:: JGRAPH_2 semantic presentation

REAL is non empty V38() set
NAT is non empty epsilon-transitive epsilon-connected ordinal Element of K19(REAL)
K19(REAL) is set
COMPLEX is non empty V38() set
omega is non empty epsilon-transitive epsilon-connected ordinal set
K19(omega) is set
K19(NAT) is set
RAT is non empty V38() set
INT is non empty V38() set
K20(REAL,REAL) is set
K19(K20(REAL,REAL)) is set
K313() is non empty V78() L8()
the carrier of K313() is non empty set
K318() is non empty V78() V100() V101() V102() V104() V151() V152() V153() V154() V155() V156() L8()
K319() is non empty V78() V102() V104() V154() V155() V156() M14(K318())
K320() is non empty V78() V100() V102() V104() V154() V155() V156() V157() M17(K318(),K319())
K322() is non empty V78() V100() V102() V104() L8()
K323() is non empty V78() V100() V102() V104() V157() M14(K322())
K408() is non empty strict TopSpace-like V204() TopStruct
the carrier of K408() is non empty V131() set
1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real ext-real positive non negative 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
K20(K20(REAL,REAL),REAL) is set
K19(K20(K20(REAL,REAL),REAL)) is set
2 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real ext-real positive non negative Element of NAT
K20(2,2) is set
K20(K20(2,2),REAL) is set
K19(K20(K20(2,2),REAL)) is set
RealSpace is strict V204() MetrStruct
R^1 is non empty strict TopSpace-like V204() TopStruct
TOP-REAL 2 is non empty V76() V141() V142() TopSpace-like V206() V207() V208() V209() V210() V211() V212() V218() L16()
the carrier of (TOP-REAL 2) is 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
ExtREAL is non empty set
{} is set
the empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V28() real ext-real non positive non negative set is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V28() real ext-real non positive non negative set
the carrier of R^1 is non empty V131() set
K19( the carrier of R^1) is set
0 is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real Element of NAT
0. (TOP-REAL 2) is Relation-like Function-like V45(2) FinSequence-like V57( TOP-REAL 2) V119() V120() V121() Element of the carrier of (TOP-REAL 2)
the ZeroF of (TOP-REAL 2) is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
|[0,0]| is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
I[01] is non empty strict TopSpace-like V204() SubSpace of R^1
the carrier of I[01] is non empty V131() set
K20( the carrier of I[01], the carrier of (TOP-REAL 2)) is set
K19(K20( the carrier of I[01], the carrier of (TOP-REAL 2))) is set
- 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 V18( the carrier of (TOP-REAL 2), REAL ) V119() V120() V121() 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 V18( the carrier of (TOP-REAL 2), REAL ) V119() V120() V121() continuous Element of K19(K20( the carrier of (TOP-REAL 2),REAL))
K0 is non empty TopSpace-like TopStruct
the carrier of K0 is non empty set
[#] K0 is non empty non proper open closed Element of K19( the carrier of K0)
K19( the carrier of K0) is set
f is non empty TopSpace-like TopStruct
the carrier of f is non empty set
K20( the carrier of K0, the carrier of f) is set
K19(K20( the carrier of K0, the carrier of f)) is set
g is non empty TopSpace-like TopStruct
the carrier of g is non empty set
K20( the carrier of g, the carrier of f) is set
K19(K20( the carrier of g, the carrier of f)) is set
[#] g is non empty non proper open closed Element of K19( the carrier of g)
K19( the carrier of g) is set
([#] K0) \/ ([#] g) is set
([#] K0) /\ ([#] g) is Element of K19( the carrier of g)
a is non empty TopSpace-like TopStruct
the carrier of a is non empty set
K19( the carrier of a) is set
[#] a is non empty non proper open closed Element of K19( the carrier of a)
K20( the carrier of a, the carrier of f) is set
K19(K20( the carrier of a, the carrier of f)) is set
b is Relation-like the carrier of K0 -defined the carrier of f -valued Function-like non empty total V18( the carrier of K0, the carrier of f) Element of K19(K20( the carrier of K0, the carrier of f))
c is Relation-like the carrier of g -defined the carrier of f -valued Function-like non empty total V18( the carrier of g, the carrier of f) Element of K19(K20( the carrier of g, the carrier of f))
b +* c is Relation-like Function-like set
d is Element of K19( the carrier of a)
O is Element of K19( the carrier of a)
dom c is Element of K19( the carrier of g)
dom b is Element of K19( the carrier of K0)
dom (b +* c) is set
rng (b +* c) is set
rng b is Element of K19( the carrier of f)
K19( the carrier of f) is set
rng c is Element of K19( the carrier of f)
(rng b) \/ (rng c) is Element of K19( the carrier of f)
A is Relation-like the carrier of a -defined the carrier of f -valued Function-like non empty total V18( the carrier of a, the carrier of f) Element of K19(K20( the carrier of a, the carrier of f))
B is Element of K19( the carrier of f)
A " B is Element of K19( the carrier of a)
b " B is Element of K19( the carrier of K0)
c " B is Element of K19( the carrier of g)
dom A is Element of K19( the carrier of a)
(dom b) \/ (dom c) is set
g2 is set
(A " B) /\ ([#] g) is Element of K19( the carrier of g)
A . g2 is set
c . g2 is set
c . g2 is set
A . g2 is set
g2 is set
A . g2 is set
b . g2 is set
c . g2 is set
g2 is set
(A " B) /\ ([#] K0) is Element of K19( the carrier of K0)
A . g2 is set
b . g2 is set
b . g2 is set
A . g2 is set
ff is Element of K19( the carrier of a)
g2 is Element of K19( the carrier of a)
g2 /\ ([#] K0) is Element of K19( the carrier of K0)
f2 is Element of K19( the carrier of a)
g2 is Element of K19( the carrier of a)
g2 /\ ([#] g) is Element of K19( the carrier of g)
(A " B) /\ (([#] K0) \/ ([#] g)) is Element of K19( the carrier of a)
((A " B) /\ ([#] K0)) \/ ((A " B) /\ ([#] g)) is set
(b " B) \/ (c " B) is set
K0 is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real Element of NAT
Euclid K0 is non empty strict Reflexive discerning V197() triangle MetrStruct
REAL K0 is non empty FinSequence-membered FinSequenceSet of REAL
K0 -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
Pitag_dist K0 is Relation-like K20((REAL K0),(REAL K0)) -defined REAL -valued Function-like total V18(K20((REAL K0),(REAL K0)), REAL ) V119() V120() V121() Element of K19(K20(K20((REAL K0),(REAL K0)),REAL))
K20((REAL K0),(REAL K0)) is set
K20(K20((REAL K0),(REAL K0)),REAL) is set
K19(K20(K20((REAL K0),(REAL K0)),REAL)) is set
MetrStruct(# (REAL K0),(Pitag_dist K0) #) is strict MetrStruct
the carrier of (Euclid K0) is non empty set
TOP-REAL K0 is non empty V76() V141() V142() TopSpace-like V206() V207() V208() V209() V210() V211() V212() V218() L16()
the carrier of (TOP-REAL K0) is non empty set
f is Element of the carrier of (Euclid K0)
g is Relation-like Function-like V45(K0) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL K0)
a is V28() real ext-real set
Ball (f,a) is Element of K19( the carrier of (Euclid K0))
K19( the carrier of (Euclid K0)) is set
{ b₁ where b₁ is Relation-like Function-like V45(K0) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL K0) : not a <= |.(g - b₁).| } is set
{ b₁ where b₁ is Element of the carrier of (Euclid K0) : not a <= dist (f,b₁) } is set
b is set
c is Element of the carrier of (Euclid K0)
dist (f,c) is V28() real ext-real Element of REAL
d is Relation-like Function-like V45(K0) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL K0)
g - d is Relation-like Function-like V45(K0) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL K0)
K296(g,d) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like V119() V120() V121() FinSequence of REAL
|.(g - d).| is V28() real ext-real non negative Element of REAL
K300((g - d)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like V119() V120() V121() FinSequence of REAL
K306(K300((g - d))) is V28() real ext-real Element of REAL
sqrt K306(K300((g - d))) is V28() real ext-real Element of REAL
b is set
c is Relation-like Function-like V45(K0) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL K0)
g - c is Relation-like Function-like V45(K0) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL K0)
K296(g,c) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like V119() V120() V121() FinSequence of REAL
|.(g - c).| is V28() real ext-real non negative Element of REAL
K300((g - c)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like V119() V120() V121() FinSequence of REAL
K306(K300((g - c))) is V28() real ext-real Element of REAL
sqrt K306(K300((g - c))) is V28() real ext-real Element of REAL
d is Element of the carrier of (Euclid K0)
dist (f,d) is V28() real ext-real Element of REAL
(0. (TOP-REAL 2)) `1 is V28() real ext-real Element of REAL
K526((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
K526((0. (TOP-REAL 2)),2) is V28() real ext-real Element of REAL
1.REAL 2 is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
1* 2 is Relation-like NAT -defined REAL -valued Function-like V45(2) FinSequence-like V119() V120() V121() Element of REAL 2
REAL 2 is non empty FinSequence-membered FinSequenceSet of REAL
2 -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
2 |-> 1 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like V119() V120() V121() Element of 2 -tuples_on REAL
<*1,1*> is set
(1.REAL 2) `1 is V28() real ext-real Element of REAL
K526((1.REAL 2),1) is V28() real ext-real Element of REAL
(1.REAL 2) `2 is V28() real ext-real Element of REAL
K526((1.REAL 2),2) is V28() real ext-real Element of REAL
dom proj1 is Element of K19( the carrier of (TOP-REAL 2))
dom proj2 is Element of K19( the carrier of (TOP-REAL 2))
K0 is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
proj1 . K0 is V28() real ext-real Element of REAL
proj2 . K0 is V28() real ext-real Element of REAL
|[(proj1 . K0),(proj2 . K0)]| is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
K0 `1 is V28() real ext-real Element of REAL
K526(K0,1) is V28() real ext-real Element of REAL
K0 `2 is V28() real ext-real Element of REAL
K526(K0,2) is V28() real ext-real Element of REAL
|[(K0 `1),(K0 `2)]| is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
{(0. (TOP-REAL 2))} is Element of K19( the carrier of (TOP-REAL 2))
K0 is Element of K19( the carrier of (TOP-REAL 2))
K0 ` is Element of K19( the carrier of (TOP-REAL 2))
the carrier of (TOP-REAL 2) \ K0 is Element of K19( the carrier of (TOP-REAL 2))
|[0,1]| is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
|[0,1]| `2 is V28() real ext-real Element of REAL
K526(|[0,1]|,2) is V28() real ext-real Element of REAL
K0 is non empty TopSpace-like TopStruct
the carrier of K0 is non empty set
f is non empty TopSpace-like TopStruct
the carrier of f is non empty set
K20( the carrier of K0, the carrier of f) is set
K19(K20( the carrier of K0, the carrier of f)) is set
K19( the carrier of f) is set
K19( the carrier of K0) is set
g is Relation-like the carrier of K0 -defined the carrier of f -valued Function-like non empty total V18( the carrier of K0, the carrier of f) Element of K19(K20( the carrier of K0, the carrier of f))
[#] f is non empty non proper open closed Element of K19( the carrier of f)
dom g is Element of K19( the carrier of K0)
a is Element of the carrier of K0
g . a is Element of the carrier of f
b is Element of K19( the carrier of f)
g " b is Element of K19( the carrier of K0)
g .: (g " b) is Element of K19( the carrier of f)
a is Element of K19( the carrier of f)
g " a is Element of K19( the carrier of K0)
b is set
g . b is set
c is Element of the carrier of K0
d is Element of K19( the carrier of K0)
g .: d is Element of K19( the carrier of f)
g " (g .: d) is Element of K19( the carrier of K0)
c is Element of K19( the carrier of K0)
d is Element of K19( the carrier of K0)
K0 is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
K0 `1 is V28() real ext-real Element of REAL
K526(K0,1) is V28() real ext-real Element of REAL
K0 `2 is V28() real ext-real Element of REAL
K526(K0,2) is V28() real ext-real Element of REAL
f is Element of K19( the carrier of (TOP-REAL 2))
the topology of (TOP-REAL 2) is non empty 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
Euclid 2 is non empty strict Reflexive discerning V197() triangle MetrStruct
Pitag_dist 2 is Relation-like K20((REAL 2),(REAL 2)) -defined REAL -valued Function-like total V18(K20((REAL 2),(REAL 2)), REAL ) V119() V120() V121() Element of K19(K20(K20((REAL 2),(REAL 2)),REAL))
K20((REAL 2),(REAL 2)) is set
K20(K20((REAL 2),(REAL 2)),REAL) is set
K19(K20(K20((REAL 2),(REAL 2)),REAL)) is set
MetrStruct(# (REAL 2),(Pitag_dist 2) #) is strict MetrStruct
the carrier of (Euclid 2) is non empty set
TopSpaceMetr (Euclid 2) is TopStruct
g is Element of K19( the carrier of TopStruct(# the carrier of (TOP-REAL 2), the topology of (TOP-REAL 2) #))
a is Element of the carrier of (Euclid 2)
b is V28() real ext-real set
Ball (a,b) is Element of K19( the carrier of (Euclid 2))
K19( the carrier of (Euclid 2)) is set
sqrt 2 is V28() real ext-real Element of REAL
b / (sqrt 2) is V28() real ext-real Element of REAL
(sqrt 2) " is V28() real ext-real set
b * ((sqrt 2) ") is V28() real ext-real set
{ b₁ where b₁ is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2) : not b <= |.(K0 - b₁).| } is set
(K0 `1) - (b / (sqrt 2)) is V28() real ext-real Element of REAL
- (b / (sqrt 2)) is V28() real ext-real set
(K0 `1) + (- (b / (sqrt 2))) is V28() real ext-real set
(K0 `1) + (b / (sqrt 2)) is V28() real ext-real Element of REAL
(K0 `2) - (b / (sqrt 2)) is V28() real ext-real Element of REAL
(K0 `2) + (- (b / (sqrt 2))) is V28() real ext-real set
(K0 `2) + (b / (sqrt 2)) is V28() real ext-real Element of REAL
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2) : ( not b<sub>1</sub> `1 <= (K0 `1) - (b / (sqrt 2)) & not (K0 `1) + (b / (sqrt 2)) <= b₁ `1 & not b<sub>1</sub> `2 <= (K0 `2) - (b / (sqrt 2)) & not (K0 `2) + (b / (sqrt 2)) <= b₁ `2 ) } is set
d is set
O is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
O `1 is V28() real ext-real Element of REAL
K526(O,1) is V28() real ext-real Element of REAL
O `2 is V28() real ext-real Element of REAL
K526(O,2) is V28() real ext-real Element of REAL
((K0 `1) + (b / (sqrt 2))) - (b / (sqrt 2)) is V28() real ext-real Element of REAL
((K0 `1) + (b / (sqrt 2))) + (- (b / (sqrt 2))) is V28() real ext-real set
(O `1) - (b / (sqrt 2)) is V28() real ext-real Element of REAL
(O `1) + (- (b / (sqrt 2))) is V28() real ext-real set
(K0 `1) - (O `1) is V28() real ext-real Element of REAL
- (O `1) is V28() real ext-real set
(K0 `1) + (- (O `1)) is V28() real ext-real set
- (b / (sqrt 2)) is V28() real ext-real Element of REAL
(O `1) + (- (b / (sqrt 2))) is V28() real ext-real Element of REAL
((O `1) + (- (b / (sqrt 2)))) - (O `1) is V28() real ext-real Element of REAL
((O `1) + (- (b / (sqrt 2)))) + (- (O `1)) is V28() real ext-real set
((K0 `2) + (b / (sqrt 2))) - (b / (sqrt 2)) is V28() real ext-real Element of REAL
((K0 `2) + (b / (sqrt 2))) + (- (b / (sqrt 2))) is V28() real ext-real set
(O `2) - (b / (sqrt 2)) is V28() real ext-real Element of REAL
(O `2) + (- (b / (sqrt 2))) is V28() real ext-real set
(K0 `2) - (O `2) is V28() real ext-real Element of REAL
- (O `2) is V28() real ext-real set
(K0 `2) + (- (O `2)) is V28() real ext-real set
(O `2) + (- (b / (sqrt 2))) is V28() real ext-real Element of REAL
((O `2) + (- (b / (sqrt 2)))) - (O `2) is V28() real ext-real Element of REAL
((O `2) + (- (b / (sqrt 2)))) + (- (O `2)) is V28() real ext-real set
(O `2) + (b / (sqrt 2)) is V28() real ext-real Element of REAL
((K0 `2) - (b / (sqrt 2))) + (b / (sqrt 2)) is V28() real ext-real Element of REAL
((O `2) + (b / (sqrt 2))) - (O `2) is V28() real ext-real Element of REAL
((O `2) + (b / (sqrt 2))) + (- (O `2)) is V28() real ext-real set
(b / (sqrt 2)) ^2 is V28() real ext-real Element of REAL
(b / (sqrt 2)) * (b / (sqrt 2)) is V28() real ext-real set
((K0 `2) - (O `2)) ^2 is V28() real ext-real Element of REAL
((K0 `2) - (O `2)) * ((K0 `2) - (O `2)) is V28() real ext-real set
b ^2 is V28() real ext-real set
b * b is V28() real ext-real set
(sqrt 2) ^2 is V28() real ext-real Element of REAL
(sqrt 2) * (sqrt 2) is V28() real ext-real set
(b ^2) / ((sqrt 2) ^2) is V28() real ext-real Element of REAL
((sqrt 2) ^2) " is V28() real ext-real set
(b ^2) * (((sqrt 2) ^2) ") is V28() real ext-real set
(b ^2) / 2 is V28() real ext-real Element of REAL
2 " is non empty V28() real ext-real positive non negative set
(b ^2) * (2 ") is V28() real ext-real set
((b / (sqrt 2)) ^2) + ((b / (sqrt 2)) ^2) is V28() real ext-real Element of REAL
(O `1) + (b / (sqrt 2)) is V28() real ext-real Element of REAL
((K0 `1) - (b / (sqrt 2))) + (b / (sqrt 2)) is V28() real ext-real Element of REAL
((O `1) + (b / (sqrt 2))) - (O `1) is V28() real ext-real Element of REAL
((O `1) + (b / (sqrt 2))) + (- (O `1)) is V28() real ext-real set
K0 - O is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
K296(K0,O) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like V119() V120() V121() FinSequence of REAL
(K0 - O) `2 is V28() real ext-real Element of REAL
K526((K0 - O),2) is V28() real ext-real Element of REAL
((K0 `1) - (O `1)) ^2 is V28() real ext-real Element of REAL
((K0 `1) - (O `1)) * ((K0 `1) - (O `1)) is V28() real ext-real set
|.(K0 - O).| is V28() real ext-real non negative Element of REAL
K300((K0 - O)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like V119() V120() V121() FinSequence of REAL
K306(K300((K0 - O))) is V28() real ext-real Element of REAL
sqrt K306(K300((K0 - O))) is V28() real ext-real Element of REAL
|.(K0 - O).| ^2 is V28() real ext-real Element of REAL
|.(K0 - O).| * |.(K0 - O).| is V28() real ext-real non negative set
(K0 - O) `1 is V28() real ext-real Element of REAL
K526((K0 - O),1) is V28() real ext-real Element of REAL
((K0 - O) `1) ^2 is V28() real ext-real Element of REAL
((K0 - O) `1) * ((K0 - O) `1) is V28() real ext-real set
((K0 - O) `2) ^2 is V28() real ext-real Element of REAL
((K0 - O) `2) * ((K0 - O) `2) is V28() real ext-real set
(((K0 - O) `1) ^2) + (((K0 - O) `2) ^2) is V28() real ext-real Element of REAL
f is non empty TopSpace-like TopStruct
the carrier of f is non empty set
K19( the carrier of f) is set
g is non empty TopSpace-like TopStruct
the carrier of g is non empty set
K19( the carrier of g) is set
K0 is non empty TopSpace-like TopStruct
the carrier of K0 is non empty set
K20( the carrier of K0, the carrier of f) is set
K19(K20( the carrier of K0, the carrier of f)) is set
K20( the carrier of K0, the carrier of g) is set
K19(K20( the carrier of K0, the carrier of g)) is set
a is Element of K19( the carrier of f)
f | a is strict TopSpace-like SubSpace of f
the carrier of (f | a) is set
b is Element of K19( the carrier of g)
g | b is strict TopSpace-like SubSpace of g
the carrier of (g | b) is set
K20( the carrier of (f | a), the carrier of (g | b)) is set
K19(K20( the carrier of (f | a), the carrier of (g | b))) is set
c is Relation-like the carrier of K0 -defined the carrier of f -valued Function-like non empty total V18( the carrier of K0, the carrier of f) Element of K19(K20( the carrier of K0, the carrier of f))
rng c is Element of K19( the carrier of f)
d is Relation-like the carrier of (f | a) -defined the carrier of (g | b) -valued Function-like V18( the carrier of (f | a), the carrier of (g | b)) Element of K19(K20( the carrier of (f | a), the carrier of (g | b)))
d * c is Relation-like the carrier of K0 -defined the carrier of (g | b) -valued Function-like Element of K19(K20( the carrier of K0, the carrier of (g | b)))
K20( the carrier of K0, the carrier of (g | b)) is set
K19(K20( the carrier of K0, the carrier of (g | b))) is set
dom c is Element of K19( the carrier of K0)
K19( the carrier of K0) is set
[#] (f | a) is non proper open closed Element of K19( the carrier of (f | a))
K19( the carrier of (f | a)) is set
K20( the carrier of K0, the carrier of (f | a)) is set
K19(K20( the carrier of K0, the carrier of (f | a))) is set
I is non empty Element of K19( the carrier of f)
f | I is non empty strict TopSpace-like SubSpace of f
A is non empty TopSpace-like TopStruct
the carrier of A is non empty set
K20( the carrier of K0, the carrier of A) is set
K19(K20( the carrier of K0, the carrier of A)) is set
O is Relation-like the carrier of K0 -defined the carrier of (f | a) -valued Function-like V18( the carrier of K0, the carrier of (f | a)) Element of K19(K20( the carrier of K0, the carrier of (f | a)))
B is non empty Element of K19( the carrier of g)
g | B is non empty strict TopSpace-like SubSpace of g
D is non empty TopSpace-like TopStruct
the carrier of D is non empty set
K20( the carrier of A, the carrier of D) is set
K19(K20( the carrier of A, the carrier of D)) is set
[#] (g | b) is non proper open closed Element of K19( the carrier of (g | b))
K19( the carrier of (g | b)) is set
C is Relation-like the carrier of K0 -defined the carrier of A -valued Function-like non empty total V18( the carrier of K0, the carrier of A) Element of K19(K20( the carrier of K0, the carrier of A))
ff is Relation-like the carrier of A -defined the carrier of D -valued Function-like non empty total V18( the carrier of A, the carrier of D) Element of K19(K20( the carrier of A, the carrier of D))
ff * C is Relation-like the carrier of K0 -defined the carrier of D -valued Function-like non empty total V18( the carrier of K0, the carrier of D) Element of K19(K20( the carrier of K0, the carrier of D))
K20( the carrier of K0, the carrier of D) is set
K19(K20( the carrier of K0, the carrier of D)) is set
d * O is Relation-like the carrier of K0 -defined the carrier of (g | b) -valued Function-like Element of K19(K20( the carrier of K0, the carrier of (g | b)))
f2 is Relation-like the carrier of K0 -defined the carrier of g -valued Function-like non empty total V18( the carrier of K0, the carrier of g) Element of K19(K20( the carrier of K0, the carrier of g))
NonZero (TOP-REAL 2) is Element of K19( the carrier of (TOP-REAL 2))
[#] (TOP-REAL 2) is non empty non proper open closed Element of K19( the carrier of (TOP-REAL 2))
{(0. (TOP-REAL 2))} is set
([#] (TOP-REAL 2)) \ {(0. (TOP-REAL 2))} is Element of K19( the carrier of (TOP-REAL 2))
K20((NonZero (TOP-REAL 2)),(NonZero (TOP-REAL 2))) is set
K19(K20((NonZero (TOP-REAL 2)),(NonZero (TOP-REAL 2)))) is set
K0 is non empty set
f is Element of K0
g is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
g `2 is V28() real ext-real Element of REAL
K526(g,2) is V28() real ext-real Element of REAL
g `1 is V28() real ext-real Element of REAL
K526(g,1) is V28() real ext-real Element of REAL
- (g `1) is V28() real ext-real Element of REAL
1 / (g `1) is V28() real ext-real Element of REAL
(g `1) " is V28() real ext-real set
1 * ((g `1) ") is V28() real ext-real set
(g `2) / (g `1) is V28() real ext-real Element of REAL
(g `2) * ((g `1) ") is V28() real ext-real set
((g `2) / (g `1)) / (g `1) is V28() real ext-real Element of REAL
((g `2) / (g `1)) * ((g `1) ") is V28() real ext-real set
|[(1 / (g `1)),(((g `2) / (g `1)) / (g `1))]| is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
(1 / (g `1)) * (g `1) is V28() real ext-real Element of REAL
a is Element of K0
b is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
b `2 is V28() real ext-real Element of REAL
K526(b,2) is V28() real ext-real Element of REAL
b `1 is V28() real ext-real Element of REAL
K526(b,1) is V28() real ext-real Element of REAL
- (b `1) is V28() real ext-real Element of REAL
1 / (b `1) is V28() real ext-real Element of REAL
(b `1) " is V28() real ext-real set
1 * ((b `1) ") is V28() real ext-real set
(b `2) / (b `1) is V28() real ext-real Element of REAL
(b `2) * ((b `1) ") is V28() real ext-real set
((b `2) / (b `1)) / (b `1) is V28() real ext-real Element of REAL
((b `2) / (b `1)) * ((b `1) ") is V28() real ext-real set
|[(1 / (b `1)),(((b `2) / (b `1)) / (b `1))]| is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
(b `1) / (b `2) is V28() real ext-real Element of REAL
(b `2) " is V28() real ext-real set
(b `1) * ((b `2) ") is V28() real ext-real set
((b `1) / (b `2)) / (b `2) is V28() real ext-real Element of REAL
((b `1) / (b `2)) * ((b `2) ") is V28() real ext-real set
1 / (b `2) is V28() real ext-real Element of REAL
1 * ((b `2) ") is V28() real ext-real set
|[(((b `1) / (b `2)) / (b `2)),(1 / (b `2))]| is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
g is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
g `2 is V28() real ext-real Element of REAL
K526(g,2) is V28() real ext-real Element of REAL
g `1 is V28() real ext-real Element of REAL
K526(g,1) is V28() real ext-real Element of REAL
- (g `1) is V28() real ext-real Element of REAL
(g `1) / (g `2) is V28() real ext-real Element of REAL
(g `2) " is V28() real ext-real set
(g `1) * ((g `2) ") is V28() real ext-real set
((g `1) / (g `2)) / (g `2) is V28() real ext-real Element of REAL
((g `1) / (g `2)) * ((g `2) ") is V28() real ext-real set
1 / (g `2) is V28() real ext-real Element of REAL
1 * ((g `2) ") is V28() real ext-real set
|[(((g `1) / (g `2)) / (g `2)),(1 / (g `2))]| is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
(1 / (g `2)) * (g `2) is V28() real ext-real Element of REAL
a is Element of K0
b is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
b `2 is V28() real ext-real Element of REAL
K526(b,2) is V28() real ext-real Element of REAL
b `1 is V28() real ext-real Element of REAL
K526(b,1) is V28() real ext-real Element of REAL
- (b `1) is V28() real ext-real Element of REAL
1 / (b `1) is V28() real ext-real Element of REAL
(b `1) " is V28() real ext-real set
1 * ((b `1) ") is V28() real ext-real set
(b `2) / (b `1) is V28() real ext-real Element of REAL
(b `2) * ((b `1) ") is V28() real ext-real set
((b `2) / (b `1)) / (b `1) is V28() real ext-real Element of REAL
((b `2) / (b `1)) * ((b `1) ") is V28() real ext-real set
|[(1 / (b `1)),(((b `2) / (b `1)) / (b `1))]| is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
(b `1) / (b `2) is V28() real ext-real Element of REAL
(b `2) " is V28() real ext-real set
(b `1) * ((b `2) ") is V28() real ext-real set
((b `1) / (b `2)) / (b `2) is V28() real ext-real Element of REAL
((b `1) / (b `2)) * ((b `2) ") is V28() real ext-real set
1 / (b `2) is V28() real ext-real Element of REAL
1 * ((b `2) ") is V28() real ext-real set
|[(((b `1) / (b `2)) / (b `2)),(1 / (b `2))]| is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
g is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
g `2 is V28() real ext-real Element of REAL
K526(g,2) is V28() real ext-real Element of REAL
g `1 is V28() real ext-real Element of REAL
K526(g,1) is V28() real ext-real Element of REAL
- (g `1) is V28() real ext-real Element of REAL
g is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
g `2 is V28() real ext-real Element of REAL
K526(g,2) is V28() real ext-real Element of REAL
g `1 is V28() real ext-real Element of REAL
K526(g,1) is V28() real ext-real Element of REAL
- (g `1) is V28() real ext-real Element of REAL
a is Element of K0
b is Element of K0
K20(K0,K0) is set
K19(K20(K0,K0)) is set
f is Relation-like K0 -defined K0 -valued Function-like non empty total V18(K0,K0) Element of K19(K20(K0,K0))
f is Relation-like K0 -defined K0 -valued Function-like non empty total V18(K0,K0) Element of K19(K20(K0,K0))
g is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
g `2 is V28() real ext-real Element of REAL
K526(g,2) is V28() real ext-real Element of REAL
g `1 is V28() real ext-real Element of REAL
K526(g,1) is V28() real ext-real Element of REAL
- (g `1) is V28() real ext-real Element of REAL
f . g is set
1 / (g `1) is V28() real ext-real Element of REAL
(g `1) " is V28() real ext-real set
1 * ((g `1) ") is V28() real ext-real set
(g `2) / (g `1) is V28() real ext-real Element of REAL
(g `2) * ((g `1) ") is V28() real ext-real set
((g `2) / (g `1)) / (g `1) is V28() real ext-real Element of REAL
((g `2) / (g `1)) * ((g `1) ") is V28() real ext-real set
|[(1 / (g `1)),(((g `2) / (g `1)) / (g `1))]| is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
(g `1) / (g `2) is V28() real ext-real Element of REAL
(g `2) " is V28() real ext-real set
(g `1) * ((g `2) ") is V28() real ext-real set
((g `1) / (g `2)) / (g `2) is V28() real ext-real Element of REAL
((g `1) / (g `2)) * ((g `2) ") is V28() real ext-real set
1 / (g `2) is V28() real ext-real Element of REAL
1 * ((g `2) ") is V28() real ext-real set
|[(((g `1) / (g `2)) / (g `2)),(1 / (g `2))]| is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
K0 is Relation-like NonZero (TOP-REAL 2) -defined NonZero (TOP-REAL 2) -valued Function-like total V18( NonZero (TOP-REAL 2), NonZero (TOP-REAL 2)) Element of K19(K20((NonZero (TOP-REAL 2)),(NonZero (TOP-REAL 2))))
f is Relation-like NonZero (TOP-REAL 2) -defined NonZero (TOP-REAL 2) -valued Function-like total V18( NonZero (TOP-REAL 2), NonZero (TOP-REAL 2)) Element of K19(K20((NonZero (TOP-REAL 2)),(NonZero (TOP-REAL 2))))
g is set
K0 . g is set
f . g is set
a is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
a `2 is V28() real ext-real Element of REAL
K526(a,2) is V28() real ext-real Element of REAL
a `1 is V28() real ext-real Element of REAL
K526(a,1) is V28() real ext-real Element of REAL
- (a `1) is V28() real ext-real Element of REAL
K0 . a is set
1 / (a `1) is V28() real ext-real Element of REAL
(a `1) " is V28() real ext-real set
1 * ((a `1) ") is V28() real ext-real set
(a `2) / (a `1) is V28() real ext-real Element of REAL
(a `2) * ((a `1) ") is V28() real ext-real set
((a `2) / (a `1)) / (a `1) is V28() real ext-real Element of REAL
((a `2) / (a `1)) * ((a `1) ") is V28() real ext-real set
|[(1 / (a `1)),(((a `2) / (a `1)) / (a `1))]| is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
a `2 is V28() real ext-real Element of REAL
K526(a,2) is V28() real ext-real Element of REAL
a `1 is V28() real ext-real Element of REAL
K526(a,1) is V28() real ext-real Element of REAL
- (a `1) is V28() real ext-real Element of REAL
K0 . a is set
(a `1) / (a `2) is V28() real ext-real Element of REAL
(a `2) " is V28() real ext-real set
(a `1) * ((a `2) ") is V28() real ext-real set
((a `1) / (a `2)) / (a `2) is V28() real ext-real Element of REAL
((a `1) / (a `2)) * ((a `2) ") is V28() real ext-real set
1 / (a `2) is V28() real ext-real Element of REAL
1 * ((a `2) ") is V28() real ext-real set
|[(((a `1) / (a `2)) / (a `2)),(1 / (a `2))]| is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
a `2 is V28() real ext-real Element of REAL
K526(a,2) is V28() real ext-real Element of REAL
a `1 is V28() real ext-real Element of REAL
K526(a,1) is V28() real ext-real Element of REAL
- (a `1) is V28() real ext-real Element of REAL
a `2 is V28() real ext-real Element of REAL
K526(a,2) is V28() real ext-real Element of REAL
a `1 is V28() real ext-real Element of REAL
K526(a,1) is V28() real ext-real Element of REAL
- (a `1) is V28() real ext-real Element of REAL
() is Relation-like NonZero (TOP-REAL 2) -defined NonZero (TOP-REAL 2) -valued Function-like total V18( NonZero (TOP-REAL 2), NonZero (TOP-REAL 2)) Element of K19(K20((NonZero (TOP-REAL 2)),(NonZero (TOP-REAL 2))))
K0 is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
K0 `2 is V28() real ext-real Element of REAL
K526(K0,2) is V28() real ext-real Element of REAL
K0 `1 is V28() real ext-real Element of REAL
K526(K0,1) is V28() real ext-real Element of REAL
- (K0 `1) is V28() real ext-real Element of REAL
- (K0 `2) is V28() real ext-real Element of REAL
- (- (K0 `1)) is V28() real ext-real Element of REAL
K0 is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
K0 `1 is V28() real ext-real Element of REAL
K526(K0,1) is V28() real ext-real Element of REAL
K0 `2 is V28() real ext-real Element of REAL
K526(K0,2) is V28() real ext-real Element of REAL
- (K0 `2) is V28() real ext-real Element of REAL
() . K0 is set
(K0 `1) / (K0 `2) is V28() real ext-real Element of REAL
(K0 `2) " is V28() real ext-real set
(K0 `1) * ((K0 `2) ") is V28() real ext-real set
((K0 `1) / (K0 `2)) / (K0 `2) is V28() real ext-real Element of REAL
((K0 `1) / (K0 `2)) * ((K0 `2) ") is V28() real ext-real set
1 / (K0 `2) is V28() real ext-real Element of REAL
1 * ((K0 `2) ") is V28() real ext-real set
|[(((K0 `1) / (K0 `2)) / (K0 `2)),(1 / (K0 `2))]| is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
1 / (K0 `1) is V28() real ext-real Element of REAL
(K0 `1) " is V28() real ext-real set
1 * ((K0 `1) ") is V28() real ext-real set
(K0 `2) / (K0 `1) is V28() real ext-real Element of REAL
(K0 `2) * ((K0 `1) ") is V28() real ext-real set
((K0 `2) / (K0 `1)) / (K0 `1) is V28() real ext-real Element of REAL
((K0 `2) / (K0 `1)) * ((K0 `1) ") is V28() real ext-real set
|[(1 / (K0 `1)),(((K0 `2) / (K0 `1)) / (K0 `1))]| is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
- (K0 `1) is V28() real ext-real Element of REAL
- (- (K0 `1)) is V28() real ext-real Element of REAL
(K0 `2) / (K0 `2) is V28() real ext-real Element of REAL
(K0 `2) * ((K0 `2) ") is V28() real ext-real set
- ((K0 `2) / (K0 `2)) is V28() real ext-real Element of REAL
(- ((K0 `2) / (K0 `2))) / (K0 `2) is V28() real ext-real Element of REAL
(- ((K0 `2) / (K0 `2))) * ((K0 `2) ") is V28() real ext-real set
- 1 is V28() real ext-real non positive Element of REAL
(- 1) / (K0 `2) is V28() real ext-real Element of REAL
(- 1) * ((K0 `2) ") is V28() real ext-real set
- (1 / (K0 `1)) is V28() real ext-real Element of REAL
((K0 `2) / (K0 `1)) / (- (K0 `1)) is V28() real ext-real Element of REAL
(- (K0 `1)) " is V28() real ext-real set
((K0 `2) / (K0 `1)) * ((- (K0 `1)) ") is V28() real ext-real set
- (((K0 `2) / (K0 `1)) / (- (K0 `1))) is V28() real ext-real Element of REAL
- (((K0 `2) / (K0 `1)) / (K0 `1)) is V28() real ext-real Element of REAL
- (- (((K0 `2) / (K0 `1)) / (K0 `1))) is V28() real ext-real Element of REAL
- (K0 `1) is V28() real ext-real Element of REAL
- (- (K0 `1)) is V28() real ext-real Element of REAL
(K0 `2) / (K0 `2) is V28() real ext-real Element of REAL
(K0 `2) * ((K0 `2) ") is V28() real ext-real set
- ((K0 `2) / (K0 `2)) is V28() real ext-real Element of REAL
(- ((K0 `2) / (K0 `2))) / (K0 `2) is V28() real ext-real Element of REAL
(- ((K0 `2) / (K0 `2))) * ((K0 `2) ") is V28() real ext-real set
- 1 is V28() real ext-real non positive Element of REAL
(- 1) / (K0 `2) is V28() real ext-real Element of REAL
(- 1) * ((K0 `2) ") is V28() real ext-real set
- (((K0 `1) / (K0 `2)) / (K0 `2)) is V28() real ext-real Element of REAL
((K0 `2) / (K0 `1)) / (- (K0 `1)) is V28() real ext-real Element of REAL
(- (K0 `1)) " is V28() real ext-real set
((K0 `2) / (K0 `1)) * ((- (K0 `1)) ") is V28() real ext-real set
- (((K0 `2) / (K0 `1)) / (- (K0 `1))) is V28() real ext-real Element of REAL
- (((K0 `2) / (K0 `1)) / (K0 `1)) is V28() real ext-real Element of REAL
- (- (((K0 `2) / (K0 `1)) / (K0 `1))) is V28() real ext-real Element of REAL
- (K0 `1) is V28() real ext-real Element of REAL
- (- (K0 `2)) is V28() real ext-real Element of REAL
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2) : ( ( ( b<sub>1</sub> `2 <= b₁ `1 & - (b<sub>1</sub> `1) <= b₁ `2 ) or ( b<sub>1</sub> `1 <= b₁ `2 & b<sub>1</sub> `2 <= - (b₁ `1) ) ) & not b<sub>1</sub> = 0. (TOP-REAL 2) ) } is set
K0 is Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | K0 is strict TopSpace-like SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | K0) is set
K19( the carrier of ((TOP-REAL 2) | K0)) is set
f is Element of K19( the carrier of ((TOP-REAL 2) | K0))
() | f is Relation-like NonZero (TOP-REAL 2) -defined NonZero (TOP-REAL 2) -valued Function-like Element of K19(K20((NonZero (TOP-REAL 2)),(NonZero (TOP-REAL 2))))
rng (() | f) is Element of K19((NonZero (TOP-REAL 2)))
K19((NonZero (TOP-REAL 2))) is set
((TOP-REAL 2) | K0) | f is strict TopSpace-like SubSpace of (TOP-REAL 2) | K0
the carrier of (((TOP-REAL 2) | K0) | f) is set
[#] ((TOP-REAL 2) | K0) is non proper open closed Element of K19( the carrier of ((TOP-REAL 2) | K0))
g is Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | g is strict TopSpace-like SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | g) is set
a is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
a `1 is V28() real ext-real Element of REAL
K526(a,1) is V28() real ext-real Element of REAL
[#] ((TOP-REAL 2) | g) is non proper open closed Element of K19( the carrier of ((TOP-REAL 2) | g))
K19( the carrier of ((TOP-REAL 2) | g)) is set
a `2 is V28() real ext-real Element of REAL
K526(a,2) is V28() real ext-real Element of REAL
b is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
b `2 is V28() real ext-real Element of REAL
K526(b,2) is V28() real ext-real Element of REAL
b `1 is V28() real ext-real Element of REAL
K526(b,1) is V28() real ext-real Element of REAL
- (b `1) is V28() real ext-real Element of REAL
b is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
b `2 is V28() real ext-real Element of REAL
K526(b,2) is V28() real ext-real Element of REAL
b `1 is V28() real ext-real Element of REAL
K526(b,1) is V28() real ext-real Element of REAL
- (b `1) is V28() real ext-real Element of REAL
a is set
dom (() | f) is Element of K19((NonZero (TOP-REAL 2)))
b is set
(() | f) . b is set
dom () is Element of K19((NonZero (TOP-REAL 2)))
(dom ()) /\ f is Element of K19( the carrier of ((TOP-REAL 2) | K0))
c is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
() . c is set
c `1 is V28() real ext-real Element of REAL
K526(c,1) is V28() real ext-real Element of REAL
1 / (c `1) is V28() real ext-real Element of REAL
(c `1) " is V28() real ext-real set
1 * ((c `1) ") is V28() real ext-real set
c `2 is V28() real ext-real Element of REAL
K526(c,2) is V28() real ext-real Element of REAL
(c `2) / (c `1) is V28() real ext-real Element of REAL
(c `2) * ((c `1) ") is V28() real ext-real set
((c `2) / (c `1)) / (c `1) is V28() real ext-real Element of REAL
((c `2) / (c `1)) * ((c `1) ") is V28() real ext-real set
|[(1 / (c `1)),(((c `2) / (c `1)) / (c `1))]| is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
d is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
d `2 is V28() real ext-real Element of REAL
K526(d,2) is V28() real ext-real Element of REAL
d `1 is V28() real ext-real Element of REAL
K526(d,1) is V28() real ext-real Element of REAL
- (d `1) is V28() real ext-real Element of REAL
[#] ((TOP-REAL 2) | g) is non proper open closed Element of K19( the carrier of ((TOP-REAL 2) | g))
K19( the carrier of ((TOP-REAL 2) | g)) is set
|[(1 / (c `1)),(((c `2) / (c `1)) / (c `1))]| `1 is V28() real ext-real Element of REAL
K526(|[(1 / (c `1)),(((c `2) / (c `1)) / (c `1))]|,1) is V28() real ext-real Element of REAL
0 * (c `1) is V28() real ext-real Element of REAL
(1 / (c `1)) * (c `1) is V28() real ext-real Element of REAL
(c `1) / (c `1) is V28() real ext-real Element of REAL
(c `1) * ((c `1) ") is V28() real ext-real set
1 * (c `1) is V28() real ext-real Element of REAL
- (1 * (c `1)) is V28() real ext-real Element of REAL
(- (1 * (c `1))) / (c `1) is V28() real ext-real Element of REAL
(- (1 * (c `1))) * ((c `1) ") is V28() real ext-real set
O is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
O `2 is V28() real ext-real Element of REAL
K526(O,2) is V28() real ext-real Element of REAL
O `1 is V28() real ext-real Element of REAL
K526(O,1) is V28() real ext-real Element of REAL
- (O `1) is V28() real ext-real Element of REAL
- 1 is V28() real ext-real non positive Element of REAL
(- 1) * (c `1) is V28() real ext-real Element of REAL
((- 1) * (c `1)) / (c `1) is V28() real ext-real Element of REAL
((- 1) * (c `1)) * ((c `1) ") is V28() real ext-real set
(- 1) / (c `1) is V28() real ext-real Element of REAL
(- 1) * ((c `1) ") is V28() real ext-real set
- (1 / (c `1)) is V28() real ext-real Element of REAL
|[(1 / (c `1)),(((c `2) / (c `1)) / (c `1))]| `2 is V28() real ext-real Element of REAL
K526(|[(1 / (c `1)),(((c `2) / (c `1)) / (c `1))]|,2) is V28() real ext-real Element of REAL
- 1 is V28() real ext-real non positive Element of REAL
1 * (c `1) is V28() real ext-real Element of REAL
- (1 * (c `1)) is V28() real ext-real Element of REAL
(c `1) / (c `1) is V28() real ext-real Element of REAL
(c `1) * ((c `1) ") is V28() real ext-real set
(- (1 * (c `1))) / (c `1) is V28() real ext-real Element of REAL
(- (1 * (c `1))) * ((c `1) ") is V28() real ext-real set
O is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
O `2 is V28() real ext-real Element of REAL
K526(O,2) is V28() real ext-real Element of REAL
O `1 is V28() real ext-real Element of REAL
K526(O,1) is V28() real ext-real Element of REAL
- (O `1) is V28() real ext-real Element of REAL
(- 1) * (c `1) is V28() real ext-real Element of REAL
((- 1) * (c `1)) / (c `1) is V28() real ext-real Element of REAL
((- 1) * (c `1)) * ((c `1) ") is V28() real ext-real set
(- 1) / (c `1) is V28() real ext-real Element of REAL
(- 1) * ((c `1) ") is V28() real ext-real set
- (1 / (c `1)) is V28() real ext-real Element of REAL
|[(1 / (c `1)),(((c `2) / (c `1)) / (c `1))]| `2 is V28() real ext-real Element of REAL
K526(|[(1 / (c `1)),(((c `2) / (c `1)) / (c `1))]|,2) is V28() real ext-real Element of REAL
[#] (((TOP-REAL 2) | K0) | f) is non proper open closed Element of K19( the carrier of (((TOP-REAL 2) | K0) | f))
K19( the carrier of (((TOP-REAL 2) | K0) | f)) is set
{ b₁ where b₁ is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2) : ( ( ( b₁ `1 <= b<sub>1</sub> `2 & - (b₁ `2) <= b<sub>1</sub> `1 ) or ( b₁ `2 <= b<sub>1</sub> `1 & b₁ `1 <= - (b<sub>1</sub> `2) ) ) & not b₁ = 0. (TOP-REAL 2) ) } is set
K0 is Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | K0 is strict TopSpace-like SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | K0) is set
K19( the carrier of ((TOP-REAL 2) | K0)) is set
