:: BORSUK_6 semantic presentation

REAL is non empty V32() complex-membered ext-real-membered real-membered V209() set
NAT is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V209() Element of bool REAL
bool REAL is non empty set
I[01] is non empty strict TopSpace-like T_0 T_1 T_2 V74() compact real-membered pathwise_connected SubSpace of R^1
R^1 is non empty strict TopSpace-like real-membered TopStruct
the carrier of I[01] is non empty complex-membered ext-real-membered real-membered set
omega is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V209() set
bool omega is non empty set
bool NAT is non empty set
{} is empty trivial Relation-like non-empty empty-yielding complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V209() set
the empty trivial Relation-like non-empty empty-yielding complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V209() set is empty trivial Relation-like non-empty empty-yielding complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V209() set
1 is non empty natural V11() real ext-real positive non negative V172() V173() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered Element of NAT
{{},1} is non empty set
COMPLEX is non empty V32() complex-membered V209() set
RAT is non empty V32() complex-membered ext-real-membered real-membered rational-membered V209() set
INT is non empty V32() complex-membered ext-real-membered real-membered rational-membered integer-membered V209() set
[:REAL,REAL:] is non empty Relation-like set
bool [:REAL,REAL:] is non empty set
K457() is non empty V100() L9()
the carrier of K457() is non empty set
K462() is non empty V100() V174() V175() V176() V178() V225() V226() V227() V228() V229() V230() L9()
K463() is non empty V100() V176() V178() V228() V229() V230() M32(K462())
K464() is non empty V100() V174() V176() V178() V228() V229() V230() V231() M35(K462(),K463())
K466() is non empty V100() V174() V176() V178() L9()
K467() is non empty V100() V174() V176() V178() V231() M32(K466())
I[01] is non empty strict TopSpace-like T_0 T_1 T_2 V74() compact real-membered pathwise_connected TopStruct
the carrier of I[01] is non empty complex-membered ext-real-membered real-membered set
[:1,1:] is non empty Relation-like set
bool [:1,1:] is non empty set
[:[:1,1:],1:] is non empty Relation-like set
bool [:[:1,1:],1:] is non empty set
[:[:1,1:],REAL:] is non empty Relation-like set
bool [:[:1,1:],REAL:] is non empty set
[:[:REAL,REAL:],REAL:] is non empty Relation-like set
bool [:[:REAL,REAL:],REAL:] is non empty set
2 is non empty natural V11() real ext-real positive non negative V172() V173() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered Element of NAT
[:2,2:] is non empty Relation-like set
[:[:2,2:],REAL:] is non empty Relation-like set
bool [:[:2,2:],REAL:] is non empty set
K551() is V237() real-membered L18()
0 is empty trivial natural V11() real ext-real non positive non negative Relation-like non-empty empty-yielding V172() V173() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V209() Element of NAT
Closed-Interval-TSpace (0,1) is non empty strict TopSpace-like real-membered SubSpace of R^1
the carrier of (Closed-Interval-TSpace (0,1)) is non empty complex-membered ext-real-membered real-membered set
TOP-REAL 2 is non empty TopSpace-like V98() V123() V124() V125() V126() V127() V128() V129() V215() V216() V257() L19()
the carrier of (TOP-REAL 2) is non empty set
NonZero (TOP-REAL 2) is Element of bool the carrier of (TOP-REAL 2)
bool the carrier of (TOP-REAL 2) is non empty set
[#] (TOP-REAL 2) is non empty non proper open closed Element of bool the carrier of (TOP-REAL 2)