f is Element of K19( the carrier of ((TOP-REAL 2) | K0))
() | f is Relation-like NonZero (TOP-REAL 2) -defined NonZero (TOP-REAL 2) -valued Function-like Element of K19(K20((NonZero (TOP-REAL 2)),(NonZero (TOP-REAL 2))))
rng (() | f) is Element of K19((NonZero (TOP-REAL 2)))
K19((NonZero (TOP-REAL 2))) is set
((TOP-REAL 2) | K0) | f is strict TopSpace-like SubSpace of (TOP-REAL 2) | K0
the carrier of (((TOP-REAL 2) | K0) | f) is set
[#] ((TOP-REAL 2) | K0) is non proper open closed Element of K19( the carrier of ((TOP-REAL 2) | K0))
g is Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | g is strict TopSpace-like SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | g) is set
a is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
a `2 is V28() real ext-real Element of REAL
K526(a,2) is V28() real ext-real Element of REAL
[#] ((TOP-REAL 2) | g) is non proper open closed Element of K19( the carrier of ((TOP-REAL 2) | g))
K19( the carrier of ((TOP-REAL 2) | g)) is set
a `1 is V28() real ext-real Element of REAL
K526(a,1) is V28() real ext-real Element of REAL
b is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
b `1 is V28() real ext-real Element of REAL
K526(b,1) is V28() real ext-real Element of REAL
b `2 is V28() real ext-real Element of REAL
K526(b,2) is V28() real ext-real Element of REAL
- (b `2) is V28() real ext-real Element of REAL
b is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
b `1 is V28() real ext-real Element of REAL
K526(b,1) is V28() real ext-real Element of REAL
b `2 is V28() real ext-real Element of REAL
K526(b,2) is V28() real ext-real Element of REAL
- (b `2) is V28() real ext-real Element of REAL
a is set
dom (() | f) is Element of K19((NonZero (TOP-REAL 2)))
b is set
(() | f) . b is set
dom () is Element of K19((NonZero (TOP-REAL 2)))
(dom ()) /\ f is Element of K19( the carrier of ((TOP-REAL 2) | K0))
c is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
() . c is set
c `1 is V28() real ext-real Element of REAL
K526(c,1) is V28() real ext-real Element of REAL
c `2 is V28() real ext-real Element of REAL
K526(c,2) is V28() real ext-real Element of REAL
(c `1) / (c `2) is V28() real ext-real Element of REAL
(c `2) " is V28() real ext-real set
(c `1) * ((c `2) ") is V28() real ext-real set
((c `1) / (c `2)) / (c `2) is V28() real ext-real Element of REAL
((c `1) / (c `2)) * ((c `2) ") is V28() real ext-real set
1 / (c `2) is V28() real ext-real Element of REAL
1 * ((c `2) ") is V28() real ext-real set
|[(((c `1) / (c `2)) / (c `2)),(1 / (c `2))]| is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
d is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
d `1 is V28() real ext-real Element of REAL
K526(d,1) is V28() real ext-real Element of REAL
d `2 is V28() real ext-real Element of REAL
K526(d,2) is V28() real ext-real Element of REAL
- (d `2) is V28() real ext-real Element of REAL
[#] ((TOP-REAL 2) | g) is non proper open closed Element of K19( the carrier of ((TOP-REAL 2) | g))
K19( the carrier of ((TOP-REAL 2) | g)) is set
|[(((c `1) / (c `2)) / (c `2)),(1 / (c `2))]| `2 is V28() real ext-real Element of REAL
K526(|[(((c `1) / (c `2)) / (c `2)),(1 / (c `2))]|,2) is V28() real ext-real Element of REAL
0 * (c `2) is V28() real ext-real Element of REAL
(1 / (c `2)) * (c `2) is V28() real ext-real Element of REAL
(c `2) / (c `2) is V28() real ext-real Element of REAL
(c `2) * ((c `2) ") is V28() real ext-real set
1 * (c `2) is V28() real ext-real Element of REAL
- (1 * (c `2)) is V28() real ext-real Element of REAL
(- (1 * (c `2))) / (c `2) is V28() real ext-real Element of REAL
(- (1 * (c `2))) * ((c `2) ") is V28() real ext-real set
O is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
O `1 is V28() real ext-real Element of REAL
K526(O,1) is V28() real ext-real Element of REAL
O `2 is V28() real ext-real Element of REAL
K526(O,2) is V28() real ext-real Element of REAL
- (O `2) is V28() real ext-real Element of REAL
- 1 is V28() real ext-real non positive Element of REAL
(- 1) * (c `2) is V28() real ext-real Element of REAL
((- 1) * (c `2)) / (c `2) is V28() real ext-real Element of REAL
((- 1) * (c `2)) * ((c `2) ") is V28() real ext-real set
(- 1) / (c `2) is V28() real ext-real Element of REAL
(- 1) * ((c `2) ") is V28() real ext-real set
- (1 / (c `2)) is V28() real ext-real Element of REAL
|[(((c `1) / (c `2)) / (c `2)),(1 / (c `2))]| `1 is V28() real ext-real Element of REAL
K526(|[(((c `1) / (c `2)) / (c `2)),(1 / (c `2))]|,1) is V28() real ext-real Element of REAL
1 * (c `2) is V28() real ext-real Element of REAL
- (1 * (c `2)) is V28() real ext-real Element of REAL
(c `2) / (c `2) is V28() real ext-real Element of REAL
(c `2) * ((c `2) ") is V28() real ext-real set
(- (1 * (c `2))) / (c `2) is V28() real ext-real Element of REAL
(- (1 * (c `2))) * ((c `2) ") is V28() real ext-real set
O is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
O `1 is V28() real ext-real Element of REAL
K526(O,1) is V28() real ext-real Element of REAL
O `2 is V28() real ext-real Element of REAL
K526(O,2) is V28() real ext-real Element of REAL
- (O `2) is V28() real ext-real Element of REAL
- 1 is V28() real ext-real non positive Element of REAL
(- 1) * (c `2) is V28() real ext-real Element of REAL
((- 1) * (c `2)) / (c `2) is V28() real ext-real Element of REAL
((- 1) * (c `2)) * ((c `2) ") is V28() real ext-real set
(- 1) / (c `2) is V28() real ext-real Element of REAL
(- 1) * ((c `2) ") is V28() real ext-real set
- (1 / (c `2)) is V28() real ext-real Element of REAL
|[(((c `1) / (c `2)) / (c `2)),(1 / (c `2))]| `1 is V28() real ext-real Element of REAL
K526(|[(((c `1) / (c `2)) / (c `2)),(1 / (c `2))]|,1) is V28() real ext-real Element of REAL
[#] (((TOP-REAL 2) | K0) | f) is non proper open closed Element of K19( the carrier of (((TOP-REAL 2) | K0) | f))
K19( the carrier of (((TOP-REAL 2) | K0) | f)) is set
0.REAL 2 is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
2 |-> 0 is Relation-like NAT -defined REAL -valued Function-like FinSequence-like V119() V120() V121() Element of 2 -tuples_on REAL
K0 is set
f is non empty Element of K19( the carrier of (TOP-REAL 2))
f ` is Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | f is non empty strict TopSpace-like SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | f) is non empty set
K19( the carrier of ((TOP-REAL 2) | f)) is set
- ((1.REAL 2) `1) is V28() real ext-real Element of REAL
g is set
(f `) ` is Element of K19( the carrier of (TOP-REAL 2))
a is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
a `2 is V28() real ext-real Element of REAL
K526(a,2) is V28() real ext-real Element of REAL
a `1 is V28() real ext-real Element of REAL
K526(a,1) is V28() real ext-real Element of REAL
- (a `1) is V28() real ext-real Element of REAL
a is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
a `2 is V28() real ext-real Element of REAL
K526(a,2) is V28() real ext-real Element of REAL
a `1 is V28() real ext-real Element of REAL
K526(a,1) is V28() real ext-real Element of REAL
- (a `1) is V28() real ext-real Element of REAL
[#] ((TOP-REAL 2) | f) is non empty non proper open closed Element of K19( the carrier of ((TOP-REAL 2) | f))
K0 is set
f is non empty Element of K19( the carrier of (TOP-REAL 2))
f ` is Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | f is non empty strict TopSpace-like SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | f) is non empty set
K19( the carrier of ((TOP-REAL 2) | f)) is set
- ((1.REAL 2) `2) is V28() real ext-real Element of REAL
g is set
(f `) ` is Element of K19( the carrier of (TOP-REAL 2))
a is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
a `1 is V28() real ext-real Element of REAL
K526(a,1) is V28() real ext-real Element of REAL
a `2 is V28() real ext-real Element of REAL
K526(a,2) is V28() real ext-real Element of REAL
- (a `2) is V28() real ext-real Element of REAL
a is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
a `1 is V28() real ext-real Element of REAL
K526(a,1) is V28() real ext-real Element of REAL
a `2 is V28() real ext-real Element of REAL
K526(a,2) is V28() real ext-real Element of REAL
- (a `2) is V28() real ext-real Element of REAL
[#] ((TOP-REAL 2) | f) is non empty non proper open closed Element of K19( the carrier of ((TOP-REAL 2) | f))
K0 is non empty TopSpace-like TopStruct
the carrier of K0 is non empty set
K20( the carrier of K0, the carrier of R^1) is V121() set
K19(K20( the carrier of K0, the carrier of R^1)) is set
f is Relation-like the carrier of K0 -defined the carrier of R^1 -valued Function-like non empty total V18( the carrier of K0, the carrier of R^1) V119() V120() V121() Element of K19(K20( the carrier of K0, the carrier of R^1))
g is Relation-like the carrier of K0 -defined the carrier of R^1 -valued Function-like non empty total V18( the carrier of K0, the carrier of R^1) V119() V120() V121() Element of K19(K20( the carrier of K0, the carrier of R^1))
a is Element of the carrier of K0
f . a is V28() real ext-real set
g . a is V28() real ext-real set
f . a is V28() real ext-real Element of the carrier of R^1
g . a is V28() real ext-real Element of the carrier of R^1
b is V28() real ext-real Element of REAL
c is V28() real ext-real Element of REAL
b + c is V28() real ext-real Element of REAL
O is V28() real ext-real set
I is V28() real ext-real set
O + I is V28() real ext-real set
K20( the carrier of K0,REAL) is set
K19(K20( the carrier of K0,REAL)) is set
a is Relation-like the carrier of K0 -defined REAL -valued Function-like non empty total V18( the carrier of K0, REAL ) V119() V120() V121() Element of K19(K20( the carrier of K0,REAL))
a is Relation-like the carrier of K0 -defined REAL -valued Function-like non empty total V18( the carrier of K0, REAL ) V119() V120() V121() Element of K19(K20( the carrier of K0,REAL))
b is Relation-like the carrier of K0 -defined the carrier of R^1 -valued Function-like non empty total V18( the carrier of K0, the carrier of R^1) V119() V120() V121() Element of K19(K20( the carrier of K0, the carrier of R^1))
K19( the carrier of K0) is set
c is Element of the carrier of K0
b . c is V28() real ext-real Element of the carrier of R^1
d is Element of K19( the carrier of R^1)
f . c is V28() real ext-real Element of the carrier of R^1
g . c is V28() real ext-real Element of the carrier of R^1
O is V28() real ext-real Element of REAL
B is V28() real ext-real Element of REAL
O - B is V28() real ext-real Element of REAL
- B is V28() real ext-real set
O + (- B) is V28() real ext-real set
O + B is V28() real ext-real Element of REAL
].(O - B),(O + B).[ is Element of K19(REAL)
I is V28() real ext-real Element of REAL
B / 2 is V28() real ext-real Element of REAL
2 " is non empty V28() real ext-real positive non negative set
B * (2 ") is V28() real ext-real set
I - (B / 2) is V28() real ext-real Element of REAL
- (B / 2) is V28() real ext-real set
I + (- (B / 2)) is V28() real ext-real set
I + (B / 2) is V28() real ext-real Element of REAL
].(I - (B / 2)),(I + (B / 2)).[ is Element of K19(REAL)
C is Element of K19( the carrier of R^1)
A is V28() real ext-real Element of REAL
A - (B / 2) is V28() real ext-real Element of REAL
A + (- (B / 2)) is V28() real ext-real set
A + (B / 2) is V28() real ext-real Element of REAL
].(A - (B / 2)),(A + (B / 2)).[ is Element of K19(REAL)
D is Element of K19( the carrier of R^1)
ff is Element of K19( the carrier of K0)
g .: ff is V129() V130() V131() Element of K19( the carrier of R^1)
f2 is Element of K19( the carrier of K0)
f .: f2 is V129() V130() V131() Element of K19( the carrier of R^1)
f2 /\ ff is Element of K19( the carrier of K0)
b .: (f2 /\ ff) is V129() V130() V131() Element of K19( the carrier of R^1)
y is set
dom b is Element of K19( the carrier of K0)
x is set
b . x is V28() real ext-real set
x2 is Element of the carrier of K0
g . x2 is V28() real ext-real Element of the carrier of R^1
f . x2 is V28() real ext-real Element of the carrier of R^1
dom g is Element of K19( the carrier of K0)
z is V28() real ext-real Element of REAL
dom f is Element of K19( the carrier of K0)
u is V28() real ext-real Element of REAL
u + z is V28() real ext-real Element of REAL
(I - (B / 2)) + (A - (B / 2)) is V28() real ext-real Element of REAL
I + A is V28() real ext-real Element of REAL
(B / 2) + (B / 2) is V28() real ext-real Element of REAL
(I + A) - ((B / 2) + (B / 2)) is V28() real ext-real Element of REAL
- ((B / 2) + (B / 2)) is V28() real ext-real set
(I + A) + (- ((B / 2) + (B / 2))) is V28() real ext-real set
(I + (B / 2)) + (A + (B / 2)) is V28() real ext-real Element of REAL
(I + A) + ((B / 2) + (B / 2)) is V28() real ext-real Element of REAL
t is V28() real ext-real Element of REAL
c is Element of the carrier of K0
f . c is V28() real ext-real Element of the carrier of R^1
d is V28() real ext-real set
g . c is V28() real ext-real Element of the carrier of R^1
O is V28() real ext-real set
b . c is V28() real ext-real Element of the carrier of R^1
d + O is V28() real ext-real set
K0 is non empty TopSpace-like TopStruct
the carrier of K0 is non empty set
K20( the carrier of K0, the carrier of R^1) is V121() set
K19(K20( the carrier of K0, the carrier of R^1)) is set
f is V28() real ext-real set
g is Element of the carrier of R^1
the carrier of K0 --> g is Relation-like the carrier of K0 -defined the carrier of R^1 -valued Function-like non empty total V18( the carrier of K0, the carrier of R^1) V119() V120() V121() Element of K19(K20( the carrier of K0, the carrier of R^1))
b is Relation-like the carrier of K0 -defined the carrier of R^1 -valued Function-like non empty total V18( the carrier of K0, the carrier of R^1) V119() V120() V121() Element of K19(K20( the carrier of K0, the carrier of R^1))
K19( the carrier of K0) is set
d is Element of the carrier of K0
b . d is V28() real ext-real Element of the carrier of R^1
O is Element of K19( the carrier of R^1)
[#] K0 is non empty non proper open closed Element of K19( the carrier of K0)
b .: ([#] K0) is V129() V130() V131() Element of K19( the carrier of R^1)
A is set
dom b is Element of K19( the carrier of K0)
B is set
b . B is V28() real ext-real set
c is Element of the carrier of K0
( the carrier of K0 --> g) . c is V28() real ext-real Element of the carrier of R^1
K0 is non empty TopSpace-like TopStruct
the carrier of K0 is non empty set
K20( the carrier of K0, the carrier of R^1) is V121() set
K19(K20( the carrier of K0, the carrier of R^1)) is set
f is Relation-like the carrier of K0 -defined the carrier of R^1 -valued Function-like non empty total V18( the carrier of K0, the carrier of R^1) V119() V120() V121() Element of K19(K20( the carrier of K0, the carrier of R^1))
g is Relation-like the carrier of K0 -defined the carrier of R^1 -valued Function-like non empty total V18( the carrier of K0, the carrier of R^1) V119() V120() V121() Element of K19(K20( the carrier of K0, the carrier of R^1))
a is Element of the carrier of K0
f . a is V28() real ext-real set
g . a is V28() real ext-real set
f . a is V28() real ext-real Element of the carrier of R^1
g . a is V28() real ext-real Element of the carrier of R^1
b is V28() real ext-real Element of REAL
c is V28() real ext-real Element of REAL
b - c is V28() real ext-real Element of REAL
- c is V28() real ext-real set
b + (- c) is V28() real ext-real set
O is V28() real ext-real set
I is V28() real ext-real set
O - I is V28() real ext-real set
- I is V28() real ext-real set
O + (- I) is V28() real ext-real set
K20( the carrier of K0,REAL) is set
K19(K20( the carrier of K0,REAL)) is set
a is Relation-like the carrier of K0 -defined REAL -valued Function-like non empty total V18( the carrier of K0, REAL ) V119() V120() V121() Element of K19(K20( the carrier of K0,REAL))
a is Relation-like the carrier of K0 -defined REAL -valued Function-like non empty total V18( the carrier of K0, REAL ) V119() V120() V121() Element of K19(K20( the carrier of K0,REAL))
b is Relation-like the carrier of K0 -defined the carrier of R^1 -valued Function-like non empty total V18( the carrier of K0, the carrier of R^1) V119() V120() V121() Element of K19(K20( the carrier of K0, the carrier of R^1))
K19( the carrier of K0) is set
c is Element of the carrier of K0
b . c is V28() real ext-real Element of the carrier of R^1
d is Element of K19( the carrier of R^1)
f . c is V28() real ext-real Element of the carrier of R^1
g . c is V28() real ext-real Element of the carrier of R^1
O is V28() real ext-real Element of REAL
B is V28() real ext-real Element of REAL
O - B is V28() real ext-real Element of REAL
- B is V28() real ext-real set
O + (- B) is V28() real ext-real set
O + B is V28() real ext-real Element of REAL
].(O - B),(O + B).[ is Element of K19(REAL)
I is V28() real ext-real Element of REAL
B / 2 is V28() real ext-real Element of REAL
2 " is non empty V28() real ext-real positive non negative set
B * (2 ") is V28() real ext-real set
I - (B / 2) is V28() real ext-real Element of REAL
- (B / 2) is V28() real ext-real set
I + (- (B / 2)) is V28() real ext-real set
I + (B / 2) is V28() real ext-real Element of REAL
].(I - (B / 2)),(I + (B / 2)).[ is Element of K19(REAL)
C is Element of K19( the carrier of R^1)
A is V28() real ext-real Element of REAL
A - (B / 2) is V28() real ext-real Element of REAL
A + (- (B / 2)) is V28() real ext-real set
A + (B / 2) is V28() real ext-real Element of REAL
].(A - (B / 2)),(A + (B / 2)).[ is Element of K19(REAL)
D is Element of K19( the carrier of R^1)
ff is Element of K19( the carrier of K0)
g .: ff is V129() V130() V131() Element of K19( the carrier of R^1)
f2 is Element of K19( the carrier of K0)
f .: f2 is V129() V130() V131() Element of K19( the carrier of R^1)
f2 /\ ff is Element of K19( the carrier of K0)
b .: (f2 /\ ff) is V129() V130() V131() Element of K19( the carrier of R^1)
y is set
dom b is Element of K19( the carrier of K0)
x is set
b . x is V28() real ext-real set
x2 is Element of the carrier of K0
g . x2 is V28() real ext-real Element of the carrier of R^1
f . x2 is V28() real ext-real Element of the carrier of R^1
dom f is Element of K19( the carrier of K0)
dom g is Element of K19( the carrier of K0)
z is V28() real ext-real Element of REAL
u is V28() real ext-real Element of REAL
u - z is V28() real ext-real Element of REAL
- z is V28() real ext-real set
u + (- z) is V28() real ext-real set
(I - (B / 2)) - (A + (B / 2)) is V28() real ext-real Element of REAL
- (A + (B / 2)) is V28() real ext-real set
(I - (B / 2)) + (- (A + (B / 2))) is V28() real ext-real set
I - A is V28() real ext-real Element of REAL
- A is V28() real ext-real set
I + (- A) is V28() real ext-real set
(B / 2) + (B / 2) is V28() real ext-real Element of REAL
(I - A) - ((B / 2) + (B / 2)) is V28() real ext-real Element of REAL
- ((B / 2) + (B / 2)) is V28() real ext-real set
(I - A) + (- ((B / 2) + (B / 2))) is V28() real ext-real set
(I + (B / 2)) - (A - (B / 2)) is V28() real ext-real Element of REAL
- (A - (B / 2)) is V28() real ext-real set
(I + (B / 2)) + (- (A - (B / 2))) is V28() real ext-real set
(I - A) + ((B / 2) + (B / 2)) is V28() real ext-real Element of REAL
t is V28() real ext-real Element of REAL
c is Element of the carrier of K0
f . c is V28() real ext-real Element of the carrier of R^1
d is V28() real ext-real set
g . c is V28() real ext-real Element of the carrier of R^1
O is V28() real ext-real set
b . c is V28() real ext-real Element of the carrier of R^1
d - O is V28() real ext-real set
- O is V28() real ext-real set
d + (- O) is V28() real ext-real set
K0 is non empty TopSpace-like TopStruct
the carrier of K0 is non empty set
K20( the carrier of K0, the carrier of R^1) is V121() set
K19(K20( the carrier of K0, the carrier of R^1)) is set
f is Relation-like the carrier of K0 -defined the carrier of R^1 -valued Function-like non empty total V18( the carrier of K0, the carrier of R^1) V119() V120() V121() Element of K19(K20( the carrier of K0, the carrier of R^1))
g is Element of the carrier of K0
f . g is V28() real ext-real set
f . g is V28() real ext-real Element of the carrier of R^1
a is V28() real ext-real Element of REAL
a * a is V28() real ext-real Element of REAL
c is V28() real ext-real set
c * c is V28() real ext-real set
K20( the carrier of K0,REAL) is set
K19(K20( the carrier of K0,REAL)) is set
g is Relation-like the carrier of K0 -defined REAL -valued Function-like non empty total V18( the carrier of K0, REAL ) V119() V120() V121() Element of K19(K20( the carrier of K0,REAL))
g is Relation-like the carrier of K0 -defined REAL -valued Function-like non empty total V18( the carrier of K0, REAL ) V119() V120() V121() Element of K19(K20( the carrier of K0,REAL))
a is Relation-like the carrier of K0 -defined the carrier of R^1 -valued Function-like non empty total V18( the carrier of K0, the carrier of R^1) V119() V120() V121() Element of K19(K20( the carrier of K0, the carrier of R^1))
K19( the carrier of K0) is set
b is Element of the carrier of K0
a . b is V28() real ext-real Element of the carrier of R^1
c is Element of K19( the carrier of R^1)
f . b is V28() real ext-real Element of the carrier of R^1
d is V28() real ext-real Element of REAL
I is V28() real ext-real Element of REAL
d - I is V28() real ext-real Element of REAL
- I is V28() real ext-real set
d + (- I) is V28() real ext-real set
d + I is V28() real ext-real Element of REAL
].(d - I),(d + I).[ is Element of K19(REAL)
O is V28() real ext-real Element of REAL
O ^2 is V28() real ext-real Element of REAL
O * O is V28() real ext-real set
O * O is V28() real ext-real Element of REAL
sqrt (d + I) is V28() real ext-real Element of REAL
(sqrt (d + I)) ^2 is V28() real ext-real Element of REAL
(sqrt (d + I)) * (sqrt (d + I)) is V28() real ext-real set
sqrt d is V28() real ext-real Element of REAL
(sqrt (d + I)) - (sqrt d) is V28() real ext-real Element of REAL
- (sqrt d) is V28() real ext-real set
(sqrt (d + I)) + (- (sqrt d)) is V28() real ext-real set
O - ((sqrt (d + I)) - (sqrt d)) is V28() real ext-real Element of REAL
- ((sqrt (d + I)) - (sqrt d)) is V28() real ext-real set
O + (- ((sqrt (d + I)) - (sqrt d))) is V28() real ext-real set
O + ((sqrt (d + I)) - (sqrt d)) is V28() real ext-real Element of REAL
].(O - ((sqrt (d + I)) - (sqrt d))),(O + ((sqrt (d + I)) - (sqrt d))).[ is Element of K19(REAL)
B is Element of K19( the carrier of R^1)
C is Element of K19( the carrier of K0)
f .: C is V129() V130() V131() Element of K19( the carrier of R^1)
((sqrt (d + I)) - (sqrt d)) ^2 is V28() real ext-real Element of REAL
((sqrt (d + I)) - (sqrt d)) * ((sqrt (d + I)) - (sqrt d)) is V28() real ext-real set
2 * (sqrt (d + I)) is V28() real ext-real Element of REAL
(2 * (sqrt (d + I))) * (sqrt d) is V28() real ext-real Element of REAL
((sqrt (d + I)) ^2) - ((2 * (sqrt (d + I))) * (sqrt d)) is V28() real ext-real Element of REAL
- ((2 * (sqrt (d + I))) * (sqrt d)) is V28() real ext-real set
((sqrt (d + I)) ^2) + (- ((2 * (sqrt (d + I))) * (sqrt d))) is V28() real ext-real set
(sqrt d) ^2 is V28() real ext-real Element of REAL
(sqrt d) * (sqrt d) is V28() real ext-real set
(((sqrt (d + I)) ^2) - ((2 * (sqrt (d + I))) * (sqrt d))) + ((sqrt d) ^2) is V28() real ext-real Element of REAL
(d + I) - ((2 * (sqrt (d + I))) * (sqrt d)) is V28() real ext-real Element of REAL
(d + I) + (- ((2 * (sqrt (d + I))) * (sqrt d))) is V28() real ext-real set
((d + I) - ((2 * (sqrt (d + I))) * (sqrt d))) + ((sqrt d) ^2) is V28() real ext-real Element of REAL
I - ((2 * (sqrt (d + I))) * (sqrt d)) is V28() real ext-real Element of REAL
I + (- ((2 * (sqrt (d + I))) * (sqrt d))) is V28() real ext-real set
d + (I - ((2 * (sqrt (d + I))) * (sqrt d))) is V28() real ext-real Element of REAL
(d + (I - ((2 * (sqrt (d + I))) * (sqrt d)))) + d is V28() real ext-real Element of REAL
2 * d is V28() real ext-real Element of REAL
(2 * d) + I is V28() real ext-real Element of REAL
((2 * d) + I) - ((2 * (sqrt (d + I))) * (sqrt d)) is V28() real ext-real Element of REAL
((2 * d) + I) + (- ((2 * (sqrt (d + I))) * (sqrt d))) is V28() real ext-real set
a .: C is V129() V130() V131() Element of K19( the carrier of R^1)
ff is set
dom a is Element of K19( the carrier of K0)
f2 is set
a . f2 is V28() real ext-real set
g2 is Element of the carrier of K0
f . g2 is V28() real ext-real Element of the carrier of R^1
dom f is Element of K19( the carrier of K0)
y is V28() real ext-real Element of REAL
- 2 is V28() real ext-real non positive Element of REAL
(- 2) * (((sqrt (d + I)) - (sqrt d)) ^2) is V28() real ext-real Element of REAL
(O - ((sqrt (d + I)) - (sqrt d))) ^2 is V28() real ext-real Element of REAL
(O - ((sqrt (d + I)) - (sqrt d))) * (O - ((sqrt (d + I)) - (sqrt d))) is V28() real ext-real set
y ^2 is V28() real ext-real Element of REAL
y * y is V28() real ext-real set
((O - ((sqrt (d + I)) - (sqrt d))) ^2) - (y ^2) is V28() real ext-real Element of REAL
- (y ^2) is V28() real ext-real set
((O - ((sqrt (d + I)) - (sqrt d))) ^2) + (- (y ^2)) is V28() real ext-real set
2 * (((sqrt (d + I)) - (sqrt d)) ^2) is V28() real ext-real Element of REAL
- (2 * (((sqrt (d + I)) - (sqrt d)) ^2)) is V28() real ext-real Element of REAL
(((O - ((sqrt (d + I)) - (sqrt d))) ^2) - (y ^2)) + (- (2 * (((sqrt (d + I)) - (sqrt d)) ^2))) is V28() real ext-real Element of REAL
(((O - ((sqrt (d + I)) - (sqrt d))) ^2) - (y ^2)) + 0 is V28() real ext-real Element of REAL
((O - ((sqrt (d + I)) - (sqrt d))) ^2) - (2 * (((sqrt (d + I)) - (sqrt d)) ^2)) is V28() real ext-real Element of REAL
- (2 * (((sqrt (d + I)) - (sqrt d)) ^2)) is V28() real ext-real set
((O - ((sqrt (d + I)) - (sqrt d))) ^2) + (- (2 * (((sqrt (d + I)) - (sqrt d)) ^2))) is V28() real ext-real set
(((O - ((sqrt (d + I)) - (sqrt d))) ^2) - (2 * (((sqrt (d + I)) - (sqrt d)) ^2))) - (y ^2) is V28() real ext-real Element of REAL
(((O - ((sqrt (d + I)) - (sqrt d))) ^2) - (2 * (((sqrt (d + I)) - (sqrt d)) ^2))) + (- (y ^2)) is V28() real ext-real set
y * y is V28() real ext-real Element of REAL
(O ^2) - (((sqrt (d + I)) - (sqrt d)) ^2) is V28() real ext-real Element of REAL
- (((sqrt (d + I)) - (sqrt d)) ^2) is V28() real ext-real set
(O ^2) + (- (((sqrt (d + I)) - (sqrt d)) ^2)) is V28() real ext-real set
0 - 0 is V28() real ext-real Element of REAL
- 0 is V28() real ext-real set
0 + (- 0) is V28() real ext-real set
2 * O is V28() real ext-real Element of REAL
(2 * O) * ((sqrt (d + I)) - (sqrt d)) is V28() real ext-real Element of REAL
((O ^2) - (((sqrt (d + I)) - (sqrt d)) ^2)) - ((2 * O) * ((sqrt (d + I)) - (sqrt d))) is V28() real ext-real Element of REAL
- ((2 * O) * ((sqrt (d + I)) - (sqrt d))) is V28() real ext-real set
((O ^2) - (((sqrt (d + I)) - (sqrt d)) ^2)) + (- ((2 * O) * ((sqrt (d + I)) - (sqrt d)))) is V28() real ext-real set
y * y is V28() real ext-real Element of REAL
y * y is V28() real ext-real Element of REAL
y * y is V28() real ext-real Element of REAL
- O is V28() real ext-real Element of REAL
(- O) - ((sqrt (d + I)) - (sqrt d)) is V28() real ext-real Element of REAL
(- O) + (- ((sqrt (d + I)) - (sqrt d))) is V28() real ext-real set
- (O + ((sqrt (d + I)) - (sqrt d))) is V28() real ext-real Element of REAL
y - (- (O + ((sqrt (d + I)) - (sqrt d)))) is V28() real ext-real Element of REAL
- (- (O + ((sqrt (d + I)) - (sqrt d)))) is V28() real ext-real set
y + (- (- (O + ((sqrt (d + I)) - (sqrt d))))) is V28() real ext-real set
(O + ((sqrt (d + I)) - (sqrt d))) - y is V28() real ext-real Element of REAL
- y is V28() real ext-real set
(O + ((sqrt (d + I)) - (sqrt d))) + (- y) is V28() real ext-real set
(O + ((sqrt (d + I)) - (sqrt d))) + y is V28() real ext-real Element of REAL
((O + ((sqrt (d + I)) - (sqrt d))) - y) * ((O + ((sqrt (d + I)) - (sqrt d))) + y) is V28() real ext-real Element of REAL
(O + ((sqrt (d + I)) - (sqrt d))) ^2 is V28() real ext-real Element of REAL
(O + ((sqrt (d + I)) - (sqrt d))) * (O + ((sqrt (d + I)) - (sqrt d))) is V28() real ext-real set
y ^2 is V28() real ext-real Element of REAL
y * y is V28() real ext-real set
((O + ((sqrt (d + I)) - (sqrt d))) ^2) - (y ^2) is V28() real ext-real Element of REAL
- (y ^2) is V28() real ext-real set
((O + ((sqrt (d + I)) - (sqrt d))) ^2) + (- (y ^2)) is V28() real ext-real set
sqrt d is V28() real ext-real Element of REAL
(sqrt (d + I)) - (sqrt d) is V28() real ext-real Element of REAL
- (sqrt d) is V28() real ext-real set
(sqrt (d + I)) + (- (sqrt d)) is V28() real ext-real set
O - ((sqrt (d + I)) - (sqrt d)) is V28() real ext-real Element of REAL
- ((sqrt (d + I)) - (sqrt d)) is V28() real ext-real set
O + (- ((sqrt (d + I)) - (sqrt d))) is V28() real ext-real set
O + ((sqrt (d + I)) - (sqrt d)) is V28() real ext-real Element of REAL
].(O - ((sqrt (d + I)) - (sqrt d))),(O + ((sqrt (d + I)) - (sqrt d))).[ is Element of K19(REAL)
B is Element of K19( the carrier of R^1)
C is Element of K19( the carrier of K0)
f .: C is V129() V130() V131() Element of K19( the carrier of R^1)
- O is V28() real ext-real Element of REAL
(- O) ^2 is V28() real ext-real Element of REAL
(- O) * (- O) is V28() real ext-real set
((sqrt (d + I)) - (sqrt d)) ^2 is V28() real ext-real Element of REAL
((sqrt (d + I)) - (sqrt d)) * ((sqrt (d + I)) - (sqrt d)) is V28() real ext-real set
2 * (sqrt (d + I)) is V28() real ext-real Element of REAL
(2 * (sqrt (d + I))) * (sqrt d) is V28() real ext-real Element of REAL
(d + I) - ((2 * (sqrt (d + I))) * (sqrt d)) is V28() real ext-real Element of REAL
- ((2 * (sqrt (d + I))) * (sqrt d)) is V28() real ext-real set
(d + I) + (- ((2 * (sqrt (d + I))) * (sqrt d))) is V28() real ext-real set
(sqrt d) ^2 is V28() real ext-real Element of REAL
(sqrt d) * (sqrt d) is V28() real ext-real set
((d + I) - ((2 * (sqrt (d + I))) * (sqrt d))) + ((sqrt d) ^2) is V28() real ext-real Element of REAL
I - ((2 * (sqrt (d + I))) * (sqrt d)) is V28() real ext-real Element of REAL
I + (- ((2 * (sqrt (d + I))) * (sqrt d))) is V28() real ext-real set
d + (I - ((2 * (sqrt (d + I))) * (sqrt d))) is V28() real ext-real Element of REAL
(d + (I - ((2 * (sqrt (d + I))) * (sqrt d)))) + d is V28() real ext-real Element of REAL
2 * d is V28() real ext-real Element of REAL
(2 * d) + I is V28() real ext-real Element of REAL
((2 * d) + I) - ((2 * (sqrt (d + I))) * (sqrt d)) is V28() real ext-real Element of REAL
((2 * d) + I) + (- ((2 * (sqrt (d + I))) * (sqrt d))) is V28() real ext-real set
2 * O is V28() real ext-real Element of REAL
(2 * O) * ((sqrt (d + I)) - (sqrt d)) is V28() real ext-real Element of REAL
- ((2 * O) * ((sqrt (d + I)) - (sqrt d))) is V28() real ext-real Element of REAL
(- ((2 * O) * ((sqrt (d + I)) - (sqrt d)))) + (((sqrt (d + I)) - (sqrt d)) ^2) is V28() real ext-real Element of REAL
a .: C is V129() V130() V131() Element of K19( the carrier of R^1)
ff is set
dom a is Element of K19( the carrier of K0)
f2 is set
a . f2 is V28() real ext-real set
g2 is Element of the carrier of K0
f . g2 is V28() real ext-real Element of the carrier of R^1
dom f is Element of K19( the carrier of K0)
y is V28() real ext-real Element of REAL
- 2 is V28() real ext-real non positive Element of REAL
(- 2) * (((sqrt (d + I)) - (sqrt d)) ^2) is V28() real ext-real Element of REAL
(O + ((sqrt (d + I)) - (sqrt d))) ^2 is V28() real ext-real Element of REAL
(O + ((sqrt (d + I)) - (sqrt d))) * (O + ((sqrt (d + I)) - (sqrt d))) is V28() real ext-real set
y ^2 is V28() real ext-real Element of REAL
y * y is V28() real ext-real set
((O + ((sqrt (d + I)) - (sqrt d))) ^2) - (y ^2) is V28() real ext-real Element of REAL
- (y ^2) is V28() real ext-real set
((O + ((sqrt (d + I)) - (sqrt d))) ^2) + (- (y ^2)) is V28() real ext-real set
2 * (((sqrt (d + I)) - (sqrt d)) ^2) is V28() real ext-real Element of REAL
- (2 * (((sqrt (d + I)) - (sqrt d)) ^2)) is V28() real ext-real Element of REAL
(((O + ((sqrt (d + I)) - (sqrt d))) ^2) - (y ^2)) + (- (2 * (((sqrt (d + I)) - (sqrt d)) ^2))) is V28() real ext-real Element of REAL
(((O + ((sqrt (d + I)) - (sqrt d))) ^2) - (y ^2)) + 0 is V28() real ext-real Element of REAL
- y is V28() real ext-real Element of REAL
- (O + ((sqrt (d + I)) - (sqrt d))) is V28() real ext-real Element of REAL
(- y) ^2 is V28() real ext-real Element of REAL
(- y) * (- y) is V28() real ext-real set
(- (O + ((sqrt (d + I)) - (sqrt d)))) ^2 is V28() real ext-real Element of REAL
(- (O + ((sqrt (d + I)) - (sqrt d)))) * (- (O + ((sqrt (d + I)) - (sqrt d)))) is V28() real ext-real set
((O + ((sqrt (d + I)) - (sqrt d))) ^2) - (2 * (((sqrt (d + I)) - (sqrt d)) ^2)) is V28() real ext-real Element of REAL
- (2 * (((sqrt (d + I)) - (sqrt d)) ^2)) is V28() real ext-real set
((O + ((sqrt (d + I)) - (sqrt d))) ^2) + (- (2 * (((sqrt (d + I)) - (sqrt d)) ^2))) is V28() real ext-real set
(((O + ((sqrt (d + I)) - (sqrt d))) ^2) - (2 * (((sqrt (d + I)) - (sqrt d)) ^2))) - (y ^2) is V28() real ext-real Element of REAL
(((O + ((sqrt (d + I)) - (sqrt d))) ^2) - (2 * (((sqrt (d + I)) - (sqrt d)) ^2))) + (- (y ^2)) is V28() real ext-real set
y * y is V28() real ext-real Element of REAL
(O + ((sqrt (d + I)) - (sqrt d))) + (- O) is V28() real ext-real Element of REAL
0 + (- O) is V28() real ext-real Element of REAL
(O ^2) - (O ^2) is V28() real ext-real Element of REAL
- (O ^2) is V28() real ext-real set
(O ^2) + (- (O ^2)) is V28() real ext-real set
(O ^2) - (((sqrt (d + I)) - (sqrt d)) ^2) is V28() real ext-real Element of REAL
- (((sqrt (d + I)) - (sqrt d)) ^2) is V28() real ext-real set
(O ^2) + (- (((sqrt (d + I)) - (sqrt d)) ^2)) is V28() real ext-real set
0 + 0 is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real Element of NAT
((O ^2) - (((sqrt (d + I)) - (sqrt d)) ^2)) + ((2 * O) * ((sqrt (d + I)) - (sqrt d))) is V28() real ext-real Element of REAL
y * y is V28() real ext-real Element of REAL
y * y is V28() real ext-real Element of REAL
y * y is V28() real ext-real Element of REAL
y - (O - ((sqrt (d + I)) - (sqrt d))) is V28() real ext-real Element of REAL
- (O - ((sqrt (d + I)) - (sqrt d))) is V28() real ext-real set
y + (- (O - ((sqrt (d + I)) - (sqrt d)))) is V28() real ext-real set
- y is V28() real ext-real Element of REAL
(- y) + (O - ((sqrt (d + I)) - (sqrt d))) is V28() real ext-real Element of REAL
- ((- y) + (O - ((sqrt (d + I)) - (sqrt d)))) is V28() real ext-real Element of REAL
(O - ((sqrt (d + I)) - (sqrt d))) + (- y) is V28() real ext-real Element of REAL
(- O) - ((sqrt (d + I)) - (sqrt d)) is V28() real ext-real Element of REAL
(- O) + (- ((sqrt (d + I)) - (sqrt d))) is V28() real ext-real set
- ((- O) - ((sqrt (d + I)) - (sqrt d))) is V28() real ext-real Element of REAL
- (O - ((sqrt (d + I)) - (sqrt d))) is V28() real ext-real Element of REAL
(- (O - ((sqrt (d + I)) - (sqrt d)))) + (O - ((sqrt (d + I)) - (sqrt d))) is V28() real ext-real Element of REAL
y + (O - ((sqrt (d + I)) - (sqrt d))) is V28() real ext-real Element of REAL
(O - ((sqrt (d + I)) - (sqrt d))) - y is V28() real ext-real Element of REAL
- y is V28() real ext-real set
(O - ((sqrt (d + I)) - (sqrt d))) + (- y) is V28() real ext-real set
(O - ((sqrt (d + I)) - (sqrt d))) + y is V28() real ext-real Element of REAL
((O - ((sqrt (d + I)) - (sqrt d))) - y) * ((O - ((sqrt (d + I)) - (sqrt d))) + y) is V28() real ext-real Element of REAL
(O - ((sqrt (d + I)) - (sqrt d))) ^2 is V28() real ext-real Element of REAL
(O - ((sqrt (d + I)) - (sqrt d))) * (O - ((sqrt (d + I)) - (sqrt d))) is V28() real ext-real set
y ^2 is V28() real ext-real Element of REAL
y * y is V28() real ext-real set
((O - ((sqrt (d + I)) - (sqrt d))) ^2) - (y ^2) is V28() real ext-real Element of REAL
- (y ^2) is V28() real ext-real set
((O - ((sqrt (d + I)) - (sqrt d))) ^2) + (- (y ^2)) is V28() real ext-real set
A is Element of K19( the carrier of K0)
a .: A is V129() V130() V131() Element of K19( the carrier of R^1)
B is Element of K19( the carrier of K0)
a .: B is V129() V130() V131() Element of K19( the carrier of R^1)
b is Element of the carrier of K0
f . b is V28() real ext-real Element of the carrier of R^1
c is V28() real ext-real set
a . b is V28() real ext-real Element of the carrier of R^1
c * c is V28() real ext-real set
K0 is non empty TopSpace-like TopStruct
the carrier of K0 is non empty set
K20( the carrier of K0, the carrier of R^1) is V121() set
K19(K20( the carrier of K0, the carrier of R^1)) is set
f is Relation-like the carrier of K0 -defined the carrier of R^1 -valued Function-like non empty total V18( the carrier of K0, the carrier of R^1) V119() V120() V121() Element of K19(K20( the carrier of K0, the carrier of R^1))
g is V28() real ext-real set
a is Element of the carrier of K0
f . a is V28() real ext-real set
f . a is V28() real ext-real Element of the carrier of R^1
b is V28() real ext-real Element of REAL
g * b is V28() real ext-real Element of REAL
c is V28() real ext-real Element of REAL
d is V28() real ext-real Element of REAL
g * d is V28() real ext-real Element of REAL
K20( the carrier of K0,REAL) is set
K19(K20( the carrier of K0,REAL)) is set
a is Relation-like the carrier of K0 -defined REAL -valued Function-like non empty total V18( the carrier of K0, REAL ) V119() V120() V121() Element of K19(K20( the carrier of K0,REAL))
a is Relation-like the carrier of K0 -defined REAL -valued Function-like non empty total V18( the carrier of K0, REAL ) V119() V120() V121() Element of K19(K20( the carrier of K0,REAL))
b is Relation-like the carrier of K0 -defined the carrier of R^1 -valued Function-like non empty total V18( the carrier of K0, the carrier of R^1) V119() V120() V121() Element of K19(K20( the carrier of K0, the carrier of R^1))
c is Element of the carrier of K0
f . c is V28() real ext-real Element of the carrier of R^1
b . c is V28() real ext-real Element of the carrier of R^1
d is V28() real ext-real set
g * d is V28() real ext-real set
O is V28() real ext-real Element of REAL
g * O is V28() real ext-real Element of REAL
K19( the carrier of K0) is set
c is Element of the carrier of K0
b . c is V28() real ext-real Element of the carrier of R^1
d is Element of K19( the carrier of R^1)
f . c is V28() real ext-real Element of the carrier of R^1
O is V28() real ext-real Element of REAL
A is V28() real ext-real Element of REAL
O - A is V28() real ext-real Element of REAL
- A is V28() real ext-real set
O + (- A) is V28() real ext-real set
O + A is V28() real ext-real Element of REAL
].(O - A),(O + A).[ is Element of K19(REAL)
I is V28() real ext-real Element of REAL
g * I is V28() real ext-real Element of REAL
A / g is V28() real ext-real Element of REAL
g " is V28() real ext-real set
A * (g ") is V28() real ext-real set
I - (A / g) is V28() real ext-real Element of REAL
- (A / g) is V28() real ext-real set
I + (- (A / g)) is V28() real ext-real set
I + (A / g) is V28() real ext-real Element of REAL
].(I - (A / g)),(I + (A / g)).[ is Element of K19(REAL)
C is Element of K19( the carrier of R^1)
D is Element of K19( the carrier of K0)
f .: D is V129() V130() V131() Element of K19( the carrier of R^1)
b .: D is V129() V130() V131() Element of K19( the carrier of R^1)
f2 is set
dom b is Element of K19( the carrier of K0)
g2 is set
b . g2 is V28() real ext-real set
y is Element of the carrier of K0
f . y is V28() real ext-real Element of the carrier of R^1
x is V28() real ext-real Element of REAL
g * x is V28() real ext-real Element of REAL
dom f is Element of K19( the carrier of K0)
g * (I - (A / g)) is V28() real ext-real Element of REAL
g * (I + (A / g)) is V28() real ext-real Element of REAL
g * (A / g) is V28() real ext-real Element of REAL
(g * I) + (g * (A / g)) is V28() real ext-real Element of REAL
(g * I) - (g * (A / g)) is V28() real ext-real Element of REAL
- (g * (A / g)) is V28() real ext-real set
(g * I) + (- (g * (A / g))) is V28() real ext-real set
x2 is V28() real ext-real Element of REAL
I - A is V28() real ext-real Element of REAL
I + (- A) is V28() real ext-real set
I + A is V28() real ext-real Element of REAL
].(I - A),(I + A).[ is Element of K19(REAL)
C is Element of K19( the carrier of R^1)
D is Element of K19( the carrier of K0)
f .: D is V129() V130() V131() Element of K19( the carrier of R^1)
b .: D is V129() V130() V131() Element of K19( the carrier of R^1)
f2 is set
dom b is Element of K19( the carrier of K0)
g2 is set
b . g2 is V28() real ext-real set
y is Element of the carrier of K0
f . y is V28() real ext-real Element of the carrier of R^1
x is V28() real ext-real Element of REAL
g * x is V28() real ext-real Element of REAL
B is Element of K19( the carrier of K0)
b .: B is V129() V130() V131() Element of K19( the carrier of R^1)
C is Element of K19( the carrier of K0)
b .: C is V129() V130() V131() Element of K19( the carrier of R^1)
- g is V28() real ext-real set
A / (- g) is V28() real ext-real Element of REAL
(- g) " is V28() real ext-real set
A * ((- g) ") is V28() real ext-real set
I - (A / (- g)) is V28() real ext-real Element of REAL
- (A / (- g)) is V28() real ext-real set
I + (- (A / (- g))) is V28() real ext-real set
I + (A / (- g)) is V28() real ext-real Element of REAL
].(I - (A / (- g))),(I + (A / (- g))).[ is Element of K19(REAL)
C is Element of K19( the carrier of R^1)
D is Element of K19( the carrier of K0)
f .: D is V129() V130() V131() Element of K19( the carrier of R^1)
(- g) * (A / (- g)) is V28() real ext-real Element of REAL
b .: D is V129() V130() V131() Element of K19( the carrier of R^1)
f2 is set
dom b is Element of K19( the carrier of K0)
g2 is set
b . g2 is V28() real ext-real set
y is Element of the carrier of K0
f . y is V28() real ext-real Element of the carrier of R^1
dom f is Element of K19( the carrier of K0)
x is V28() real ext-real Element of REAL
g * (I - (A / (- g))) is V28() real ext-real Element of REAL
g * x is V28() real ext-real Element of REAL
g * (I + (A / (- g))) is V28() real ext-real Element of REAL
g * (A / (- g)) is V28() real ext-real Element of REAL
- (g * (A / (- g))) is V28() real ext-real Element of REAL
(g * I) - (- (g * (A / (- g)))) is V28() real ext-real Element of REAL
- (- (g * (A / (- g)))) is V28() real ext-real set
(g * I) + (- (- (g * (A / (- g))))) is V28() real ext-real set
(g * I) + (- (g * (A / (- g)))) is V28() real ext-real Element of REAL
B is Element of K19( the carrier of K0)
b .: B is V129() V130() V131() Element of K19( the carrier of R^1)
C is Element of K19( the carrier of K0)
b .: C is V129() V130() V131() Element of K19( the carrier of R^1)
K0 is non empty TopSpace-like TopStruct
the carrier of K0 is non empty set
K20( the carrier of K0, the carrier of R^1) is V121() set
K19(K20( the carrier of K0, the carrier of R^1)) is set
f is Relation-like the carrier of K0 -defined the carrier of R^1 -valued Function-like non empty total V18( the carrier of K0, the carrier of R^1) V119() V120() V121() Element of K19(K20( the carrier of K0, the carrier of R^1))
g is V28() real ext-real set
b is Element of the carrier of K0
f . b is V28() real ext-real set
f . b is V28() real ext-real Element of the carrier of R^1
c is V28() real ext-real Element of REAL
a is V28() real ext-real Element of REAL
c + a is V28() real ext-real Element of REAL
O is V28() real ext-real Element of REAL
O + a is V28() real ext-real Element of REAL
K20( the carrier of K0,REAL) is set
K19(K20( the carrier of K0,REAL)) is set
a is Relation-like the carrier of K0 -defined REAL -valued Function-like non empty total V18( the carrier of K0, REAL ) V119() V120() V121() Element of K19(K20( the carrier of K0,REAL))
a is Relation-like the carrier of K0 -defined REAL -valued Function-like non empty total V18( the carrier of K0, REAL ) V119() V120() V121() Element of K19(K20( the carrier of K0,REAL))
b is Relation-like the carrier of K0 -defined the carrier of R^1 -valued Function-like non empty total V18( the carrier of K0, the carrier of R^1) V119() V120() V121() Element of K19(K20( the carrier of K0, the carrier of R^1))
K19( the carrier of K0) is set
c is Element of the carrier of K0
b . c is V28() real ext-real Element of the carrier of R^1
d is Element of K19( the carrier of R^1)
f . c is V28() real ext-real Element of the carrier of R^1
O is V28() real ext-real Element of REAL
A is V28() real ext-real Element of REAL
O - A is V28() real ext-real Element of REAL
- A is V28() real ext-real set
O + (- A) is V28() real ext-real set
O + A is V28() real ext-real Element of REAL
].(O - A),(O + A).[ is Element of K19(REAL)
I is V28() real ext-real Element of REAL
I - A is V28() real ext-real Element of REAL
I + (- A) is V28() real ext-real set
I + A is V28() real ext-real Element of REAL
].(I - A),(I + A).[ is Element of K19(REAL)
C is Element of K19( the carrier of R^1)
D is Element of K19( the carrier of K0)
f .: D is V129() V130() V131() Element of K19( the carrier of R^1)
b .: D is V129() V130() V131() Element of K19( the carrier of R^1)
f2 is set
dom b is Element of K19( the carrier of K0)
g2 is set
b . g2 is V28() real ext-real set
y is Element of the carrier of K0
f . y is V28() real ext-real Element of the carrier of R^1
dom f is Element of K19( the carrier of K0)
x is V28() real ext-real Element of REAL
x + g is V28() real ext-real Element of REAL
(I - A) + g is V28() real ext-real Element of REAL
I + g is V28() real ext-real Element of REAL
(I + g) - A is V28() real ext-real Element of REAL
(I + g) + (- A) is V28() real ext-real set
(I + A) + g is V28() real ext-real Element of REAL
c is Element of the carrier of K0
f . c is V28() real ext-real Element of the carrier of R^1
b . c is V28() real ext-real Element of the carrier of R^1
d is V28() real ext-real set
d + g is V28() real ext-real set
O is V28() real ext-real Element of REAL
O + g is V28() real ext-real Element of REAL
K0 is non empty TopSpace-like TopStruct
the carrier of K0 is non empty set
K20( the carrier of K0, the carrier of R^1) is V121() set
K19(K20( the carrier of K0, the carrier of R^1)) is set
f is Relation-like the carrier of K0 -defined the carrier of R^1 -valued Function-like non empty total V18( the carrier of K0, the carrier of R^1) V119() V120() V121() Element of K19(K20( the carrier of K0, the carrier of R^1))
g is Relation-like the carrier of K0 -defined the carrier of R^1 -valued Function-like non empty total V18( the carrier of K0, the carrier of R^1) V119() V120() V121() Element of K19(K20( the carrier of K0, the carrier of R^1))
a is Relation-like the carrier of K0 -defined the carrier of R^1 -valued Function-like non empty total V18( the carrier of K0, the carrier of R^1) V119() V120() V121() Element of K19(K20( the carrier of K0, the carrier of R^1))
b is Relation-like the carrier of K0 -defined the carrier of R^1 -valued Function-like non empty total V18( the carrier of K0, the carrier of R^1) V119() V120() V121() Element of K19(K20( the carrier of K0, the carrier of R^1))
c is Relation-like the carrier of K0 -defined the carrier of R^1 -valued Function-like non empty total V18( the carrier of K0, the carrier of R^1) V119() V120() V121() Element of K19(K20( the carrier of K0, the carrier of R^1))
d is Relation-like the carrier of K0 -defined the carrier of R^1 -valued Function-like non empty total V18( the carrier of K0, the carrier of R^1) V119() V120() V121() Element of K19(K20( the carrier of K0, the carrier of R^1))
O is Relation-like the carrier of K0 -defined the carrier of R^1 -valued Function-like non empty total V18( the carrier of K0, the carrier of R^1) V119() V120() V121() Element of K19(K20( the carrier of K0, the carrier of R^1))
4 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real ext-real positive non negative Element of NAT
1 / 4 is V28() real ext-real non negative Element of REAL
4 " is non empty V28() real ext-real positive non negative set
1 * (4 ") is V28() real ext-real non negative set
I is Relation-like the carrier of K0 -defined the carrier of R^1 -valued Function-like non empty total V18( the carrier of K0, the carrier of R^1) V119() V120() V121() Element of K19(K20( the carrier of K0, the carrier of R^1))
A is Element of the carrier of K0
f . A is V28() real ext-real Element of the carrier of R^1
g . A is V28() real ext-real Element of the carrier of R^1
I . A is V28() real ext-real Element of the carrier of R^1
B is V28() real ext-real set
C is V28() real ext-real set
B * C is V28() real ext-real set
c . A is V28() real ext-real Element of the carrier of R^1
B - C is V28() real ext-real set
- C is V28() real ext-real set
B + (- C) is V28() real ext-real set
d . A is V28() real ext-real Element of the carrier of R^1
(B - C) ^2 is V28() real ext-real set
(B - C) * (B - C) is V28() real ext-real set
a . A is V28() real ext-real Element of the carrier of R^1
B + C is V28() real ext-real set
b . A is V28() real ext-real Element of the carrier of R^1
(B + C) ^2 is V28() real ext-real set
(B + C) * (B + C) is V28() real ext-real set
O . A is V28() real ext-real Element of the carrier of R^1
((B + C) ^2) - ((B - C) ^2) is V28() real ext-real set
- ((B - C) ^2) is V28() real ext-real set
((B + C) ^2) + (- ((B - C) ^2)) is V28() real ext-real set
B ^2 is V28() real ext-real set
B * B is V28() real ext-real set
2 * B is V28() real ext-real Element of REAL
(2 * B) * C is V28() real ext-real Element of REAL
(B ^2) + ((2 * B) * C) is V28() real ext-real Element of REAL
C ^2 is V28() real ext-real set
C * C is V28() real ext-real set
((B ^2) + ((2 * B) * C)) + (C ^2) is V28() real ext-real Element of REAL
(((B ^2) + ((2 * B) * C)) + (C ^2)) - ((B - C) ^2) is V28() real ext-real Element of REAL
(((B ^2) + ((2 * B) * C)) + (C ^2)) + (- ((B - C) ^2)) is V28() real ext-real set
(1 / 4) * ((((B ^2) + ((2 * B) * C)) + (C ^2)) - ((B - C) ^2)) is V28() real ext-real Element of REAL
K0 is non empty TopSpace-like TopStruct
the carrier of K0 is non empty set
K20( the carrier of K0, the carrier of R^1) is V121() set
K19(K20( the carrier of K0, the carrier of R^1)) is set
f is Relation-like the carrier of K0 -defined the carrier of R^1 -valued Function-like non empty total V18( the carrier of K0, the carrier of R^1) V119() V120() V121() Element of K19(K20( the carrier of K0, the carrier of R^1))
g is Element of the carrier of K0
f . g is V28() real ext-real set
f . g is V28() real ext-real Element of the carrier of R^1
a is V28() real ext-real Element of REAL
1 / a is V28() real ext-real Element of REAL
a " is V28() real ext-real set
1 * (a ") is V28() real ext-real set
c is V28() real ext-real Element of REAL
1 / c is V28() real ext-real Element of REAL
c " is V28() real ext-real set
1 * (c ") is V28() real ext-real set
K20( the carrier of K0,REAL) is set
K19(K20( the carrier of K0,REAL)) is set
g is Relation-like the carrier of K0 -defined REAL -valued Function-like non empty total V18( the carrier of K0, REAL ) V119() V120() V121() Element of K19(K20( the carrier of K0,REAL))
g is Relation-like the carrier of K0 -defined REAL -valued Function-like non empty total V18( the carrier of K0, REAL ) V119() V120() V121() Element of K19(K20( the carrier of K0,REAL))
a is Relation-like the carrier of K0 -defined the carrier of R^1 -valued Function-like non empty total V18( the carrier of K0, the carrier of R^1) V119() V120() V121() Element of K19(K20( the carrier of K0, the carrier of R^1))
K19( the carrier of K0) is set
b is Element of the carrier of K0
a . b is V28() real ext-real Element of the carrier of R^1
c is Element of K19( the carrier of R^1)
f . b is V28() real ext-real Element of the carrier of R^1
d is V28() real ext-real Element of REAL
I is V28() real ext-real Element of REAL
d - I is V28() real ext-real Element of REAL
- I is V28() real ext-real set
d + (- I) is V28() real ext-real set
d + I is V28() real ext-real Element of REAL
].(d - I),(d + I).[ is Element of K19(REAL)
O is V28() real ext-real Element of REAL
1 / O is V28() real ext-real Element of REAL
O " is V28() real ext-real set
1 * (O ") is V28() real ext-real set
I / d is V28() real ext-real Element of REAL
d " is V28() real ext-real set
I * (d ") is V28() real ext-real set
(I / d) / (d + I) is V28() real ext-real Element of REAL
(d + I) " is V28() real ext-real set
(I / d) * ((d + I) ") is V28() real ext-real set
O - ((I / d) / (d + I)) is V28() real ext-real Element of REAL
- ((I / d) / (d + I)) is V28() real ext-real set
O + (- ((I / d) / (d + I))) is V28() real ext-real set
O + ((I / d) / (d + I)) is V28() real ext-real Element of REAL
].(O - ((I / d) / (d + I))),(O + ((I / d) / (d + I))).[ is Element of K19(REAL)
B is Element of K19( the carrier of R^1)
d / (d + I) is V28() real ext-real Element of REAL
d * ((d + I) ") is V28() real ext-real set
C is Element of K19( the carrier of K0)
f .: C is V129() V130() V131() Element of K19( the carrier of R^1)
1 / d is V28() real ext-real Element of REAL
1 * (d ") is V28() real ext-real set
I / (d + I) is V28() real ext-real Element of REAL
I * ((d + I) ") is V28() real ext-real set
(I / (d + I)) / d is V28() real ext-real Element of REAL
(I / (d + I)) * (d ") is V28() real ext-real set
(1 / d) - ((I / (d + I)) / d) is V28() real ext-real Element of REAL
- ((I / (d + I)) / d) is V28() real ext-real set
(1 / d) + (- ((I / (d + I)) / d)) is V28() real ext-real set
1 - (I / (d + I)) is V28() real ext-real Element of REAL
- (I / (d + I)) is V28() real ext-real set
1 + (- (I / (d + I))) is V28() real ext-real set
(1 - (I / (d + I))) / d is V28() real ext-real Element of REAL
(1 - (I / (d + I))) * (d ") is V28() real ext-real set
(d + I) / (d + I) is V28() real ext-real Element of REAL
(d + I) * ((d + I) ") is V28() real ext-real set
((d + I) / (d + I)) - (I / (d + I)) is V28() real ext-real Element of REAL
((d + I) / (d + I)) + (- (I / (d + I))) is V28() real ext-real set
(((d + I) / (d + I)) - (I / (d + I))) / d is V28() real ext-real Element of REAL
(((d + I) / (d + I)) - (I / (d + I))) * (d ") is V28() real ext-real set
(d + I) - I is V28() real ext-real Element of REAL
(d + I) + (- I) is V28() real ext-real set
((d + I) - I) / (d + I) is V28() real ext-real Element of REAL
((d + I) - I) * ((d + I) ") is V28() real ext-real set
(((d + I) - I) / (d + I)) / d is V28() real ext-real Element of REAL
(((d + I) - I) / (d + I)) * (d ") is V28() real ext-real set
(d / (d + I)) / d is V28() real ext-real Element of REAL
(d / (d + I)) * (d ") is V28() real ext-real set
a .: C is V129() V130() V131() Element of K19( the carrier of R^1)
I ^2 is V28() real ext-real Element of REAL
I * I is V28() real ext-real set
I * d is V28() real ext-real Element of REAL
I * I is V28() real ext-real Element of REAL
(I * I) + (I * I) is V28() real ext-real Element of REAL
(I * d) + ((I * I) + (I * I)) is V28() real ext-real Element of REAL
(I * d) - ((I * I) + (I * I)) is V28() real ext-real Element of REAL
- ((I * I) + (I * I)) is V28() real ext-real set
(I * d) + (- ((I * I) + (I * I))) is V28() real ext-real set
d * d is V28() real ext-real Element of REAL
(d * d) + (I * d) is V28() real ext-real Element of REAL
((I * d) - ((I * I) + (I * I))) + (d * d) is V28() real ext-real Element of REAL
d * (d + I) is V28() real ext-real Element of REAL
(d + I) + I is V28() real ext-real Element of REAL
(d * (d + I)) / ((d + I) + I) is V28() real ext-real Element of REAL
((d + I) + I) " is V28() real ext-real set
(d * (d + I)) * (((d + I) + I) ") is V28() real ext-real set
(d - I) * ((d + I) + I) is V28() real ext-real Element of REAL
((d - I) * ((d + I) + I)) / ((d + I) + I) is V28() real ext-real Element of REAL
((d - I) * ((d + I) + I)) * (((d + I) + I) ") is V28() real ext-real set
((d + I) + I) / (d + I) is V28() real ext-real Element of REAL
((d + I) + I) * ((d + I) ") is V28() real ext-real set
d / (((d + I) + I) / (d + I)) is V28() real ext-real Element of REAL
(((d + I) + I) / (d + I)) " is V28() real ext-real set
d * ((((d + I) + I) / (d + I)) ") is V28() real ext-real set
((d + I) / (d + I)) + (I / (d + I)) is V28() real ext-real Element of REAL
d / (((d + I) / (d + I)) + (I / (d + I))) is V28() real ext-real Element of REAL
(((d + I) / (d + I)) + (I / (d + I))) " is V28() real ext-real set
d * ((((d + I) / (d + I)) + (I / (d + I))) ") is V28() real ext-real set
d * 1 is V28() real ext-real Element of REAL
1 + (I / (d + I)) is V28() real ext-real Element of REAL
(d * 1) / (1 + (I / (d + I))) is V28() real ext-real Element of REAL
(1 + (I / (d + I))) " is V28() real ext-real set
(d * 1) * ((1 + (I / (d + I))) ") is V28() real ext-real set
(1 + (I / (d + I))) / d is V28() real ext-real Element of REAL
(1 + (I / (d + I))) * (d ") is V28() real ext-real set
1 / ((1 + (I / (d + I))) / d) is V28() real ext-real Element of REAL
((1 + (I / (d + I))) / d) " is V28() real ext-real set
1 * (((1 + (I / (d + I))) / d) ") is V28() real ext-real set
ff is set
dom a is Element of K19( the carrier of K0)
f2 is set
a . f2 is V28() real ext-real set
g2 is Element of the carrier of K0
f . g2 is V28() real ext-real Element of the carrier of R^1
y is V28() real ext-real Element of REAL
1 / y is V28() real ext-real Element of REAL
y " is V28() real ext-real set
1 * (y ") is V28() real ext-real set
dom f is Element of K19( the carrier of K0)
1 / (O - ((I / d) / (d + I))) is V28() real ext-real Element of REAL
(O - ((I / d) / (d + I))) " is V28() real ext-real set
1 * ((O - ((I / d) / (d + I))) ") is V28() real ext-real set
(1 / d) + ((I / d) / (d + I)) is V28() real ext-real Element of REAL
1 / ((1 / d) + ((I / d) / (d + I))) is V28() real ext-real Element of REAL
((1 / d) + ((I / d) / (d + I))) " is V28() real ext-real set
1 * (((1 / d) + ((I / d) / (d + I))) ") is V28() real ext-real set
d " is V28() real ext-real Element of REAL
I * (d ") is V28() real ext-real Element of REAL
(I * (d ")) / (d + I) is V28() real ext-real Element of REAL
(I * (d ")) * ((d + I) ") is V28() real ext-real set
O - ((I * (d ")) / (d + I)) is V28() real ext-real Element of REAL
- ((I * (d ")) / (d + I)) is V28() real ext-real set
O + (- ((I * (d ")) / (d + I))) is V28() real ext-real set
1 / (O - ((I * (d ")) / (d + I))) is V28() real ext-real Element of REAL
(O - ((I * (d ")) / (d + I))) " is V28() real ext-real set
1 * ((O - ((I * (d ")) / (d + I))) ") is V28() real ext-real set
I * (1 / d) is V28() real ext-real Element of REAL
(I * (1 / d)) / (d + I) is V28() real ext-real Element of REAL
(I * (1 / d)) * ((d + I) ") is V28() real ext-real set
O - ((I * (1 / d)) / (d + I)) is V28() real ext-real Element of REAL
- ((I * (1 / d)) / (d + I)) is V28() real ext-real set
O + (- ((I * (1 / d)) / (d + I))) is V28() real ext-real set
1 / (O - ((I * (1 / d)) / (d + I))) is V28() real ext-real Element of REAL
(O - ((I * (1 / d)) / (d + I))) " is V28() real ext-real set
1 * ((O - ((I * (1 / d)) / (d + I))) ") is V28() real ext-real set
(d + I) / O is V28() real ext-real Element of REAL
(d + I) * (O ") is V28() real ext-real set
I / ((d + I) / O) is V28() real ext-real Element of REAL
((d + I) / O) " is V28() real ext-real set
I * (((d + I) / O) ") is V28() real ext-real set
O - (I / ((d + I) / O)) is V28() real ext-real Element of REAL
- (I / ((d + I) / O)) is V28() real ext-real set
O + (- (I / ((d + I) / O))) is V28() real ext-real set
1 / (O - (I / ((d + I) / O))) is V28() real ext-real Element of REAL
(O - (I / ((d + I) / O))) " is V28() real ext-real set
1 * ((O - (I / ((d + I) / O))) ") is V28() real ext-real set
O * 1 is V28() real ext-real Element of REAL
O * (I / (d + I)) is V28() real ext-real Element of REAL
(O * 1) - (O * (I / (d + I))) is V28() real ext-real Element of REAL
- (O * (I / (d + I))) is V28() real ext-real set
(O * 1) + (- (O * (I / (d + I)))) is V28() real ext-real set
1 / ((O * 1) - (O * (I / (d + I)))) is V28() real ext-real Element of REAL
((O * 1) - (O * (I / (d + I)))) " is V28() real ext-real set
1 * (((O * 1) - (O * (I / (d + I)))) ") is V28() real ext-real set
(1 - (I / (d + I))) * O is V28() real ext-real Element of REAL
1 / ((1 - (I / (d + I))) * O) is V28() real ext-real Element of REAL
((1 - (I / (d + I))) * O) " is V28() real ext-real set
1 * (((1 - (I / (d + I))) * O) ") is V28() real ext-real set
(((d + I) / (d + I)) - (I / (d + I))) * O is V28() real ext-real Element of REAL
1 / ((((d + I) / (d + I)) - (I / (d + I))) * O) is V28() real ext-real Element of REAL
((((d + I) / (d + I)) - (I / (d + I))) * O) " is V28() real ext-real set
1 * (((((d + I) / (d + I)) - (I / (d + I))) * O) ") is V28() real ext-real set
(((d + I) - I) / (d + I)) * O is V28() real ext-real Element of REAL
1 / ((((d + I) - I) / (d + I)) * O) is V28() real ext-real Element of REAL
((((d + I) - I) / (d + I)) * O) " is V28() real ext-real set
1 * (((((d + I) - I) / (d + I)) * O) ") is V28() real ext-real set
d / ((d + I) / O) is V28() real ext-real Element of REAL
d * (((d + I) / O) ") is V28() real ext-real set
1 / (d / ((d + I) / O)) is V28() real ext-real Element of REAL
(d / ((d + I) / O)) " is V28() real ext-real set
1 * ((d / ((d + I) / O)) ") is V28() real ext-real set
d * O is V28() real ext-real Element of REAL
(d * O) / (d + I) is V28() real ext-real Element of REAL
(d * O) * ((d + I) ") is V28() real ext-real set
1 / ((d * O) / (d + I)) is V28() real ext-real Element of REAL
((d * O) / (d + I)) " is V28() real ext-real set
1 * (((d * O) / (d + I)) ") is V28() real ext-real set
(d + I) / (d * O) is V28() real ext-real Element of REAL
(d * O) " is V28() real ext-real set
(d + I) * ((d * O) ") is V28() real ext-real set
((d + I) / (d * O)) * 1 is V28() real ext-real Element of REAL
(d + I) / 1 is V28() real ext-real Element of REAL
1 " is non empty V28() real ext-real positive non negative set
(d + I) * (1 ") is V28() real ext-real set
- d is V28() real ext-real Element of REAL
I / (- d) is V28() real ext-real Element of REAL
(- d) " is V28() real ext-real set
I * ((- d) ") is V28() real ext-real set
(- d) + I is V28() real ext-real Element of REAL
(I / (- d)) / ((- d) + I) is V28() real ext-real Element of REAL
((- d) + I) " is V28() real ext-real set
(I / (- d)) * (((- d) + I) ") is V28() real ext-real set
O - ((I / (- d)) / ((- d) + I)) is V28() real ext-real Element of REAL
- ((I / (- d)) / ((- d) + I)) is V28() real ext-real set
O + (- ((I / (- d)) / ((- d) + I))) is V28() real ext-real set
O + ((I / (- d)) / ((- d) + I)) is V28() real ext-real Element of REAL
].(O - ((I / (- d)) / ((- d) + I))),(O + ((I / (- d)) / ((- d) + I))).[ is Element of K19(REAL)
B is Element of K19( the carrier of R^1)
(- d) / ((- d) + I) is V28() real ext-real Element of REAL
(- d) * (((- d) + I) ") is V28() real ext-real set
d / ((- d) + I) is V28() real ext-real Element of REAL
d * (((- d) + I) ") is V28() real ext-real set
- (d / ((- d) + I)) is V28() real ext-real Element of REAL
C is Element of K19( the carrier of K0)
f .: C is V129() V130() V131() Element of K19( the carrier of R^1)
1 / (- d) is V28() real ext-real Element of REAL
1 * ((- d) ") is V28() real ext-real set
(- d) * (1 / (- d)) is V28() real ext-real Element of REAL
O * ((- d) * (1 / (- d))) is V28() real ext-real Element of REAL
O * 1 is V28() real ext-real Element of REAL
d * O is V28() real ext-real Element of REAL
- (d * O) is V28() real ext-real Element of REAL
(- (d * O)) * (1 / (- d)) is V28() real ext-real Element of REAL
- 1 is V28() real ext-real non positive Element of REAL
(- 1) * (1 / (- d)) is V28() real ext-real Element of REAL
- (1 / (- d)) is V28() real ext-real Element of REAL
I / ((- d) + I) is V28() real ext-real Element of REAL
I * (((- d) + I) ") is V28() real ext-real set
(I / ((- d) + I)) / (- d) is V28() real ext-real Element of REAL
(I / ((- d) + I)) * ((- d) ") is V28() real ext-real set
(- (1 / (- d))) + ((I / ((- d) + I)) / (- d)) is V28() real ext-real Element of REAL
(- 1) / (- d) is V28() real ext-real Element of REAL
(- 1) * ((- d) ") is V28() real ext-real set
((- 1) / (- d)) + ((I / ((- d) + I)) / (- d)) is V28() real ext-real Element of REAL
(- 1) + (I / ((- d) + I)) is V28() real ext-real Element of REAL
((- 1) + (I / ((- d) + I))) / (- d) is V28() real ext-real Element of REAL
((- 1) + (I / ((- d) + I))) * ((- d) ") is V28() real ext-real set
((- d) + I) / ((- d) + I) is V28() real ext-real Element of REAL
((- d) + I) * (((- d) + I) ") is V28() real ext-real set
- (((- d) + I) / ((- d) + I)) is V28() real ext-real Element of REAL
(- (((- d) + I) / ((- d) + I))) + (I / ((- d) + I)) is V28() real ext-real Element of REAL
((- (((- d) + I) / ((- d) + I))) + (I / ((- d) + I))) / (- d) is V28() real ext-real Element of REAL
((- (((- d) + I) / ((- d) + I))) + (I / ((- d) + I))) * ((- d) ") is V28() real ext-real set
- ((- d) + I) is V28() real ext-real Element of REAL
(- ((- d) + I)) / ((- d) + I) is V28() real ext-real Element of REAL
(- ((- d) + I)) * (((- d) + I) ") is V28() real ext-real set
((- ((- d) + I)) / ((- d) + I)) + (I / ((- d) + I)) is V28() real ext-real Element of REAL
(((- ((- d) + I)) / ((- d) + I)) + (I / ((- d) + I))) / (- d) is V28() real ext-real Element of REAL
(((- ((- d) + I)) / ((- d) + I)) + (I / ((- d) + I))) * ((- d) ") is V28() real ext-real set
(d - I) + I is V28() real ext-real Element of REAL
((d - I) + I) / ((- d) + I) is V28() real ext-real Element of REAL
((d - I) + I) * (((- d) + I) ") is V28() real ext-real set
(((d - I) + I) / ((- d) + I)) / (- d) is V28() real ext-real Element of REAL
(((d - I) + I) / ((- d) + I)) * ((- d) ") is V28() real ext-real set
(d / ((- d) + I)) / (- d) is V28() real ext-real Element of REAL
(d / ((- d) + I)) * ((- d) ") is V28() real ext-real set
a .: C is V129() V130() V131() Element of K19( the carrier of R^1)
I ^2 is V28() real ext-real Element of REAL
I * I is V28() real ext-real set
I * (- d) is V28() real ext-real Element of REAL
I * I is V28() real ext-real Element of REAL
(I * I) + (I * I) is V28() real ext-real Element of REAL
(I * (- d)) + ((I * I) + (I * I)) is V28() real ext-real Element of REAL
(I * (- d)) - ((I * I) + (I * I)) is V28() real ext-real Element of REAL
- ((I * I) + (I * I)) is V28() real ext-real set
(I * (- d)) + (- ((I * I) + (I * I))) is V28() real ext-real set
(- d) * (- d) is V28() real ext-real Element of REAL
(I * (- d)) + ((- d) * (- d)) is V28() real ext-real Element of REAL
((I * (- d)) - ((I * I) + (I * I))) + ((- d) * (- d)) is V28() real ext-real Element of REAL
(- d) * ((- d) + I) is V28() real ext-real Element of REAL
((- d) + I) + I is V28() real ext-real Element of REAL
((- d) * ((- d) + I)) / (((- d) + I) + I) is V28() real ext-real Element of REAL
(((- d) + I) + I) " is V28() real ext-real set
((- d) * ((- d) + I)) * ((((- d) + I) + I) ") is V28() real ext-real set
(- d) - I is V28() real ext-real Element of REAL
(- d) + (- I) is V28() real ext-real set
((- d) - I) * (((- d) + I) + I) is V28() real ext-real Element of REAL
(((- d) - I) * (((- d) + I) + I)) / (((- d) + I) + I) is V28() real ext-real Element of REAL
(((- d) - I) * (((- d) + I) + I)) * ((((- d) + I) + I) ") is V28() real ext-real set
(((- d) + I) + I) / ((- d) + I) is V28() real ext-real Element of REAL
(((- d) + I) + I) * (((- d) + I) ") is V28() real ext-real set
(- d) / ((((- d) + I) + I) / ((- d) + I)) is V28() real ext-real Element of REAL
((((- d) + I) + I) / ((- d) + I)) " is V28() real ext-real set
(- d) * (((((- d) + I) + I) / ((- d) + I)) ") is V28() real ext-real set
(((- d) + I) / ((- d) + I)) + (I / ((- d) + I)) is V28() real ext-real Element of REAL
(- d) / ((((- d) + I) / ((- d) + I)) + (I / ((- d) + I))) is V28() real ext-real Element of REAL
((((- d) + I) / ((- d) + I)) + (I / ((- d) + I))) " is V28() real ext-real set
(- d) * (((((- d) + I) / ((- d) + I)) + (I / ((- d) + I))) ") is V28() real ext-real set
(- d) * 1 is V28() real ext-real Element of REAL
1 + (I / ((- d) + I)) is V28() real ext-real Element of REAL
((- d) * 1) / (1 + (I / ((- d) + I))) is V28() real ext-real Element of REAL
(1 + (I / ((- d) + I))) " is V28() real ext-real set
((- d) * 1) * ((1 + (I / ((- d) + I))) ") is V28() real ext-real set
(1 + (I / ((- d) + I))) / (- d) is V28() real ext-real Element of REAL
(1 + (I / ((- d) + I))) * ((- d) ") is V28() real ext-real set
1 / ((1 + (I / ((- d) + I))) / (- d)) is V28() real ext-real Element of REAL
((1 + (I / ((- d) + I))) / (- d)) " is V28() real ext-real set
1 * (((1 + (I / ((- d) + I))) / (- d)) ") is V28() real ext-real set
(1 / (- d)) + ((I / (- d)) / ((- d) + I)) is V28() real ext-real Element of REAL
1 / ((1 / (- d)) + ((I / (- d)) / ((- d) + I))) is V28() real ext-real Element of REAL
((1 / (- d)) + ((I / (- d)) / ((- d) + I))) " is V28() real ext-real set
1 * (((1 / (- d)) + ((I / (- d)) / ((- d) + I))) ") is V28() real ext-real set
- (d + I) is V28() real ext-real Element of REAL
- (1 / ((1 / (- d)) + ((I / (- d)) / ((- d) + I)))) is V28() real ext-real Element of REAL
- ((1 / (- d)) + ((I / (- d)) / ((- d) + I))) is V28() real ext-real Element of REAL
1 / (- ((1 / (- d)) + ((I / (- d)) / ((- d) + I)))) is V28() real ext-real Element of REAL
(- ((1 / (- d)) + ((I / (- d)) / ((- d) + I)))) " is V28() real ext-real set
1 * ((- ((1 / (- d)) + ((I / (- d)) / ((- d) + I)))) ") is V28() real ext-real set
ff is set
dom a is Element of K19( the carrier of K0)
f2 is set
a . f2 is V28() real ext-real set
g2 is Element of the carrier of K0
f . g2 is V28() real ext-real Element of the carrier of R^1
y is V28() real ext-real Element of REAL
1 / y is V28() real ext-real Element of REAL
y " is V28() real ext-real set
1 * (y ") is V28() real ext-real set
dom f is Element of K19( the carrier of K0)
1 / (O + ((I / (- d)) / ((- d) + I))) is V28() real ext-real Element of REAL
(O + ((I / (- d)) / ((- d) + I))) " is V28() real ext-real set
1 * ((O + ((I / (- d)) / ((- d) + I))) ") is V28() real ext-real set
(- (1 / (- d))) - ((I / (- d)) / ((- d) + I)) is V28() real ext-real Element of REAL
(- (1 / (- d))) + (- ((I / (- d)) / ((- d) + I))) is V28() real ext-real set
1 / ((- (1 / (- d))) - ((I / (- d)) / ((- d) + I))) is V28() real ext-real Element of REAL
((- (1 / (- d))) - ((I / (- d)) / ((- d) + I))) " is V28() real ext-real set
1 * (((- (1 / (- d))) - ((I / (- d)) / ((- d) + I))) ") is V28() real ext-real set
(- d) " is V28() real ext-real Element of REAL
I * ((- d) ") is V28() real ext-real Element of REAL
(I * ((- d) ")) / ((- d) + I) is V28() real ext-real Element of REAL
(I * ((- d) ")) * (((- d) + I) ") is V28() real ext-real set
O + ((I * ((- d) ")) / ((- d) + I)) is V28() real ext-real Element of REAL
1 / (O + ((I * ((- d) ")) / ((- d) + I))) is V28() real ext-real Element of REAL
(O + ((I * ((- d) ")) / ((- d) + I))) " is V28() real ext-real set
1 * ((O + ((I * ((- d) ")) / ((- d) + I))) ") is V28() real ext-real set
I * (1 / (- d)) is V28() real ext-real Element of REAL
(I * (1 / (- d))) / ((- d) + I) is V28() real ext-real Element of REAL
(I * (1 / (- d))) * (((- d) + I) ") is V28() real ext-real set
O + ((I * (1 / (- d))) / ((- d) + I)) is V28() real ext-real Element of REAL
1 / (O + ((I * (1 / (- d))) / ((- d) + I))) is V28() real ext-real Element of REAL
(O + ((I * (1 / (- d))) / ((- d) + I))) " is V28() real ext-real set
1 * ((O + ((I * (1 / (- d))) / ((- d) + I))) ") is V28() real ext-real set
O * I is V28() real ext-real Element of REAL
- (O * I) is V28() real ext-real Element of REAL
(- (O * I)) / ((- d) + I) is V28() real ext-real Element of REAL
(- (O * I)) * (((- d) + I) ") is V28() real ext-real set
O + ((- (O * I)) / ((- d) + I)) is V28() real ext-real Element of REAL
1 / (O + ((- (O * I)) / ((- d) + I))) is V28() real ext-real Element of REAL
(O + ((- (O * I)) / ((- d) + I))) " is V28() real ext-real set
1 * ((O + ((- (O * I)) / ((- d) + I))) ") is V28() real ext-real set
(O * I) / ((- d) + I) is V28() real ext-real Element of REAL
(O * I) * (((- d) + I) ") is V28() real ext-real set
- ((O * I) / ((- d) + I)) is V28() real ext-real Element of REAL
O + (- ((O * I) / ((- d) + I))) is V28() real ext-real Element of REAL
1 / (O + (- ((O * I) / ((- d) + I)))) is V28() real ext-real Element of REAL
(O + (- ((O * I) / ((- d) + I)))) " is V28() real ext-real set
1 * ((O + (- ((O * I) / ((- d) + I)))) ") is V28() real ext-real set
O - ((O * I) / ((- d) + I)) is V28() real ext-real Element of REAL
- ((O * I) / ((- d) + I)) is V28() real ext-real set
O + (- ((O * I) / ((- d) + I))) is V28() real ext-real set
1 / (O - ((O * I) / ((- d) + I))) is V28() real ext-real Element of REAL
(O - ((O * I) / ((- d) + I))) " is V28() real ext-real set
1 * ((O - ((O * I) / ((- d) + I))) ") is V28() real ext-real set
((- d) + I) / O is V28() real ext-real Element of REAL
((- d) + I) * (O ") is V28() real ext-real set
I / (((- d) + I) / O) is V28() real ext-real Element of REAL
(((- d) + I) / O) " is V28() real ext-real set
I * ((((- d) + I) / O) ") is V28() real ext-real set
O - (I / (((- d) + I) / O)) is V28() real ext-real Element of REAL
- (I / (((- d) + I) / O)) is V28() real ext-real set
O + (- (I / (((- d) + I) / O))) is V28() real ext-real set
1 / (O - (I / (((- d) + I) / O))) is V28() real ext-real Element of REAL
(O - (I / (((- d) + I) / O))) " is V28() real ext-real set
1 * ((O - (I / (((- d) + I) / O))) ") is V28() real ext-real set
O * (I / ((- d) + I)) is V28() real ext-real Element of REAL
(O * 1) - (O * (I / ((- d) + I))) is V28() real ext-real Element of REAL
- (O * (I / ((- d) + I))) is V28() real ext-real set
(O * 1) + (- (O * (I / ((- d) + I)))) is V28() real ext-real set
1 / ((O * 1) - (O * (I / ((- d) + I)))) is V28() real ext-real Element of REAL
((O * 1) - (O * (I / ((- d) + I)))) " is V28() real ext-real set
1 * (((O * 1) - (O * (I / ((- d) + I)))) ") is V28() real ext-real set
1 - (I / ((- d) + I)) is V28() real ext-real Element of REAL
- (I / ((- d) + I)) is V28() real ext-real set
1 + (- (I / ((- d) + I))) is V28() real ext-real set
O * (1 - (I / ((- d) + I))) is V28() real ext-real Element of REAL
1 / (O * (1 - (I / ((- d) + I)))) is V28() real ext-real Element of REAL
(O * (1 - (I / ((- d) + I)))) " is V28() real ext-real set
1 * ((O * (1 - (I / ((- d) + I)))) ") is V28() real ext-real set
(((- d) + I) / ((- d) + I)) - (I / ((- d) + I)) is V28() real ext-real Element of REAL
(((- d) + I) / ((- d) + I)) + (- (I / ((- d) + I))) is V28() real ext-real set
((((- d) + I) / ((- d) + I)) - (I / ((- d) + I))) * O is V28() real ext-real Element of REAL
1 / (((((- d) + I) / ((- d) + I)) - (I / ((- d) + I))) * O) is V28() real ext-real Element of REAL
(((((- d) + I) / ((- d) + I)) - (I / ((- d) + I))) * O) " is V28() real ext-real set
1 * ((((((- d) + I) / ((- d) + I)) - (I / ((- d) + I))) * O) ") is V28() real ext-real set
((- d) + I) - I is V28() real ext-real Element of REAL
((- d) + I) + (- I) is V28() real ext-real set
- (d - I) is V28() real ext-real Element of REAL
(((- d) + I) - I) / (- (d - I)) is V28() real ext-real Element of REAL
(- (d - I)) " is V28() real ext-real set
(((- d) + I) - I) * ((- (d - I)) ") is V28() real ext-real set
((((- d) + I) - I) / (- (d - I))) * O is V28() real ext-real Element of REAL
1 / (((((- d) + I) - I) / (- (d - I))) * O) is V28() real ext-real Element of REAL
(((((- d) + I) - I) / (- (d - I))) * O) " is V28() real ext-real set
1 * ((((((- d) + I) - I) / (- (d - I))) * O) ") is V28() real ext-real set
(((- d) + I) - I) / (d - I) is V28() real ext-real Element of REAL
(d - I) " is V28() real ext-real set
(((- d) + I) - I) * ((d - I) ") is V28() real ext-real set
- ((((- d) + I) - I) / (d - I)) is V28() real ext-real Element of REAL
(- ((((- d) + I) - I) / (d - I))) * O is V28() real ext-real Element of REAL
1 / ((- ((((- d) + I) - I) / (d - I))) * O) is V28() real ext-real Element of REAL
((- ((((- d) + I) - I) / (d - I))) * O) " is V28() real ext-real set
1 * (((- ((((- d) + I) - I) / (d - I))) * O) ") is V28() real ext-real set
- O is V28() real ext-real Element of REAL
((((- d) + I) - I) / (d - I)) * (- O) is V28() real ext-real Element of REAL
1 / (((((- d) + I) - I) / (d - I)) * (- O)) is V28() real ext-real Element of REAL
(((((- d) + I) - I) / (d - I)) * (- O)) " is V28() real ext-real set
1 * ((((((- d) + I) - I) / (d - I)) * (- O)) ") is V28() real ext-real set
(d - I) / (- O) is V28() real ext-real Element of REAL
(- O) " is V28() real ext-real set
(d - I) * ((- O) ") is V28() real ext-real set
(- d) / ((d - I) / (- O)) is V28() real ext-real Element of REAL
((d - I) / (- O)) " is V28() real ext-real set
(- d) * (((d - I) / (- O)) ") is V28() real ext-real set
1 / ((- d) / ((d - I) / (- O))) is V28() real ext-real Element of REAL
((- d) / ((d - I) / (- O))) " is V28() real ext-real set
1 * (((- d) / ((d - I) / (- O))) ") is V28() real ext-real set
(- d) * (- O) is V28() real ext-real Element of REAL
((- d) * (- O)) / (d - I) is V28() real ext-real Element of REAL
((- d) * (- O)) * ((d - I) ") is V28() real ext-real set
1 / (((- d) * (- O)) / (d - I)) is V28() real ext-real Element of REAL
(((- d) * (- O)) / (d - I)) " is V28() real ext-real set
1 * ((((- d) * (- O)) / (d - I)) ") is V28() real ext-real set
(d - I) / ((- d) * (- O)) is V28() real ext-real Element of REAL
((- d) * (- O)) " is V28() real ext-real set
(d - I) * (((- d) * (- O)) ") is V28() real ext-real set
((d - I) / ((- d) * (- O))) * 1 is V28() real ext-real Element of REAL
(- d) * ((- d) ") is V28() real ext-real Element of REAL
(d - I) / ((- d) * ((- d) ")) is V28() real ext-real Element of REAL
((- d) * ((- d) ")) " is V28() real ext-real set
(d - I) * (((- d) * ((- d) ")) ") is V28() real ext-real set
(d - I) / 1 is V28() real ext-real Element of REAL
1 " is non empty V28() real ext-real positive non negative set
(d - I) * (1 ") is V28() real ext-real set
A is Element of K19( the carrier of K0)
a .: A is V129() V130() V131() Element of K19( the carrier of R^1)
B is Element of K19( the carrier of K0)
a .: B is V129() V130() V131() Element of K19( the carrier of R^1)
b is Element of the carrier of K0
f . b is V28() real ext-real Element of the carrier of R^1
a . b is V28() real ext-real Element of the carrier of R^1
c is V28() real ext-real set
1 / c is V28() real ext-real Element of REAL
c " is V28() real ext-real set
1 * (c ") is V28() real ext-real set
d is V28() real ext-real Element of REAL
1 / d is V28() real ext-real Element of REAL
d " is V28() real ext-real set
1 * (d ") is V28() real ext-real set
K0 is non empty TopSpace-like TopStruct
the carrier of K0 is non empty set
K20( the carrier of K0, the carrier of R^1) is V121() set
K19(K20( the carrier of K0, the carrier of R^1)) is set
f is Relation-like the carrier of K0 -defined the carrier of R^1 -valued Function-like non empty total V18( the carrier of K0, the carrier of R^1) V119() V120() V121() Element of K19(K20( the carrier of K0, the carrier of R^1))
g is Relation-like the carrier of K0 -defined the carrier of R^1 -valued Function-like non empty total V18( the carrier of K0, the carrier of R^1) V119() V120() V121() Element of K19(K20( the carrier of K0, the carrier of R^1))
a is Relation-like the carrier of K0 -defined the carrier of R^1 -valued Function-like non empty total V18( the carrier of K0, the carrier of R^1) V119() V120() V121() Element of K19(K20( the carrier of K0, the carrier of R^1))
b is Relation-like the carrier of K0 -defined the carrier of R^1 -valued Function-like non empty total V18( the carrier of K0, the carrier of R^1) V119() V120() V121() Element of K19(K20( the carrier of K0, the carrier of R^1))
c is Element of the carrier of K0
f . c is V28() real ext-real Element of the carrier of R^1
g . c is V28() real ext-real Element of the carrier of R^1
b . c is V28() real ext-real Element of the carrier of R^1
d is V28() real ext-real set
O is V28() real ext-real set
d / O is V28() real ext-real set
O " is V28() real ext-real set
d * (O ") is V28() real ext-real set
a . c is V28() real ext-real Element of the carrier of R^1
1 / O is V28() real ext-real Element of REAL
1 * (O ") is V28() real ext-real set
d * (1 / O) is V28() real ext-real Element of REAL
K0 is non empty TopSpace-like TopStruct
the carrier of K0 is non empty set
K20( the carrier of K0, the carrier of R^1) is V121() set
K19(K20( the carrier of K0, the carrier of R^1)) is set
f is Relation-like the carrier of K0 -defined the carrier of R^1 -valued Function-like non empty total V18( the carrier of K0, the carrier of R^1) V119() V120() V121() Element of K19(K20( the carrier of K0, the carrier of R^1))
g is Relation-like the carrier of K0 -defined the carrier of R^1 -valued Function-like non empty total V18( the carrier of K0, the carrier of R^1) V119() V120() V121() Element of K19(K20( the carrier of K0, the carrier of R^1))
a is Relation-like the carrier of K0 -defined the carrier of R^1 -valued Function-like non empty total V18( the carrier of K0, the carrier of R^1) V119() V120() V121() Element of K19(K20( the carrier of K0, the carrier of R^1))
b is Relation-like the carrier of K0 -defined the carrier of R^1 -valued Function-like non empty total V18( the carrier of K0, the carrier of R^1) V119() V120() V121() Element of K19(K20( the carrier of K0, the carrier of R^1))
c is Element of the carrier of K0
f . c is V28() real ext-real Element of the carrier of R^1
g . c is V28() real ext-real Element of the carrier of R^1
b . c is V28() real ext-real Element of the carrier of R^1
d is V28() real ext-real set
O is V28() real ext-real set
d / O is V28() real ext-real set
O " is V28() real ext-real set
d * (O ") is V28() real ext-real set
(d / O) / O is V28() real ext-real set
(d / O) * (O ") is V28() real ext-real set
a . c is V28() real ext-real Element of the carrier of R^1
K20( the carrier of (TOP-REAL 2), the carrier of R^1) is V121() set
K19(K20( the carrier of (TOP-REAL 2), the carrier of R^1)) is set
f is Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | f is strict TopSpace-like SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | f) is set
K20( the carrier of ((TOP-REAL 2) | f), the carrier of R^1) is V121() set
K19(K20( the carrier of ((TOP-REAL 2) | f), the carrier of R^1)) is set
g is Relation-like the carrier of ((TOP-REAL 2) | f) -defined the carrier of R^1 -valued Function-like total V18( the carrier of ((TOP-REAL 2) | f), the carrier of R^1) V119() V120() V121() Element of K19(K20( the carrier of ((TOP-REAL 2) | f), the carrier of R^1))
dom g is Element of K19( the carrier of ((TOP-REAL 2) | f))
K19( the carrier of ((TOP-REAL 2) | f)) is set
the carrier of (TOP-REAL 2) /\ f is Element of K19( the carrier of (TOP-REAL 2))
K0 is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of R^1 -valued Function-like non empty total V18( the carrier of (TOP-REAL 2), the carrier of R^1) V119() V120() V121() Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of R^1))
a is set
g . a is V28() real ext-real set
proj1 . a is V28() real ext-real set
[#] ((TOP-REAL 2) | f) is non proper open closed Element of K19( the carrier of ((TOP-REAL 2) | f))
K0 | f is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of R^1 -valued Function-like V119() V120() V121() Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of R^1))
K0 is Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | K0 is strict TopSpace-like SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | K0) is set
K20( the carrier of ((TOP-REAL 2) | K0), the carrier of R^1) is V121() set
K19(K20( the carrier of ((TOP-REAL 2) | K0), the carrier of R^1)) is set
f is Relation-like the carrier of ((TOP-REAL 2) | K0) -defined the carrier of R^1 -valued Function-like total V18( the carrier of ((TOP-REAL 2) | K0), the carrier of R^1) V119() V120() V121() Element of K19(K20( the carrier of ((TOP-REAL 2) | K0), the carrier of R^1))
dom f is Element of K19( the carrier of ((TOP-REAL 2) | K0))
K19( the carrier of ((TOP-REAL 2) | K0)) is set
the carrier of (TOP-REAL 2) /\ K0 is Element of K19( the carrier of (TOP-REAL 2))
g is set
f . g is V28() real ext-real set
proj2 . g is V28() real ext-real set
[#] ((TOP-REAL 2) | K0) is non proper open closed Element of K19( the carrier of ((TOP-REAL 2) | K0))