K164((TOP-REAL 2)) is Relation-like Function-like V39(2) FinSequence-like V55( TOP-REAL 2) V195() Element of the carrier of (TOP-REAL 2)
the ZeroF of (TOP-REAL 2) is Relation-like Function-like V39(2) FinSequence-like V195() Element of the carrier of (TOP-REAL 2)
{K164((TOP-REAL 2))} is non empty trivial set
([#] (TOP-REAL 2)) \ {K164((TOP-REAL 2))} is Element of bool the carrier of (TOP-REAL 2)
[:(NonZero (TOP-REAL 2)),(NonZero (TOP-REAL 2)):] is Relation-like set
bool [:(NonZero (TOP-REAL 2)),(NonZero (TOP-REAL 2)):] is non empty set
[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):] is non empty Relation-like set
bool [: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):] is non empty set
K638(K551()) is TopStruct
the carrier of K638(K551()) is set
bool the carrier of K638(K551()) is non empty set
[.0,1.] is complex-membered ext-real-membered real-membered Element of bool REAL
0[01] is V11() real ext-real Element of the carrier of I[01]
1[01] is V11() real ext-real Element of the carrier of I[01]
(#) (0,1) is V11() real ext-real Element of the carrier of (Closed-Interval-TSpace (0,1))
(0,1) (#) is V11() real ext-real Element of the carrier of (Closed-Interval-TSpace (0,1))
the carrier of R^1 is non empty complex-membered ext-real-membered real-membered set
bool the carrier of I[01] is non empty set
1 / 2 is V11() real ext-real non negative Element of REAL
[:I[01],I[01]:] is non empty strict TopSpace-like T_0 T_1 T_2 compact TopStruct
the carrier of [:I[01],I[01]:] is non empty set
{ b₁ where b₁ is Relation-like Function-like V39(2) FinSequence-like V195() 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 V39(2) FinSequence-like V195() 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 V39(2) FinSequence-like V195() 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 V39(2) FinSequence-like V195() Element of the carrier of (TOP-REAL 2) : b₁ `2 <= - (b<sub>1</sub> `1) } is set
[:R^1,R^1:] is non empty strict TopSpace-like TopStruct
the carrier of [:R^1,R^1:] is non empty set
[: the carrier of [:R^1,R^1:], the carrier of (TOP-REAL 2):] is non empty Relation-like set
bool [: the carrier of [:R^1,R^1:], the carrier of (TOP-REAL 2):] is non empty set
1 / 2 is V11() real ext-real non negative set
F₁() is non empty set
T is set
T is set
T is Relation-like Function-like set
proj1 T is set
T is Relation-like Function-like set
proj1 T is set
a is Element of F₁()
T . a is set
F₂(a) is set
F₃(a) is set
F₄(a) is set
[:[.0,1.],[.0,1.]:] is Relation-like REAL -defined REAL -valued Element of bool [:REAL,REAL:]
T is V11() real ext-real set
b is V11() real ext-real set
a is V11() real ext-real set
b - T is V11() real ext-real set
a - T is V11() real ext-real set
(b - T) / (a - T) is V11() real ext-real set
T is V11() real ext-real Element of the carrier of I[01]
2 * T is V11() real ext-real Element of REAL
2 * (1 / 2) is V11() real ext-real non negative Element of REAL
T is V11() real ext-real Element of the carrier of I[01]
2 * T is V11() real ext-real Element of REAL
(2 * T) - 1 is V11() real ext-real Element of REAL
2 * 1 is V11() real ext-real non negative Element of REAL
2 - 1 is V11() real ext-real Element of REAL
2 * (1 / 2) is V11() real ext-real non negative Element of REAL
1 - 1 is V11() real ext-real Element of REAL
T is V11() real ext-real Element of the carrier of I[01]
a is V11() real ext-real Element of the carrier of I[01]
T * a is V11() real ext-real set
T is V11() real ext-real Element of the carrier of I[01]
(1 / 2) * T is V11() real ext-real Element of REAL
(1 / 2) * 1 is V11() real ext-real non negative Element of REAL
4 is non empty natural V11() real ext-real positive non negative V172() V173() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered Element of NAT
1 / 4 is V11() real ext-real non negative Element of REAL
T is V11() real ext-real Element of the carrier of I[01]
T - (1 / 4) is V11() real ext-real Element of REAL
1 + (1 / 4) is non empty V11() real ext-real positive non negative Element of REAL
(1 / 4) + 0 is V11() real ext-real non negative Element of REAL
id I[01] is non empty Relation-like the carrier of I[01] -defined the carrier of I[01] -valued Function-like V43( the carrier of I[01]) quasi_total continuous being_homeomorphism V171( I[01] , I[01] ) Element of bool [: the carrier of I[01], the carrier of I[01]:]
[: the carrier of I[01], the carrier of I[01]:] is non empty Relation-like set
bool [: the carrier of I[01], the carrier of I[01]:] is non empty set
id the carrier of I[01] is non empty Relation-like the carrier of I[01] -defined the carrier of I[01] -valued V43( the carrier of I[01]) quasi_total Element of bool [: the carrier of I[01], the carrier of I[01]:]
(id I[01]) . 0 is set
(id I[01]) . 1 is set
bool the carrier of [:I[01],I[01]:] is non empty set
T is V11() real ext-real Element of the carrier of I[01]
a is V11() real ext-real Element of the carrier of I[01]
b is V11() real ext-real Element of the carrier of I[01]
P is V11() real ext-real Element of the carrier of I[01]
[.T,a.] is complex-membered ext-real-membered real-membered Element of bool REAL
[.b,P.] is complex-membered ext-real-membered real-membered Element of bool REAL
[:[.T,a.],[.b,P.]:] is Relation-like REAL -defined REAL -valued Element of bool [:REAL,REAL:]
Q is non empty Element of bool the carrier of [:I[01],I[01]:]
{ b₁ where b₁ is Relation-like Function-like V39(2) FinSequence-like V195() Element of the carrier of (TOP-REAL 2) : b₁ `2 <= (2 * (b<sub>1</sub> `1)) - 1 } is set
AffineMap (1,0,(1 / 2),(1 / 2)) is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like V43( the carrier of (TOP-REAL 2)) quasi_total continuous Element of bool [: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):]
Q is Element of bool the carrier of (TOP-REAL 2)
e2 is Element of bool the carrier of (TOP-REAL 2)
(AffineMap (1,0,(1 / 2),(1 / 2))) .: Q is Element of bool the carrier of (TOP-REAL 2)
gg is set
dom (AffineMap (1,0,(1 / 2),(1 / 2))) is non empty Element of bool the carrier of (TOP-REAL 2)
gg is set
(AffineMap (1,0,(1 / 2),(1 / 2))) . gg is set
S2 is Relation-like Function-like V39(2) FinSequence-like V195() Element of the carrier of (TOP-REAL 2)
S2 `2 is V11() real ext-real Element of REAL
K599(S2,2) is V11() real ext-real Element of REAL
S2 `1 is V11() real ext-real Element of REAL
K599(S2,1) is V11() real ext-real Element of REAL
2 * (S2 `1) is V11() real ext-real Element of REAL
(2 * (S2 `1)) - 1 is V11() real ext-real Element of REAL
(AffineMap (1,0,(1 / 2),(1 / 2))) . S2 is Relation-like Function-like V39(2) FinSequence-like V195() Element of the carrier of (TOP-REAL 2)
1 * (S2 `1) is V11() real ext-real Element of REAL
(1 * (S2 `1)) + 0 is V11() real ext-real Element of REAL
(1 / 2) * (S2 `2) is V11() real ext-real Element of REAL
((1 / 2) * (S2 `2)) + (1 / 2) is V11() real ext-real Element of REAL
|[((1 * (S2 `1)) + 0),(((1 / 2) * (S2 `2)) + (1 / 2))]| is Relation-like Function-like V39(2) FinSequence-like V195() Element of the carrier of (TOP-REAL 2)
((AffineMap (1,0,(1 / 2),(1 / 2))) . S2) `1 is V11() real ext-real Element of REAL
K599(((AffineMap (1,0,(1 / 2),(1 / 2))) . S2),1) is V11() real ext-real Element of REAL
((AffineMap (1,0,(1 / 2),(1 / 2))) . S2) `2 is V11() real ext-real Element of REAL