proj2 | K0 is Relation-like the carrier of ((TOP-REAL 2) | K0) -defined REAL -valued Function-like total V18( the carrier of ((TOP-REAL 2) | K0), REAL ) V119() V120() V121() continuous Element of K19(K20( the carrier of ((TOP-REAL 2) | K0),REAL))
K20( the carrier of ((TOP-REAL 2) | K0),REAL) is set
K19(K20( the carrier of ((TOP-REAL 2) | K0),REAL)) is set
K0 is non empty Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | K0 is non empty strict TopSpace-like SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | K0) is non empty set
K20( the carrier of ((TOP-REAL 2) | K0), the carrier of R^1) is V121() set
K19(K20( the carrier of ((TOP-REAL 2) | K0), the carrier of R^1)) is set
f is Relation-like the carrier of ((TOP-REAL 2) | K0) -defined the carrier of R^1 -valued Function-like non empty total V18( the carrier of ((TOP-REAL 2) | K0), the carrier of R^1) V119() V120() V121() Element of K19(K20( the carrier of ((TOP-REAL 2) | K0), the carrier of R^1))
proj1 | K0 is Relation-like the carrier of ((TOP-REAL 2) | K0) -defined REAL -valued Function-like non empty total V18( the carrier of ((TOP-REAL 2) | K0), REAL ) V119() V120() V121() continuous Element of K19(K20( the carrier of ((TOP-REAL 2) | K0),REAL))
K20( the carrier of ((TOP-REAL 2) | K0),REAL) is set
K19(K20( the carrier of ((TOP-REAL 2) | K0),REAL)) is set
[#] ((TOP-REAL 2) | K0) is non empty non proper open closed Element of K19( the carrier of ((TOP-REAL 2) | K0))
K19( the carrier of ((TOP-REAL 2) | K0)) is set
g is Relation-like the carrier of ((TOP-REAL 2) | K0) -defined the carrier of R^1 -valued Function-like non empty total V18( the carrier of ((TOP-REAL 2) | K0), the carrier of R^1) V119() V120() V121() Element of K19(K20( the carrier of ((TOP-REAL 2) | K0), the carrier of R^1))
a is Element of the carrier of ((TOP-REAL 2) | K0)
g . a is V28() real ext-real Element of the carrier of R^1
proj1 . a is V28() real ext-real set
(dom proj1) /\ K0 is Element of K19( the carrier of (TOP-REAL 2))
a is Element of the carrier of ((TOP-REAL 2) | K0)
g . a is V28() real ext-real Element of the carrier of R^1
proj1 . a is V28() real ext-real set
b is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
b `1 is V28() real ext-real Element of REAL
K526(b,1) is V28() real ext-real Element of REAL
a is Relation-like the carrier of ((TOP-REAL 2) | K0) -defined the carrier of R^1 -valued Function-like non empty total V18( the carrier of ((TOP-REAL 2) | K0), the carrier of R^1) V119() V120() V121() Element of K19(K20( the carrier of ((TOP-REAL 2) | K0), the carrier of R^1))
dom f is Element of K19( the carrier of ((TOP-REAL 2) | K0))
b is set
f . b is V28() real ext-real set
a . b is V28() real ext-real set
c is Element of the carrier of ((TOP-REAL 2) | K0)
g . c is V28() real ext-real Element of the carrier of R^1
proj1 . c is V28() real ext-real set
d is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
proj1 . d is V28() real ext-real Element of REAL
d `1 is V28() real ext-real Element of REAL
K526(d,1) is V28() real ext-real Element of REAL
f . d is V28() real ext-real set
1 / (d `1) is V28() real ext-real Element of REAL
(d `1) " is V28() real ext-real set
1 * ((d `1) ") is V28() real ext-real set
dom a is Element of K19( the carrier of ((TOP-REAL 2) | K0))
K0 is non empty Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | K0 is non empty strict TopSpace-like SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | K0) is non empty set
K20( the carrier of ((TOP-REAL 2) | K0), the carrier of R^1) is V121() set
K19(K20( the carrier of ((TOP-REAL 2) | K0), the carrier of R^1)) is set
f is Relation-like the carrier of ((TOP-REAL 2) | K0) -defined the carrier of R^1 -valued Function-like non empty total V18( the carrier of ((TOP-REAL 2) | K0), the carrier of R^1) V119() V120() V121() Element of K19(K20( the carrier of ((TOP-REAL 2) | K0), the carrier of R^1))
proj2 | K0 is Relation-like the carrier of ((TOP-REAL 2) | K0) -defined REAL -valued Function-like non empty total V18( the carrier of ((TOP-REAL 2) | K0), REAL ) V119() V120() V121() continuous Element of K19(K20( the carrier of ((TOP-REAL 2) | K0),REAL))
K20( the carrier of ((TOP-REAL 2) | K0),REAL) is set
K19(K20( the carrier of ((TOP-REAL 2) | K0),REAL)) is set
[#] ((TOP-REAL 2) | K0) is non empty non proper open closed Element of K19( the carrier of ((TOP-REAL 2) | K0))
K19( the carrier of ((TOP-REAL 2) | K0)) is set
g is Relation-like the carrier of ((TOP-REAL 2) | K0) -defined the carrier of R^1 -valued Function-like non empty total V18( the carrier of ((TOP-REAL 2) | K0), the carrier of R^1) V119() V120() V121() Element of K19(K20( the carrier of ((TOP-REAL 2) | K0), the carrier of R^1))
a is Element of the carrier of ((TOP-REAL 2) | K0)
g . a is V28() real ext-real Element of the carrier of R^1
proj2 . a is V28() real ext-real set
(dom proj2) /\ K0 is Element of K19( the carrier of (TOP-REAL 2))
a is Element of the carrier of ((TOP-REAL 2) | K0)
g . a is V28() real ext-real Element of the carrier of R^1
proj2 . a is V28() real ext-real set
b is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
b `2 is V28() real ext-real Element of REAL
K526(b,2) is V28() real ext-real Element of REAL
a is Relation-like the carrier of ((TOP-REAL 2) | K0) -defined the carrier of R^1 -valued Function-like non empty total V18( the carrier of ((TOP-REAL 2) | K0), the carrier of R^1) V119() V120() V121() Element of K19(K20( the carrier of ((TOP-REAL 2) | K0), the carrier of R^1))
dom f is Element of K19( the carrier of ((TOP-REAL 2) | K0))
b is set
f . b is V28() real ext-real set
a . b is V28() real ext-real set
c is Element of the carrier of ((TOP-REAL 2) | K0)
g . c is V28() real ext-real Element of the carrier of R^1
proj2 . c is V28() real ext-real set
d is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
proj2 . d is V28() real ext-real Element of REAL
d `2 is V28() real ext-real Element of REAL
K526(d,2) is V28() real ext-real Element of REAL
f . d is V28() real ext-real set
1 / (d `2) is V28() real ext-real Element of REAL
(d `2) " is V28() real ext-real set
1 * ((d `2) ") is V28() real ext-real set
dom a is Element of K19( the carrier of ((TOP-REAL 2) | K0))
K0 is non empty Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | K0 is non empty strict TopSpace-like SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | K0) is non empty set
K20( the carrier of ((TOP-REAL 2) | K0), the carrier of R^1) is V121() set
K19(K20( the carrier of ((TOP-REAL 2) | K0), the carrier of R^1)) is set
f is Relation-like the carrier of ((TOP-REAL 2) | K0) -defined the carrier of R^1 -valued Function-like non empty total V18( the carrier of ((TOP-REAL 2) | K0), the carrier of R^1) V119() V120() V121() Element of K19(K20( the carrier of ((TOP-REAL 2) | K0), the carrier of R^1))
proj2 | K0 is Relation-like the carrier of ((TOP-REAL 2) | K0) -defined REAL -valued Function-like non empty total V18( the carrier of ((TOP-REAL 2) | K0), REAL ) V119() V120() V121() continuous Element of K19(K20( the carrier of ((TOP-REAL 2) | K0),REAL))
K20( the carrier of ((TOP-REAL 2) | K0),REAL) is set
K19(K20( the carrier of ((TOP-REAL 2) | K0),REAL)) is set
proj1 | K0 is Relation-like the carrier of ((TOP-REAL 2) | K0) -defined REAL -valued Function-like non empty total V18( the carrier of ((TOP-REAL 2) | K0), REAL ) V119() V120() V121() continuous Element of K19(K20( the carrier of ((TOP-REAL 2) | K0),REAL))
[#] ((TOP-REAL 2) | K0) is non empty non proper open closed Element of K19( the carrier of ((TOP-REAL 2) | K0))
K19( the carrier of ((TOP-REAL 2) | K0)) is set
a is Relation-like the carrier of ((TOP-REAL 2) | K0) -defined the carrier of R^1 -valued Function-like non empty total V18( the carrier of ((TOP-REAL 2) | K0), the carrier of R^1) V119() V120() V121() Element of K19(K20( the carrier of ((TOP-REAL 2) | K0), the carrier of R^1))
b is Element of the carrier of ((TOP-REAL 2) | K0)
a . b is V28() real ext-real Element of the carrier of R^1
proj1 . b is V28() real ext-real set
(dom proj1) /\ K0 is Element of K19( the carrier of (TOP-REAL 2))
b is Element of the carrier of ((TOP-REAL 2) | K0)
a . b is V28() real ext-real Element of the carrier of R^1
proj1 . b is V28() real ext-real set
c is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
c `1 is V28() real ext-real Element of REAL
K526(c,1) is V28() real ext-real Element of REAL
g is Relation-like the carrier of ((TOP-REAL 2) | K0) -defined the carrier of R^1 -valued Function-like non empty total V18( the carrier of ((TOP-REAL 2) | K0), the carrier of R^1) V119() V120() V121() Element of K19(K20( the carrier of ((TOP-REAL 2) | K0), the carrier of R^1))
b is Element of the carrier of ((TOP-REAL 2) | K0)
g . b is V28() real ext-real Element of the carrier of R^1
proj2 . b is V28() real ext-real set
(dom proj2) /\ K0 is Element of K19( the carrier of (TOP-REAL 2))
b is Relation-like the carrier of ((TOP-REAL 2) | K0) -defined the carrier of R^1 -valued Function-like non empty total V18( the carrier of ((TOP-REAL 2) | K0), the carrier of R^1) V119() V120() V121() Element of K19(K20( the carrier of ((TOP-REAL 2) | K0), the carrier of R^1))
dom f is Element of K19( the carrier of ((TOP-REAL 2) | K0))
c is set
f . c is V28() real ext-real set
b . c is V28() real ext-real set
O is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
proj2 . O is V28() real ext-real Element of REAL
O `2 is V28() real ext-real Element of REAL
K526(O,2) is V28() real ext-real Element of REAL
proj1 . O is V28() real ext-real Element of REAL
O `1 is V28() real ext-real Element of REAL
K526(O,1) is V28() real ext-real Element of REAL
d is Element of the carrier of ((TOP-REAL 2) | K0)
g . d is V28() real ext-real Element of the carrier of R^1
proj2 . d is V28() real ext-real set
a . d is V28() real ext-real Element of the carrier of R^1
proj1 . d is V28() real ext-real set
f . O is V28() real ext-real set
(O `2) / (O `1) is V28() real ext-real Element of REAL
(O `1) " is V28() real ext-real set
(O `2) * ((O `1) ") is V28() real ext-real set
((O `2) / (O `1)) / (O `1) is V28() real ext-real Element of REAL
((O `2) / (O `1)) * ((O `1) ") is V28() real ext-real set
dom b is Element of K19( the carrier of ((TOP-REAL 2) | K0))
K0 is non empty Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | K0 is non empty strict TopSpace-like SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | K0) is non empty set
K20( the carrier of ((TOP-REAL 2) | K0), the carrier of R^1) is V121() set
K19(K20( the carrier of ((TOP-REAL 2) | K0), the carrier of R^1)) is set
f is Relation-like the carrier of ((TOP-REAL 2) | K0) -defined the carrier of R^1 -valued Function-like non empty total V18( the carrier of ((TOP-REAL 2) | K0), the carrier of R^1) V119() V120() V121() Element of K19(K20( the carrier of ((TOP-REAL 2) | K0), the carrier of R^1))
proj1 | K0 is Relation-like the carrier of ((TOP-REAL 2) | K0) -defined REAL -valued Function-like non empty total V18( the carrier of ((TOP-REAL 2) | K0), REAL ) V119() V120() V121() continuous Element of K19(K20( the carrier of ((TOP-REAL 2) | K0),REAL))
K20( the carrier of ((TOP-REAL 2) | K0),REAL) is set
K19(K20( the carrier of ((TOP-REAL 2) | K0),REAL)) is set
proj2 | K0 is Relation-like the carrier of ((TOP-REAL 2) | K0) -defined REAL -valued Function-like non empty total V18( the carrier of ((TOP-REAL 2) | K0), REAL ) V119() V120() V121() continuous Element of K19(K20( the carrier of ((TOP-REAL 2) | K0),REAL))
[#] ((TOP-REAL 2) | K0) is non empty non proper open closed Element of K19( the carrier of ((TOP-REAL 2) | K0))
K19( the carrier of ((TOP-REAL 2) | K0)) is set
a is Relation-like the carrier of ((TOP-REAL 2) | K0) -defined the carrier of R^1 -valued Function-like non empty total V18( the carrier of ((TOP-REAL 2) | K0), the carrier of R^1) V119() V120() V121() Element of K19(K20( the carrier of ((TOP-REAL 2) | K0), the carrier of R^1))
b is Element of the carrier of ((TOP-REAL 2) | K0)
a . b is V28() real ext-real Element of the carrier of R^1
proj2 . b is V28() real ext-real set
(dom proj2) /\ K0 is Element of K19( the carrier of (TOP-REAL 2))
b is Element of the carrier of ((TOP-REAL 2) | K0)
a . b is V28() real ext-real Element of the carrier of R^1
proj2 . b is V28() real ext-real set
c is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
c `2 is V28() real ext-real Element of REAL
K526(c,2) is V28() real ext-real Element of REAL
g is Relation-like the carrier of ((TOP-REAL 2) | K0) -defined the carrier of R^1 -valued Function-like non empty total V18( the carrier of ((TOP-REAL 2) | K0), the carrier of R^1) V119() V120() V121() Element of K19(K20( the carrier of ((TOP-REAL 2) | K0), the carrier of R^1))
b is Element of the carrier of ((TOP-REAL 2) | K0)
g . b is V28() real ext-real Element of the carrier of R^1
proj1 . b is V28() real ext-real set
(dom proj1) /\ K0 is Element of K19( the carrier of (TOP-REAL 2))
b is Relation-like the carrier of ((TOP-REAL 2) | K0) -defined the carrier of R^1 -valued Function-like non empty total V18( the carrier of ((TOP-REAL 2) | K0), the carrier of R^1) V119() V120() V121() Element of K19(K20( the carrier of ((TOP-REAL 2) | K0), the carrier of R^1))
dom f is Element of K19( the carrier of ((TOP-REAL 2) | K0))
c is set
f . c is V28() real ext-real set
b . c is V28() real ext-real set
O is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
proj1 . O is V28() real ext-real Element of REAL
O `1 is V28() real ext-real Element of REAL
K526(O,1) is V28() real ext-real Element of REAL
proj2 . O is V28() real ext-real Element of REAL
O `2 is V28() real ext-real Element of REAL
K526(O,2) is V28() real ext-real Element of REAL
d is Element of the carrier of ((TOP-REAL 2) | K0)
g . d is V28() real ext-real Element of the carrier of R^1
proj1 . d is V28() real ext-real set
a . d is V28() real ext-real Element of the carrier of R^1
proj2 . d is V28() real ext-real set
f . O is V28() real ext-real set
(O `1) / (O `2) is V28() real ext-real Element of REAL
(O `2) " is V28() real ext-real set
(O `1) * ((O `2) ") is V28() real ext-real set
((O `1) / (O `2)) / (O `2) is V28() real ext-real Element of REAL
((O `1) / (O `2)) * ((O `2) ") is V28() real ext-real set
dom b is Element of K19( the carrier of ((TOP-REAL 2) | K0))
K0 is Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | K0 is strict TopSpace-like SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | K0) is set
f is Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | f is strict TopSpace-like SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | f) is set
K20( the carrier of ((TOP-REAL 2) | K0), the carrier of ((TOP-REAL 2) | f)) is set
K19(K20( the carrier of ((TOP-REAL 2) | K0), the carrier of ((TOP-REAL 2) | f))) is set
K20( the carrier of ((TOP-REAL 2) | K0), the carrier of R^1) is V121() set
K19(K20( the carrier of ((TOP-REAL 2) | K0), the carrier of R^1)) is set
g is Relation-like the carrier of ((TOP-REAL 2) | K0) -defined the carrier of ((TOP-REAL 2) | f) -valued Function-like V18( the carrier of ((TOP-REAL 2) | K0), the carrier of ((TOP-REAL 2) | f)) Element of K19(K20( the carrier of ((TOP-REAL 2) | K0), the carrier of ((TOP-REAL 2) | f)))
a is Relation-like the carrier of ((TOP-REAL 2) | K0) -defined the carrier of R^1 -valued Function-like total V18( the carrier of ((TOP-REAL 2) | K0), the carrier of R^1) V119() V120() V121() Element of K19(K20( the carrier of ((TOP-REAL 2) | K0), the carrier of R^1))
b is Relation-like the carrier of ((TOP-REAL 2) | K0) -defined the carrier of R^1 -valued Function-like total V18( the carrier of ((TOP-REAL 2) | K0), the carrier of R^1) V119() V120() V121() Element of K19(K20( the carrier of ((TOP-REAL 2) | K0), the carrier of R^1))
d is non empty Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | d is non empty strict TopSpace-like SubSpace of TOP-REAL 2
c is non empty Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | c is non empty strict TopSpace-like SubSpace of TOP-REAL 2
O is non empty TopSpace-like TopStruct
the carrier of O is non empty set
I is non empty TopSpace-like TopStruct
the carrier of I is non empty set
K20( the carrier of O, the carrier of I) is set
K19(K20( the carrier of O, the carrier of I)) is set
K19( the carrier of I) is set
A is Relation-like the carrier of O -defined the carrier of I -valued Function-like non empty total V18( the carrier of O, the carrier of I) Element of K19(K20( the carrier of O, the carrier of I))
K19( the carrier of O) is set
B is Element of the carrier of O
A . B is Element of the carrier of I
C is Element of K19( the carrier of I)
[#] I is non empty non proper open closed Element of K19( the carrier of I)
D is Element of K19( the carrier of (TOP-REAL 2))
D /\ ([#] I) is Element of K19( the carrier of I)
ff is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
ff `1 is V28() real ext-real Element of REAL
K526(ff,1) is V28() real ext-real Element of REAL
ff `2 is V28() real ext-real Element of REAL
K526(ff,2) is V28() real ext-real Element of REAL
f2 is V28() real ext-real set
(ff `1) - f2 is V28() real ext-real Element of REAL
- f2 is V28() real ext-real set
(ff `1) + (- f2) is V28() real ext-real set
(ff `1) + f2 is V28() real ext-real Element of REAL
(ff `2) - f2 is V28() real ext-real Element of REAL
(ff `2) + (- f2) is V28() real ext-real set
(ff `2) + f2 is V28() real ext-real Element of REAL
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2) : ( not b<sub>1</sub> `1 <= (ff `1) - f2 & not (ff `1) + f2 <= b₁ `1 & not b<sub>1</sub> `2 <= (ff `2) - f2 & not (ff `2) + f2 <= b₁ `2 ) } is set
].((ff `1) - f2),((ff `1) + f2).[ is Element of K19(REAL)
].((ff `2) - f2),((ff `2) + f2).[ is Element of K19(REAL)
g2 is Element of K19( the carrier of R^1)
dom b is Element of K19( the carrier of ((TOP-REAL 2) | K0))
K19( the carrier of ((TOP-REAL 2) | K0)) is set
b . B is V28() real ext-real set
rng b is V129() V130() V131() Element of K19( the carrier of R^1)
dom a is Element of K19( the carrier of ((TOP-REAL 2) | K0))
a . B is V28() real ext-real set
rng a is V129() V130() V131() Element of K19( the carrier of R^1)
[#] O is non empty non proper open closed Element of K19( the carrier of O)
z is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
z `1 is V28() real ext-real Element of REAL
K526(z,1) is V28() real ext-real Element of REAL
z `2 is V28() real ext-real Element of REAL
K526(z,2) is V28() real ext-real Element of REAL
|[(z `1),(z `2)]| is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
A . |[(z `1),(z `2)]| is set
x is V28() real ext-real Element of REAL
x2 is V28() real ext-real Element of REAL
|[x,x2]| is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
y is Element of K19( the carrier of R^1)
u is Element of K19( the carrier of O)
b .: u is V129() V130() V131() Element of K19( the carrier of R^1)
t is Element of K19( the carrier of O)
a .: t is V129() V130() V131() Element of K19( the carrier of R^1)
t /\ u is Element of K19( the carrier of O)
W5 is Element of K19( the carrier of O)
b .: W5 is V129() V130() V131() Element of K19( the carrier of R^1)
a .: W5 is V129() V130() V131() Element of K19( the carrier of R^1)
A .: W5 is Element of K19( the carrier of I)
v is set
dom A is Element of K19( the carrier of O)
q2 is Element of the carrier of I
k is set
A . k is set
the carrier of ((TOP-REAL 2) | d) is non empty set
[#] ((TOP-REAL 2) | d) is non empty non proper open closed Element of K19( the carrier of ((TOP-REAL 2) | d))
K19( the carrier of ((TOP-REAL 2) | d)) is set
r8 is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
r8 `1 is V28() real ext-real Element of REAL
K526(r8,1) is V28() real ext-real Element of REAL
r8 `2 is V28() real ext-real Element of REAL
K526(r8,2) is V28() real ext-real Element of REAL
|[(r8 `1),(r8 `2)]| is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
[#] ((TOP-REAL 2) | K0) is non proper open closed Element of K19( the carrier of ((TOP-REAL 2) | K0))
b . |[(r8 `1),(r8 `2)]| is V28() real ext-real set
a . |[(r8 `1),(r8 `2)]| is V28() real ext-real set
r7 is V28() real ext-real Element of REAL
s7 is V28() real ext-real Element of REAL
|[r7,s7]| is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
|[r7,s7]| `1 is V28() real ext-real Element of REAL
K526(|[r7,s7]|,1) is V28() real ext-real Element of REAL
|[r7,s7]| `2 is V28() real ext-real Element of REAL
K526(|[r7,s7]|,2) is V28() real ext-real Element of REAL
K0 is Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | K0 is strict TopSpace-like SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | K0) is set
f is Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | f is strict TopSpace-like SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | f) is set
K20( the carrier of ((TOP-REAL 2) | K0), the carrier of ((TOP-REAL 2) | f)) is set
K19(K20( the carrier of ((TOP-REAL 2) | K0), the carrier of ((TOP-REAL 2) | f))) is set
() | K0 is Relation-like NonZero (TOP-REAL 2) -defined NonZero (TOP-REAL 2) -valued Function-like Element of K19(K20((NonZero (TOP-REAL 2)),(NonZero (TOP-REAL 2))))
g is Relation-like the carrier of ((TOP-REAL 2) | K0) -defined the carrier of ((TOP-REAL 2) | f) -valued Function-like V18( the carrier of ((TOP-REAL 2) | K0), the carrier of ((TOP-REAL 2) | f)) Element of K19(K20( the carrier of ((TOP-REAL 2) | K0), the carrier of ((TOP-REAL 2) | f)))
a is set
b is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
b `2 is V28() real ext-real Element of REAL
K526(b,2) is V28() real ext-real Element of REAL
b `1 is V28() real ext-real Element of REAL
K526(b,1) is V28() real ext-real Element of REAL
- (b `1) is V28() real ext-real Element of REAL
- ((1.REAL 2) `1) is V28() real ext-real Element of REAL
a is non empty Element of K19( the carrier of (TOP-REAL 2))
b is set
c is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
c `2 is V28() real ext-real Element of REAL
K526(c,2) is V28() real ext-real Element of REAL
c `1 is V28() real ext-real Element of REAL
K526(c,1) is V28() real ext-real Element of REAL
- (c `1) is V28() real ext-real Element of REAL
() | a is Relation-like NonZero (TOP-REAL 2) -defined NonZero (TOP-REAL 2) -valued Function-like Element of K19(K20((NonZero (TOP-REAL 2)),(NonZero (TOP-REAL 2))))
dom (() | a) is Element of K19((NonZero (TOP-REAL 2)))
K19((NonZero (TOP-REAL 2))) is set
proj2 * (() | a) is Relation-like NonZero (TOP-REAL 2) -defined REAL -valued Function-like V119() V120() V121() Element of K19(K20((NonZero (TOP-REAL 2)),REAL))
K20((NonZero (TOP-REAL 2)),REAL) is set
K19(K20((NonZero (TOP-REAL 2)),REAL)) is set
dom (proj2 * (() | a)) is Element of K19((NonZero (TOP-REAL 2)))
b is set
dom () is Element of K19((NonZero (TOP-REAL 2)))
(dom ()) /\ a is Element of K19( the carrier of (TOP-REAL 2))
() . b is set
rng () is Element of K19((NonZero (TOP-REAL 2)))
(() | a) . b is set
rng (proj2 * (() | a)) is V129() V130() V131() Element of K19(REAL)
proj1 * (() | a) is Relation-like NonZero (TOP-REAL 2) -defined REAL -valued Function-like V119() V120() V121() Element of K19(K20((NonZero (TOP-REAL 2)),REAL))
dom (proj1 * (() | a)) is Element of K19((NonZero (TOP-REAL 2)))
b is set
dom () is Element of K19((NonZero (TOP-REAL 2)))
(dom ()) /\ a is Element of K19( the carrier of (TOP-REAL 2))
() . b is set
rng () is Element of K19((NonZero (TOP-REAL 2)))
(() | a) . b is set
rng (proj1 * (() | a)) is V129() V130() V131() Element of K19(REAL)
dom () is Element of K19((NonZero (TOP-REAL 2)))
(dom ()) /\ a is Element of K19( the carrier of (TOP-REAL 2))
(NonZero (TOP-REAL 2)) /\ a is Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | a is non empty strict TopSpace-like SubSpace of TOP-REAL 2
[#] ((TOP-REAL 2) | a) is non empty non proper open closed Element of K19( the carrier of ((TOP-REAL 2) | a))
the carrier of ((TOP-REAL 2) | a) is non empty set
K19( the carrier of ((TOP-REAL 2) | a)) is set
K20( the carrier of ((TOP-REAL 2) | a), the carrier of R^1) is V121() set
K19(K20( the carrier of ((TOP-REAL 2) | a), the carrier of R^1)) is set
b is Relation-like the carrier of ((TOP-REAL 2) | a) -defined the carrier of R^1 -valued Function-like non empty total V18( the carrier of ((TOP-REAL 2) | a), the carrier of R^1) V119() V120() V121() Element of K19(K20( the carrier of ((TOP-REAL 2) | a), the carrier of R^1))
c is set
d is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
d `2 is V28() real ext-real Element of REAL
K526(d,2) is V28() real ext-real Element of REAL
d `1 is V28() real ext-real Element of REAL
K526(d,1) is V28() real ext-real Element of REAL
- (d `1) is V28() real ext-real Element of REAL
c is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
b . c is V28() real ext-real set
c `1 is V28() real ext-real Element of REAL
K526(c,1) is V28() real ext-real Element of REAL
1 / (c `1) is V28() real ext-real Element of REAL
(c `1) " is V28() real ext-real set
1 * ((c `1) ") is V28() real ext-real set
() . c is set
c `2 is V28() real ext-real Element of REAL
K526(c,2) is V28() real ext-real Element of REAL
(c `2) / (c `1) is V28() real ext-real Element of REAL
(c `2) * ((c `1) ") is V28() real ext-real set
((c `2) / (c `1)) / (c `1) is V28() real ext-real Element of REAL
((c `2) / (c `1)) * ((c `1) ") is V28() real ext-real set
|[(1 / (c `1)),(((c `2) / (c `1)) / (c `1))]| is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
d is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
d `2 is V28() real ext-real Element of REAL
K526(d,2) is V28() real ext-real Element of REAL
d `1 is V28() real ext-real Element of REAL
K526(d,1) is V28() real ext-real Element of REAL
- (d `1) is V28() real ext-real Element of REAL
(() | a) . c is set
proj1 . |[(1 / (c `1)),(((c `2) / (c `1)) / (c `1))]| is V28() real ext-real Element of REAL
|[(1 / (c `1)),(((c `2) / (c `1)) / (c `1))]| `1 is V28() real ext-real Element of REAL
K526(|[(1 / (c `1)),(((c `2) / (c `1)) / (c `1))]|,1) is V28() real ext-real Element of REAL
c is Relation-like the carrier of ((TOP-REAL 2) | a) -defined the carrier of R^1 -valued Function-like non empty total V18( the carrier of ((TOP-REAL 2) | a), the carrier of R^1) V119() V120() V121() Element of K19(K20( the carrier of ((TOP-REAL 2) | a), the carrier of R^1))
d is Relation-like the carrier of ((TOP-REAL 2) | a) -defined the carrier of R^1 -valued Function-like non empty total V18( the carrier of ((TOP-REAL 2) | a), the carrier of R^1) V119() V120() V121() Element of K19(K20( the carrier of ((TOP-REAL 2) | a), the carrier of R^1))
O is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
d . O is V28() real ext-real set
O `2 is V28() real ext-real Element of REAL
K526(O,2) is V28() real ext-real Element of REAL
O `1 is V28() real ext-real Element of REAL
K526(O,1) is V28() real ext-real Element of REAL
(O `2) / (O `1) is V28() real ext-real Element of REAL
(O `1) " is V28() real ext-real set
(O `2) * ((O `1) ") is V28() real ext-real set
((O `2) / (O `1)) / (O `1) is V28() real ext-real Element of REAL
((O `2) / (O `1)) * ((O `1) ") is V28() real ext-real set
() . O is set
1 / (O `1) is V28() real ext-real Element of REAL
1 * ((O `1) ") is V28() real ext-real set
|[(1 / (O `1)),(((O `2) / (O `1)) / (O `1))]| is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
I is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
I `2 is V28() real ext-real Element of REAL
K526(I,2) is V28() real ext-real Element of REAL
I `1 is V28() real ext-real Element of REAL
K526(I,1) is V28() real ext-real Element of REAL
- (I `1) is V28() real ext-real Element of REAL
(() | a) . O is set
proj2 . |[(1 / (O `1)),(((O `2) / (O `1)) / (O `1))]| is V28() real ext-real Element of REAL
|[(1 / (O `1)),(((O `2) / (O `1)) / (O `1))]| `2 is V28() real ext-real Element of REAL
K526(|[(1 / (O `1)),(((O `2) / (O `1)) / (O `1))]|,2) is V28() real ext-real Element of REAL
O is Relation-like the carrier of ((TOP-REAL 2) | a) -defined the carrier of R^1 -valued Function-like non empty total V18( the carrier of ((TOP-REAL 2) | a), the carrier of R^1) V119() V120() V121() Element of K19(K20( the carrier of ((TOP-REAL 2) | a), the carrier of R^1))
I is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
I `1 is V28() real ext-real Element of REAL
K526(I,1) is V28() real ext-real Element of REAL
I `2 is V28() real ext-real Element of REAL
K526(I,2) is V28() real ext-real Element of REAL
A is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
A `2 is V28() real ext-real Element of REAL
K526(A,2) is V28() real ext-real Element of REAL
A `1 is V28() real ext-real Element of REAL
K526(A,1) is V28() real ext-real Element of REAL
- (A `1) is V28() real ext-real Element of REAL
A is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
A `2 is V28() real ext-real Element of REAL
K526(A,2) is V28() real ext-real Element of REAL
A `1 is V28() real ext-real Element of REAL
K526(A,1) is V28() real ext-real Element of REAL
- (A `1) is V28() real ext-real Element of REAL
I is V28() real ext-real set
A is V28() real ext-real set
|[I,A]| is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
B is V28() real ext-real set
c . |[I,A]| is V28() real ext-real set
C is V28() real ext-real set
O . |[I,A]| is V28() real ext-real set
g . |[I,A]| is set
|[B,C]| is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
|[I,A]| `1 is V28() real ext-real Element of REAL
K526(|[I,A]|,1) is V28() real ext-real Element of REAL
1 / (|[I,A]| `1) is V28() real ext-real Element of REAL
(|[I,A]| `1) " is V28() real ext-real set
1 * ((|[I,A]| `1) ") is V28() real ext-real set
|[I,A]| `2 is V28() real ext-real Element of REAL
K526(|[I,A]|,2) is V28() real ext-real Element of REAL
- (|[I,A]| `1) is V28() real ext-real Element of REAL
() . |[I,A]| is set
(|[I,A]| `2) / (|[I,A]| `1) is V28() real ext-real Element of REAL
(|[I,A]| `2) * ((|[I,A]| `1) ") is V28() real ext-real set
((|[I,A]| `2) / (|[I,A]| `1)) / (|[I,A]| `1) is V28() real ext-real Element of REAL
((|[I,A]| `2) / (|[I,A]| `1)) * ((|[I,A]| `1) ") is V28() real ext-real set
|[(1 / (|[I,A]| `1)),(((|[I,A]| `2) / (|[I,A]| `1)) / (|[I,A]| `1))]| is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
ff is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
ff `2 is V28() real ext-real Element of REAL
K526(ff,2) is V28() real ext-real Element of REAL
ff `1 is V28() real ext-real Element of REAL
K526(ff,1) is V28() real ext-real Element of REAL
- (ff `1) is V28() real ext-real Element of REAL
(() | K0) . |[I,A]| is set
ff is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
ff `2 is V28() real ext-real Element of REAL
K526(ff,2) is V28() real ext-real Element of REAL
ff `1 is V28() real ext-real Element of REAL
K526(ff,1) is V28() real ext-real Element of REAL
- (ff `1) is V28() real ext-real Element of REAL
K0 is Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | K0 is strict TopSpace-like SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | K0) is set
f is Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | f is strict TopSpace-like SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | f) is set
K20( the carrier of ((TOP-REAL 2) | K0), the carrier of ((TOP-REAL 2) | f)) is set
K19(K20( the carrier of ((TOP-REAL 2) | K0), the carrier of ((TOP-REAL 2) | f))) is set
() | K0 is Relation-like NonZero (TOP-REAL 2) -defined NonZero (TOP-REAL 2) -valued Function-like Element of K19(K20((NonZero (TOP-REAL 2)),(NonZero (TOP-REAL 2))))
g is Relation-like the carrier of ((TOP-REAL 2) | K0) -defined the carrier of ((TOP-REAL 2) | f) -valued Function-like V18( the carrier of ((TOP-REAL 2) | K0), the carrier of ((TOP-REAL 2) | f)) Element of K19(K20( the carrier of ((TOP-REAL 2) | K0), the carrier of ((TOP-REAL 2) | f)))
a is set
b is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
b `1 is V28() real ext-real Element of REAL
K526(b,1) is V28() real ext-real Element of REAL
b `2 is V28() real ext-real Element of REAL
K526(b,2) is V28() real ext-real Element of REAL
- (b `2) is V28() real ext-real Element of REAL
- ((1.REAL 2) `2) is V28() real ext-real Element of REAL
a is non empty Element of K19( the carrier of (TOP-REAL 2))
b is set
c is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
c `1 is V28() real ext-real Element of REAL
K526(c,1) is V28() real ext-real Element of REAL
c `2 is V28() real ext-real Element of REAL
K526(c,2) is V28() real ext-real Element of REAL
- (c `2) is V28() real ext-real Element of REAL
() | a is Relation-like NonZero (TOP-REAL 2) -defined NonZero (TOP-REAL 2) -valued Function-like Element of K19(K20((NonZero (TOP-REAL 2)),(NonZero (TOP-REAL 2))))
dom (() | a) is Element of K19((NonZero (TOP-REAL 2)))
K19((NonZero (TOP-REAL 2))) is set
proj1 * (() | a) is Relation-like NonZero (TOP-REAL 2) -defined REAL -valued Function-like V119() V120() V121() Element of K19(K20((NonZero (TOP-REAL 2)),REAL))
K20((NonZero (TOP-REAL 2)),REAL) is set
K19(K20((NonZero (TOP-REAL 2)),REAL)) is set
dom (proj1 * (() | a)) is Element of K19((NonZero (TOP-REAL 2)))
b is set
dom () is Element of K19((NonZero (TOP-REAL 2)))
(dom ()) /\ a is Element of K19( the carrier of (TOP-REAL 2))
() . b is set
rng () is Element of K19((NonZero (TOP-REAL 2)))
(() | a) . b is set
rng (proj1 * (() | a)) is V129() V130() V131() Element of K19(REAL)
proj2 * (() | a) is Relation-like NonZero (TOP-REAL 2) -defined REAL -valued Function-like V119() V120() V121() Element of K19(K20((NonZero (TOP-REAL 2)),REAL))
dom (proj2 * (() | a)) is Element of K19((NonZero (TOP-REAL 2)))
b is set
dom () is Element of K19((NonZero (TOP-REAL 2)))
(dom ()) /\ a is Element of K19( the carrier of (TOP-REAL 2))
() . b is set
rng () is Element of K19((NonZero (TOP-REAL 2)))
(() | a) . b is set
rng (proj2 * (() | a)) is V129() V130() V131() Element of K19(REAL)
dom () is Element of K19((NonZero (TOP-REAL 2)))
(dom ()) /\ a is Element of K19( the carrier of (TOP-REAL 2))
(NonZero (TOP-REAL 2)) /\ a is Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | a is non empty strict TopSpace-like SubSpace of TOP-REAL 2
[#] ((TOP-REAL 2) | a) is non empty non proper open closed Element of K19( the carrier of ((TOP-REAL 2) | a))
the carrier of ((TOP-REAL 2) | a) is non empty set
K19( the carrier of ((TOP-REAL 2) | a)) is set
K20( the carrier of ((TOP-REAL 2) | a), the carrier of R^1) is V121() set
K19(K20( the carrier of ((TOP-REAL 2) | a), the carrier of R^1)) is set
b is Relation-like the carrier of ((TOP-REAL 2) | a) -defined the carrier of R^1 -valued Function-like non empty total V18( the carrier of ((TOP-REAL 2) | a), the carrier of R^1) V119() V120() V121() Element of K19(K20( the carrier of ((TOP-REAL 2) | a), the carrier of R^1))
c is set
d is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
d `1 is V28() real ext-real Element of REAL
K526(d,1) is V28() real ext-real Element of REAL
d `2 is V28() real ext-real Element of REAL
K526(d,2) is V28() real ext-real Element of REAL
- (d `2) is V28() real ext-real Element of REAL
c is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
b . c is V28() real ext-real set
c `2 is V28() real ext-real Element of REAL
K526(c,2) is V28() real ext-real Element of REAL
1 / (c `2) is V28() real ext-real Element of REAL
(c `2) " is V28() real ext-real set
1 * ((c `2) ") is V28() real ext-real set
() . c is set
c `1 is V28() real ext-real Element of REAL
K526(c,1) is V28() real ext-real Element of REAL
(c `1) / (c `2) is V28() real ext-real Element of REAL
(c `1) * ((c `2) ") is V28() real ext-real set
((c `1) / (c `2)) / (c `2) is V28() real ext-real Element of REAL
((c `1) / (c `2)) * ((c `2) ") is V28() real ext-real set
|[(((c `1) / (c `2)) / (c `2)),(1 / (c `2))]| is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
d is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
d `1 is V28() real ext-real Element of REAL
K526(d,1) is V28() real ext-real Element of REAL
d `2 is V28() real ext-real Element of REAL
K526(d,2) is V28() real ext-real Element of REAL
- (d `2) is V28() real ext-real Element of REAL
(() | a) . c is set
proj2 . |[(((c `1) / (c `2)) / (c `2)),(1 / (c `2))]| is V28() real ext-real Element of REAL
|[(((c `1) / (c `2)) / (c `2)),(1 / (c `2))]| `2 is V28() real ext-real Element of REAL
K526(|[(((c `1) / (c `2)) / (c `2)),(1 / (c `2))]|,2) is V28() real ext-real Element of REAL
c is Relation-like the carrier of ((TOP-REAL 2) | a) -defined the carrier of R^1 -valued Function-like non empty total V18( the carrier of ((TOP-REAL 2) | a), the carrier of R^1) V119() V120() V121() Element of K19(K20( the carrier of ((TOP-REAL 2) | a), the carrier of R^1))
d is Relation-like the carrier of ((TOP-REAL 2) | a) -defined the carrier of R^1 -valued Function-like non empty total V18( the carrier of ((TOP-REAL 2) | a), the carrier of R^1) V119() V120() V121() Element of K19(K20( the carrier of ((TOP-REAL 2) | a), the carrier of R^1))
O is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
d . O is V28() real ext-real set
O `1 is V28() real ext-real Element of REAL
K526(O,1) is V28() real ext-real Element of REAL
O `2 is V28() real ext-real Element of REAL
K526(O,2) is V28() real ext-real Element of REAL
(O `1) / (O `2) is V28() real ext-real Element of REAL
(O `2) " is V28() real ext-real set
(O `1) * ((O `2) ") is V28() real ext-real set
((O `1) / (O `2)) / (O `2) is V28() real ext-real Element of REAL
((O `1) / (O `2)) * ((O `2) ") is V28() real ext-real set
() . O is set
1 / (O `2) is V28() real ext-real Element of REAL
1 * ((O `2) ") is V28() real ext-real set
|[(((O `1) / (O `2)) / (O `2)),(1 / (O `2))]| is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
I is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
I `1 is V28() real ext-real Element of REAL
K526(I,1) is V28() real ext-real Element of REAL
I `2 is V28() real ext-real Element of REAL
K526(I,2) is V28() real ext-real Element of REAL
- (I `2) is V28() real ext-real Element of REAL
(() | a) . O is set
proj1 . |[(((O `1) / (O `2)) / (O `2)),(1 / (O `2))]| is V28() real ext-real Element of REAL
|[(((O `1) / (O `2)) / (O `2)),(1 / (O `2))]| `1 is V28() real ext-real Element of REAL
K526(|[(((O `1) / (O `2)) / (O `2)),(1 / (O `2))]|,1) is V28() real ext-real Element of REAL
O is Relation-like the carrier of ((TOP-REAL 2) | a) -defined the carrier of R^1 -valued Function-like non empty total V18( the carrier of ((TOP-REAL 2) | a), the carrier of R^1) V119() V120() V121() Element of K19(K20( the carrier of ((TOP-REAL 2) | a), the carrier of R^1))
I is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
I `2 is V28() real ext-real Element of REAL
K526(I,2) is V28() real ext-real Element of REAL
I `1 is V28() real ext-real Element of REAL
K526(I,1) is V28() real ext-real Element of REAL
A is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
A `1 is V28() real ext-real Element of REAL
K526(A,1) is V28() real ext-real Element of REAL
A `2 is V28() real ext-real Element of REAL
K526(A,2) is V28() real ext-real Element of REAL
- (A `2) is V28() real ext-real Element of REAL
A is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
A `1 is V28() real ext-real Element of REAL
K526(A,1) is V28() real ext-real Element of REAL
A `2 is V28() real ext-real Element of REAL
K526(A,2) is V28() real ext-real Element of REAL
- (A `2) is V28() real ext-real Element of REAL
I is V28() real ext-real set
A is V28() real ext-real set
|[I,A]| is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
B is V28() real ext-real set
O . |[I,A]| is V28() real ext-real set
C is V28() real ext-real set
c . |[I,A]| is V28() real ext-real set
g . |[I,A]| is set
|[B,C]| is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
|[I,A]| `2 is V28() real ext-real Element of REAL
K526(|[I,A]|,2) is V28() real ext-real Element of REAL
1 / (|[I,A]| `2) is V28() real ext-real Element of REAL
(|[I,A]| `2) " is V28() real ext-real set
1 * ((|[I,A]| `2) ") is V28() real ext-real set
(() | K0) . |[I,A]| is set
() . |[I,A]| is set
|[I,A]| `1 is V28() real ext-real Element of REAL
K526(|[I,A]|,1) is V28() real ext-real Element of REAL
(|[I,A]| `1) / (|[I,A]| `2) is V28() real ext-real Element of REAL
(|[I,A]| `1) * ((|[I,A]| `2) ") is V28() real ext-real set
((|[I,A]| `1) / (|[I,A]| `2)) / (|[I,A]| `2) is V28() real ext-real Element of REAL
((|[I,A]| `1) / (|[I,A]| `2)) * ((|[I,A]| `2) ") is V28() real ext-real set
|[(((|[I,A]| `1) / (|[I,A]| `2)) / (|[I,A]| `2)),(1 / (|[I,A]| `2))]| is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
ff is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
ff `1 is V28() real ext-real Element of REAL
K526(ff,1) is V28() real ext-real Element of REAL
ff `2 is V28() real ext-real Element of REAL
K526(ff,2) is V28() real ext-real Element of REAL
- (ff `2) is V28() real ext-real Element of REAL
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2) : P<sub>1</sub>[b<sub>1</sub>] } is set
K0 is set
f is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
F<sub>1</sub>() is Element of K19( the carrier of (TOP-REAL 2))
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2) : P<sub>1</sub>[b<sub>1</sub>] } is set
F<sub>1</sub>() ` is Element of K19( the carrier of (TOP-REAL 2))
{ b₁ where b₁ is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2) : P₁[b₁] } is set
K0 is set
the carrier of (TOP-REAL 2) \ F₁() is Element of K19( the carrier of (TOP-REAL 2))
f is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
K0 is set
f is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
g is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
the carrier of (TOP-REAL 2) \ F₁() is Element of K19( the carrier of (TOP-REAL 2))
f is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
K0 is V28() real ext-real set
f is V28() real ext-real set
K0 - f is V28() real ext-real set
- f is V28() real ext-real set
K0 + (- f) is V28() real ext-real set
4 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real ext-real positive non negative Element of NAT
(K0 - f) / 4 is V28() real ext-real Element of REAL
4 " is non empty V28() real ext-real positive non negative set
(K0 - f) * (4 ") is V28() real ext-real set
g is V28() real ext-real set
K0 - g is V28() real ext-real set
- g is V28() real ext-real set
K0 + (- g) is V28() real ext-real set
a is V28() real ext-real set
f - a is V28() real ext-real set
- a is V28() real ext-real set
f + (- a) is V28() real ext-real set
(K0 - g) - (f - a) is V28() real ext-real set
- (f - a) is V28() real ext-real set
(K0 - g) + (- (f - a)) is V28() real ext-real set
- ((K0 - f) / 4) is V28() real ext-real Element of REAL
((K0 - f) / 4) - (- ((K0 - f) / 4)) is V28() real ext-real Element of REAL
- (- ((K0 - f) / 4)) is V28() real ext-real set
((K0 - f) / 4) + (- (- ((K0 - f) / 4))) is V28() real ext-real set
g - a is V28() real ext-real set
g + (- a) is V28() real ext-real set
(K0 - f) - (g - a) is V28() real ext-real set
- (g - a) is V28() real ext-real set
(K0 - f) + (- (g - a)) is V28() real ext-real set
((K0 - f) / 4) + ((K0 - f) / 4) is V28() real ext-real Element of REAL
(g - a) + (((K0 - f) / 4) + ((K0 - f) / 4)) is V28() real ext-real Element of REAL
(K0 - f) / 2 is V28() real ext-real Element of REAL
2 " is non empty V28() real ext-real positive non negative set
(K0 - f) * (2 ") is V28() real ext-real set
(K0 - f) - ((K0 - f) / 2) is V28() real ext-real Element of REAL
- ((K0 - f) / 2) is V28() real ext-real set
(K0 - f) + (- ((K0 - f) / 2)) is V28() real ext-real set
{ b₁ where b₁ is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2) : F₁(b₁) <= F₂(b₁) } is set
{ b₁ where b₁ is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2) : S₁[b₁] } is set
the topology of (TOP-REAL 2) is non empty 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
Euclid 2 is non empty strict Reflexive discerning V197() triangle MetrStruct
Pitag_dist 2 is Relation-like K20((REAL 2),(REAL 2)) -defined REAL -valued Function-like total V18(K20((REAL 2),(REAL 2)), REAL ) V119() V120() V121() Element of K19(K20(K20((REAL 2),(REAL 2)),REAL))
K20((REAL 2),(REAL 2)) is set
K20(K20((REAL 2),(REAL 2)),REAL) is set
K19(K20(K20((REAL 2),(REAL 2)),REAL)) is set
MetrStruct(# (REAL 2),(Pitag_dist 2) #) is strict MetrStruct
TopSpaceMetr (Euclid 2) is TopStruct
the carrier of (TopSpaceMetr (Euclid 2)) is set
K19( the carrier of (TopSpaceMetr (Euclid 2))) is set
K0 is Element of K19( the carrier of (TOP-REAL 2))
K0 ` is Element of K19( the carrier of (TOP-REAL 2))
{ b₁ where b₁ is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2) : not S₁[b₁] } is set
the carrier of (Euclid 2) is non empty set
f is Element of K19( the carrier of (TopSpaceMetr (Euclid 2)))
g is Element of the carrier of (Euclid 2)
a is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
F₁(a) is V28() real ext-real set
F₂(a) is V28() real ext-real set
F₁(a) - F₂(a) is V28() real ext-real set
- F₂(a) is V28() real ext-real set
F₁(a) + (- F₂(a)) is V28() real ext-real set
(F₁(a) - F₂(a)) / 4 is V28() real ext-real Element of REAL
(F₁(a) - F₂(a)) * (4 ") is V28() real ext-real set
c is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
F₁(c) is V28() real ext-real set
F₂(c) is V28() real ext-real set
(F₁(a) - F₂(a)) / 2 is V28() real ext-real Element of REAL
(F₁(a) - F₂(a)) * (2 ") is V28() real ext-real set
Ball (g,((F₁(a) - F₂(a)) / 4)) is Element of K19( the carrier of (Euclid 2))
K19( the carrier of (Euclid 2)) is set
c is set
{ b₁ where b₁ is Element of the carrier of (Euclid 2) : not (F₁(a) - F₂(a)) / 4 <= dist (g,b₁) } is set
O is Element of the carrier of (Euclid 2)
dist (g,O) is V28() real ext-real Element of REAL
d is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
a - d is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
K296(a,d) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like V119() V120() V121() FinSequence of REAL
|.(a - d).| is V28() real ext-real non negative Element of REAL
K300((a - d)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like V119() V120() V121() FinSequence of REAL
K306(K300((a - d))) is V28() real ext-real Element of REAL
sqrt K306(K300((a - d))) is V28() real ext-real Element of REAL
|.(a - d).| ^2 is V28() real ext-real Element of REAL
|.(a - d).| * |.(a - d).| is V28() real ext-real non negative set
((F₁(a) - F₂(a)) / 4) ^2 is V28() real ext-real Element of REAL
((F₁(a) - F₂(a)) / 4) * ((F₁(a) - F₂(a)) / 4) is V28() real ext-real set
F₁((a - d)) is V28() real ext-real set
F₁(d) is V28() real ext-real set
F₁(a) - F₁(d) is V28() real ext-real set
- F₁(d) is V28() real ext-real set
F₁(a) + (- F₁(d)) is V28() real ext-real set
F₁((a - d)) ^2 is V28() real ext-real set
F₁((a - d)) * F₁((a - d)) is V28() real ext-real set
F₂((a - d)) is V28() real ext-real set
F₂((a - d)) ^2 is V28() real ext-real set
F₂((a - d)) * F₂((a - d)) is V28() real ext-real set
(F₁((a - d)) ^2) + (F₂((a - d)) ^2) is V28() real ext-real set
0 + (F₁((a - d)) ^2) is V28() real ext-real Element of REAL
(F₂((a - d)) ^2) + (F₁((a - d)) ^2) is V28() real ext-real set
F₂(d) is V28() real ext-real set
F₂(a) - F₂(d) is V28() real ext-real set
- F₂(d) is V28() real ext-real set
F₂(a) + (- F₂(d)) is V28() real ext-real set
(F₂((a - d)) ^2) + 0 is V28() real ext-real Element of REAL
- ((F₁(a) - F₂(a)) / 4) is V28() real ext-real Element of REAL
(F₁(a) - F₁(d)) - (F₂(a) - F₂(d)) is V28() real ext-real set
- (F₂(a) - F₂(d)) is V28() real ext-real set
(F₁(a) - F₁(d)) + (- (F₂(a) - F₂(d))) is V28() real ext-real set
((F₁(a) - F₂(a)) / 4) - (- ((F₁(a) - F₂(a)) / 4)) is V28() real ext-real Element of REAL
- (- ((F₁(a) - F₂(a)) / 4)) is V28() real ext-real set
((F₁(a) - F₂(a)) / 4) + (- (- ((F₁(a) - F₂(a)) / 4))) is V28() real ext-real set
F₁(d) - F₂(d) is V28() real ext-real set
F₁(d) + (- F₂(d)) is V28() real ext-real set
K0 is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
f is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
K0 - f is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
K296(K0,f) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like V119() V120() V121() FinSequence of REAL
(K0 - f) `1 is V28() real ext-real Element of REAL
K526((K0 - f),1) is V28() real ext-real Element of REAL
K0 `1 is V28() real ext-real Element of REAL
K526(K0,1) is V28() real ext-real Element of REAL
f `1 is V28() real ext-real Element of REAL
K526(f,1) is V28() real ext-real Element of REAL
(K0 `1) - (f `1) is V28() real ext-real Element of REAL
- (f `1) is V28() real ext-real set
(K0 `1) + (- (f `1)) is V28() real ext-real set
g is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
a is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
g - a is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
K296(g,a) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like V119() V120() V121() FinSequence of REAL
(g - a) `2 is V28() real ext-real Element of REAL
K526((g - a),2) is V28() real ext-real Element of REAL
g `2 is V28() real ext-real Element of REAL
K526(g,2) is V28() real ext-real Element of REAL
a `2 is V28() real ext-real Element of REAL
K526(a,2) is V28() real ext-real Element of REAL
(g `2) - (a `2) is V28() real ext-real Element of REAL
- (a `2) is V28() real ext-real set
(g `2) + (- (a `2)) is V28() real ext-real set
K0 is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
f is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
K0 - f is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
K296(K0,f) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like V119() V120() V121() FinSequence of REAL
|.(K0 - f).| is V28() real ext-real non negative Element of REAL
K300((K0 - f)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like V119() V120() V121() FinSequence of REAL
K306(K300((K0 - f))) is V28() real ext-real Element of REAL
sqrt K306(K300((K0 - f))) is V28() real ext-real Element of REAL
|.(K0 - f).| ^2 is V28() real ext-real Element of REAL
|.(K0 - f).| * |.(K0 - f).| is V28() real ext-real non negative set
(K0 - f) `1 is V28() real ext-real Element of REAL
K526((K0 - f),1) is V28() real ext-real Element of REAL
((K0 - f) `1) ^2 is V28() real ext-real Element of REAL
((K0 - f) `1) * ((K0 - f) `1) is V28() real ext-real set
(K0 - f) `2 is V28() real ext-real Element of REAL
K526((K0 - f),2) is V28() real ext-real Element of REAL
((K0 - f) `2) ^2 is V28() real ext-real Element of REAL
((K0 - f) `2) * ((K0 - f) `2) is V28() real ext-real set
(((K0 - f) `1) ^2) + (((K0 - f) `2) ^2) is V28() real ext-real Element of REAL
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2) : H<sub>1</sub>(b<sub>1</sub>) <= H<sub>2</sub>(b<sub>1</sub>) } is set
K0 is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
f is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
K0 - f is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
K296(K0,f) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like V119() V120() V121() FinSequence of REAL
(K0 - f) `2 is V28() real ext-real Element of REAL
K526((K0 - f),2) is V28() real ext-real Element of REAL
K0 `2 is V28() real ext-real Element of REAL
K526(K0,2) is V28() real ext-real Element of REAL
f `2 is V28() real ext-real Element of REAL
K526(f,2) is V28() real ext-real Element of REAL
(K0 `2) - (f `2) is V28() real ext-real Element of REAL
- (f `2) is V28() real ext-real set
(K0 `2) + (- (f `2)) is V28() real ext-real set
g is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
a is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
g - a is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
K296(g,a) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like V119() V120() V121() FinSequence of REAL
(g - a) `1 is V28() real ext-real Element of REAL
K526((g - a),1) is V28() real ext-real Element of REAL
g `1 is V28() real ext-real Element of REAL
K526(g,1) is V28() real ext-real Element of REAL
a `1 is V28() real ext-real Element of REAL
K526(a,1) is V28() real ext-real Element of REAL
(g `1) - (a `1) is V28() real ext-real Element of REAL
- (a `1) is V28() real ext-real set
(g `1) + (- (a `1)) is V28() real ext-real set
K0 is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
f is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
K0 - f is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
K296(K0,f) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like V119() V120() V121() FinSequence of REAL
|.(K0 - f).| is V28() real ext-real non negative Element of REAL
K300((K0 - f)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like V119() V120() V121() FinSequence of REAL
K306(K300((K0 - f))) is V28() real ext-real Element of REAL
sqrt K306(K300((K0 - f))) is V28() real ext-real Element of REAL
|.(K0 - f).| ^2 is V28() real ext-real Element of REAL
|.(K0 - f).| * |.(K0 - f).| is V28() real ext-real non negative set
(K0 - f) `2 is V28() real ext-real Element of REAL
K526((K0 - f),2) is V28() real ext-real Element of REAL
((K0 - f) `2) ^2 is V28() real ext-real Element of REAL
((K0 - f) `2) * ((K0 - f) `2) is V28() real ext-real set
(K0 - f) `1 is V28() real ext-real Element of REAL
K526((K0 - f),1) is V28() real ext-real Element of REAL
((K0 - f) `1) ^2 is V28() real ext-real Element of REAL
((K0 - f) `1) * ((K0 - f) `1) is V28() real ext-real set
(((K0 - f) `2) ^2) + (((K0 - f) `1) ^2) is V28() real ext-real Element of REAL
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2) : H<sub>2</sub>(b<sub>1</sub>) <= H<sub>1</sub>(b<sub>1</sub>) } is set
K0 is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
f is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
K0 - f is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
K296(K0,f) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like V119() V120() V121() FinSequence of REAL
(K0 - f) `1 is V28() real ext-real Element of REAL
K526((K0 - f),1) is V28() real ext-real Element of REAL
- ((K0 - f) `1) is V28() real ext-real Element of REAL
K0 `1 is V28() real ext-real Element of REAL
K526(K0,1) is V28() real ext-real Element of REAL
f `1 is V28() real ext-real Element of REAL
K526(f,1) is V28() real ext-real Element of REAL
(K0 `1) - (f `1) is V28() real ext-real Element of REAL
- (f `1) is V28() real ext-real set
(K0 `1) + (- (f `1)) is V28() real ext-real set
- ((K0 `1) - (f `1)) is V28() real ext-real Element of REAL
- (K0 `1) is V28() real ext-real Element of REAL
- (f `1) is V28() real ext-real Element of REAL
H₃(K0) - H₃(f) is V28() real ext-real Element of REAL
- (- (f `1)) is V28() real ext-real set
(- (K0 `1)) + (- (- (f `1))) is V28() real ext-real set
(K0 - f) `2 is V28() real ext-real Element of REAL
K526((K0 - f),2) is V28() real ext-real Element of REAL
K0 `2 is V28() real ext-real Element of REAL
K526(K0,2) is V28() real ext-real Element of REAL
f `2 is V28() real ext-real Element of REAL
K526(f,2) is V28() real ext-real Element of REAL
H₂(K0) - H₂(f) is V28() real ext-real Element of REAL
- (f `2) is V28() real ext-real set
(K0 `2) + (- (f `2)) is V28() real ext-real set
K0 is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
f is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
K0 - f is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
K296(K0,f) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like V119() V120() V121() FinSequence of REAL
(K0 - f) `1 is V28() real ext-real Element of REAL
K526((K0 - f),1) is V28() real ext-real Element of REAL
- ((K0 - f) `1) is V28() real ext-real Element of REAL
H<sub>3</sub>(K0 - f) ^2 is V28() real ext-real Element of REAL
(- ((K0 - f) `1)) * (- ((K0 - f) `1)) is V28() real ext-real set
H<sub>1</sub>(K0 - f) ^2 is V28() real ext-real Element of REAL
((K0 - f) `1) * ((K0 - f) `1) is V28() real ext-real set
|.(K0 - f).| is V28() real ext-real non negative Element of REAL
K300((K0 - f)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like V119() V120() V121() FinSequence of REAL
K306(K300((K0 - f))) is V28() real ext-real Element of REAL
sqrt K306(K300((K0 - f))) is V28() real ext-real Element of REAL
|.(K0 - f).| ^2 is V28() real ext-real Element of REAL
|.(K0 - f).| * |.(K0 - f).| is V28() real ext-real non negative set
(K0 - f) `2 is V28() real ext-real Element of REAL
K526((K0 - f),2) is V28() real ext-real Element of REAL
H₂(K0 - f) ^2 is V28() real ext-real Element of REAL
((K0 - f) `2) * ((K0 - f) `2) is V28() real ext-real set
(H₃(K0 - f) ^2) + (H₂(K0 - f) ^2) is V28() real ext-real Element of REAL
{ b₁ where b₁ is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2) : H₃(b₁) <= H₂(b₁) } is set
K0 is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
f is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
K0 - f is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
K296(K0,f) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like V119() V120() V121() FinSequence of REAL
(K0 - f) `2 is V28() real ext-real Element of REAL
K526((K0 - f),2) is V28() real ext-real Element of REAL
K0 `2 is V28() real ext-real Element of REAL
K526(K0,2) is V28() real ext-real Element of REAL
f `2 is V28() real ext-real Element of REAL
K526(f,2) is V28() real ext-real Element of REAL
H₂(K0) - H₂(f) is V28() real ext-real Element of REAL
- (f `2) is V28() real ext-real set
(K0 `2) + (- (f `2)) is V28() real ext-real set
(K0 - f) `1 is V28() real ext-real Element of REAL
K526((K0 - f),1) is V28() real ext-real Element of REAL
- ((K0 - f) `1) is V28() real ext-real Element of REAL
K0 `1 is V28() real ext-real Element of REAL
K526(K0,1) is V28() real ext-real Element of REAL
f `1 is V28() real ext-real Element of REAL
K526(f,1) is V28() real ext-real Element of REAL
(K0 `1) - (f `1) is V28() real ext-real Element of REAL
- (f `1) is V28() real ext-real set
(K0 `1) + (- (f `1)) is V28() real ext-real set
- ((K0 `1) - (f `1)) is V28() real ext-real Element of REAL
- (K0 `1) is V28() real ext-real Element of REAL
- (f `1) is V28() real ext-real Element of REAL
H₃(K0) - H₃(f) is V28() real ext-real Element of REAL
- (- (f `1)) is V28() real ext-real set
(- (K0 `1)) + (- (- (f `1))) is V28() real ext-real set
K0 is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
f is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
K0 - f is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
K296(K0,f) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like V119() V120() V121() FinSequence of REAL
(K0 - f) `1 is V28() real ext-real Element of REAL
K526((K0 - f),1) is V28() real ext-real Element of REAL
- ((K0 - f) `1) is V28() real ext-real Element of REAL
(- ((K0 - f) `1)) ^2 is V28() real ext-real Element of REAL
(- ((K0 - f) `1)) * (- ((K0 - f) `1)) is V28() real ext-real set
((K0 - f) `1) ^2 is V28() real ext-real Element of REAL
((K0 - f) `1) * ((K0 - f) `1) is V28() real ext-real set
|.(K0 - f).| is V28() real ext-real non negative Element of REAL
K300((K0 - f)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like V119() V120() V121() FinSequence of REAL
K306(K300((K0 - f))) is V28() real ext-real Element of REAL
sqrt K306(K300((K0 - f))) is V28() real ext-real Element of REAL
|.(K0 - f).| ^2 is V28() real ext-real Element of REAL
|.(K0 - f).| * |.(K0 - f).| is V28() real ext-real non negative set
(K0 - f) `2 is V28() real ext-real Element of REAL
K526((K0 - f),2) is V28() real ext-real Element of REAL
H₂(K0 - f) ^2 is V28() real ext-real Element of REAL
((K0 - f) `2) * ((K0 - f) `2) is V28() real ext-real set
H₃(K0 - f) ^2 is V28() real ext-real Element of REAL
(H₂(K0 - f) ^2) + (H₃(K0 - f) ^2) is V28() real ext-real Element of REAL
{ b₁ where b₁ is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2) : H₂(b₁) <= H₃(b₁) } is set
K0 is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
f is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
K0 - f is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
K296(K0,f) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like V119() V120() V121() FinSequence of REAL
(K0 - f) `2 is V28() real ext-real Element of REAL
K526((K0 - f),2) is V28() real ext-real Element of REAL
- ((K0 - f) `2) is V28() real ext-real Element of REAL
K0 `2 is V28() real ext-real Element of REAL
K526(K0,2) is V28() real ext-real Element of REAL
f `2 is V28() real ext-real Element of REAL
K526(f,2) is V28() real ext-real Element of REAL
(K0 `2) - (f `2) is V28() real ext-real Element of REAL
- (f `2) is V28() real ext-real set
(K0 `2) + (- (f `2)) is V28() real ext-real set
- ((K0 `2) - (f `2)) is V28() real ext-real Element of REAL
- (K0 `2) is V28() real ext-real Element of REAL
- (f `2) is V28() real ext-real Element of REAL
H₄(K0) - H₄(f) is V28() real ext-real Element of REAL
- (- (f `2)) is V28() real ext-real set
(- (K0 `2)) + (- (- (f `2))) is V28() real ext-real set
(K0 - f) `1 is V28() real ext-real Element of REAL
K526((K0 - f),1) is V28() real ext-real Element of REAL
K0 `1 is V28() real ext-real Element of REAL
K526(K0,1) is V28() real ext-real Element of REAL
f `1 is V28() real ext-real Element of REAL
K526(f,1) is V28() real ext-real Element of REAL
H₁(K0) - H₁(f) is V28() real ext-real Element of REAL
- (f `1) is V28() real ext-real set
(K0 `1) + (- (f `1)) is V28() real ext-real set
K0 is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
f is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
K0 - f is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
K296(K0,f) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like V119() V120() V121() FinSequence of REAL
(K0 - f) `2 is V28() real ext-real Element of REAL
K526((K0 - f),2) is V28() real ext-real Element of REAL
- ((K0 - f) `2) is V28() real ext-real Element of REAL
(- ((K0 - f) `2)) ^2 is V28() real ext-real Element of REAL
(- ((K0 - f) `2)) * (- ((K0 - f) `2)) is V28() real ext-real set
((K0 - f) `2) ^2 is V28() real ext-real Element of REAL
((K0 - f) `2) * ((K0 - f) `2) is V28() real ext-real set
|.(K0 - f).| is V28() real ext-real non negative Element of REAL
K300((K0 - f)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like V119() V120() V121() FinSequence of REAL
K306(K300((K0 - f))) is V28() real ext-real Element of REAL
sqrt K306(K300((K0 - f))) is V28() real ext-real Element of REAL
|.(K0 - f).| ^2 is V28() real ext-real Element of REAL
|.(K0 - f).| * |.(K0 - f).| is V28() real ext-real non negative set
H<sub>4</sub>(K0 - f) ^2 is V28() real ext-real Element of REAL
(K0 - f) `1 is V28() real ext-real Element of REAL
K526((K0 - f),1) is V28() real ext-real Element of REAL
H₁(K0 - f) ^2 is V28() real ext-real Element of REAL
((K0 - f) `1) * ((K0 - f) `1) is V28() real ext-real set
(H₄(K0 - f) ^2) + (H₁(K0 - f) ^2) is V28() real ext-real Element of REAL
{ b₁ where b₁ is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2) : H₄(b₁) <= H₁(b₁) } is set
K0 is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
f is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
K0 - f is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
K296(K0,f) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like V119() V120() V121() FinSequence of REAL
(K0 - f) `1 is V28() real ext-real Element of REAL
K526((K0 - f),1) is V28() real ext-real Element of REAL
K0 `1 is V28() real ext-real Element of REAL
K526(K0,1) is V28() real ext-real Element of REAL
f `1 is V28() real ext-real Element of REAL
K526(f,1) is V28() real ext-real Element of REAL
H₁(K0) - H₁(f) is V28() real ext-real Element of REAL
- (f `1) is V28() real ext-real set
(K0 `1) + (- (f `1)) is V28() real ext-real set
(K0 - f) `2 is V28() real ext-real Element of REAL
K526((K0 - f),2) is V28() real ext-real Element of REAL
- ((K0 - f) `2) is V28() real ext-real Element of REAL
K0 `2 is V28() real ext-real Element of REAL
K526(K0,2) is V28() real ext-real Element of REAL
f `2 is V28() real ext-real Element of REAL
K526(f,2) is V28() real ext-real Element of REAL
(K0 `2) - (f `2) is V28() real ext-real Element of REAL
- (f `2) is V28() real ext-real set
(K0 `2) + (- (f `2)) is V28() real ext-real set
- ((K0 `2) - (f `2)) is V28() real ext-real Element of REAL
- (K0 `2) is V28() real ext-real Element of REAL
- (f `2) is V28() real ext-real Element of REAL
H₄(K0) - H₄(f) is V28() real ext-real Element of REAL
- (- (f `2)) is V28() real ext-real set
(- (K0 `2)) + (- (- (f `2))) is V28() real ext-real set
K0 is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
f is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
K0 - f is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
K296(K0,f) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like V119() V120() V121() FinSequence of REAL
(K0 - f) `2 is V28() real ext-real Element of REAL
K526((K0 - f),2) is V28() real ext-real Element of REAL
- ((K0 - f) `2) is V28() real ext-real Element of REAL
H<sub>4</sub>(K0 - f) ^2 is V28() real ext-real Element of REAL
(- ((K0 - f) `2)) * (- ((K0 - f) `2)) is V28() real ext-real set
H<sub>2</sub>(K0 - f) ^2 is V28() real ext-real Element of REAL
((K0 - f) `2) * ((K0 - f) `2) is V28() real ext-real set
|.(K0 - f).| is V28() real ext-real non negative Element of REAL
K300((K0 - f)) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like V119() V120() V121() FinSequence of REAL
K306(K300((K0 - f))) is V28() real ext-real Element of REAL
sqrt K306(K300((K0 - f))) is V28() real ext-real Element of REAL
|.(K0 - f).| ^2 is V28() real ext-real Element of REAL
|.(K0 - f).| * |.(K0 - f).| is V28() real ext-real non negative set
(K0 - f) `1 is V28() real ext-real Element of REAL
K526((K0 - f),1) is V28() real ext-real Element of REAL
H₁(K0 - f) ^2 is V28() real ext-real Element of REAL
((K0 - f) `1) * ((K0 - f) `1) is V28() real ext-real set
(H₁(K0 - f) ^2) + (H₄(K0 - f) ^2) is V28() real ext-real Element of REAL
{ b₁ where b₁ is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2) : H₁(b₁) <= H₄(b₁) } is set
{ b₁ where b₁ is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2) : b₁ `2 <= - (b<sub>1</sub> `1) } is set
{ b₁ where b₁ is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2) : b₁ `1 <= b<sub>1</sub> `2 } is set
{ b₁ where b₁ is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2) : - (b₁ `1) <= b<sub>1</sub> `2 } is set
{ b₁ where b₁ is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2) : b₁ `2 <= b<sub>1</sub> `1 } is set
b is Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | b is strict TopSpace-like SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | b) is set
K19( the carrier of ((TOP-REAL 2) | b)) is set
c is Element of K19( the carrier of ((TOP-REAL 2) | b))
((TOP-REAL 2) | b) | c is strict TopSpace-like SubSpace of (TOP-REAL 2) | b
the carrier of (((TOP-REAL 2) | b) | c) is set
K20( the carrier of (((TOP-REAL 2) | b) | c), the carrier of ((TOP-REAL 2) | b)) is set
K19(K20( the carrier of (((TOP-REAL 2) | b) | c), the carrier of ((TOP-REAL 2) | b))) is set
() | c is Relation-like NonZero (TOP-REAL 2) -defined NonZero (TOP-REAL 2) -valued Function-like Element of K19(K20((NonZero (TOP-REAL 2)),(NonZero (TOP-REAL 2))))
d is Relation-like the carrier of (((TOP-REAL 2) | b) | c) -defined the carrier of ((TOP-REAL 2) | b) -valued Function-like V18( the carrier of (((TOP-REAL 2) | b) | c), the carrier of ((TOP-REAL 2) | b)) Element of K19(K20( the carrier of (((TOP-REAL 2) | b) | c), the carrier of ((TOP-REAL 2) | b)))
[#] ((TOP-REAL 2) | b) is non proper open closed Element of K19( the carrier of ((TOP-REAL 2) | b))
I is set
A is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
A `2 is V28() real ext-real Element of REAL
K526(A,2) is V28() real ext-real Element of REAL
A `1 is V28() real ext-real Element of REAL
K526(A,1) is V28() real ext-real Element of REAL
- (A `1) is V28() real ext-real Element of REAL
A is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
A `2 is V28() real ext-real Element of REAL
K526(A,2) is V28() real ext-real Element of REAL
A `1 is V28() real ext-real Element of REAL
K526(A,1) is V28() real ext-real Element of REAL
- (A `1) is V28() real ext-real Element of REAL
O is Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | O is strict TopSpace-like SubSpace of TOP-REAL 2
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2) : S<sub>1</sub>[b<sub>1</sub>] } is set
I is Element of K19( the carrier of (TOP-REAL 2))
I /\ b is Element of K19( the carrier of (TOP-REAL 2))
A is set
B is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
B `2 is V28() real ext-real Element of REAL
K526(B,2) is V28() real ext-real Element of REAL
B `1 is V28() real ext-real Element of REAL
K526(B,1) is V28() real ext-real Element of REAL
- (B `1) is V28() real ext-real Element of REAL
a is closed Element of K19( the carrier of (TOP-REAL 2))
g is closed Element of K19( the carrier of (TOP-REAL 2))
a /\ g is closed Element of K19( the carrier of (TOP-REAL 2))
f is closed Element of K19( the carrier of (TOP-REAL 2))
K0 is closed Element of K19( the carrier of (TOP-REAL 2))
f /\ K0 is closed Element of K19( the carrier of (TOP-REAL 2))
(a /\ g) \/ (f /\ K0) is closed Element of K19( the carrier of (TOP-REAL 2))
A is set
B is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
B `2 is V28() real ext-real Element of REAL
K526(B,2) is V28() real ext-real Element of REAL
B `1 is V28() real ext-real Element of REAL
K526(B,1) is V28() real ext-real Element of REAL
C is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
C `1 is V28() real ext-real Element of REAL
K526(C,1) is V28() real ext-real Element of REAL
- (C `1) is V28() real ext-real Element of REAL
C `2 is V28() real ext-real Element of REAL
K526(C,2) is V28() real ext-real Element of REAL
B is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
B `1 is V28() real ext-real Element of REAL
K526(B,1) is V28() real ext-real Element of REAL
B `2 is V28() real ext-real Element of REAL
K526(B,2) is V28() real ext-real Element of REAL
C is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
C `2 is V28() real ext-real Element of REAL
K526(C,2) is V28() real ext-real Element of REAL
C `1 is V28() real ext-real Element of REAL
K526(C,1) is V28() real ext-real Element of REAL
- (C `1) is V28() real ext-real Element of REAL
A is set
B is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
B `2 is V28() real ext-real Element of REAL
K526(B,2) is V28() real ext-real Element of REAL
B `1 is V28() real ext-real Element of REAL
K526(B,1) is V28() real ext-real Element of REAL
- (B `1) is V28() real ext-real Element of REAL
A is set
B is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
B `2 is V28() real ext-real Element of REAL
K526(B,2) is V28() real ext-real Element of REAL
B `1 is V28() real ext-real Element of REAL
K526(B,1) is V28() real ext-real Element of REAL
- (B `1) is V28() real ext-real Element of REAL
B is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
B `2 is V28() real ext-real Element of REAL
K526(B,2) is V28() real ext-real Element of REAL
B `1 is V28() real ext-real Element of REAL
K526(B,1) is V28() real ext-real Element of REAL
- (B `1) is V28() real ext-real Element of REAL
B is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
B `2 is V28() real ext-real Element of REAL
K526(B,2) is V28() real ext-real Element of REAL
B `1 is V28() real ext-real Element of REAL
K526(B,1) is V28() real ext-real Element of REAL
- (B `1) is V28() real ext-real Element of REAL
I /\ ([#] ((TOP-REAL 2) | b)) is Element of K19( the carrier of ((TOP-REAL 2) | b))
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2) : b<sub>1</sub> `1 <= - (b₁ `2) } is set
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2) : b<sub>1</sub> `2 <= b₁ `1 } is set
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2) : - (b<sub>1</sub> `2) <= b₁ `1 } is set
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2) : b<sub>1</sub> `1 <= b₁ `2 } is set
b is Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | b is strict TopSpace-like SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | b) is set
K19( the carrier of ((TOP-REAL 2) | b)) is set
c is Element of K19( the carrier of ((TOP-REAL 2) | b))
((TOP-REAL 2) | b) | c is strict TopSpace-like SubSpace of (TOP-REAL 2) | b
the carrier of (((TOP-REAL 2) | b) | c) is set
K20( the carrier of (((TOP-REAL 2) | b) | c), the carrier of ((TOP-REAL 2) | b)) is set
K19(K20( the carrier of (((TOP-REAL 2) | b) | c), the carrier of ((TOP-REAL 2) | b))) is set
() | c is Relation-like NonZero (TOP-REAL 2) -defined NonZero (TOP-REAL 2) -valued Function-like Element of K19(K20((NonZero (TOP-REAL 2)),(NonZero (TOP-REAL 2))))
d is Relation-like the carrier of (((TOP-REAL 2) | b) | c) -defined the carrier of ((TOP-REAL 2) | b) -valued Function-like V18( the carrier of (((TOP-REAL 2) | b) | c), the carrier of ((TOP-REAL 2) | b)) Element of K19(K20( the carrier of (((TOP-REAL 2) | b) | c), the carrier of ((TOP-REAL 2) | b)))
[#] ((TOP-REAL 2) | b) is non proper open closed Element of K19( the carrier of ((TOP-REAL 2) | b))
I is set
A is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
A `1 is V28() real ext-real Element of REAL
K526(A,1) is V28() real ext-real Element of REAL
A `2 is V28() real ext-real Element of REAL
K526(A,2) is V28() real ext-real Element of REAL
- (A `2) is V28() real ext-real Element of REAL
A is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
A `1 is V28() real ext-real Element of REAL
K526(A,1) is V28() real ext-real Element of REAL
A `2 is V28() real ext-real Element of REAL
K526(A,2) is V28() real ext-real Element of REAL
- (A `2) is V28() real ext-real Element of REAL
O is Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | O is strict TopSpace-like SubSpace of TOP-REAL 2
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2) : S<sub>1</sub>[b<sub>1</sub>] } is set
I is Element of K19( the carrier of (TOP-REAL 2))
I /\ b is Element of K19( the carrier of (TOP-REAL 2))
A is set
B is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
B `1 is V28() real ext-real Element of REAL
K526(B,1) is V28() real ext-real Element of REAL
B `2 is V28() real ext-real Element of REAL
K526(B,2) is V28() real ext-real Element of REAL
- (B `2) is V28() real ext-real Element of REAL
a is closed Element of K19( the carrier of (TOP-REAL 2))
g is closed Element of K19( the carrier of (TOP-REAL 2))
a /\ g is closed Element of K19( the carrier of (TOP-REAL 2))
f is closed Element of K19( the carrier of (TOP-REAL 2))
K0 is closed Element of K19( the carrier of (TOP-REAL 2))
f /\ K0 is closed Element of K19( the carrier of (TOP-REAL 2))
(a /\ g) \/ (f /\ K0) is closed Element of K19( the carrier of (TOP-REAL 2))
A is set
B is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
B `1 is V28() real ext-real Element of REAL
K526(B,1) is V28() real ext-real Element of REAL
B `2 is V28() real ext-real Element of REAL
K526(B,2) is V28() real ext-real Element of REAL
C is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
C `2 is V28() real ext-real Element of REAL
K526(C,2) is V28() real ext-real Element of REAL
- (C `2) is V28() real ext-real Element of REAL
C `1 is V28() real ext-real Element of REAL
K526(C,1) is V28() real ext-real Element of REAL
B is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
B `2 is V28() real ext-real Element of REAL
K526(B,2) is V28() real ext-real Element of REAL
B `1 is V28() real ext-real Element of REAL
K526(B,1) is V28() real ext-real Element of REAL
C is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
C `1 is V28() real ext-real Element of REAL
K526(C,1) is V28() real ext-real Element of REAL
C `2 is V28() real ext-real Element of REAL
K526(C,2) is V28() real ext-real Element of REAL
- (C `2) is V28() real ext-real Element of REAL
A is set
B is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
B `1 is V28() real ext-real Element of REAL
K526(B,1) is V28() real ext-real Element of REAL
B `2 is V28() real ext-real Element of REAL
K526(B,2) is V28() real ext-real Element of REAL
- (B `2) is V28() real ext-real Element of REAL
A is set
B is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
B `1 is V28() real ext-real Element of REAL
K526(B,1) is V28() real ext-real Element of REAL
B `2 is V28() real ext-real Element of REAL
K526(B,2) is V28() real ext-real Element of REAL
- (B `2) is V28() real ext-real Element of REAL
B is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
B `1 is V28() real ext-real Element of REAL
K526(B,1) is V28() real ext-real Element of REAL
B `2 is V28() real ext-real Element of REAL
K526(B,2) is V28() real ext-real Element of REAL
- (B `2) is V28() real ext-real Element of REAL
B is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
B `1 is V28() real ext-real Element of REAL
K526(B,1) is V28() real ext-real Element of REAL
B `2 is V28() real ext-real Element of REAL
K526(B,2) is V28() real ext-real Element of REAL
- (B `2) is V28() real ext-real Element of REAL
I /\ ([#] ((TOP-REAL 2) | b)) is Element of K19( the carrier of ((TOP-REAL 2) | b))
- 1 is V28() real ext-real non positive Element of REAL
|[(- 1),1]| is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
g is non empty Element of K19( the carrier of (TOP-REAL 2))
g ` is Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | g is non empty strict TopSpace-like SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | g) is non empty set
K20( the carrier of ((TOP-REAL 2) | g), the carrier of ((TOP-REAL 2) | g)) is set
K19(K20( the carrier of ((TOP-REAL 2) | g), the carrier of ((TOP-REAL 2) | g))) is set
f is Element of K19( the carrier of (TOP-REAL 2))
f ` is Element of K19( the carrier of (TOP-REAL 2))
a is set
the carrier of (TOP-REAL 2) \ g is Element of K19( the carrier of (TOP-REAL 2))
b is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
b `2 is V28() real ext-real Element of REAL
K526(b,2) is V28() real ext-real Element of REAL
b `1 is V28() real ext-real Element of REAL
K526(b,1) is V28() real ext-real Element of REAL
- (b `1) is V28() real ext-real Element of REAL
b is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
b `2 is V28() real ext-real Element of REAL
K526(b,2) is V28() real ext-real Element of REAL
b `1 is V28() real ext-real Element of REAL
K526(b,1) is V28() real ext-real Element of REAL
- (b `1) is V28() real ext-real Element of REAL
[#] ((TOP-REAL 2) | g) is non empty non proper open closed Element of K19( the carrier of ((TOP-REAL 2) | g))
K19( the carrier of ((TOP-REAL 2) | g)) is set
- ((1.REAL 2) `1) is V28() real ext-real Element of REAL
K19( the carrier of ((TOP-REAL 2) | g)) is set
a is non empty Element of K19( the carrier of ((TOP-REAL 2) | g))
((TOP-REAL 2) | g) | a is non empty strict TopSpace-like SubSpace of (TOP-REAL 2) | g
[#] (((TOP-REAL 2) | g) | a) is non empty non proper open closed Element of K19( the carrier of (((TOP-REAL 2) | g) | a))
the carrier of (((TOP-REAL 2) | g) | a) is non empty set
K19( the carrier of (((TOP-REAL 2) | g) | a)) is set
b is set
the carrier of (TOP-REAL 2) \ g is Element of K19( the carrier of (TOP-REAL 2))
c is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
c `1 is V28() real ext-real Element of REAL
K526(c,1) is V28() real ext-real Element of REAL
c `2 is V28() real ext-real Element of REAL
K526(c,2) is V28() real ext-real Element of REAL
- (c `2) is V28() real ext-real Element of REAL
c is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
c `1 is V28() real ext-real Element of REAL
K526(c,1) is V28() real ext-real Element of REAL
c `2 is V28() real ext-real Element of REAL
K526(c,2) is V28() real ext-real Element of REAL
- (c `2) is V28() real ext-real Element of REAL
[#] ((TOP-REAL 2) | g) is non empty non proper open closed Element of K19( the carrier of ((TOP-REAL 2) | g))
|[(- 1),1]| `1 is V28() real ext-real Element of REAL
K526(|[(- 1),1]|,1) is V28() real ext-real Element of REAL
|[(- 1),1]| `2 is V28() real ext-real Element of REAL
K526(|[(- 1),1]|,2) is V28() real ext-real Element of REAL
b is non empty Element of K19( the carrier of ((TOP-REAL 2) | g))
((TOP-REAL 2) | g) | b is non empty strict TopSpace-like SubSpace of (TOP-REAL 2) | g
[#] (((TOP-REAL 2) | g) | b) is non empty non proper open closed Element of K19( the carrier of (((TOP-REAL 2) | g) | b))
the carrier of (((TOP-REAL 2) | g) | b) is non empty set
K19( the carrier of (((TOP-REAL 2) | g) | b)) is set
[#] ((TOP-REAL 2) | g) is non empty non proper open closed Element of K19( the carrier of ((TOP-REAL 2) | g))
() | b is Relation-like NonZero (TOP-REAL 2) -defined NonZero (TOP-REAL 2) -valued Function-like Element of K19(K20((NonZero (TOP-REAL 2)),(NonZero (TOP-REAL 2))))
rng (() | b) is Element of K19((NonZero (TOP-REAL 2)))
K19((NonZero (TOP-REAL 2))) is set
d is set
c is Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | c is strict TopSpace-like SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | c) is set
O is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
O `2 is V28() real ext-real Element of REAL
K526(O,2) is V28() real ext-real Element of REAL
[#] ((TOP-REAL 2) | c) is non proper open closed Element of K19( the carrier of ((TOP-REAL 2) | c))
K19( the carrier of ((TOP-REAL 2) | c)) is set
O `1 is V28() real ext-real Element of REAL
K526(O,1) is V28() real ext-real Element of REAL
I is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
I `1 is V28() real ext-real Element of REAL
K526(I,1) is V28() real ext-real Element of REAL
I `2 is V28() real ext-real Element of REAL
K526(I,2) is V28() real ext-real Element of REAL
- (I `2) is V28() real ext-real Element of REAL
I is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
I `1 is V28() real ext-real Element of REAL
K526(I,1) is V28() real ext-real Element of REAL
I `2 is V28() real ext-real Element of REAL
K526(I,2) is V28() real ext-real Element of REAL
- (I `2) is V28() real ext-real Element of REAL
dom (() | b) is Element of K19((NonZero (TOP-REAL 2)))
O is set
(() | b) . O is set
dom () is Element of K19((NonZero (TOP-REAL 2)))
(dom ()) /\ b is Element of K19( the carrier of ((TOP-REAL 2) | g))
I is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
() . I is set
I `1 is V28() real ext-real Element of REAL
K526(I,1) is V28() real ext-real Element of REAL
I `2 is V28() real ext-real Element of REAL
K526(I,2) is V28() real ext-real Element of REAL
(I `1) / (I `2) is V28() real ext-real Element of REAL
(I `2) " is V28() real ext-real set
(I `1) * ((I `2) ") is V28() real ext-real set
((I `1) / (I `2)) / (I `2) is V28() real ext-real Element of REAL
((I `1) / (I `2)) * ((I `2) ") is V28() real ext-real set
1 / (I `2) is V28() real ext-real Element of REAL
1 * ((I `2) ") is V28() real ext-real set
|[(((I `1) / (I `2)) / (I `2)),(1 / (I `2))]| is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
[#] ((TOP-REAL 2) | c) is non proper open closed Element of K19( the carrier of ((TOP-REAL 2) | c))
K19( the carrier of ((TOP-REAL 2) | c)) is set
|[(((I `1) / (I `2)) / (I `2)),(1 / (I `2))]| `2 is V28() real ext-real Element of REAL
K526(|[(((I `1) / (I `2)) / (I `2)),(1 / (I `2))]|,2) is V28() real ext-real Element of REAL
0 * (I `2) is V28() real ext-real Element of REAL
(1 / (I `2)) * (I `2) is V28() real ext-real Element of REAL
B is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
B `1 is V28() real ext-real Element of REAL
K526(B,1) is V28() real ext-real Element of REAL
B `2 is V28() real ext-real Element of REAL
K526(B,2) is V28() real ext-real Element of REAL
- (B `2) is V28() real ext-real Element of REAL
(I `2) / (I `2) is V28() real ext-real Element of REAL
(I `2) * ((I `2) ") is V28() real ext-real set
1 * (I `2) is V28() real ext-real Element of REAL
- (1 * (I `2)) is V28() real ext-real Element of REAL
(- (1 * (I `2))) / (I `2) is V28() real ext-real Element of REAL
(- (1 * (I `2))) * ((I `2) ") is V28() real ext-real set
B is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
B `1 is V28() real ext-real Element of REAL
K526(B,1) is V28() real ext-real Element of REAL
B `2 is V28() real ext-real Element of REAL
K526(B,2) is V28() real ext-real Element of REAL