K599(((AffineMap (1,0,(1 / 2),(1 / 2))) . S2),2) is V11() real ext-real Element of REAL
(1 / 2) * ((2 * (S2 `1)) - 1) is V11() real ext-real Element of REAL
(S2 `1) - (1 / 2) is V11() real ext-real Element of REAL
((S2 `1) - (1 / 2)) + (1 / 2) is V11() real ext-real Element of REAL
gg is set
rng (AffineMap (1,0,(1 / 2),(1 / 2))) is non empty Element of bool the carrier of (TOP-REAL 2)
dom (AffineMap (1,0,(1 / 2),(1 / 2))) is non empty Element of bool the carrier of (TOP-REAL 2)
gg is set
(AffineMap (1,0,(1 / 2),(1 / 2))) . gg is set
S2 is Relation-like Function-like V39(2) FinSequence-like V195() Element of the carrier of (TOP-REAL 2)
(AffineMap (1,0,(1 / 2),(1 / 2))) . S2 is Relation-like Function-like V39(2) FinSequence-like V195() Element of the carrier of (TOP-REAL 2)
S2 `1 is V11() real ext-real Element of REAL
K599(S2,1) is V11() real ext-real Element of REAL
1 * (S2 `1) is V11() real ext-real Element of REAL
(1 * (S2 `1)) + 0 is V11() real ext-real Element of REAL
S2 `2 is V11() real ext-real Element of REAL
K599(S2,2) is V11() real ext-real Element of REAL
(1 / 2) * (S2 `2) is V11() real ext-real Element of REAL
((1 / 2) * (S2 `2)) + (1 / 2) is V11() real ext-real Element of REAL
|[((1 * (S2 `1)) + 0),(((1 / 2) * (S2 `2)) + (1 / 2))]| is Relation-like Function-like V39(2) FinSequence-like V195() Element of the carrier of (TOP-REAL 2)
((AffineMap (1,0,(1 / 2),(1 / 2))) . S2) `1 is V11() real ext-real Element of REAL
K599(((AffineMap (1,0,(1 / 2),(1 / 2))) . S2),1) is V11() real ext-real Element of REAL
((AffineMap (1,0,(1 / 2),(1 / 2))) . S2) `2 is V11() real ext-real Element of REAL
K599(((AffineMap (1,0,(1 / 2),(1 / 2))) . S2),2) is V11() real ext-real Element of REAL
2 * (((AffineMap (1,0,(1 / 2),(1 / 2))) . S2) `2) is V11() real ext-real Element of REAL
2 * (S2 `1) is V11() real ext-real Element of REAL
g is Relation-like Function-like V39(2) FinSequence-like V195() Element of the carrier of (TOP-REAL 2)
g `2 is V11() real ext-real Element of REAL
K599(g,2) is V11() real ext-real Element of REAL
g `1 is V11() real ext-real Element of REAL
K599(g,1) is V11() real ext-real Element of REAL
(2 * (((AffineMap (1,0,(1 / 2),(1 / 2))) . S2) `2)) - 1 is V11() real ext-real Element of REAL
(2 * (S2 `1)) - 1 is V11() real ext-real Element of REAL
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V39(2) FinSequence-like V195() Element of the carrier of (TOP-REAL 2) : (2 * (b<sub>1</sub> `1)) - 1 <= b₁ `2 } is set
Q is Element of bool the carrier of (TOP-REAL 2)
e2 is Element of bool the carrier of (TOP-REAL 2)
(AffineMap (1,0,(1 / 2),(1 / 2))) .: Q is Element of bool the carrier of (TOP-REAL 2)
gg is set
dom (AffineMap (1,0,(1 / 2),(1 / 2))) is non empty Element of bool the carrier of (TOP-REAL 2)
gg is set
(AffineMap (1,0,(1 / 2),(1 / 2))) . gg is set
S2 is Relation-like Function-like V39(2) FinSequence-like V195() Element of the carrier of (TOP-REAL 2)
S2 `1 is V11() real ext-real Element of REAL
K599(S2,1) is V11() real ext-real Element of REAL
2 * (S2 `1) is V11() real ext-real Element of REAL
(2 * (S2 `1)) - 1 is V11() real ext-real Element of REAL
S2 `2 is V11() real ext-real Element of REAL
K599(S2,2) is V11() real ext-real Element of REAL
(1 / 2) * ((2 * (S2 `1)) - 1) is V11() real ext-real Element of REAL
(1 / 2) * (S2 `2) is V11() real ext-real Element of REAL
(AffineMap (1,0,(1 / 2),(1 / 2))) . S2 is Relation-like Function-like V39(2) FinSequence-like V195() Element of the carrier of (TOP-REAL 2)
1 * (S2 `1) is V11() real ext-real Element of REAL
(1 * (S2 `1)) + 0 is V11() real ext-real Element of REAL
((1 / 2) * (S2 `2)) + (1 / 2) is V11() real ext-real Element of REAL