- (B `2) is V28() real ext-real Element of REAL
(- 1) * (I `2) is V28() real ext-real Element of REAL
((- 1) * (I `2)) / (I `2) is V28() real ext-real Element of REAL
((- 1) * (I `2)) * ((I `2) ") is V28() real ext-real set
(- 1) / (I `2) is V28() real ext-real Element of REAL
(- 1) * ((I `2) ") is V28() real ext-real set
- (1 / (I `2)) is V28() real ext-real Element of REAL
|[(((I `1) / (I `2)) / (I `2)),(1 / (I `2))]| `1 is V28() real ext-real Element of REAL
K526(|[(((I `1) / (I `2)) / (I `2)),(1 / (I `2))]|,1) is V28() real ext-real Element of REAL
1 * (I `2) is V28() real ext-real Element of REAL
- (1 * (I `2)) is V28() real ext-real Element of REAL
(I `2) / (I `2) is V28() real ext-real Element of REAL
(I `2) * ((I `2) ") is V28() real ext-real set
(- (1 * (I `2))) / (I `2) is V28() real ext-real Element of REAL
(- (1 * (I `2))) * ((I `2) ") is V28() real ext-real set
B is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
B `1 is V28() real ext-real Element of REAL
K526(B,1) is V28() real ext-real Element of REAL
B `2 is V28() real ext-real Element of REAL
K526(B,2) is V28() real ext-real Element of REAL
- (B `2) is V28() real ext-real Element of REAL
(- 1) * (I `2) is V28() real ext-real Element of REAL
((- 1) * (I `2)) / (I `2) is V28() real ext-real Element of REAL
((- 1) * (I `2)) * ((I `2) ") is V28() real ext-real set
(- 1) / (I `2) is V28() real ext-real Element of REAL
(- 1) * ((I `2) ") is V28() real ext-real set
- (1 / (I `2)) is V28() real ext-real Element of REAL
|[(((I `1) / (I `2)) / (I `2)),(1 / (I `2))]| `1 is V28() real ext-real Element of REAL
K526(|[(((I `1) / (I `2)) / (I `2)),(1 / (I `2))]|,1) is V28() real ext-real Element of REAL
a \/ b is Element of K19( the carrier of ((TOP-REAL 2) | g))
c is set
d is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
d `2 is V28() real ext-real Element of REAL
K526(d,2) is V28() real ext-real Element of REAL
d `1 is V28() real ext-real Element of REAL
K526(d,1) is V28() real ext-real Element of REAL
- (d `1) is V28() real ext-real Element of REAL
- (d `2) is V28() real ext-real Element of REAL
c is set
d is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
d `1 is V28() real ext-real Element of REAL
K526(d,1) is V28() real ext-real Element of REAL
d `2 is V28() real ext-real Element of REAL
K526(d,2) is V28() real ext-real Element of REAL
- (d `2) is V28() real ext-real Element of REAL
d is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
d `1 is V28() real ext-real Element of REAL
K526(d,1) is V28() real ext-real Element of REAL
d `2 is V28() real ext-real Element of REAL
K526(d,2) is V28() real ext-real Element of REAL
- (d `2) is V28() real ext-real Element of REAL
() | a is Relation-like NonZero (TOP-REAL 2) -defined NonZero (TOP-REAL 2) -valued Function-like Element of K19(K20((NonZero (TOP-REAL 2)),(NonZero (TOP-REAL 2))))
rng (() | a) is Element of K19((NonZero (TOP-REAL 2)))
d is set
c is Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | c is strict TopSpace-like SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | c) is set
O is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
O `1 is V28() real ext-real Element of REAL
K526(O,1) is V28() real ext-real Element of REAL
[#] ((TOP-REAL 2) | c) is non proper open closed Element of K19( the carrier of ((TOP-REAL 2) | c))
K19( the carrier of ((TOP-REAL 2) | c)) is set
O `2 is V28() real ext-real Element of REAL
K526(O,2) is V28() real ext-real Element of REAL
I is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
I `2 is V28() real ext-real Element of REAL
K526(I,2) is V28() real ext-real Element of REAL
I `1 is V28() real ext-real Element of REAL
K526(I,1) is V28() real ext-real Element of REAL
- (I `1) is V28() real ext-real Element of REAL
I is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
I `2 is V28() real ext-real Element of REAL
K526(I,2) is V28() real ext-real Element of REAL
I `1 is V28() real ext-real Element of REAL
K526(I,1) is V28() real ext-real Element of REAL
- (I `1) is V28() real ext-real Element of REAL
dom (() | a) is Element of K19((NonZero (TOP-REAL 2)))
O is set
(() | a) . O is set
dom () is Element of K19((NonZero (TOP-REAL 2)))
(dom ()) /\ a is Element of K19( the carrier of ((TOP-REAL 2) | g))
I is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
() . I is set
I `1 is V28() real ext-real Element of REAL
K526(I,1) is V28() real ext-real Element of REAL
1 / (I `1) is V28() real ext-real Element of REAL
(I `1) " is V28() real ext-real set
1 * ((I `1) ") is V28() real ext-real set
I `2 is V28() real ext-real Element of REAL
K526(I,2) is V28() real ext-real Element of REAL
(I `2) / (I `1) is V28() real ext-real Element of REAL
(I `2) * ((I `1) ") is V28() real ext-real set
((I `2) / (I `1)) / (I `1) is V28() real ext-real Element of REAL
((I `2) / (I `1)) * ((I `1) ") is V28() real ext-real set
|[(1 / (I `1)),(((I `2) / (I `1)) / (I `1))]| is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
[#] ((TOP-REAL 2) | c) is non proper open closed Element of K19( the carrier of ((TOP-REAL 2) | c))
K19( the carrier of ((TOP-REAL 2) | c)) is set
|[(1 / (I `1)),(((I `2) / (I `1)) / (I `1))]| `1 is V28() real ext-real Element of REAL
K526(|[(1 / (I `1)),(((I `2) / (I `1)) / (I `1))]|,1) is V28() real ext-real Element of REAL
0 * (I `1) is V28() real ext-real Element of REAL
(1 / (I `1)) * (I `1) is V28() real ext-real Element of REAL
B is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
B `2 is V28() real ext-real Element of REAL
K526(B,2) is V28() real ext-real Element of REAL
B `1 is V28() real ext-real Element of REAL
K526(B,1) is V28() real ext-real Element of REAL
- (B `1) is V28() real ext-real Element of REAL
(I `1) / (I `1) is V28() real ext-real Element of REAL
(I `1) * ((I `1) ") is V28() real ext-real set
1 * (I `1) is V28() real ext-real Element of REAL
- (1 * (I `1)) is V28() real ext-real Element of REAL
(- (1 * (I `1))) / (I `1) is V28() real ext-real Element of REAL
(- (1 * (I `1))) * ((I `1) ") is V28() real ext-real set
B is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
B `2 is V28() real ext-real Element of REAL
K526(B,2) is V28() real ext-real Element of REAL
B `1 is V28() real ext-real Element of REAL
K526(B,1) is V28() real ext-real Element of REAL
- (B `1) is V28() real ext-real Element of REAL
(- 1) * (I `1) is V28() real ext-real Element of REAL
((- 1) * (I `1)) / (I `1) is V28() real ext-real Element of REAL
((- 1) * (I `1)) * ((I `1) ") is V28() real ext-real set
(- 1) / (I `1) is V28() real ext-real Element of REAL
(- 1) * ((I `1) ") is V28() real ext-real set
- (1 / (I `1)) is V28() real ext-real Element of REAL
|[(1 / (I `1)),(((I `2) / (I `1)) / (I `1))]| `2 is V28() real ext-real Element of REAL
K526(|[(1 / (I `1)),(((I `2) / (I `1)) / (I `1))]|,2) is V28() real ext-real Element of REAL
1 * (I `1) is V28() real ext-real Element of REAL
- (1 * (I `1)) is V28() real ext-real Element of REAL
(I `1) / (I `1) is V28() real ext-real Element of REAL
(I `1) * ((I `1) ") is V28() real ext-real set
(- (1 * (I `1))) / (I `1) is V28() real ext-real Element of REAL
(- (1 * (I `1))) * ((I `1) ") is V28() real ext-real set
B is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
B `2 is V28() real ext-real Element of REAL
K526(B,2) is V28() real ext-real Element of REAL
B `1 is V28() real ext-real Element of REAL
K526(B,1) is V28() real ext-real Element of REAL
- (B `1) is V28() real ext-real Element of REAL
(- 1) * (I `1) is V28() real ext-real Element of REAL
((- 1) * (I `1)) / (I `1) is V28() real ext-real Element of REAL
((- 1) * (I `1)) * ((I `1) ") is V28() real ext-real set
(- 1) / (I `1) is V28() real ext-real Element of REAL
(- 1) * ((I `1) ") is V28() real ext-real set
- (1 / (I `1)) is V28() real ext-real Element of REAL
|[(1 / (I `1)),(((I `2) / (I `1)) / (I `1))]| `2 is V28() real ext-real Element of REAL
K526(|[(1 / (I `1)),(((I `2) / (I `1)) / (I `1))]|,2) is V28() real ext-real Element of REAL
c is set
d is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
d `2 is V28() real ext-real Element of REAL
K526(d,2) is V28() real ext-real Element of REAL
d `1 is V28() real ext-real Element of REAL
K526(d,1) is V28() real ext-real Element of REAL
- (d `1) is V28() real ext-real Element of REAL
d is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
d `2 is V28() real ext-real Element of REAL
K526(d,2) is V28() real ext-real Element of REAL
d `1 is V28() real ext-real Element of REAL
K526(d,1) is V28() real ext-real Element of REAL
- (d `1) is V28() real ext-real Element of REAL
dom (() | a) is Element of K19((NonZero (TOP-REAL 2)))
dom () is Element of K19((NonZero (TOP-REAL 2)))
(dom ()) /\ a is Element of K19( the carrier of ((TOP-REAL 2) | g))
(NonZero (TOP-REAL 2)) /\ a is Element of K19( the carrier of ((TOP-REAL 2) | g))
K20( the carrier of (((TOP-REAL 2) | g) | a), the carrier of ((TOP-REAL 2) | g)) is set
K19(K20( the carrier of (((TOP-REAL 2) | g) | a), the carrier of ((TOP-REAL 2) | g))) is set
dom (() | b) is Element of K19((NonZero (TOP-REAL 2)))
(dom ()) /\ b is Element of K19( the carrier of ((TOP-REAL 2) | g))
(NonZero (TOP-REAL 2)) /\ b is Element of K19( the carrier of ((TOP-REAL 2) | g))
K20( the carrier of (((TOP-REAL 2) | g) | b), the carrier of ((TOP-REAL 2) | g)) is set
K19(K20( the carrier of (((TOP-REAL 2) | g) | b), the carrier of ((TOP-REAL 2) | g))) is set
d is Relation-like the carrier of (((TOP-REAL 2) | g) | b) -defined the carrier of ((TOP-REAL 2) | g) -valued Function-like non empty total V18( the carrier of (((TOP-REAL 2) | g) | b), the carrier of ((TOP-REAL 2) | g)) Element of K19(K20( the carrier of (((TOP-REAL 2) | g) | b), the carrier of ((TOP-REAL 2) | g)))
dom d is Element of K19( the carrier of (((TOP-REAL 2) | g) | b))
([#] (((TOP-REAL 2) | g) | a)) /\ ([#] (((TOP-REAL 2) | g) | b)) is Element of K19( the carrier of (((TOP-REAL 2) | g) | b))
c is Relation-like the carrier of (((TOP-REAL 2) | g) | a) -defined the carrier of ((TOP-REAL 2) | g) -valued Function-like non empty total V18( the carrier of (((TOP-REAL 2) | g) | a), the carrier of ((TOP-REAL 2) | g)) Element of K19(K20( the carrier of (((TOP-REAL 2) | g) | a), the carrier of ((TOP-REAL 2) | g)))
O is set
c . O is set
d . O is set
() . O is set
dom c is Element of K19( the carrier of (((TOP-REAL 2) | g) | a))
([#] (((TOP-REAL 2) | g) | a)) \/ ([#] (((TOP-REAL 2) | g) | b)) is set
c +* d is Relation-like Function-like set
O is Relation-like the carrier of ((TOP-REAL 2) | g) -defined the carrier of ((TOP-REAL 2) | g) -valued Function-like non empty total V18( the carrier of ((TOP-REAL 2) | g), the carrier of ((TOP-REAL 2) | g)) Element of K19(K20( the carrier of ((TOP-REAL 2) | g), the carrier of ((TOP-REAL 2) | g)))
dom O is Element of K19( the carrier of ((TOP-REAL 2) | g))
I is set
O . I is set
() . I is set
A is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
O . A is set
d +* c is Relation-like Function-like set
(d +* c) . A is set
c . A is set
A is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
A `2 is V28() real ext-real Element of REAL
K526(A,2) is V28() real ext-real Element of REAL
A `1 is V28() real ext-real Element of REAL
K526(A,1) is V28() real ext-real Element of REAL
- (A `1) is V28() real ext-real Element of REAL
- (A `2) is V28() real ext-real Element of REAL
() . A is set
d . A is set
- 1 is V28() real ext-real non positive Element of REAL
{ b₁ where b₁ is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2) : ( not b₁ `1 <= - 1 & not 1 <= b<sub>1</sub> `1 & not b₁ `2 <= - 1 & not 1 <= b<sub>1</sub> `2 ) } is set
{ b₁ where b₁ is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2) : ( ( - 1 = b₁ `1 & - 1 <= b<sub>1</sub> `2 & b₁ `2 <= 1 ) or ( b<sub>1</sub> `1 = 1 & - 1 <= b₁ `2 & b<sub>1</sub> `2 <= 1 ) or ( - 1 = b₁ `2 & - 1 <= b<sub>1</sub> `1 & b₁ `1 <= 1 ) or ( 1 = b<sub>1</sub> `2 & - 1 <= b₁ `1 & b<sub>1</sub> `1 <= 1 ) ) } is set
g is Element of K19( the carrier of (TOP-REAL 2))
a is Element of K19( the carrier of (TOP-REAL 2))
b is Element of K19( the carrier of (TOP-REAL 2))
g ` is Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (g `) is strict TopSpace-like SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | (g `)) is set
K20( the carrier of ((TOP-REAL 2) | (g `)), the carrier of ((TOP-REAL 2) | (g `))) is set
K19(K20( the carrier of ((TOP-REAL 2) | (g `)), the carrier of ((TOP-REAL 2) | (g `)))) is set
a \/ b is Element of K19( the carrier of (TOP-REAL 2))
c is non empty Element of K19( the carrier of (TOP-REAL 2))
c ` is Element of K19( the carrier of (TOP-REAL 2))
d is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
() . d is set
O is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
O `1 is V28() real ext-real Element of REAL
K526(O,1) is V28() real ext-real Element of REAL
O `2 is V28() real ext-real Element of REAL
K526(O,2) is V28() real ext-real Element of REAL
d `2 is V28() real ext-real Element of REAL
K526(d,2) is V28() real ext-real Element of REAL
d `1 is V28() real ext-real Element of REAL
K526(d,1) is V28() real ext-real Element of REAL
- (d `1) is V28() real ext-real Element of REAL
1 / (d `1) is V28() real ext-real Element of REAL
(d `1) " is V28() real ext-real set
1 * ((d `1) ") is V28() real ext-real set
(d `2) / (d `1) is V28() real ext-real Element of REAL
(d `2) * ((d `1) ") is V28() real ext-real set
((d `2) / (d `1)) / (d `1) is V28() real ext-real Element of REAL
((d `2) / (d `1)) * ((d `1) ") is V28() real ext-real set
|[(1 / (d `1)),(((d `2) / (d `1)) / (d `1))]| is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
1 * (d `1) is V28() real ext-real Element of REAL
(1 / (d `1)) * (d `1) is V28() real ext-real Element of REAL
I is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
I `1 is V28() real ext-real Element of REAL
K526(I,1) is V28() real ext-real Element of REAL
I `2 is V28() real ext-real Element of REAL
K526(I,2) is V28() real ext-real Element of REAL
(- 1) * (d `1) is V28() real ext-real Element of REAL
(1 / (d `1)) * (d `1) is V28() real ext-real Element of REAL
- (- (d `1)) is V28() real ext-real Element of REAL
I is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
I `1 is V28() real ext-real Element of REAL
K526(I,1) is V28() real ext-real Element of REAL
I `2 is V28() real ext-real Element of REAL
K526(I,2) is V28() real ext-real Element of REAL
d `2 is V28() real ext-real Element of REAL
K526(d,2) is V28() real ext-real Element of REAL
d `1 is V28() real ext-real Element of REAL
K526(d,1) is V28() real ext-real Element of REAL
- (d `1) is V28() real ext-real Element of REAL
(d `1) / (d `2) is V28() real ext-real Element of REAL
(d `2) " is V28() real ext-real set
(d `1) * ((d `2) ") is V28() real ext-real set
((d `1) / (d `2)) / (d `2) is V28() real ext-real Element of REAL
((d `1) / (d `2)) * ((d `2) ") is V28() real ext-real set
1 / (d `2) is V28() real ext-real Element of REAL
1 * ((d `2) ") is V28() real ext-real set
|[(((d `1) / (d `2)) / (d `2)),(1 / (d `2))]| is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
1 * (d `2) is V28() real ext-real Element of REAL
(1 / (d `2)) * (d `2) is V28() real ext-real Element of REAL
I is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
I `1 is V28() real ext-real Element of REAL
K526(I,1) is V28() real ext-real Element of REAL
I `2 is V28() real ext-real Element of REAL
K526(I,2) is V28() real ext-real Element of REAL
(- 1) * (d `2) is V28() real ext-real Element of REAL
(1 / (d `2)) * (d `2) is V28() real ext-real Element of REAL
- (d `2) is V28() real ext-real Element of REAL
- (- (d `2)) is V28() real ext-real Element of REAL
I is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
I `1 is V28() real ext-real Element of REAL
K526(I,1) is V28() real ext-real Element of REAL
I `2 is V28() real ext-real Element of REAL
K526(I,2) is V28() real ext-real Element of REAL
d `2 is V28() real ext-real Element of REAL
K526(d,2) is V28() real ext-real Element of REAL
d `1 is V28() real ext-real Element of REAL
K526(d,1) is V28() real ext-real Element of REAL
- (d `1) is V28() real ext-real Element of REAL
d `2 is V28() real ext-real Element of REAL
K526(d,2) is V28() real ext-real Element of REAL
d `1 is V28() real ext-real Element of REAL
K526(d,1) is V28() real ext-real Element of REAL
- (d `1) is V28() real ext-real Element of REAL
O is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
O `1 is V28() real ext-real Element of REAL
K526(O,1) is V28() real ext-real Element of REAL
O `2 is V28() real ext-real Element of REAL
K526(O,2) is V28() real ext-real Element of REAL
d `2 is V28() real ext-real Element of REAL
K526(d,2) is V28() real ext-real Element of REAL
d `1 is V28() real ext-real Element of REAL
K526(d,1) is V28() real ext-real Element of REAL
- (d `1) is V28() real ext-real Element of REAL
1 / (d `1) is V28() real ext-real Element of REAL
(d `1) " is V28() real ext-real set
1 * ((d `1) ") is V28() real ext-real set
(d `2) / (d `1) is V28() real ext-real Element of REAL
(d `2) * ((d `1) ") is V28() real ext-real set
((d `2) / (d `1)) / (d `1) is V28() real ext-real Element of REAL
((d `2) / (d `1)) * ((d `1) ") is V28() real ext-real set
|[(1 / (d `1)),(((d `2) / (d `1)) / (d `1))]| is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
(d `1) " is V28() real ext-real Element of REAL
(d `1) * ((d `1) ") is V28() real ext-real Element of REAL
I is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
I `1 is V28() real ext-real Element of REAL
K526(I,1) is V28() real ext-real Element of REAL
I `2 is V28() real ext-real Element of REAL
K526(I,2) is V28() real ext-real Element of REAL
(d `1) " is V28() real ext-real Element of REAL
(d `1) * ((d `1) ") is V28() real ext-real Element of REAL
I is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
I `1 is V28() real ext-real Element of REAL
K526(I,1) is V28() real ext-real Element of REAL
I `2 is V28() real ext-real Element of REAL
K526(I,2) is V28() real ext-real Element of REAL
(TOP-REAL 2) | c is non empty strict TopSpace-like SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | c) is non empty set
K19( the carrier of ((TOP-REAL 2) | c)) is set
I is non empty Element of K19( the carrier of ((TOP-REAL 2) | c))
((TOP-REAL 2) | c) | I is non empty strict TopSpace-like SubSpace of (TOP-REAL 2) | c
the carrier of (((TOP-REAL 2) | c) | I) is non empty set
[#] (((TOP-REAL 2) | c) | I) is non empty non proper open closed Element of K19( the carrier of (((TOP-REAL 2) | c) | I))
K19( the carrier of (((TOP-REAL 2) | c) | I)) is set
() | I is Relation-like NonZero (TOP-REAL 2) -defined NonZero (TOP-REAL 2) -valued Function-like Element of K19(K20((NonZero (TOP-REAL 2)),(NonZero (TOP-REAL 2))))
dom (() | I) is Element of K19((NonZero (TOP-REAL 2)))
K19((NonZero (TOP-REAL 2))) is set
dom () is Element of K19((NonZero (TOP-REAL 2)))
(dom ()) /\ I is Element of K19( the carrier of ((TOP-REAL 2) | c))
c /\ I is Element of K19( the carrier of ((TOP-REAL 2) | c))
[#] ((TOP-REAL 2) | c) is non empty non proper open closed Element of K19( the carrier of ((TOP-REAL 2) | c))
([#] ((TOP-REAL 2) | c)) /\ I is Element of K19( the carrier of ((TOP-REAL 2) | c))
the carrier of ((TOP-REAL 2) | c) /\ I is Element of K19( the carrier of ((TOP-REAL 2) | c))
(() | I) . d is set
rng (() | I) is Element of K19((NonZero (TOP-REAL 2)))
((d `2) / (d `1)) * 1 is V28() real ext-real Element of REAL
(d `2) * 1 is V28() real ext-real Element of REAL
A is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
A `1 is V28() real ext-real Element of REAL
K526(A,1) is V28() real ext-real Element of REAL
A `2 is V28() real ext-real Element of REAL
K526(A,2) is V28() real ext-real Element of REAL
((d `2) / (d `1)) * (- 1) is V28() real ext-real Element of REAL
- ((d `2) / (d `1)) is V28() real ext-real Element of REAL
(d `2) * (- 1) is V28() real ext-real Element of REAL
- ((d `2) * (- 1)) is V28() real ext-real Element of REAL
A is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
A `1 is V28() real ext-real Element of REAL
K526(A,1) is V28() real ext-real Element of REAL
A `2 is V28() real ext-real Element of REAL
K526(A,2) is V28() real ext-real Element of REAL
A is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
A `2 is V28() real ext-real Element of REAL
K526(A,2) is V28() real ext-real Element of REAL
A `1 is V28() real ext-real Element of REAL
K526(A,1) is V28() real ext-real Element of REAL
- (A `1) is V28() real ext-real Element of REAL
(TOP-REAL 2) | c is non empty strict TopSpace-like SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | c) is non empty set
K19( the carrier of ((TOP-REAL 2) | c)) is set
I is non empty Element of K19( the carrier of ((TOP-REAL 2) | c))
() | I is Relation-like NonZero (TOP-REAL 2) -defined NonZero (TOP-REAL 2) -valued Function-like Element of K19(K20((NonZero (TOP-REAL 2)),(NonZero (TOP-REAL 2))))
(() | I) . d is set
dom (() | I) is Element of K19((NonZero (TOP-REAL 2)))
K19((NonZero (TOP-REAL 2))) is set
dom () is Element of K19((NonZero (TOP-REAL 2)))
(dom ()) /\ I is Element of K19( the carrier of ((TOP-REAL 2) | c))
c /\ I is Element of K19( the carrier of ((TOP-REAL 2) | c))
[#] ((TOP-REAL 2) | c) is non empty non proper open closed Element of K19( the carrier of ((TOP-REAL 2) | c))
([#] ((TOP-REAL 2) | c)) /\ I is Element of K19( the carrier of ((TOP-REAL 2) | c))
the carrier of ((TOP-REAL 2) | c) /\ I is Element of K19( the carrier of ((TOP-REAL 2) | c))
rng (() | I) is Element of K19((NonZero (TOP-REAL 2)))
((TOP-REAL 2) | c) | I is non empty strict TopSpace-like SubSpace of (TOP-REAL 2) | c
the carrier of (((TOP-REAL 2) | c) | I) is non empty set
[#] (((TOP-REAL 2) | c) | I) is non empty non proper open closed Element of K19( the carrier of (((TOP-REAL 2) | c) | I))
K19( the carrier of (((TOP-REAL 2) | c) | I)) is set
((d `2) / (d `1)) * 1 is V28() real ext-real Element of REAL
(d `2) * 1 is V28() real ext-real Element of REAL
A is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
A `1 is V28() real ext-real Element of REAL
K526(A,1) is V28() real ext-real Element of REAL
A `2 is V28() real ext-real Element of REAL
K526(A,2) is V28() real ext-real Element of REAL
((d `2) / (d `1)) * (- 1) is V28() real ext-real Element of REAL
- ((d `2) / (d `1)) is V28() real ext-real Element of REAL
(d `2) * (- 1) is V28() real ext-real Element of REAL
- ((d `2) * (- 1)) is V28() real ext-real Element of REAL
A is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
A `1 is V28() real ext-real Element of REAL
K526(A,1) is V28() real ext-real Element of REAL
A `2 is V28() real ext-real Element of REAL
K526(A,2) is V28() real ext-real Element of REAL
A is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
A `2 is V28() real ext-real Element of REAL
K526(A,2) is V28() real ext-real Element of REAL
A `1 is V28() real ext-real Element of REAL
K526(A,1) is V28() real ext-real Element of REAL
- (A `1) is V28() real ext-real Element of REAL
d `2 is V28() real ext-real Element of REAL
K526(d,2) is V28() real ext-real Element of REAL
d `1 is V28() real ext-real Element of REAL
K526(d,1) is V28() real ext-real Element of REAL
- (d `1) is V28() real ext-real Element of REAL
(d `1) / (d `2) is V28() real ext-real Element of REAL
(d `2) " is V28() real ext-real set
(d `1) * ((d `2) ") is V28() real ext-real set
((d `1) / (d `2)) / (d `2) is V28() real ext-real Element of REAL
((d `1) / (d `2)) * ((d `2) ") is V28() real ext-real set
1 / (d `2) is V28() real ext-real Element of REAL
1 * ((d `2) ") is V28() real ext-real set
|[(((d `1) / (d `2)) / (d `2)),(1 / (d `2))]| is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
(d `2) " is V28() real ext-real Element of REAL
(d `2) * ((d `2) ") is V28() real ext-real Element of REAL
- (d `2) is V28() real ext-real Element of REAL
I is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
I `1 is V28() real ext-real Element of REAL
K526(I,1) is V28() real ext-real Element of REAL
I `2 is V28() real ext-real Element of REAL
K526(I,2) is V28() real ext-real Element of REAL
(d `2) " is V28() real ext-real Element of REAL
(d `2) * ((d `2) ") is V28() real ext-real Element of REAL
I is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
I `1 is V28() real ext-real Element of REAL
K526(I,1) is V28() real ext-real Element of REAL
I `2 is V28() real ext-real Element of REAL
K526(I,2) is V28() real ext-real Element of REAL
(TOP-REAL 2) | c is non empty strict TopSpace-like SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | c) is non empty set
K19( the carrier of ((TOP-REAL 2) | c)) is set
I is non empty Element of K19( the carrier of ((TOP-REAL 2) | c))
() | I is Relation-like NonZero (TOP-REAL 2) -defined NonZero (TOP-REAL 2) -valued Function-like Element of K19(K20((NonZero (TOP-REAL 2)),(NonZero (TOP-REAL 2))))
dom (() | I) is Element of K19((NonZero (TOP-REAL 2)))
K19((NonZero (TOP-REAL 2))) is set
dom () is Element of K19((NonZero (TOP-REAL 2)))
(dom ()) /\ I is Element of K19( the carrier of ((TOP-REAL 2) | c))
c /\ I is Element of K19( the carrier of ((TOP-REAL 2) | c))
[#] ((TOP-REAL 2) | c) is non empty non proper open closed Element of K19( the carrier of ((TOP-REAL 2) | c))
([#] ((TOP-REAL 2) | c)) /\ I is Element of K19( the carrier of ((TOP-REAL 2) | c))
the carrier of ((TOP-REAL 2) | c) /\ I is Element of K19( the carrier of ((TOP-REAL 2) | c))
- (d `2) is V28() real ext-real Element of REAL
(() | I) . d is set
rng (() | I) is Element of K19((NonZero (TOP-REAL 2)))
((TOP-REAL 2) | c) | I is non empty strict TopSpace-like SubSpace of (TOP-REAL 2) | c
the carrier of (((TOP-REAL 2) | c) | I) is non empty set
[#] (((TOP-REAL 2) | c) | I) is non empty non proper open closed Element of K19( the carrier of (((TOP-REAL 2) | c) | I))
K19( the carrier of (((TOP-REAL 2) | c) | I)) is set
((d `1) / (d `2)) * 1 is V28() real ext-real Element of REAL
(d `1) * 1 is V28() real ext-real Element of REAL
A is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
A `1 is V28() real ext-real Element of REAL
K526(A,1) is V28() real ext-real Element of REAL
A `2 is V28() real ext-real Element of REAL
K526(A,2) is V28() real ext-real Element of REAL
((d `1) / (d `2)) * (- 1) is V28() real ext-real Element of REAL
- ((d `1) / (d `2)) is V28() real ext-real Element of REAL
(d `1) * (- 1) is V28() real ext-real Element of REAL
- ((d `1) * (- 1)) is V28() real ext-real Element of REAL
A is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
A `1 is V28() real ext-real Element of REAL
K526(A,1) is V28() real ext-real Element of REAL
A `2 is V28() real ext-real Element of REAL
K526(A,2) is V28() real ext-real Element of REAL
A is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
A `1 is V28() real ext-real Element of REAL
K526(A,1) is V28() real ext-real Element of REAL
A `2 is V28() real ext-real Element of REAL
K526(A,2) is V28() real ext-real Element of REAL
- (A `2) is V28() real ext-real Element of REAL
(TOP-REAL 2) | c is non empty strict TopSpace-like SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | c) is non empty set
K19( the carrier of ((TOP-REAL 2) | c)) is set
I is non empty Element of K19( the carrier of ((TOP-REAL 2) | c))
((TOP-REAL 2) | c) | I is non empty strict TopSpace-like SubSpace of (TOP-REAL 2) | c
the carrier of (((TOP-REAL 2) | c) | I) is non empty set
[#] (((TOP-REAL 2) | c) | I) is non empty non proper open closed Element of K19( the carrier of (((TOP-REAL 2) | c) | I))
K19( the carrier of (((TOP-REAL 2) | c) | I)) is set
() | I is Relation-like NonZero (TOP-REAL 2) -defined NonZero (TOP-REAL 2) -valued Function-like Element of K19(K20((NonZero (TOP-REAL 2)),(NonZero (TOP-REAL 2))))
dom (() | I) is Element of K19((NonZero (TOP-REAL 2)))
K19((NonZero (TOP-REAL 2))) is set
dom () is Element of K19((NonZero (TOP-REAL 2)))
(dom ()) /\ I is Element of K19( the carrier of ((TOP-REAL 2) | c))
c /\ I is Element of K19( the carrier of ((TOP-REAL 2) | c))
[#] ((TOP-REAL 2) | c) is non empty non proper open closed Element of K19( the carrier of ((TOP-REAL 2) | c))
([#] ((TOP-REAL 2) | c)) /\ I is Element of K19( the carrier of ((TOP-REAL 2) | c))
the carrier of ((TOP-REAL 2) | c) /\ I is Element of K19( the carrier of ((TOP-REAL 2) | c))
- (d `2) is V28() real ext-real Element of REAL
(() | I) . d is set
rng (() | I) is Element of K19((NonZero (TOP-REAL 2)))
((d `1) / (d `2)) * 1 is V28() real ext-real Element of REAL
(d `1) * 1 is V28() real ext-real Element of REAL
A is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
A `1 is V28() real ext-real Element of REAL
K526(A,1) is V28() real ext-real Element of REAL
A `2 is V28() real ext-real Element of REAL
K526(A,2) is V28() real ext-real Element of REAL
((d `1) / (d `2)) * (- 1) is V28() real ext-real Element of REAL
- ((d `1) / (d `2)) is V28() real ext-real Element of REAL
(d `1) * (- 1) is V28() real ext-real Element of REAL
- ((d `1) * (- 1)) is V28() real ext-real Element of REAL
A is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
A `1 is V28() real ext-real Element of REAL
K526(A,1) is V28() real ext-real Element of REAL
A `2 is V28() real ext-real Element of REAL
K526(A,2) is V28() real ext-real Element of REAL
A is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
A `1 is V28() real ext-real Element of REAL
K526(A,1) is V28() real ext-real Element of REAL
A `2 is V28() real ext-real Element of REAL
K526(A,2) is V28() real ext-real Element of REAL
- (A `2) is V28() real ext-real Element of REAL
d `2 is V28() real ext-real Element of REAL
K526(d,2) is V28() real ext-real Element of REAL
d `1 is V28() real ext-real Element of REAL
K526(d,1) is V28() real ext-real Element of REAL
- (d `1) is V28() real ext-real Element of REAL
d `2 is V28() real ext-real Element of REAL
K526(d,2) is V28() real ext-real Element of REAL
d `1 is V28() real ext-real Element of REAL
K526(d,1) is V28() real ext-real Element of REAL
- (d `1) is V28() real ext-real Element of REAL
d is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
() . d is set
d `2 is V28() real ext-real Element of REAL
K526(d,2) is V28() real ext-real Element of REAL
d `1 is V28() real ext-real Element of REAL
K526(d,1) is V28() real ext-real Element of REAL
- (d `1) is V28() real ext-real Element of REAL
(d `1) ^2 is V28() real ext-real Element of REAL
(d `1) * (d `1) is V28() real ext-real set
((d `1) ^2) / (d `1) is V28() real ext-real Element of REAL
(d `1) " is V28() real ext-real set
((d `1) ^2) * ((d `1) ") is V28() real ext-real set
(d `2) / (d `1) is V28() real ext-real Element of REAL
(d `2) * ((d `1) ") is V28() real ext-real set
(d `1) / (d `1) is V28() real ext-real Element of REAL
(d `1) * ((d `1) ") is V28() real ext-real set
((d `2) / (d `1)) / (d `1) is V28() real ext-real Element of REAL
((d `2) / (d `1)) * ((d `1) ") is V28() real ext-real set
(- 1) * (d `1) is V28() real ext-real Element of REAL
((- 1) * (d `1)) / (d `1) is V28() real ext-real Element of REAL
((- 1) * (d `1)) * ((d `1) ") is V28() real ext-real set
1 / (d `1) is V28() real ext-real Element of REAL
1 * ((d `1) ") is V28() real ext-real set
(d `1) ^2 is V28() real ext-real Element of REAL
(d `1) * (d `1) is V28() real ext-real set
- (d `2) is V28() real ext-real Element of REAL
- (- (d `1)) is V28() real ext-real Element of REAL
((d `1) ^2) / (d `1) is V28() real ext-real Element of REAL
(d `1) " is V28() real ext-real set
((d `1) ^2) * ((d `1) ") is V28() real ext-real set
(- (d `2)) / (d `1) is V28() real ext-real Element of REAL
(- (d `2)) * ((d `1) ") is V28() real ext-real set
(d `2) / (d `1) is V28() real ext-real Element of REAL
(d `2) * ((d `1) ") is V28() real ext-real set
- ((d `2) / (d `1)) is V28() real ext-real Element of REAL
- (- ((d `2) / (d `1))) is V28() real ext-real Element of REAL
((d `2) / (d `1)) / (d `1) is V28() real ext-real Element of REAL
((d `2) / (d `1)) * ((d `1) ") is V28() real ext-real set
(- 1) * (d `1) is V28() real ext-real Element of REAL
((- 1) * (d `1)) / (d `1) is V28() real ext-real Element of REAL
((- 1) * (d `1)) * ((d `1) ") is V28() real ext-real set
(d `1) / (d `1) is V28() real ext-real Element of REAL
(d `1) * ((d `1) ") is V28() real ext-real set
1 / (d `1) is V28() real ext-real Element of REAL
1 * ((d `1) ") is V28() real ext-real set
1 / (d `1) is V28() real ext-real Element of REAL
(d `1) " is V28() real ext-real set
1 * ((d `1) ") is V28() real ext-real set
(d `2) / (d `1) is V28() real ext-real Element of REAL
(d `2) * ((d `1) ") is V28() real ext-real set
((d `2) / (d `1)) / (d `1) is V28() real ext-real Element of REAL
((d `2) / (d `1)) * ((d `1) ") is V28() real ext-real set
1 / (d `1) is V28() real ext-real Element of REAL
(d `1) " is V28() real ext-real set
1 * ((d `1) ") is V28() real ext-real set
(d `2) / (d `1) is V28() real ext-real Element of REAL
(d `2) * ((d `1) ") is V28() real ext-real set
((d `2) / (d `1)) / (d `1) is V28() real ext-real Element of REAL
((d `2) / (d `1)) * ((d `1) ") is V28() real ext-real set
- (- (d `1)) is V28() real ext-real Element of REAL
(d `1) / (d `1) is V28() real ext-real Element of REAL
(d `1) " is V28() real ext-real set
(d `1) * ((d `1) ") is V28() real ext-real set
(- 1) / (d `1) is V28() real ext-real Element of REAL
(- 1) * ((d `1) ") is V28() real ext-real set
- ((- 1) / (d `1)) is V28() real ext-real Element of REAL
- ((d `1) / (d `1)) is V28() real ext-real Element of REAL
(d `1) ^2 is V28() real ext-real Element of REAL
(d `1) * (d `1) is V28() real ext-real set
(d `2) / (d `1) is V28() real ext-real Element of REAL
(d `2) * ((d `1) ") is V28() real ext-real set
((d `1) ^2) / (d `1) is V28() real ext-real Element of REAL
((d `1) ^2) * ((d `1) ") is V28() real ext-real set
((d `2) / (d `1)) / (d `1) is V28() real ext-real Element of REAL
((d `2) / (d `1)) * ((d `1) ") is V28() real ext-real set
(- 1) * (d `1) is V28() real ext-real Element of REAL
((- 1) * (d `1)) / (d `1) is V28() real ext-real Element of REAL
((- 1) * (d `1)) * ((d `1) ") is V28() real ext-real set
1 / (d `1) is V28() real ext-real Element of REAL
1 * ((d `1) ") is V28() real ext-real set
(d `1) ^2 is V28() real ext-real Element of REAL
(d `1) * (d `1) is V28() real ext-real set
- (d `2) is V28() real ext-real Element of REAL
(- (d `2)) / (d `1) is V28() real ext-real Element of REAL
(d `1) " is V28() real ext-real set
(- (d `2)) * ((d `1) ") is V28() real ext-real set
((d `1) ^2) / (d `1) is V28() real ext-real Element of REAL
((d `1) ^2) * ((d `1) ") is V28() real ext-real set
(d `2) / (d `1) is V28() real ext-real Element of REAL
(d `2) * ((d `1) ") is V28() real ext-real set
- ((d `2) / (d `1)) is V28() real ext-real Element of REAL
- (- ((d `2) / (d `1))) is V28() real ext-real Element of REAL
((d `2) / (d `1)) / (d `1) is V28() real ext-real Element of REAL
((d `2) / (d `1)) * ((d `1) ") is V28() real ext-real set
(- 1) * (d `1) is V28() real ext-real Element of REAL
((- 1) * (d `1)) / (d `1) is V28() real ext-real Element of REAL
((- 1) * (d `1)) * ((d `1) ") is V28() real ext-real set
(d `1) / (d `1) is V28() real ext-real Element of REAL
(d `1) * ((d `1) ") is V28() real ext-real set
(- 1) / (d `1) is V28() real ext-real Element of REAL
(- 1) * ((d `1) ") is V28() real ext-real set
- ((- 1) / (d `1)) is V28() real ext-real Element of REAL
1 / (d `1) is V28() real ext-real Element of REAL
1 * ((d `1) ") is V28() real ext-real set
1 / (d `1) is V28() real ext-real Element of REAL
(d `1) " is V28() real ext-real set
1 * ((d `1) ") is V28() real ext-real set
(d `2) / (d `1) is V28() real ext-real Element of REAL
(d `2) * ((d `1) ") is V28() real ext-real set
((d `2) / (d `1)) / (d `1) is V28() real ext-real Element of REAL
((d `2) / (d `1)) * ((d `1) ") is V28() real ext-real set
1 / (d `1) is V28() real ext-real Element of REAL
(d `1) " is V28() real ext-real set
1 * ((d `1) ") is V28() real ext-real set
(d `2) / (d `1) is V28() real ext-real Element of REAL
(d `2) * ((d `1) ") is V28() real ext-real set
((d `2) / (d `1)) / (d `1) is V28() real ext-real Element of REAL
((d `2) / (d `1)) * ((d `1) ") is V28() real ext-real set
1 / (d `1) is V28() real ext-real Element of REAL
(d `1) " is V28() real ext-real set
1 * ((d `1) ") is V28() real ext-real set
(d `2) / (d `1) is V28() real ext-real Element of REAL
(d `2) * ((d `1) ") is V28() real ext-real set
((d `2) / (d `1)) / (d `1) is V28() real ext-real Element of REAL
((d `2) / (d `1)) * ((d `1) ") is V28() real ext-real set
1 / (d `1) is V28() real ext-real Element of REAL
(d `1) " is V28() real ext-real set
1 * ((d `1) ") is V28() real ext-real set
(d `2) / (d `1) is V28() real ext-real Element of REAL
(d `2) * ((d `1) ") is V28() real ext-real set
((d `2) / (d `1)) / (d `1) is V28() real ext-real Element of REAL
((d `2) / (d `1)) * ((d `1) ") is V28() real ext-real set
1 / (d `1) is V28() real ext-real Element of REAL
(d `1) " is V28() real ext-real set
1 * ((d `1) ") is V28() real ext-real set
(d `2) / (d `1) is V28() real ext-real Element of REAL
(d `2) * ((d `1) ") is V28() real ext-real set
((d `2) / (d `1)) / (d `1) is V28() real ext-real Element of REAL
((d `2) / (d `1)) * ((d `1) ") is V28() real ext-real set
1 / (d `1) is V28() real ext-real Element of REAL
(d `1) " is V28() real ext-real set
1 * ((d `1) ") is V28() real ext-real set
(d `2) / (d `1) is V28() real ext-real Element of REAL
(d `2) * ((d `1) ") is V28() real ext-real set
((d `2) / (d `1)) / (d `1) is V28() real ext-real Element of REAL
((d `2) / (d `1)) * ((d `1) ") is V28() real ext-real set
|[(1 / (d `1)),(((d `2) / (d `1)) / (d `1))]| is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
O is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
O `1 is V28() real ext-real Element of REAL
K526(O,1) is V28() real ext-real Element of REAL
O `2 is V28() real ext-real Element of REAL
K526(O,2) is V28() real ext-real Element of REAL
d `2 is V28() real ext-real Element of REAL
K526(d,2) is V28() real ext-real Element of REAL
d `1 is V28() real ext-real Element of REAL
K526(d,1) is V28() real ext-real Element of REAL
- (d `1) is V28() real ext-real Element of REAL
- (d `2) is V28() real ext-real Element of REAL
(d `2) ^2 is V28() real ext-real Element of REAL
(d `2) * (d `2) is V28() real ext-real set
((d `2) ^2) / (d `2) is V28() real ext-real Element of REAL
(d `2) " is V28() real ext-real set
((d `2) ^2) * ((d `2) ") is V28() real ext-real set
(d `1) / (d `2) is V28() real ext-real Element of REAL
(d `1) * ((d `2) ") is V28() real ext-real set
(d `2) / (d `2) is V28() real ext-real Element of REAL
(d `2) * ((d `2) ") is V28() real ext-real set
((d `1) / (d `2)) / (d `2) is V28() real ext-real Element of REAL
((d `1) / (d `2)) * ((d `2) ") is V28() real ext-real set
(- 1) * (d `2) is V28() real ext-real Element of REAL
((- 1) * (d `2)) / (d `2) is V28() real ext-real Element of REAL
((- 1) * (d `2)) * ((d `2) ") is V28() real ext-real set
1 / (d `2) is V28() real ext-real Element of REAL
1 * ((d `2) ") is V28() real ext-real set
(d `2) ^2 is V28() real ext-real Element of REAL
(d `2) * (d `2) is V28() real ext-real set
((d `2) ^2) / (d `2) is V28() real ext-real Element of REAL
(d `2) " is V28() real ext-real set
((d `2) ^2) * ((d `2) ") is V28() real ext-real set
(- (d `1)) / (d `2) is V28() real ext-real Element of REAL
(- (d `1)) * ((d `2) ") is V28() real ext-real set
(d `1) / (d `2) is V28() real ext-real Element of REAL
(d `1) * ((d `2) ") is V28() real ext-real set
- ((d `1) / (d `2)) is V28() real ext-real Element of REAL
- (- ((d `1) / (d `2))) is V28() real ext-real Element of REAL
((d `1) / (d `2)) / (d `2) is V28() real ext-real Element of REAL
((d `1) / (d `2)) * ((d `2) ") is V28() real ext-real set
(- 1) * (d `2) is V28() real ext-real Element of REAL
((- 1) * (d `2)) / (d `2) is V28() real ext-real Element of REAL
((- 1) * (d `2)) * ((d `2) ") is V28() real ext-real set
(d `2) / (d `2) is V28() real ext-real Element of REAL
(d `2) * ((d `2) ") is V28() real ext-real set
1 / (d `2) is V28() real ext-real Element of REAL
1 * ((d `2) ") is V28() real ext-real set
1 / (d `2) is V28() real ext-real Element of REAL
(d `2) " is V28() real ext-real set
1 * ((d `2) ") is V28() real ext-real set
(d `1) / (d `2) is V28() real ext-real Element of REAL
(d `1) * ((d `2) ") is V28() real ext-real set
((d `1) / (d `2)) / (d `2) is V28() real ext-real Element of REAL
((d `1) / (d `2)) * ((d `2) ") is V28() real ext-real set
1 / (d `2) is V28() real ext-real Element of REAL
(d `2) " is V28() real ext-real set
1 * ((d `2) ") is V28() real ext-real set
(d `1) / (d `2) is V28() real ext-real Element of REAL
(d `1) * ((d `2) ") is V28() real ext-real set
((d `1) / (d `2)) / (d `2) is V28() real ext-real Element of REAL
((d `1) / (d `2)) * ((d `2) ") is V28() real ext-real set
- (- (d `2)) is V28() real ext-real Element of REAL
(d `2) / (d `2) is V28() real ext-real Element of REAL
(d `2) " is V28() real ext-real set
(d `2) * ((d `2) ") is V28() real ext-real set
(- 1) / (d `2) is V28() real ext-real Element of REAL
(- 1) * ((d `2) ") is V28() real ext-real set
- ((- 1) / (d `2)) is V28() real ext-real Element of REAL
- ((d `2) / (d `2)) is V28() real ext-real Element of REAL
(d `2) ^2 is V28() real ext-real Element of REAL
(d `2) * (d `2) is V28() real ext-real set
(d `1) / (d `2) is V28() real ext-real Element of REAL
(d `1) * ((d `2) ") is V28() real ext-real set
((d `2) ^2) / (d `2) is V28() real ext-real Element of REAL
((d `2) ^2) * ((d `2) ") is V28() real ext-real set
((d `1) / (d `2)) / (d `2) is V28() real ext-real Element of REAL
((d `1) / (d `2)) * ((d `2) ") is V28() real ext-real set
(- 1) * (d `2) is V28() real ext-real Element of REAL
((- 1) * (d `2)) / (d `2) is V28() real ext-real Element of REAL
((- 1) * (d `2)) * ((d `2) ") is V28() real ext-real set
1 / (d `2) is V28() real ext-real Element of REAL
1 * ((d `2) ") is V28() real ext-real set
(d `2) ^2 is V28() real ext-real Element of REAL
(d `2) * (d `2) is V28() real ext-real set
(- (d `1)) / (d `2) is V28() real ext-real Element of REAL
(d `2) " is V28() real ext-real set
(- (d `1)) * ((d `2) ") is V28() real ext-real set
((d `2) ^2) / (d `2) is V28() real ext-real Element of REAL
((d `2) ^2) * ((d `2) ") is V28() real ext-real set
(d `1) / (d `2) is V28() real ext-real Element of REAL
(d `1) * ((d `2) ") is V28() real ext-real set
- ((d `1) / (d `2)) is V28() real ext-real Element of REAL
- (- ((d `1) / (d `2))) is V28() real ext-real Element of REAL
((d `1) / (d `2)) / (d `2) is V28() real ext-real Element of REAL
((d `1) / (d `2)) * ((d `2) ") is V28() real ext-real set
(- 1) * (d `2) is V28() real ext-real Element of REAL
((- 1) * (d `2)) / (d `2) is V28() real ext-real Element of REAL
((- 1) * (d `2)) * ((d `2) ") is V28() real ext-real set
(d `2) / (d `2) is V28() real ext-real Element of REAL
(d `2) * ((d `2) ") is V28() real ext-real set
(- 1) / (d `2) is V28() real ext-real Element of REAL
(- 1) * ((d `2) ") is V28() real ext-real set
- ((- 1) / (d `2)) is V28() real ext-real Element of REAL
1 / (d `2) is V28() real ext-real Element of REAL
1 * ((d `2) ") is V28() real ext-real set
1 / (d `2) is V28() real ext-real Element of REAL
(d `2) " is V28() real ext-real set
1 * ((d `2) ") is V28() real ext-real set
(d `1) / (d `2) is V28() real ext-real Element of REAL
(d `1) * ((d `2) ") is V28() real ext-real set
((d `1) / (d `2)) / (d `2) is V28() real ext-real Element of REAL
((d `1) / (d `2)) * ((d `2) ") is V28() real ext-real set
1 / (d `2) is V28() real ext-real Element of REAL
(d `2) " is V28() real ext-real set
1 * ((d `2) ") is V28() real ext-real set
(d `1) / (d `2) is V28() real ext-real Element of REAL
(d `1) * ((d `2) ") is V28() real ext-real set
((d `1) / (d `2)) / (d `2) is V28() real ext-real Element of REAL
((d `1) / (d `2)) * ((d `2) ") is V28() real ext-real set
1 / (d `2) is V28() real ext-real Element of REAL
(d `2) " is V28() real ext-real set
1 * ((d `2) ") is V28() real ext-real set
(d `1) / (d `2) is V28() real ext-real Element of REAL
(d `1) * ((d `2) ") is V28() real ext-real set
((d `1) / (d `2)) / (d `2) is V28() real ext-real Element of REAL
((d `1) / (d `2)) * ((d `2) ") is V28() real ext-real set
1 / (d `2) is V28() real ext-real Element of REAL
(d `2) " is V28() real ext-real set
1 * ((d `2) ") is V28() real ext-real set
(d `1) / (d `2) is V28() real ext-real Element of REAL
(d `1) * ((d `2) ") is V28() real ext-real set
((d `1) / (d `2)) / (d `2) is V28() real ext-real Element of REAL
((d `1) / (d `2)) * ((d `2) ") is V28() real ext-real set
|[(((d `1) / (d `2)) / (d `2)),(1 / (d `2))]| is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
O is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
O `2 is V28() real ext-real Element of REAL
K526(O,2) is V28() real ext-real Element of REAL
O `1 is V28() real ext-real Element of REAL
K526(O,1) is V28() real ext-real Element of REAL
d `2 is V28() real ext-real Element of REAL
K526(d,2) is V28() real ext-real Element of REAL
d `1 is V28() real ext-real Element of REAL
K526(d,1) is V28() real ext-real Element of REAL
- (d `1) is V28() real ext-real Element of REAL
d `2 is V28() real ext-real Element of REAL
K526(d,2) is V28() real ext-real Element of REAL
d `1 is V28() real ext-real Element of REAL
K526(d,1) is V28() real ext-real Element of REAL
- (d `1) is V28() real ext-real Element of REAL
dom () is Element of K19((NonZero (TOP-REAL 2)))
K19((NonZero (TOP-REAL 2))) is set
d is set
O is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
O `1 is V28() real ext-real Element of REAL
K526(O,1) is V28() real ext-real Element of REAL
O `2 is V28() real ext-real Element of REAL
K526(O,2) is V28() real ext-real Element of REAL
- (O `2) is V28() real ext-real Element of REAL
O is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
O `1 is V28() real ext-real Element of REAL
K526(O,1) is V28() real ext-real Element of REAL
O `2 is V28() real ext-real Element of REAL
K526(O,2) is V28() real ext-real Element of REAL
- (O `2) is V28() real ext-real Element of REAL
- ((1.REAL 2) `2) is V28() real ext-real Element of REAL
(TOP-REAL 2) | c is non empty strict TopSpace-like SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | c) is non empty set
[#] ((TOP-REAL 2) | c) is non empty non proper open closed Element of K19( the carrier of ((TOP-REAL 2) | c))
K19( the carrier of ((TOP-REAL 2) | c)) is set
I is set
A is set
() . I is set
() . A is set
O is non empty Element of K19( the carrier of ((TOP-REAL 2) | c))
d is non empty Element of K19( the carrier of ((TOP-REAL 2) | c))
O \/ d is Element of K19( the carrier of ((TOP-REAL 2) | c))
D is set
ff is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
ff `2 is V28() real ext-real Element of REAL
K526(ff,2) is V28() real ext-real Element of REAL
ff `1 is V28() real ext-real Element of REAL
K526(ff,1) is V28() real ext-real Element of REAL
- (ff `1) is V28() real ext-real Element of REAL
- (ff `2) is V28() real ext-real Element of REAL
B is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
() . B is set
B `1 is V28() real ext-real Element of REAL
K526(B,1) is V28() real ext-real Element of REAL
1 / (B `1) is V28() real ext-real Element of REAL
(B `1) " is V28() real ext-real set
1 * ((B `1) ") is V28() real ext-real set
B `2 is V28() real ext-real Element of REAL
K526(B,2) is V28() real ext-real Element of REAL
(B `2) / (B `1) is V28() real ext-real Element of REAL
(B `2) * ((B `1) ") is V28() real ext-real set
((B `2) / (B `1)) / (B `1) is V28() real ext-real Element of REAL
((B `2) / (B `1)) * ((B `1) ") is V28() real ext-real set
|[(1 / (B `1)),(((B `2) / (B `1)) / (B `1))]| is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
D is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
D `2 is V28() real ext-real Element of REAL
K526(D,2) is V28() real ext-real Element of REAL
D `1 is V28() real ext-real Element of REAL
K526(D,1) is V28() real ext-real Element of REAL
- (D `1) is V28() real ext-real Element of REAL
C is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
C `1 is V28() real ext-real Element of REAL
K526(C,1) is V28() real ext-real Element of REAL
1 / (C `1) is V28() real ext-real Element of REAL
(C `1) " is V28() real ext-real set
1 * ((C `1) ") is V28() real ext-real set
C `2 is V28() real ext-real Element of REAL
K526(C,2) is V28() real ext-real Element of REAL
(C `2) / (C `1) is V28() real ext-real Element of REAL
(C `2) * ((C `1) ") is V28() real ext-real set
((C `2) / (C `1)) / (C `1) is V28() real ext-real Element of REAL
((C `2) / (C `1)) * ((C `1) ") is V28() real ext-real set
|[(1 / (C `1)),(((C `2) / (C `1)) / (C `1))]| is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
D is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
D `2 is V28() real ext-real Element of REAL
K526(D,2) is V28() real ext-real Element of REAL
D `1 is V28() real ext-real Element of REAL
K526(D,1) is V28() real ext-real Element of REAL
- (D `1) is V28() real ext-real Element of REAL
|[(B `1),(B `2)]| is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
(1 / (B `1)) " is V28() real ext-real Element of REAL
(B `1) " is V28() real ext-real Element of REAL
((B `1) ") " is V28() real ext-real Element of REAL
ff is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
ff `2 is V28() real ext-real Element of REAL
K526(ff,2) is V28() real ext-real Element of REAL
ff `1 is V28() real ext-real Element of REAL
K526(ff,1) is V28() real ext-real Element of REAL
- (ff `1) is V28() real ext-real Element of REAL
ff is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
ff `2 is V28() real ext-real Element of REAL
K526(ff,2) is V28() real ext-real Element of REAL
ff `1 is V28() real ext-real Element of REAL
K526(ff,1) is V28() real ext-real Element of REAL
- (ff `1) is V28() real ext-real Element of REAL
|[(1 / (C `1)),(((C `2) / (C `1)) / (C `1))]| `1 is V28() real ext-real Element of REAL
K526(|[(1 / (C `1)),(((C `2) / (C `1)) / (C `1))]|,1) is V28() real ext-real Element of REAL
|[(1 / (C `1)),(((C `2) / (C `1)) / (C `1))]| `2 is V28() real ext-real Element of REAL
K526(|[(1 / (C `1)),(((C `2) / (C `1)) / (C `1))]|,2) is V28() real ext-real Element of REAL
(C `2) / (B `1) is V28() real ext-real Element of REAL
(C `2) * ((B `1) ") is V28() real ext-real set
D is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
D `2 is V28() real ext-real Element of REAL
K526(D,2) is V28() real ext-real Element of REAL
D `1 is V28() real ext-real Element of REAL
K526(D,1) is V28() real ext-real Element of REAL
- (D `1) is V28() real ext-real Element of REAL
D is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
D `2 is V28() real ext-real Element of REAL
K526(D,2) is V28() real ext-real Element of REAL
D `1 is V28() real ext-real Element of REAL
K526(D,1) is V28() real ext-real Element of REAL
- (D `1) is V28() real ext-real Element of REAL
- (B `1) is V28() real ext-real Element of REAL
(B `1) / (B `1) is V28() real ext-real Element of REAL
(B `1) * ((B `1) ") is V28() real ext-real set
- (B `1) is V28() real ext-real Element of REAL
(B `1) / (B `1) is V28() real ext-real Element of REAL
(B `1) * ((B `1) ") is V28() real ext-real set
- (B `1) is V28() real ext-real Element of REAL
D is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
D `2 is V28() real ext-real Element of REAL
K526(D,2) is V28() real ext-real Element of REAL
D `1 is V28() real ext-real Element of REAL
K526(D,1) is V28() real ext-real Element of REAL
- (D `1) is V28() real ext-real Element of REAL
- (B `1) is V28() real ext-real Element of REAL
(- (B `1)) / (B `1) is V28() real ext-real Element of REAL
(- (B `1)) * ((B `1) ") is V28() real ext-real set
- (- (B `1)) is V28() real ext-real Element of REAL
- (B `2) is V28() real ext-real Element of REAL
(B `1) / (- (B `1)) is V28() real ext-real Element of REAL
(- (B `1)) " is V28() real ext-real set
(B `1) * ((- (B `1)) ") is V28() real ext-real set
(- (B `2)) / (- (B `1)) is V28() real ext-real Element of REAL
(- (B `2)) * ((- (B `1)) ") is V28() real ext-real set
D is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
D `2 is V28() real ext-real Element of REAL
K526(D,2) is V28() real ext-real Element of REAL
D `1 is V28() real ext-real Element of REAL
K526(D,1) is V28() real ext-real Element of REAL
- (D `1) is V28() real ext-real Element of REAL
C is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
C `2 is V28() real ext-real Element of REAL
K526(C,2) is V28() real ext-real Element of REAL
C `1 is V28() real ext-real Element of REAL
K526(C,1) is V28() real ext-real Element of REAL
D is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
D `1 is V28() real ext-real Element of REAL
K526(D,1) is V28() real ext-real Element of REAL
D `2 is V28() real ext-real Element of REAL
K526(D,2) is V28() real ext-real Element of REAL
- (D `2) is V28() real ext-real Element of REAL
D is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
D `1 is V28() real ext-real Element of REAL
K526(D,1) is V28() real ext-real Element of REAL
D `2 is V28() real ext-real Element of REAL
K526(D,2) is V28() real ext-real Element of REAL
- (D `2) is V28() real ext-real Element of REAL
- (C `1) is V28() real ext-real Element of REAL
() . C is set
(C `1) / (C `2) is V28() real ext-real Element of REAL
(C `2) " is V28() real ext-real set
(C `1) * ((C `2) ") is V28() real ext-real set
((C `1) / (C `2)) / (C `2) is V28() real ext-real Element of REAL
((C `1) / (C `2)) * ((C `2) ") is V28() real ext-real set
1 / (C `2) is V28() real ext-real Element of REAL
1 * ((C `2) ") is V28() real ext-real set
|[(((C `1) / (C `2)) / (C `2)),(1 / (C `2))]| is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
D is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
D `1 is V28() real ext-real Element of REAL
K526(D,1) is V28() real ext-real Element of REAL
D `2 is V28() real ext-real Element of REAL
K526(D,2) is V28() real ext-real Element of REAL
- (D `2) is V28() real ext-real Element of REAL
(1 / (C `2)) * (B `1) is V28() real ext-real Element of REAL
(B `1) / (C `2) is V28() real ext-real Element of REAL
(B `1) * ((C `2) ") is V28() real ext-real set
(1 / (B `1)) * (C `2) is V28() real ext-real Element of REAL
(C `2) / (B `1) is V28() real ext-real Element of REAL
(C `2) * ((B `1) ") is V28() real ext-real set
((C `1) / (C `2)) * ((B `2) / (B `1)) is V28() real ext-real Element of REAL
(((C `1) / (C `2)) * ((B `2) / (B `1))) * (B `1) is V28() real ext-real Element of REAL
1 * (B `1) is V28() real ext-real Element of REAL
- (C `2) is V28() real ext-real Element of REAL
(- (C `2)) / (C `2) is V28() real ext-real Element of REAL
(- (C `2)) * ((C `2) ") is V28() real ext-real set
- (C `2) is V28() real ext-real Element of REAL
- (- (C `2)) is V28() real ext-real Element of REAL
(C `2) / (- (C `2)) is V28() real ext-real Element of REAL
(- (C `2)) " is V28() real ext-real set
(C `2) * ((- (C `2)) ") is V28() real ext-real set
(- (C `1)) / (- (C `2)) is V28() real ext-real Element of REAL
(- (C `1)) * ((- (C `2)) ") is V28() real ext-real set
- (C `2) is V28() real ext-real Element of REAL
D is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
D `1 is V28() real ext-real Element of REAL
K526(D,1) is V28() real ext-real Element of REAL
D `2 is V28() real ext-real Element of REAL
K526(D,2) is V28() real ext-real Element of REAL
- (D `2) is V28() real ext-real Element of REAL
- (C `2) is V28() real ext-real Element of REAL
((B `2) / (B `1)) * (B `1) is V28() real ext-real Element of REAL
((C `1) / (C `2)) * (((B `2) / (B `1)) * (B `1)) is V28() real ext-real Element of REAL
((C `1) / (C `2)) * (B `2) is V28() real ext-real Element of REAL
(B `1) / (B `2) is V28() real ext-real Element of REAL
(B `2) " is V28() real ext-real set
(B `1) * ((B `2) ") is V28() real ext-real set
(C `2) / (C `2) is V28() real ext-real Element of REAL
(C `2) * ((C `2) ") is V28() real ext-real set
(C `2) / (C `2) is V28() real ext-real Element of REAL
(C `2) * ((C `2) ") is V28() real ext-real set
D is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
D `1 is V28() real ext-real Element of REAL
K526(D,1) is V28() real ext-real Element of REAL
D `2 is V28() real ext-real Element of REAL
K526(D,2) is V28() real ext-real Element of REAL
- (D `2) is V28() real ext-real Element of REAL
((C `1) / (C `2)) * (C `2) is V28() real ext-real Element of REAL
1 * (C `2) is V28() real ext-real Element of REAL
D is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
D `1 is V28() real ext-real Element of REAL
K526(D,1) is V28() real ext-real Element of REAL
D `2 is V28() real ext-real Element of REAL
K526(D,2) is V28() real ext-real Element of REAL
- (D `2) is V28() real ext-real Element of REAL
(- 1) * (B `1) is V28() real ext-real Element of REAL
- (B `2) is V28() real ext-real Element of REAL
(- 1) * (C `2) is V28() real ext-real Element of REAL
D is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
D `1 is V28() real ext-real Element of REAL
K526(D,1) is V28() real ext-real Element of REAL
D `2 is V28() real ext-real Element of REAL
K526(D,2) is V28() real ext-real Element of REAL
- (D `2) is V28() real ext-real Element of REAL
B is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
() . B is set
B `1 is V28() real ext-real Element of REAL
K526(B,1) is V28() real ext-real Element of REAL
B `2 is V28() real ext-real Element of REAL
K526(B,2) is V28() real ext-real Element of REAL
(B `1) / (B `2) is V28() real ext-real Element of REAL
(B `2) " is V28() real ext-real set
(B `1) * ((B `2) ") is V28() real ext-real set
((B `1) / (B `2)) / (B `2) is V28() real ext-real Element of REAL
((B `1) / (B `2)) * ((B `2) ") is V28() real ext-real set
1 / (B `2) is V28() real ext-real Element of REAL
1 * ((B `2) ") is V28() real ext-real set
|[(((B `1) / (B `2)) / (B `2)),(1 / (B `2))]| is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
D is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
D `1 is V28() real ext-real Element of REAL
K526(D,1) is V28() real ext-real Element of REAL
D `2 is V28() real ext-real Element of REAL
K526(D,2) is V28() real ext-real Element of REAL
- (D `2) is V28() real ext-real Element of REAL
C is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
C `1 is V28() real ext-real Element of REAL
K526(C,1) is V28() real ext-real Element of REAL
C `2 is V28() real ext-real Element of REAL
K526(C,2) is V28() real ext-real Element of REAL
(C `1) / (C `2) is V28() real ext-real Element of REAL
(C `2) " is V28() real ext-real set
(C `1) * ((C `2) ") is V28() real ext-real set
((C `1) / (C `2)) / (C `2) is V28() real ext-real Element of REAL
((C `1) / (C `2)) * ((C `2) ") is V28() real ext-real set
1 / (C `2) is V28() real ext-real Element of REAL
1 * ((C `2) ") is V28() real ext-real set
|[(((C `1) / (C `2)) / (C `2)),(1 / (C `2))]| is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
D is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
D `1 is V28() real ext-real Element of REAL
K526(D,1) is V28() real ext-real Element of REAL
D `2 is V28() real ext-real Element of REAL
K526(D,2) is V28() real ext-real Element of REAL
- (D `2) is V28() real ext-real Element of REAL
|[(B `1),(B `2)]| is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
(1 / (B `2)) " is V28() real ext-real Element of REAL
(B `2) " is V28() real ext-real Element of REAL
((B `2) ") " is V28() real ext-real Element of REAL
ff is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
ff `1 is V28() real ext-real Element of REAL
K526(ff,1) is V28() real ext-real Element of REAL
ff `2 is V28() real ext-real Element of REAL
K526(ff,2) is V28() real ext-real Element of REAL
- (ff `2) is V28() real ext-real Element of REAL
ff is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
ff `1 is V28() real ext-real Element of REAL
K526(ff,1) is V28() real ext-real Element of REAL
ff `2 is V28() real ext-real Element of REAL
K526(ff,2) is V28() real ext-real Element of REAL
- (ff `2) is V28() real ext-real Element of REAL
|[(((C `1) / (C `2)) / (C `2)),(1 / (C `2))]| `2 is V28() real ext-real Element of REAL
K526(|[(((C `1) / (C `2)) / (C `2)),(1 / (C `2))]|,2) is V28() real ext-real Element of REAL
|[(((C `1) / (C `2)) / (C `2)),(1 / (C `2))]| `1 is V28() real ext-real Element of REAL
K526(|[(((C `1) / (C `2)) / (C `2)),(1 / (C `2))]|,1) is V28() real ext-real Element of REAL
(C `1) / (B `2) is V28() real ext-real Element of REAL
(C `1) * ((B `2) ") is V28() real ext-real set
D is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
D `1 is V28() real ext-real Element of REAL
K526(D,1) is V28() real ext-real Element of REAL
D `2 is V28() real ext-real Element of REAL
K526(D,2) is V28() real ext-real Element of REAL
- (D `2) is V28() real ext-real Element of REAL
D is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
D `1 is V28() real ext-real Element of REAL
K526(D,1) is V28() real ext-real Element of REAL
D `2 is V28() real ext-real Element of REAL
K526(D,2) is V28() real ext-real Element of REAL
- (D `2) is V28() real ext-real Element of REAL
- (B `2) is V28() real ext-real Element of REAL
(B `2) / (B `2) is V28() real ext-real Element of REAL
(B `2) * ((B `2) ") is V28() real ext-real set
- (B `2) is V28() real ext-real Element of REAL
(B `2) / (B `2) is V28() real ext-real Element of REAL
(B `2) * ((B `2) ") is V28() real ext-real set
- (B `2) is V28() real ext-real Element of REAL
D is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
D `1 is V28() real ext-real Element of REAL
K526(D,1) is V28() real ext-real Element of REAL
D `2 is V28() real ext-real Element of REAL
K526(D,2) is V28() real ext-real Element of REAL
- (D `2) is V28() real ext-real Element of REAL
- (B `2) is V28() real ext-real Element of REAL
(- (B `2)) / (B `2) is V28() real ext-real Element of REAL
(- (B `2)) * ((B `2) ") is V28() real ext-real set
- (- (B `2)) is V28() real ext-real Element of REAL
- (B `1) is V28() real ext-real Element of REAL
(B `2) / (- (B `2)) is V28() real ext-real Element of REAL
(- (B `2)) " is V28() real ext-real set
(B `2) * ((- (B `2)) ") is V28() real ext-real set
(- (B `1)) / (- (B `2)) is V28() real ext-real Element of REAL
(- (B `1)) * ((- (B `2)) ") is V28() real ext-real set
D is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
D `1 is V28() real ext-real Element of REAL
K526(D,1) is V28() real ext-real Element of REAL
D `2 is V28() real ext-real Element of REAL
K526(D,2) is V28() real ext-real Element of REAL
- (D `2) is V28() real ext-real Element of REAL
C is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
C `1 is V28() real ext-real Element of REAL
K526(C,1) is V28() real ext-real Element of REAL
C `2 is V28() real ext-real Element of REAL
K526(C,2) is V28() real ext-real Element of REAL
D is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
D `2 is V28() real ext-real Element of REAL
K526(D,2) is V28() real ext-real Element of REAL
D `1 is V28() real ext-real Element of REAL
K526(D,1) is V28() real ext-real Element of REAL
- (D `1) is V28() real ext-real Element of REAL
D is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
D `2 is V28() real ext-real Element of REAL
K526(D,2) is V28() real ext-real Element of REAL
D `1 is V28() real ext-real Element of REAL
K526(D,1) is V28() real ext-real Element of REAL
- (D `1) is V28() real ext-real Element of REAL
- (C `1) is V28() real ext-real Element of REAL
(- (C `1)) / (C `1) is V28() real ext-real Element of REAL
(C `1) " is V28() real ext-real set
(- (C `1)) * ((C `1) ") is V28() real ext-real set
(C `2) / (C `1) is V28() real ext-real Element of REAL
(C `2) * ((C `1) ") is V28() real ext-real set
- (C `1) is V28() real ext-real Element of REAL
- (- (C `1)) is V28() real ext-real Element of REAL
- (C `2) is V28() real ext-real Element of REAL
(C `1) / (- (C `1)) is V28() real ext-real Element of REAL
(- (C `1)) " is V28() real ext-real set
(C `1) * ((- (C `1)) ") is V28() real ext-real set
(- (C `2)) / (- (C `1)) is V28() real ext-real Element of REAL
(- (C `2)) * ((- (C `1)) ") is V28() real ext-real set
(C `2) / (C `1) is V28() real ext-real Element of REAL
(C `1) " is V28() real ext-real set
(C `2) * ((C `1) ") is V28() real ext-real set
- (C `1) is V28() real ext-real Element of REAL
D is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
D `2 is V28() real ext-real Element of REAL
K526(D,2) is V28() real ext-real Element of REAL
D `1 is V28() real ext-real Element of REAL
K526(D,1) is V28() real ext-real Element of REAL
- (D `1) is V28() real ext-real Element of REAL
(C `2) / (C `1) is V28() real ext-real Element of REAL
(C `1) " is V28() real ext-real set
(C `2) * ((C `1) ") is V28() real ext-real set
- (C `1) is V28() real ext-real Element of REAL
(C `2) / (C `1) is V28() real ext-real Element of REAL
(C `1) " is V28() real ext-real set
(C `2) * ((C `1) ") is V28() real ext-real set
() . C is set
1 / (C `1) is V28() real ext-real Element of REAL
1 * ((C `1) ") is V28() real ext-real set
((C `2) / (C `1)) / (C `1) is V28() real ext-real Element of REAL
((C `2) / (C `1)) * ((C `1) ") is V28() real ext-real set
|[(1 / (C `1)),(((C `2) / (C `1)) / (C `1))]| is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
D is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
D `2 is V28() real ext-real Element of REAL
K526(D,2) is V28() real ext-real Element of REAL
D `1 is V28() real ext-real Element of REAL
K526(D,1) is V28() real ext-real Element of REAL
- (D `1) is V28() real ext-real Element of REAL
(1 / (B `2)) * (C `1) is V28() real ext-real Element of REAL
(C `1) / (B `2) is V28() real ext-real Element of REAL
(C `1) * ((B `2) ") is V28() real ext-real set
(1 / (C `1)) * (B `2) is V28() real ext-real Element of REAL
(B `2) / (C `1) is V28() real ext-real Element of REAL
(B `2) * ((C `1) ") is V28() real ext-real set
((C `2) / (C `1)) * ((B `1) / (B `2)) is V28() real ext-real Element of REAL
(((C `2) / (C `1)) * ((B `1) / (B `2))) * (B `2) is V28() real ext-real Element of REAL
((B `1) / (B `2)) * (B `2) is V28() real ext-real Element of REAL
((C `2) / (C `1)) * (((B `1) / (B `2)) * (B `2)) is V28() real ext-real Element of REAL
((C `2) / (C `1)) * (B `1) is V28() real ext-real Element of REAL
(B `2) / (B `1) is V28() real ext-real Element of REAL
(B `1) " is V28() real ext-real set
(B `2) * ((B `1) ") is V28() real ext-real set
(C `1) / (C `1) is V28() real ext-real Element of REAL
(C `1) * ((C `1) ") is V28() real ext-real set
(C `1) / (C `1) is V28() real ext-real Element of REAL
(C `1) * ((C `1) ") is V28() real ext-real set
D is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
D `2 is V28() real ext-real Element of REAL
K526(D,2) is V28() real ext-real Element of REAL
D `1 is V28() real ext-real Element of REAL
K526(D,1) is V28() real ext-real Element of REAL
- (D `1) is V28() real ext-real Element of REAL
1 * (B `2) is V28() real ext-real Element of REAL
((C `2) / (C `1)) * (C `1) is V28() real ext-real Element of REAL
1 * (C `1) is V28() real ext-real Element of REAL
D is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
D `2 is V28() real ext-real Element of REAL
K526(D,2) is V28() real ext-real Element of REAL
D `1 is V28() real ext-real Element of REAL
K526(D,1) is V28() real ext-real Element of REAL
- (D `1) is V28() real ext-real Element of REAL
(- 1) * (B `2) is V28() real ext-real Element of REAL
- (B `1) is V28() real ext-real Element of REAL
(- 1) * (C `1) is V28() real ext-real Element of REAL
- (C `2) is V28() real ext-real Element of REAL
D is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
D `2 is V28() real ext-real Element of REAL
K526(D,2) is V28() real ext-real Element of REAL
D `1 is V28() real ext-real Element of REAL
K526(D,1) is V28() real ext-real Element of REAL
- (D `1) is V28() real ext-real Element of REAL
d is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
() . d is set
O is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
O `1 is V28() real ext-real Element of REAL
K526(O,1) is V28() real ext-real Element of REAL
O `2 is V28() real ext-real Element of REAL
K526(O,2) is V28() real ext-real Element of REAL
O is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
O `1 is V28() real ext-real Element of REAL
K526(O,1) is V28() real ext-real Element of REAL
O `2 is V28() real ext-real Element of REAL
K526(O,2) is V28() real ext-real Element of REAL
d `2 is V28() real ext-real Element of REAL
K526(d,2) is V28() real ext-real Element of REAL
d `1 is V28() real ext-real Element of REAL
K526(d,1) is V28() real ext-real Element of REAL
- (d `1) is V28() real ext-real Element of REAL
1 / (d `1) is V28() real ext-real Element of REAL
(d `1) " is V28() real ext-real set
1 * ((d `1) ") is V28() real ext-real set
(d `2) / (d `1) is V28() real ext-real Element of REAL
(d `2) * ((d `1) ") is V28() real ext-real set
((d `2) / (d `1)) / (d `1) is V28() real ext-real Element of REAL
((d `2) / (d `1)) * ((d `1) ") is V28() real ext-real set
|[(1 / (d `1)),(((d `2) / (d `1)) / (d `1))]| is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
- (- (d `1)) is V28() real ext-real Element of REAL
O is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
O `1 is V28() real ext-real Element of REAL
K526(O,1) is V28() real ext-real Element of REAL
O `2 is V28() real ext-real Element of REAL
K526(O,2) is V28() real ext-real Element of REAL
O is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
O `1 is V28() real ext-real Element of REAL
K526(O,1) is V28() real ext-real Element of REAL
O `2 is V28() real ext-real Element of REAL
K526(O,2) is V28() real ext-real Element of REAL
d `2 is V28() real ext-real Element of REAL
K526(d,2) is V28() real ext-real Element of REAL
d `1 is V28() real ext-real Element of REAL
K526(d,1) is V28() real ext-real Element of REAL
- (d `1) is V28() real ext-real Element of REAL
(d `1) / (d `2) is V28() real ext-real Element of REAL
(d `2) " is V28() real ext-real set
(d `1) * ((d `2) ") is V28() real ext-real set
((d `1) / (d `2)) / (d `2) is V28() real ext-real Element of REAL
((d `1) / (d `2)) * ((d `2) ") is V28() real ext-real set
1 / (d `2) is V28() real ext-real Element of REAL
1 * ((d `2) ") is V28() real ext-real set
|[(((d `1) / (d `2)) / (d `2)),(1 / (d `2))]| is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
O is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
O `1 is V28() real ext-real Element of REAL
K526(O,1) is V28() real ext-real Element of REAL
O `2 is V28() real ext-real Element of REAL
K526(O,2) is V28() real ext-real Element of REAL
d `2 is V28() real ext-real Element of REAL
K526(d,2) is V28() real ext-real Element of REAL
d `1 is V28() real ext-real Element of REAL
K526(d,1) is V28() real ext-real Element of REAL
- (d `1) is V28() real ext-real Element of REAL
d `2 is V28() real ext-real Element of REAL
K526(d,2) is V28() real ext-real Element of REAL
d `1 is V28() real ext-real Element of REAL
K526(d,1) is V28() real ext-real Element of REAL
- (d `1) is V28() real ext-real Element of REAL
(TOP-REAL 2) | c is non empty strict TopSpace-like SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | c) is non empty set
K20( the carrier of ((TOP-REAL 2) | c), the carrier of ((TOP-REAL 2) | c)) is set
K19(K20( the carrier of ((TOP-REAL 2) | c), the carrier of ((TOP-REAL 2) | c))) is set
d is Relation-like the carrier of ((TOP-REAL 2) | c) -defined the carrier of ((TOP-REAL 2) | c) -valued Function-like non empty total V18( the carrier of ((TOP-REAL 2) | c), the carrier of ((TOP-REAL 2) | c)) Element of K19(K20( the carrier of ((TOP-REAL 2) | c), the carrier of ((TOP-REAL 2) | c)))
K0 is Element of K19( the carrier of (TOP-REAL 2))
K0 ` is Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (K0 `) is strict TopSpace-like SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | (K0 `)) is set
[#] ((TOP-REAL 2) | (K0 `)) is non proper open closed Element of K19( the carrier of ((TOP-REAL 2) | (K0 `)))
K19( the carrier of ((TOP-REAL 2) | (K0 `))) is set
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2) : S<sub>1</sub>[b<sub>1</sub>] } is set
a is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total V18( the carrier of I[01], the carrier of (TOP-REAL 2)) Element of K19(K20( the carrier of I[01], the carrier of (TOP-REAL 2)))
b is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total V18( the carrier of I[01], the carrier of (TOP-REAL 2)) Element of K19(K20( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng a is Element of K19( the carrier of (TOP-REAL 2))
rng b is Element of K19( the carrier of (TOP-REAL 2))
c is Element of K19( the carrier of (TOP-REAL 2))
d is Element of the carrier of I[01]
O is Element of the carrier of I[01]
a . d is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
(a . d) `1 is V28() real ext-real Element of REAL
K526((a . d),1) is V28() real ext-real Element of REAL
a . O is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
(a . O) `1 is V28() real ext-real Element of REAL
K526((a . O),1) is V28() real ext-real Element of REAL
(a . d) `2 is V28() real ext-real Element of REAL
K526((a . d),2) is V28() real ext-real Element of REAL
(a . O) `2 is V28() real ext-real Element of REAL
K526((a . O),2) is V28() real ext-real Element of REAL
b . d is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
(b . d) `2 is V28() real ext-real Element of REAL
K526((b . d),2) is V28() real ext-real Element of REAL
b . O is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
(b . O) `2 is V28() real ext-real Element of REAL
K526((b . O),2) is V28() real ext-real Element of REAL
(b . d) `1 is V28() real ext-real Element of REAL
K526((b . d),1) is V28() real ext-real Element of REAL
(b . O) `1 is V28() real ext-real Element of REAL
K526((b . O),1) is V28() real ext-real Element of REAL
dom a is Element of K19( the carrier of I[01])
K19( the carrier of I[01]) is set
(rng a) /\ c is Element of K19( the carrier of (TOP-REAL 2))
(rng b) /\ c is Element of K19( the carrier of (TOP-REAL 2))
K20( the carrier of ((TOP-REAL 2) | (K0 `)), the carrier of ((TOP-REAL 2) | (K0 `))) is set
K19(K20( the carrier of ((TOP-REAL 2) | (K0 `)), the carrier of ((TOP-REAL 2) | (K0 `)))) is set
g is Element of K19( the carrier of (TOP-REAL 2))
c \/ g is Element of K19( the carrier of (TOP-REAL 2))
I is Relation-like the carrier of ((TOP-REAL 2) | (K0 `)) -defined the carrier of ((TOP-REAL 2) | (K0 `)) -valued Function-like total V18( the carrier of ((TOP-REAL 2) | (K0 `)), the carrier of ((TOP-REAL 2) | (K0 `))) Element of K19(K20( the carrier of ((TOP-REAL 2) | (K0 `)), the carrier of ((TOP-REAL 2) | (K0 `))))
A is set
the carrier of (TOP-REAL 2) \ K0 is Element of K19( the carrier of (TOP-REAL 2))
I * a is Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL 2) | (K0 `)) -valued Function-like Element of K19(K20( the carrier of I[01], the carrier of ((TOP-REAL 2) | (K0 `))))
K20( the carrier of I[01], the carrier of ((TOP-REAL 2) | (K0 `))) is set
K19(K20( the carrier of I[01], the carrier of ((TOP-REAL 2) | (K0 `)))) is set
B is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total V18( the carrier of I[01], the carrier of (TOP-REAL 2)) Element of K19(K20( the carrier of I[01], the carrier of (TOP-REAL 2)))
f is non empty Element of K19( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | f is non empty strict TopSpace-like SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | f) is non empty set
dom I is Element of K19( the carrier of ((TOP-REAL 2) | (K0 `)))
B is set
the carrier of (TOP-REAL 2) \ K0 is Element of K19( the carrier of (TOP-REAL 2))
I * b is Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL 2) | (K0 `)) -valued Function-like Element of K19(K20( the carrier of I[01], the carrier of ((TOP-REAL 2) | (K0 `))))
C is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total V18( the carrier of I[01], the carrier of (TOP-REAL 2)) Element of K19(K20( the carrier of I[01], the carrier of (TOP-REAL 2)))
dom b is Element of K19( the carrier of I[01])
A is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total V18( the carrier of I[01], the carrier of (TOP-REAL 2)) Element of K19(K20( the carrier of I[01], the carrier of (TOP-REAL 2)))
B is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total V18( the carrier of I[01], the carrier of (TOP-REAL 2)) Element of K19(K20( the carrier of I[01], the carrier of (TOP-REAL 2)))
C is Element of the carrier of I[01]
A . C is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
(A . C) `1 is V28() real ext-real Element of REAL
K526((A . C),1) is V28() real ext-real Element of REAL
B . C is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
(B . C) `1 is V28() real ext-real Element of REAL
K526((B . C),1) is V28() real ext-real Element of REAL
(A . C) `2 is V28() real ext-real Element of REAL
K526((A . C),2) is V28() real ext-real Element of REAL
(B . C) `2 is V28() real ext-real Element of REAL
K526((B . C),2) is V28() real ext-real Element of REAL
b . C is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
I . (b . C) is set
a . C is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
I . (a . C) is set
I . (b . C) is set
I . (a . C) is set
D is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
D `1 is V28() real ext-real Element of REAL
K526(D,1) is V28() real ext-real Element of REAL
D `2 is V28() real ext-real Element of REAL
K526(D,2) is V28() real ext-real Element of REAL
ff is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
ff `1 is V28() real ext-real Element of REAL
K526(ff,1) is V28() real ext-real Element of REAL
ff `2 is V28() real ext-real Element of REAL
K526(ff,2) is V28() real ext-real Element of REAL
D is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
D `1 is V28() real ext-real Element of REAL
K526(D,1) is V28() real ext-real Element of REAL
D `2 is V28() real ext-real Element of REAL
K526(D,2) is V28() real ext-real Element of REAL
ff is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
ff `1 is V28() real ext-real Element of REAL
K526(ff,1) is V28() real ext-real Element of REAL
ff `2 is V28() real ext-real Element of REAL
K526(ff,2) is V28() real ext-real Element of REAL
D is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
D `1 is V28() real ext-real Element of REAL
K526(D,1) is V28() real ext-real Element of REAL
D `2 is V28() real ext-real Element of REAL
K526(D,2) is V28() real ext-real Element of REAL
ff is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
ff `1 is V28() real ext-real Element of REAL
K526(ff,1) is V28() real ext-real Element of REAL
ff `2 is V28() real ext-real Element of REAL
K526(ff,2) is V28() real ext-real Element of REAL
D is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
D `1 is V28() real ext-real Element of REAL
K526(D,1) is V28() real ext-real Element of REAL
D `2 is V28() real ext-real Element of REAL
K526(D,2) is V28() real ext-real Element of REAL
ff is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
ff `1 is V28() real ext-real Element of REAL
K526(ff,1) is V28() real ext-real Element of REAL
ff `2 is V28() real ext-real Element of REAL
K526(ff,2) is V28() real ext-real Element of REAL
I . (a . O) is set
A . O is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
(A . O) `1 is V28() real ext-real Element of REAL
K526((A . O),1) is V28() real ext-real Element of REAL
I . (a . d) is set
A . d is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
(A . d) `1 is V28() real ext-real Element of REAL
K526((A . d),1) is V28() real ext-real Element of REAL
I . (b . O) is set
B . O is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
(B . O) `2 is V28() real ext-real Element of REAL
K526((B . O),2) is V28() real ext-real Element of REAL
I . (b . d) is set
B . d is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
(B . d) `2 is V28() real ext-real Element of REAL
K526((B . d),2) is V28() real ext-real Element of REAL
rng A is Element of K19( the carrier of (TOP-REAL 2))
rng B is Element of K19( the carrier of (TOP-REAL 2))
(rng A) /\ (rng B) is Element of K19( the carrier of (TOP-REAL 2))
the Element of (rng A) /\ (rng B) is Element of (rng A) /\ (rng B)
D is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total V18( the carrier of I[01], the carrier of (TOP-REAL 2)) Element of K19(K20( the carrier of I[01], the carrier of (TOP-REAL 2)))
ff is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total V18( the carrier of I[01], the carrier of (TOP-REAL 2)) Element of K19(K20( the carrier of I[01], the carrier of (TOP-REAL 2)))
dom A is Element of K19( the carrier of I[01])
D is set
A . D is set
a . D is set
dom B is Element of K19( the carrier of I[01])
ff is set
B . ff is set
I . (a . D) is set
b . ff is set
I . (b . ff) is set
the carrier of (TOP-REAL 2) \ K0 is Element of K19( the carrier of (TOP-REAL 2))
f2 is set
f2 is set
(rng a) /\ (rng b) is Element of K19( the carrier of (TOP-REAL 2))
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
K20( the carrier of (TOP-REAL 2), the carrier of R^1) is V121() set
K19(K20( the carrier of (TOP-REAL 2), the carrier of R^1)) is set
g is V28() real ext-real set
a is V28() real ext-real set
b is V28() real ext-real set
c is V28() real ext-real set
d is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total V18( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)) Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
(TOP-REAL 2) | ([#] (TOP-REAL 2)) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
the topology of (TOP-REAL 2) is non empty 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 ((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 V121() set
K19(K20( the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))), the carrier of R^1)) is set
K0 is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of R^1 -valued Function-like non empty total V18( the carrier of (TOP-REAL 2), the carrier of R^1) V119() V120() V121() Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of R^1))
O is Relation-like the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))) -defined the carrier of R^1 -valued Function-like non empty total V18( the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))), the carrier of R^1) V119() V120() V121() Element of K19(K20( the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))), the carrier of R^1))
I is Relation-like the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))) -defined the carrier of R^1 -valued Function-like non empty total V18( the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))), the carrier of R^1) V119() V120() V121() Element of K19(K20( the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))), the carrier of R^1))
proj1 * d is Relation-like the carrier of (TOP-REAL 2) -defined REAL -valued Function-like non empty total V18( the carrier of (TOP-REAL 2), REAL ) V119() V120() V121() Element of K19(K20( the carrier of (TOP-REAL 2),REAL))
B is Relation-like the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))) -defined the carrier of R^1 -valued Function-like non empty total V18( the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))), the carrier of R^1) V119() V120() V121() Element of K19(K20( the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))), the carrier of R^1))
proj2 * d is Relation-like the carrier of (TOP-REAL 2) -defined REAL -valued Function-like non empty total V18( the carrier of (TOP-REAL 2), REAL ) V119() V120() V121() Element of K19(K20( the carrier of (TOP-REAL 2),REAL))
D is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of R^1 -valued Function-like non empty total V18( the carrier of (TOP-REAL 2), the carrier of R^1) V119() V120() V121() Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of R^1))
A is Relation-like the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))) -defined the carrier of R^1 -valued Function-like non empty total V18( the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))), the carrier of R^1) V119() V120() V121() Element of K19(K20( the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))), the carrier of R^1))
dom A is Element of K19( the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))))
K19( the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2)))) is set
dom B is Element of K19( the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))))
f2 is set
A . f2 is V28() real ext-real set
B . f2 is V28() real ext-real set
d . f2 is set
proj1 . (d . f2) is V28() real ext-real set
g2 is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
g2 `1 is V28() real ext-real Element of REAL
K526(g2,1) is V28() real ext-real Element of REAL
g * (g2 `1) is V28() real ext-real Element of REAL
(g * (g2 `1)) + a is V28() real ext-real Element of REAL
g2 `2 is V28() real ext-real Element of REAL
K526(g2,2) is V28() real ext-real Element of REAL
b * (g2 `2) is V28() real ext-real Element of REAL
(b * (g2 `2)) + c is V28() real ext-real Element of REAL
|[((g * (g2 `1)) + a),((b * (g2 `2)) + c)]| is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
proj1 . |[((g * (g2 `1)) + a),((b * (g2 `2)) + c)]| is V28() real ext-real Element of REAL
proj1 . g2 is V28() real ext-real Element of REAL
g * (proj1 . g2) is V28() real ext-real Element of REAL
(g * (proj1 . g2)) + a is V28() real ext-real Element of REAL
I . g2 is V28() real ext-real set
ff is Relation-like the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))) -defined the carrier of R^1 -valued Function-like non empty total V18( the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))), the carrier of R^1) V119() V120() V121() Element of K19(K20( the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))), the carrier of R^1))
f2 is Relation-like the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))) -defined the carrier of R^1 -valued Function-like non empty total V18( the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))), the carrier of R^1) V119() V120() V121() Element of K19(K20( the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))), the carrier of R^1))
g2 is Relation-like the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))) -defined the carrier of R^1 -valued Function-like non empty total V18( the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))), the carrier of R^1) V119() V120() V121() Element of K19(K20( the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))), the carrier of R^1))
C is Relation-like the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))) -defined the carrier of R^1 -valued Function-like non empty total V18( the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))), the carrier of R^1) V119() V120() V121() Element of K19(K20( the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))), the carrier of R^1))
dom C is Element of K19( the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))))
y is set
C . y is V28() real ext-real set
g2 . y is V28() real ext-real set
d . y is set
proj2 . (d . y) is V28() real ext-real set
x is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
x `1 is V28() real ext-real Element of REAL
K526(x,1) is V28() real ext-real Element of REAL
g * (x `1) is V28() real ext-real Element of REAL
(g * (x `1)) + a is V28() real ext-real Element of REAL
x `2 is V28() real ext-real Element of REAL
K526(x,2) is V28() real ext-real Element of REAL
b * (x `2) is V28() real ext-real Element of REAL
(b * (x `2)) + c is V28() real ext-real Element of REAL
|[((g * (x `1)) + a),((b * (x `2)) + c)]| is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
proj2 . |[((g * (x `1)) + a),((b * (x `2)) + c)]| is V28() real ext-real Element of REAL
proj2 . x is V28() real ext-real Element of REAL
b * (proj2 . x) is V28() real ext-real Element of REAL
(b * (proj2 . x)) + c is V28() real ext-real Element of REAL
f2 . x is V28() real ext-real set
K20( the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))), the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2)))) is set
K19(K20( the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))), the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))))) is set
y is Relation-like the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))) -defined the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))) -valued Function-like non empty total V18( the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))), the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2)))) Element of K19(K20( the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))), the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2)))))
x is V28() real ext-real set
x2 is V28() real ext-real set
|[x,x2]| is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
z is V28() real ext-real set
A . |[x,x2]| is V28() real ext-real set
u is V28() real ext-real set
C . |[x,x2]| is V28() real ext-real set
y . |[x,x2]| is set
|[z,u]| is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
d . |[x,x2]| is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
dom d is Element of K19( the carrier of (TOP-REAL 2))
proj1 . (y . |[x,x2]|) is V28() real ext-real set
proj2 . (y . |[x,x2]|) is V28() real ext-real set
dom g2 is Element of K19( the carrier of ((TOP-REAL 2) | ([#] (TOP-REAL 2))))
K0 is V28() real ext-real set
f is V28() real ext-real set
g is V28() real ext-real set
a is V28() real ext-real set
b is set
c is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
c `1 is V28() real ext-real Element of REAL
K526(c,1) is V28() real ext-real Element of REAL
K0 * (c `1) is V28() real ext-real Element of REAL
(K0 * (c `1)) + f is V28() real ext-real Element of REAL
c `2 is V28() real ext-real Element of REAL
K526(c,2) is V28() real ext-real Element of REAL
g * (c `2) is V28() real ext-real Element of REAL
(g * (c `2)) + a is V28() real ext-real Element of REAL
|[((K0 * (c `1)) + f),((g * (c `2)) + a)]| is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
d is set
O is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
O `1 is V28() real ext-real Element of REAL
K526(O,1) is V28() real ext-real Element of REAL
K0 * (O `1) is V28() real ext-real Element of REAL
(K0 * (O `1)) + f is V28() real ext-real Element of REAL
O `2 is V28() real ext-real Element of REAL
K526(O,2) is V28() real ext-real Element of REAL
g * (O `2) is V28() real ext-real Element of REAL
(g * (O `2)) + a is V28() real ext-real Element of REAL
|[((K0 * (O `1)) + f),((g * (O `2)) + a)]| is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
b is Relation-like Function-like set
dom b is set
b is Relation-like Function-like set
dom b is set
c is set
b . c is set
d is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
b . d is set
d `1 is V28() real ext-real Element of REAL
K526(d,1) is V28() real ext-real Element of REAL
K0 * (d `1) is V28() real ext-real Element of REAL
(K0 * (d `1)) + f is V28() real ext-real Element of REAL
d `2 is V28() real ext-real Element of REAL
K526(d,2) is V28() real ext-real Element of REAL
g * (d `2) is V28() real ext-real Element of REAL
(g * (d `2)) + a is V28() real ext-real Element of REAL
|[((K0 * (d `1)) + f),((g * (d `2)) + a)]| is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
c is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total V18( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)) Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
d is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
c . d is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
d `1 is V28() real ext-real Element of REAL
K526(d,1) is V28() real ext-real Element of REAL
K0 * (d `1) is V28() real ext-real Element of REAL
(K0 * (d `1)) + f is V28() real ext-real Element of REAL
d `2 is V28() real ext-real Element of REAL
K526(d,2) is V28() real ext-real Element of REAL
g * (d `2) is V28() real ext-real Element of REAL
(g * (d `2)) + a is V28() real ext-real Element of REAL
|[((K0 * (d `1)) + f),((g * (d `2)) + a)]| is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
b is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total V18( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)) Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
c is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total V18( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)) Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
d is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
b . d is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
c . d is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
d `1 is V28() real ext-real Element of REAL
K526(d,1) is V28() real ext-real Element of REAL
K0 * (d `1) is V28() real ext-real Element of REAL
(K0 * (d `1)) + f is V28() real ext-real Element of REAL
d `2 is V28() real ext-real Element of REAL
K526(d,2) is V28() real ext-real Element of REAL
g * (d `2) is V28() real ext-real Element of REAL
(g * (d `2)) + a is V28() real ext-real Element of REAL
|[((K0 * (d `1)) + f),((g * (d `2)) + a)]| is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
K0 is V28() real ext-real set
f is V28() real ext-real set
g is V28() real ext-real set
a is V28() real ext-real set
(K0,f,g,a) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total V18( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)) Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
b is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
(K0,f,g,a) . b is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
b `1 is V28() real ext-real Element of REAL
K526(b,1) is V28() real ext-real Element of REAL
K0 * (b `1) is V28() real ext-real Element of REAL
(K0 * (b `1)) + f is V28() real ext-real Element of REAL
b `2 is V28() real ext-real Element of REAL
K526(b,2) is V28() real ext-real Element of REAL
g * (b `2) is V28() real ext-real Element of REAL
(g * (b `2)) + a is V28() real ext-real Element of REAL
|[((K0 * (b `1)) + f),((g * (b `2)) + a)]| is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
K0 is V28() real ext-real set
g is V28() real ext-real set
f is V28() real ext-real set
a is V28() real ext-real set
(K0,f,g,a) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total V18( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)) continuous Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
dom (K0,f,g,a) is Element of K19( the carrier of (TOP-REAL 2))
c is set
d is set
(K0,f,g,a) . c is set
(K0,f,g,a) . d is set
I is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
I `1 is V28() real ext-real Element of REAL
K526(I,1) is V28() real ext-real Element of REAL
K0 * (I `1) is V28() real ext-real Element of REAL
(K0 * (I `1)) + f is V28() real ext-real Element of REAL
I `2 is V28() real ext-real Element of REAL
K526(I,2) is V28() real ext-real Element of REAL
g * (I `2) is V28() real ext-real Element of REAL
(g * (I `2)) + a is V28() real ext-real Element of REAL
|[((K0 * (I `1)) + f),((g * (I `2)) + a)]| is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
O is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
O `1 is V28() real ext-real Element of REAL
K526(O,1) is V28() real ext-real Element of REAL
K0 * (O `1) is V28() real ext-real Element of REAL
(K0 * (O `1)) + f is V28() real ext-real Element of REAL
O `2 is V28() real ext-real Element of REAL
K526(O,2) is V28() real ext-real Element of REAL
g * (O `2) is V28() real ext-real Element of REAL
(g * (O `2)) + a is V28() real ext-real Element of REAL
|[((K0 * (O `1)) + f),((g * (O `2)) + a)]| is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
(K0 * (O `1)) / K0 is V28() real ext-real Element of REAL
K0 " is V28() real ext-real set
(K0 * (O `1)) * (K0 ") is V28() real ext-real set
(g * (O `2)) / g is V28() real ext-real Element of REAL
g " is V28() real ext-real set
(g * (O `2)) * (g ") is V28() real ext-real set
{ b₁ where b₁ is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2) : S₁[b₁] } is set
f is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total V18( the carrier of I[01], the carrier of (TOP-REAL 2)) Element of K19(K20( the carrier of I[01], the carrier of (TOP-REAL 2)))
g is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total V18( the carrier of I[01], the carrier of (TOP-REAL 2)) Element of K19(K20( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng f is Element of K19( the carrier of (TOP-REAL 2))
rng g is Element of K19( the carrier of (TOP-REAL 2))
a is V28() real ext-real set
b is V28() real ext-real set
c is V28() real ext-real set
d is V28() real ext-real set
O is Element of the carrier of I[01]
I is Element of the carrier of I[01]
f . O is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
(f . O) `1 is V28() real ext-real Element of REAL
K526((f . O),1) is V28() real ext-real Element of REAL
f . I is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
(f . I) `1 is V28() real ext-real Element of REAL
K526((f . I),1) is V28() real ext-real Element of REAL
(f . O) `2 is V28() real ext-real Element of REAL
K526((f . O),2) is V28() real ext-real Element of REAL
(f . I) `2 is V28() real ext-real Element of REAL
K526((f . I),2) is V28() real ext-real Element of REAL
g . O is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
(g . O) `2 is V28() real ext-real Element of REAL
K526((g . O),2) is V28() real ext-real Element of REAL
g . I is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
(g . I) `2 is V28() real ext-real Element of REAL
K526((g . I),2) is V28() real ext-real Element of REAL
(g . O) `1 is V28() real ext-real Element of REAL
K526((g . O),1) is V28() real ext-real Element of REAL
(g . I) `1 is V28() real ext-real Element of REAL
K526((g . I),1) is V28() real ext-real Element of REAL
b - a is V28() real ext-real set
- a is V28() real ext-real set
b + (- a) is V28() real ext-real set
2 / (b - a) is V28() real ext-real Element of REAL
(b - a) " is V28() real ext-real set
2 * ((b - a) ") is V28() real ext-real set
2 * b is V28() real ext-real Element of REAL
(2 * b) / (b - a) is V28() real ext-real Element of REAL
(2 * b) * ((b - a) ") is V28() real ext-real set
1 - ((2 * b) / (b - a)) is V28() real ext-real Element of REAL
- ((2 * b) / (b - a)) is V28() real ext-real set
1 + (- ((2 * b) / (b - a))) is V28() real ext-real set
d - c is V28() real ext-real set
- c is V28() real ext-real set
d + (- c) is V28() real ext-real set
2 / (d - c) is V28() real ext-real Element of REAL
(d - c) " is V28() real ext-real set
2 * ((d - c) ") is V28() real ext-real set
2 * d is V28() real ext-real Element of REAL
(2 * d) / (d - c) is V28() real ext-real Element of REAL
(2 * d) * ((d - c) ") is V28() real ext-real set
1 - ((2 * d) / (d - c)) is V28() real ext-real Element of REAL
- ((2 * d) / (d - c)) is V28() real ext-real set
1 + (- ((2 * d) / (d - c))) is V28() real ext-real set
((2 / (b - a)),(1 - ((2 * b) / (b - a))),(2 / (d - c)),(1 - ((2 * d) / (d - c)))) is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total V18( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)) continuous Element of K19(K20( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
((2 / (b - a)),(1 - ((2 * b) / (b - a))),(2 / (d - c)),(1 - ((2 * d) / (d - c)))) * f is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total V18( the carrier of I[01], the carrier of (TOP-REAL 2)) Element of K19(K20( the carrier of I[01], the carrier of (TOP-REAL 2)))
((2 / (b - a)),(1 - ((2 * b) / (b - a))),(2 / (d - c)),(1 - ((2 * d) / (d - c)))) * g is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total V18( the carrier of I[01], the carrier of (TOP-REAL 2)) Element of K19(K20( the carrier of I[01], the carrier of (TOP-REAL 2)))
dom g is Element of K19( the carrier of I[01])
K19( the carrier of I[01]) is set
g2 is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total V18( the carrier of I[01], the carrier of (TOP-REAL 2)) Element of K19(K20( the carrier of I[01], the carrier of (TOP-REAL 2)))
g2 . I is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
((2 / (b - a)),(1 - ((2 * b) / (b - a))),(2 / (d - c)),(1 - ((2 * d) / (d - c)))) . (g . I) is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
(2 / (b - a)) * ((g . I) `1) is V28() real ext-real Element of REAL
((2 / (b - a)) * ((g . I) `1)) + (1 - ((2 * b) / (b - a))) is V28() real ext-real Element of REAL
(2 / (d - c)) * d is V28() real ext-real Element of REAL
((2 / (d - c)) * d) + (1 - ((2 * d) / (d - c))) is V28() real ext-real Element of REAL
|[(((2 / (b - a)) * ((g . I) `1)) + (1 - ((2 * b) / (b - a)))),(((2 / (d - c)) * d) + (1 - ((2 * d) / (d - c))))]| is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
(g2 . I) `2 is V28() real ext-real Element of REAL
K526((g2 . I),2) is V28() real ext-real Element of REAL
d * 2 is V28() real ext-real Element of REAL
(d * 2) / (d - c) is V28() real ext-real Element of REAL
(d * 2) * ((d - c) ") is V28() real ext-real set
((d * 2) / (d - c)) + (1 - ((2 * d) / (d - c))) is V28() real ext-real Element of REAL
g2 . O is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
((2 / (b - a)),(1 - ((2 * b) / (b - a))),(2 / (d - c)),(1 - ((2 * d) / (d - c)))) . (g . O) is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
(2 / (b - a)) * ((g . O) `1) is V28() real ext-real Element of REAL
((2 / (b - a)) * ((g . O) `1)) + (1 - ((2 * b) / (b - a))) is V28() real ext-real Element of REAL
(2 / (d - c)) * c is V28() real ext-real Element of REAL
((2 / (d - c)) * c) + (1 - ((2 * d) / (d - c))) is V28() real ext-real Element of REAL
|[(((2 / (b - a)) * ((g . O) `1)) + (1 - ((2 * b) / (b - a)))),(((2 / (d - c)) * c) + (1 - ((2 * d) / (d - c))))]| is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
(g2 . O) `2 is V28() real ext-real Element of REAL
K526((g2 . O),2) is V28() real ext-real Element of REAL
c * 2 is V28() real ext-real Element of REAL
(c * 2) / (d - c) is V28() real ext-real Element of REAL
(c * 2) * ((d - c) ") is V28() real ext-real set
((c * 2) / (d - c)) + (1 - ((2 * d) / (d - c))) is V28() real ext-real Element of REAL
(d - c) / (d - c) is V28() real ext-real set
(d - c) * ((d - c) ") is V28() real ext-real set
((d - c) / (d - c)) - ((2 * d) / (d - c)) is V28() real ext-real Element of REAL
((d - c) / (d - c)) + (- ((2 * d) / (d - c))) is V28() real ext-real set
((c * 2) / (d - c)) + (((d - c) / (d - c)) - ((2 * d) / (d - c))) is V28() real ext-real Element of REAL
(d - c) - (2 * d) is V28() real ext-real Element of REAL
- (2 * d) is V28() real ext-real set
(d - c) + (- (2 * d)) is V28() real ext-real set
((d - c) - (2 * d)) / (d - c) is V28() real ext-real Element of REAL
((d - c) - (2 * d)) * ((d - c) ") is V28() real ext-real set
((c * 2) / (d - c)) + (((d - c) - (2 * d)) / (d - c)) is V28() real ext-real Element of REAL
(c * 2) + ((d - c) - (2 * d)) is V28() real ext-real Element of REAL
((c * 2) + ((d - c) - (2 * d))) / (d - c) is V28() real ext-real Element of REAL
((c * 2) + ((d - c) - (2 * d))) * ((d - c) ") is V28() real ext-real set
- (d - c) is V28() real ext-real set
(- (d - c)) / (d - c) is V28() real ext-real set
(- (d - c)) * ((d - c) ") is V28() real ext-real set
- ((d - c) / (d - c)) is V28() real ext-real set
(g2 . O) `1 is V28() real ext-real Element of REAL
K526((g2 . O),1) is V28() real ext-real Element of REAL
(g2 . I) `1 is V28() real ext-real Element of REAL
K526((g2 . I),1) is V28() real ext-real Element of REAL
a - b is V28() real ext-real set
- b is V28() real ext-real set
a + (- b) is V28() real ext-real set
(a - b) / (b - a) is V28() real ext-real set
(a - b) * ((b - a) ") is V28() real ext-real set
- (b - a) is V28() real ext-real set
(- (b - a)) / (b - a) is V28() real ext-real set
(- (b - a)) * ((b - a) ") is V28() real ext-real set
(b - a) / (b - a) is V28() real ext-real set
(b - a) * ((b - a) ") is V28() real ext-real set
- ((b - a) / (b - a)) is V28() real ext-real set
y is V28() real ext-real Element of REAL
(2 / (b - a)) * y is V28() real ext-real Element of REAL
((2 / (b - a)) * y) + (1 - ((2 * b) / (b - a))) is V28() real ext-real Element of REAL
y * 2 is V28() real ext-real Element of REAL
(y * 2) / (b - a) is V28() real ext-real Element of REAL
(y * 2) * ((b - a) ") is V28() real ext-real set
((y * 2) / (b - a)) + (1 - ((2 * b) / (b - a))) is V28() real ext-real Element of REAL
((b - a) / (b - a)) - ((2 * b) / (b - a)) is V28() real ext-real Element of REAL
((b - a) / (b - a)) + (- ((2 * b) / (b - a))) is V28() real ext-real set
((y * 2) / (b - a)) + (((b - a) / (b - a)) - ((2 * b) / (b - a))) is V28() real ext-real Element of REAL
(b - a) - (2 * b) is V28() real ext-real Element of REAL
- (2 * b) is V28() real ext-real set
(b - a) + (- (2 * b)) is V28() real ext-real set
((b - a) - (2 * b)) / (b - a) is V28() real ext-real Element of REAL
((b - a) - (2 * b)) * ((b - a) ") is V28() real ext-real set
((y * 2) / (b - a)) + (((b - a) - (2 * b)) / (b - a)) is V28() real ext-real Element of REAL
(y * 2) + ((b - a) - (2 * b)) is V28() real ext-real Element of REAL
((y * 2) + ((b - a) - (2 * b))) / (b - a) is V28() real ext-real Element of REAL
((y * 2) + ((b - a) - (2 * b))) * ((b - a) ") is V28() real ext-real set
y - b is V28() real ext-real Element of REAL
y + (- b) is V28() real ext-real set
(y - b) + (y - b) is V28() real ext-real Element of REAL
((y - b) + (y - b)) - (a - b) is V28() real ext-real Element of REAL
- (a - b) is V28() real ext-real set
((y - b) + (y - b)) + (- (a - b)) is V28() real ext-real set
(((y - b) + (y - b)) - (a - b)) / (b - a) is V28() real ext-real Element of REAL
(((y - b) + (y - b)) - (a - b)) * ((b - a) ") is V28() real ext-real set
x is V28() real ext-real Element of REAL
x - b is V28() real ext-real Element of REAL
x + (- b) is V28() real ext-real set
b - b is V28() real ext-real set
b + (- b) is V28() real ext-real set
(x - b) + (x - b) is V28() real ext-real Element of REAL
((x - b) + (x - b)) - (a - b) is V28() real ext-real Element of REAL
((x - b) + (x - b)) + (- (a - b)) is V28() real ext-real set
0 + (b - b) is V28() real ext-real Element of REAL
(0 + (b - b)) - (a - b) is V28() real ext-real Element of REAL
(0 + (b - b)) + (- (a - b)) is V28() real ext-real set
(((x - b) + (x - b)) - (a - b)) / (b - a) is V28() real ext-real Element of REAL
(((x - b) + (x - b)) - (a - b)) * ((b - a) ") is V28() real ext-real set
(a - b) + (a - b) is V28() real ext-real set
((a - b) + (a - b)) - (a - b) is V28() real ext-real set
((a - b) + (a - b)) + (- (a - b)) is V28() real ext-real set
(2 / (b - a)) * x is V28() real ext-real Element of REAL
((2 / (b - a)) * x) + (1 - ((2 * b) / (b - a))) is V28() real ext-real Element of REAL
x * 2 is V28() real ext-real Element of REAL
(x * 2) / (b - a) is V28() real ext-real Element of REAL
(x * 2) * ((b - a) ") is V28() real ext-real set
((x * 2) / (b - a)) + (1 - ((2 * b) / (b - a))) is V28() real ext-real Element of REAL
((x * 2) / (b - a)) + (((b - a) / (b - a)) - ((2 * b) / (b - a))) is V28() real ext-real Element of REAL
((x * 2) / (b - a)) + (((b - a) - (2 * b)) / (b - a)) is V28() real ext-real Element of REAL
(x * 2) + ((b - a) - (2 * b)) is V28() real ext-real Element of REAL
((x * 2) + ((b - a) - (2 * b))) / (b - a) is V28() real ext-real Element of REAL
((x * 2) + ((b - a) - (2 * b))) * ((b - a) ") is V28() real ext-real set
f2 is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total V18( the carrier of I[01], the carrier of (TOP-REAL 2)) Element of K19(K20( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng f2 is Element of K19( the carrier of (TOP-REAL 2))
K0 is Element of K19( the carrier of (TOP-REAL 2))
y is set
x is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
x2 is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
x2 `1 is V28() real ext-real Element of REAL
K526(x2,1) is V28() real ext-real Element of REAL
x2 `2 is V28() real ext-real Element of REAL
K526(x2,2) is V28() real ext-real Element of REAL
dom f2 is Element of K19( the carrier of I[01])
z is set
f2 . z is set
u is Element of the carrier of I[01]
f . u is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
t is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
t `1 is V28() real ext-real Element of REAL
K526(t,1) is V28() real ext-real Element of REAL
(2 / (b - a)) * (t `1) is V28() real ext-real Element of REAL
((2 / (b - a)) * (t `1)) + (1 - ((2 * b) / (b - a))) is V28() real ext-real Element of REAL
(t `1) * 2 is V28() real ext-real Element of REAL
((t `1) * 2) / (b - a) is V28() real ext-real Element of REAL
((t `1) * 2) * ((b - a) ") is V28() real ext-real set
(((t `1) * 2) / (b - a)) + (1 - ((2 * b) / (b - a))) is V28() real ext-real Element of REAL
(b - a) / (b - a) is V28() real ext-real set
(b - a) * ((b - a) ") is V28() real ext-real set
((b - a) / (b - a)) - ((2 * b) / (b - a)) is V28() real ext-real Element of REAL
((b - a) / (b - a)) + (- ((2 * b) / (b - a))) is V28() real ext-real set
(((t `1) * 2) / (b - a)) + (((b - a) / (b - a)) - ((2 * b) / (b - a))) is V28() real ext-real Element of REAL
(b - a) - (2 * b) is V28() real ext-real Element of REAL
- (2 * b) is V28() real ext-real set
(b - a) + (- (2 * b)) is V28() real ext-real set
((b - a) - (2 * b)) / (b - a) is V28() real ext-real Element of REAL
((b - a) - (2 * b)) * ((b - a) ") is V28() real ext-real set
(((t `1) * 2) / (b - a)) + (((b - a) - (2 * b)) / (b - a)) is V28() real ext-real Element of REAL
((t `1) * 2) + ((b - a) - (2 * b)) is V28() real ext-real Element of REAL
(((t `1) * 2) + ((b - a) - (2 * b))) / (b - a) is V28() real ext-real Element of REAL
(((t `1) * 2) + ((b - a) - (2 * b))) * ((b - a) ") is V28() real ext-real set
(t `1) - b is V28() real ext-real Element of REAL
- b is V28() real ext-real set
(t `1) + (- b) is V28() real ext-real set
2 * ((t `1) - b) is V28() real ext-real Element of REAL
a - b is V28() real ext-real set
a + (- b) is V28() real ext-real set
(2 * ((t `1) - b)) - (a - b) is V28() real ext-real Element of REAL
- (a - b) is V28() real ext-real set
(2 * ((t `1) - b)) + (- (a - b)) is V28() real ext-real set
((2 * ((t `1) - b)) - (a - b)) / (b - a) is V28() real ext-real Element of REAL
((2 * ((t `1) - b)) - (a - b)) * ((b - a) ") is V28() real ext-real set
((2 / (b - a)),(1 - ((2 * b) / (b - a))),(2 / (d - c)),(1 - ((2 * d) / (d - c)))) . t is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
t `2 is V28() real ext-real Element of REAL
K526(t,2) is V28() real ext-real Element of REAL
(2 / (d - c)) * (t `2) is V28() real ext-real Element of REAL
((2 / (d - c)) * (t `2)) + (1 - ((2 * d) / (d - c))) is V28() real ext-real Element of REAL
(t `2) * 2 is V28() real ext-real Element of REAL
((t `2) * 2) / (d - c) is V28() real ext-real Element of REAL
((t `2) * 2) * ((d - c) ") is V28() real ext-real set
(((t `2) * 2) / (d - c)) + (1 - ((2 * d) / (d - c))) is V28() real ext-real Element of REAL
(((t `2) * 2) / (d - c)) + (((d - c) / (d - c)) - ((2 * d) / (d - c))) is V28() real ext-real Element of REAL
(((t `2) * 2) / (d - c)) + (((d - c) - (2 * d)) / (d - c)) is V28() real ext-real Element of REAL
((t `2) * 2) + ((d - c) - (2 * d)) is V28() real ext-real Element of REAL
(((t `2) * 2) + ((d - c) - (2 * d))) / (d - c) is V28() real ext-real Element of REAL
(((t `2) * 2) + ((d - c) - (2 * d))) * ((d - c) ") is V28() real ext-real set
(t `2) - d is V28() real ext-real Element of REAL
- d is V28() real ext-real set
(t `2) + (- d) is V28() real ext-real set
2 * ((t `2) - d) is V28() real ext-real Element of REAL
c - d is V28() real ext-real set
c + (- d) is V28() real ext-real set
(2 * ((t `2) - d)) - (c - d) is V28() real ext-real Element of REAL
- (c - d) is V28() real ext-real set
(2 * ((t `2) - d)) + (- (c - d)) is V28() real ext-real set
((2 * ((t `2) - d)) - (c - d)) / (d - c) is V28() real ext-real Element of REAL
((2 * ((t `2) - d)) - (c - d)) * ((d - c) ") is V28() real ext-real set
|[(((2 / (b - a)) * (t `1)) + (1 - ((2 * b) / (b - a)))),(((2 / (d - c)) * (t `2)) + (1 - ((2 * d) / (d - c))))]| is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
(((2 * ((t `2) - d)) - (c - d)) / (d - c)) * (d - c) is V28() real ext-real Element of REAL
(- 1) * (d - c) is V28() real ext-real Element of REAL
((2 * ((t `2) - d)) - (c - d)) + (c - d) is V28() real ext-real Element of REAL
((- 1) * (d - c)) + (c - d) is V28() real ext-real Element of REAL
(2 * ((t `2) - d)) / 2 is V28() real ext-real Element of REAL
(2 * ((t `2) - d)) * (2 ") is V28() real ext-real set
2 * (c - d) is V28() real ext-real Element of REAL
(2 * (c - d)) / 2 is V28() real ext-real Element of REAL
(2 * (c - d)) * (2 ") is V28() real ext-real set
1 * (d - c) is V28() real ext-real Element of REAL
(1 * (d - c)) + (c - d) is V28() real ext-real Element of REAL
0 / 2 is V28() real ext-real Element of REAL
0 * (2 ") is V28() real ext-real set
((t `2) - d) * 2 is V28() real ext-real Element of REAL
(((t `2) - d) * 2) / 2 is V28() real ext-real Element of REAL
(((t `2) - d) * 2) * (2 ") is V28() real ext-real set
0 + d is V28() real ext-real Element of REAL
1 * (b - a) is V28() real ext-real Element of REAL
(((2 * ((t `1) - b)) - (a - b)) / (b - a)) * (b - a) is V28() real ext-real Element of REAL
(1 * (b - a)) + (a - b) is V28() real ext-real Element of REAL
((2 * ((t `1) - b)) - (a - b)) + (a - b) is V28() real ext-real Element of REAL
((t `1) - b) * 2 is V28() real ext-real Element of REAL
(((t `1) - b) * 2) / 2 is V28() real ext-real Element of REAL
(((t `1) - b) * 2) * (2 ") is V28() real ext-real set
0 + b is V28() real ext-real Element of REAL
(- 1) * (b - a) is V28() real ext-real Element of REAL
((- 1) * (b - a)) + (a - b) is V28() real ext-real Element of REAL
(2 * ((t `1) - b)) / 2 is V28() real ext-real Element of REAL
(2 * ((t `1) - b)) * (2 ") is V28() real ext-real set
2 * (a - b) is V28() real ext-real Element of REAL
(2 * (a - b)) / 2 is V28() real ext-real Element of REAL
(2 * (a - b)) * (2 ") is V28() real ext-real set
dom f is Element of K19( the carrier of I[01])
f2 . I is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
((2 / (b - a)),(1 - ((2 * b) / (b - a))),(2 / (d - c)),(1 - ((2 * d) / (d - c)))) . (f . I) is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
(2 / (b - a)) * b is V28() real ext-real Element of REAL
((2 / (b - a)) * b) + (1 - ((2 * b) / (b - a))) is V28() real ext-real Element of REAL
(2 / (d - c)) * ((f . I) `2) is V28() real ext-real Element of REAL
((2 / (d - c)) * ((f . I) `2)) + (1 - ((2 * d) / (d - c))) is V28() real ext-real Element of REAL
|[(((2 / (b - a)) * b) + (1 - ((2 * b) / (b - a)))),(((2 / (d - c)) * ((f . I) `2)) + (1 - ((2 * d) / (d - c))))]| is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
(f2 . I) `1 is V28() real ext-real Element of REAL
K526((f2 . I),1) is V28() real ext-real Element of REAL
b * 2 is V28() real ext-real Element of REAL
(b * 2) / (b - a) is V28() real ext-real Element of REAL
(b * 2) * ((b - a) ") is V28() real ext-real set
((b * 2) / (b - a)) + (1 - ((2 * b) / (b - a))) is V28() real ext-real Element of REAL
f2 . O is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
((2 / (b - a)),(1 - ((2 * b) / (b - a))),(2 / (d - c)),(1 - ((2 * d) / (d - c)))) . (f . O) is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
(2 / (b - a)) * a is V28() real ext-real Element of REAL
((2 / (b - a)) * a) + (1 - ((2 * b) / (b - a))) is V28() real ext-real Element of REAL
(2 / (d - c)) * ((f . O) `2) is V28() real ext-real Element of REAL
((2 / (d - c)) * ((f . O) `2)) + (1 - ((2 * d) / (d - c))) is V28() real ext-real Element of REAL
|[(((2 / (b - a)) * a) + (1 - ((2 * b) / (b - a)))),(((2 / (d - c)) * ((f . O) `2)) + (1 - ((2 * d) / (d - c))))]| is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
(f2 . O) `1 is V28() real ext-real Element of REAL
K526((f2 . O),1) is V28() real ext-real Element of REAL
a * 2 is V28() real ext-real Element of REAL
(a * 2) / (b - a) is V28() real ext-real Element of REAL
(a * 2) * ((b - a) ") is V28() real ext-real set
((a * 2) / (b - a)) + (1 - ((2 * b) / (b - a))) is V28() real ext-real Element of REAL
((a * 2) / (b - a)) + (((b - a) / (b - a)) - ((2 * b) / (b - a))) is V28() real ext-real Element of REAL
((a * 2) / (b - a)) + (((b - a) - (2 * b)) / (b - a)) is V28() real ext-real Element of REAL
(a * 2) + ((b - a) - (2 * b)) is V28() real ext-real Element of REAL
((a * 2) + ((b - a) - (2 * b))) / (b - a) is V28() real ext-real Element of REAL
((a * 2) + ((b - a) - (2 * b))) * ((b - a) ") is V28() real ext-real set
- (b - a) is V28() real ext-real set
(- (b - a)) / (b - a) is V28() real ext-real set
(- (b - a)) * ((b - a) ") is V28() real ext-real set
- ((b - a) / (b - a)) is V28() real ext-real set
rng g2 is Element of K19( the carrier of (TOP-REAL 2))
y is set
x is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
x2 is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
x2 `1 is V28() real ext-real Element of REAL
K526(x2,1) is V28() real ext-real Element of REAL
x2 `2 is V28() real ext-real Element of REAL
K526(x2,2) is V28() real ext-real Element of REAL
dom g2 is Element of K19( the carrier of I[01])
z is set
g2 . z is set
u is Element of the carrier of I[01]
g . u is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
t is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
t `1 is V28() real ext-real Element of REAL
K526(t,1) is V28() real ext-real Element of REAL
(2 / (b - a)) * (t `1) is V28() real ext-real Element of REAL
((2 / (b - a)) * (t `1)) + (1 - ((2 * b) / (b - a))) is V28() real ext-real Element of REAL
(t `1) * 2 is V28() real ext-real Element of REAL
((t `1) * 2) / (b - a) is V28() real ext-real Element of REAL
((t `1) * 2) * ((b - a) ") is V28() real ext-real set
(((t `1) * 2) / (b - a)) + (1 - ((2 * b) / (b - a))) is V28() real ext-real Element of REAL
(((t `1) * 2) / (b - a)) + (((b - a) / (b - a)) - ((2 * b) / (b - a))) is V28() real ext-real Element of REAL
(((t `1) * 2) / (b - a)) + (((b - a) - (2 * b)) / (b - a)) is V28() real ext-real Element of REAL
((t `1) * 2) + ((b - a) - (2 * b)) is V28() real ext-real Element of REAL
(((t `1) * 2) + ((b - a) - (2 * b))) / (b - a) is V28() real ext-real Element of REAL
(((t `1) * 2) + ((b - a) - (2 * b))) * ((b - a) ") is V28() real ext-real set
(t `1) - b is V28() real ext-real Element of REAL
(t `1) + (- b) is V28() real ext-real set
2 * ((t `1) - b) is V28() real ext-real Element of REAL
(2 * ((t `1) - b)) - (a - b) is V28() real ext-real Element of REAL
(2 * ((t `1) - b)) + (- (a - b)) is V28() real ext-real set
((2 * ((t `1) - b)) - (a - b)) / (b - a) is V28() real ext-real Element of REAL
((2 * ((t `1) - b)) - (a - b)) * ((b - a) ") is V28() real ext-real set
((2 / (b - a)),(1 - ((2 * b) / (b - a))),(2 / (d - c)),(1 - ((2 * d) / (d - c)))) . t is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
t `2 is V28() real ext-real Element of REAL
K526(t,2) is V28() real ext-real Element of REAL
(2 / (d - c)) * (t `2) is V28() real ext-real Element of REAL
((2 / (d - c)) * (t `2)) + (1 - ((2 * d) / (d - c))) is V28() real ext-real Element of REAL
(t `2) * 2 is V28() real ext-real Element of REAL
((t `2) * 2) / (d - c) is V28() real ext-real Element of REAL
((t `2) * 2) * ((d - c) ") is V28() real ext-real set
(((t `2) * 2) / (d - c)) + (1 - ((2 * d) / (d - c))) is V28() real ext-real Element of REAL
(((t `2) * 2) / (d - c)) + (((d - c) / (d - c)) - ((2 * d) / (d - c))) is V28() real ext-real Element of REAL
(((t `2) * 2) / (d - c)) + (((d - c) - (2 * d)) / (d - c)) is V28() real ext-real Element of REAL
((t `2) * 2) + ((d - c) - (2 * d)) is V28() real ext-real Element of REAL
(((t `2) * 2) + ((d - c) - (2 * d))) / (d - c) is V28() real ext-real Element of REAL
(((t `2) * 2) + ((d - c) - (2 * d))) * ((d - c) ") is V28() real ext-real set
(t `2) - d is V28() real ext-real Element of REAL
(t `2) + (- d) is V28() real ext-real set
2 * ((t `2) - d) is V28() real ext-real Element of REAL
(2 * ((t `2) - d)) - (c - d) is V28() real ext-real Element of REAL
(2 * ((t `2) - d)) + (- (c - d)) is V28() real ext-real set
((2 * ((t `2) - d)) - (c - d)) / (d - c) is V28() real ext-real Element of REAL
((2 * ((t `2) - d)) - (c - d)) * ((d - c) ") is V28() real ext-real set
|[(((2 / (b - a)) * (t `1)) + (1 - ((2 * b) / (b - a)))),(((2 / (d - c)) * (t `2)) + (1 - ((2 * d) / (d - c))))]| is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2)
(((2 * ((t `2) - d)) - (c - d)) / (d - c)) * (d - c) is V28() real ext-real Element of REAL
((2 * ((t `2) - d)) - (c - d)) + (c - d) is V28() real ext-real Element of REAL
(2 * ((t `2) - d)) / 2 is V28() real ext-real Element of REAL
(2 * ((t `2) - d)) * (2 ") is V28() real ext-real set
((t `2) - d) * 2 is V28() real ext-real Element of REAL
(((t `2) - d) * 2) / 2 is V28() real ext-real Element of REAL
(((t `2) - d) * 2) * (2 ") is V28() real ext-real set
(((2 * ((t `1) - b)) - (a - b)) / (b - a)) * (b - a) is V28() real ext-real Element of REAL
((2 * ((t `1) - b)) - (a - b)) + (a - b) is V28() real ext-real Element of REAL
((t `1) - b) * 2 is V28() real ext-real Element of REAL
(((t `1) - b) * 2) / 2 is V28() real ext-real Element of REAL
(((t `1) - b) * 2) * (2 ") is V28() real ext-real set
(2 * ((t `1) - b)) / 2 is V28() real ext-real Element of REAL
(2 * ((t `1) - b)) * (2 ") is V28() real ext-real set
(f2 . O) `2 is V28() real ext-real Element of REAL
K526((f2 . O),2) is V28() real ext-real Element of REAL
(f2 . I) `2 is V28() real ext-real Element of REAL
K526((f2 . I),2) is V28() real ext-real Element of REAL
(c - d) / (d - c) is V28() real ext-real set
(c - d) * ((d - c) ") is V28() real ext-real set
y is V28() real ext-real Element of REAL
(2 / (d - c)) * y is V28() real ext-real Element of REAL
((2 / (d - c)) * y) + (1 - ((2 * d) / (d - c))) is V28() real ext-real Element of REAL
y * 2 is V28() real ext-real Element of REAL
(y * 2) / (d - c) is V28() real ext-real Element of REAL
(y * 2) * ((d - c) ") is V28() real ext-real set
((y * 2) / (d - c)) + (1 - ((2 * d) / (d - c))) is V28() real ext-real Element of REAL
((y * 2) / (d - c)) + (((d - c) / (d - c)) - ((2 * d) / (d - c))) is V28() real ext-real Element of REAL
((y * 2) / (d - c)) + (((d - c) - (2 * d)) / (d - c)) is V28() real ext-real Element of REAL
(y * 2) + ((d - c) - (2 * d)) is V28() real ext-real Element of REAL
((y * 2) + ((d - c) - (2 * d))) / (d - c) is V28() real ext-real Element of REAL
((y * 2) + ((d - c) - (2 * d))) * ((d - c) ") is V28() real ext-real set
y - d is V28() real ext-real Element of REAL
y + (- d) is V28() real ext-real set
(y - d) + (y - d) is V28() real ext-real Element of REAL
((y - d) + (y - d)) - (c - d) is V28() real ext-real Element of REAL
((y - d) + (y - d)) + (- (c - d)) is V28() real ext-real set
(((y - d) + (y - d)) - (c - d)) / (d - c) is V28() real ext-real Element of REAL
(((y - d) + (y - d)) - (c - d)) * ((d - c) ") is V28() real ext-real set
x is V28() real ext-real Element of REAL
x - d is V28() real ext-real Element of REAL
x + (- d) is V28() real ext-real set
d - d is V28() real ext-real set
d + (- d) is V28() real ext-real set
(x - d) + (x - d) is V28() real ext-real Element of REAL
((x - d) + (x - d)) - (c - d) is V28() real ext-real Element of REAL
((x - d) + (x - d)) + (- (c - d)) is V28() real ext-real set
0 + (d - d) is V28() real ext-real Element of REAL
(0 + (d - d)) - (c - d) is V28() real ext-real Element of REAL
(0 + (d - d)) + (- (c - d)) is V28() real ext-real set
(((x - d) + (x - d)) - (c - d)) / (d - c) is V28() real ext-real Element of REAL
(((x - d) + (x - d)) - (c - d)) * ((d - c) ") is V28() real ext-real set
(c - d) + (c - d) is V28() real ext-real set
((c - d) + (c - d)) - (c - d) is V28() real ext-real set
((c - d) + (c - d)) + (- (c - d)) is V28() real ext-real set
(2 / (d - c)) * x is V28() real ext-real Element of REAL
((2 / (d - c)) * x) + (1 - ((2 * d) / (d - c))) is V28() real ext-real Element of REAL
x * 2 is V28() real ext-real Element of REAL
(x * 2) / (d - c) is V28() real ext-real Element of REAL
(x * 2) * ((d - c) ") is V28() real ext-real set
((x * 2) / (d - c)) + (1 - ((2 * d) / (d - c))) is V28() real ext-real Element of REAL
((x * 2) / (d - c)) + (((d - c) / (d - c)) - ((2 * d) / (d - c))) is V28() real ext-real Element of REAL
((x * 2) / (d - c)) + (((d - c) - (2 * d)) / (d - c)) is V28() real ext-real Element of REAL
(x * 2) + ((d - c) - (2 * d)) is V28() real ext-real Element of REAL
((x * 2) + ((d - c) - (2 * d))) / (d - c) is V28() real ext-real Element of REAL
((x * 2) + ((d - c) - (2 * d))) * ((d - c) ") is V28() real ext-real set
(rng f2) /\ (rng g2) is Element of K19( the carrier of (TOP-REAL 2))
the Element of (rng f2) /\ (rng g2) is Element of (rng f2) /\ (rng g2)
x is set
f2 . x is set
f . x is set
x2 is set
g2 . x2 is set
g . x2 is set
((2 / (b - a)),(1 - ((2 * b) / (b - a))),(2 / (d - c)),(1 - ((2 * d) / (d - c)))) . (g . x2) is set
dom ((2 / (b - a)),(1 - ((2 * b) / (b - a))),(2 / (d - c)),(1 - ((2 * d) / (d - c)))) is Element of K19( the carrier of (TOP-REAL 2))
((2 / (b - a)),(1 - ((2 * b) / (b - a))),(2 / (d - c)),(1 - ((2 * d) / (d - c)))) . (f . x) is set
(rng f) /\ (rng g) is Element of K19( the carrier of (TOP-REAL 2))
{ b₁ where b₁ is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2) : b₁ `2 <= b<sub>1</sub> `1 } is set
{ b₁ where b₁ is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2) : b₁ `1 <= b<sub>1</sub> `2 } is set
{ b₁ where b₁ is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2) : - (b₁ `1) <= b<sub>1</sub> `2 } is set
{ b₁ where b₁ is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2) : b₁ `2 <= - (b<sub>1</sub> `1) } is set
{ b₁ where b₁ is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2) : - (b₁ `2) <= b<sub>1</sub> `1 } is set
{ b₁ where b₁ is Relation-like Function-like V45(2) FinSequence-like V119() V120() V121() Element of the carrier of (TOP-REAL 2) : b₁ `1 <= - (b<sub>1</sub> `2) } is set