|[((1 * (S2 `1)) + 0),(((1 / 2) * (S2 `2)) + (1 / 2))]| is Relation-like Function-like V39(2) FinSequence-like V195() Element of the carrier of (TOP-REAL 2)
((AffineMap (1,0,(1 / 2),(1 / 2))) . S2) `1 is V11() real ext-real Element of REAL
K599(((AffineMap (1,0,(1 / 2),(1 / 2))) . S2),1) is V11() real ext-real Element of REAL
((AffineMap (1,0,(1 / 2),(1 / 2))) . S2) `2 is V11() real ext-real Element of REAL
K599(((AffineMap (1,0,(1 / 2),(1 / 2))) . S2),2) is V11() real ext-real Element of REAL
(S2 `1) - (1 / 2) is V11() real ext-real Element of REAL
((S2 `1) - (1 / 2)) + (1 / 2) is V11() real ext-real Element of REAL
gg is set
rng (AffineMap (1,0,(1 / 2),(1 / 2))) is non empty Element of bool the carrier of (TOP-REAL 2)
dom (AffineMap (1,0,(1 / 2),(1 / 2))) is non empty Element of bool the carrier of (TOP-REAL 2)
gg is set
(AffineMap (1,0,(1 / 2),(1 / 2))) . gg is set
S2 is Relation-like Function-like V39(2) FinSequence-like V195() Element of the carrier of (TOP-REAL 2)
(AffineMap (1,0,(1 / 2),(1 / 2))) . S2 is Relation-like Function-like V39(2) FinSequence-like V195() Element of the carrier of (TOP-REAL 2)
S2 `1 is V11() real ext-real Element of REAL
K599(S2,1) is V11() real ext-real Element of REAL
1 * (S2 `1) is V11() real ext-real Element of REAL
(1 * (S2 `1)) + 0 is V11() real ext-real Element of REAL
S2 `2 is V11() real ext-real Element of REAL
K599(S2,2) is V11() real ext-real Element of REAL
(1 / 2) * (S2 `2) is V11() real ext-real Element of REAL
((1 / 2) * (S2 `2)) + (1 / 2) is V11() real ext-real Element of REAL
|[((1 * (S2 `1)) + 0),(((1 / 2) * (S2 `2)) + (1 / 2))]| is Relation-like Function-like V39(2) FinSequence-like V195() Element of the carrier of (TOP-REAL 2)
((AffineMap (1,0,(1 / 2),(1 / 2))) . S2) `1 is V11() real ext-real Element of REAL
K599(((AffineMap (1,0,(1 / 2),(1 / 2))) . S2),1) is V11() real ext-real Element of REAL
2 * (S2 `1) is V11() real ext-real Element of REAL
((AffineMap (1,0,(1 / 2),(1 / 2))) . S2) `2 is V11() real ext-real Element of REAL
K599(((AffineMap (1,0,(1 / 2),(1 / 2))) . S2),2) is V11() real ext-real Element of REAL
2 * (((AffineMap (1,0,(1 / 2),(1 / 2))) . S2) `2) is V11() real ext-real Element of REAL
g is Relation-like Function-like V39(2) FinSequence-like V195() Element of the carrier of (TOP-REAL 2)
g `1 is V11() real ext-real Element of REAL
K599(g,1) is V11() real ext-real Element of REAL
g `2 is V11() real ext-real Element of REAL
K599(g,2) is V11() real ext-real Element of REAL
(2 * (S2 `1)) - 1 is V11() real ext-real Element of REAL
(2 * (((AffineMap (1,0,(1 / 2),(1 / 2))) . S2) `2)) - 1 is V11() real ext-real Element of REAL
{ b₁ where b₁ is Relation-like Function-like V39(2) FinSequence-like V195() Element of the carrier of (TOP-REAL 2) : 1 - (2 * (b₁ `1)) <= b<sub>1</sub> `2 } is set
- (1 / 2) is V11() real ext-real non positive Element of REAL
AffineMap (1,0,(1 / 2),(- (1 / 2))) is non empty Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like V43( the carrier of (TOP-REAL 2)) quasi_total continuous Element of bool [: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):]
Q is Element of bool the carrier of (TOP-REAL 2)
e2 is Element of bool the carrier of (TOP-REAL 2)
(AffineMap (1,0,(1 / 2),(- (1 / 2)))) .: Q is Element of bool the carrier of (TOP-REAL 2)
gg is set
dom (AffineMap (1,0,(1 / 2),(- (1 / 2)))) is non empty Element of bool the carrier of (TOP-REAL 2)
gg is set
(AffineMap (1,0,(1 / 2),(- (1 / 2)))) . gg is set
S2 is Relation-like Function-like V39(2) FinSequence-like V195() Element of the carrier of (TOP-REAL 2)
S2 `1 is V11() real ext-real Element of REAL
K599(S2,1) is V11() real ext-real Element of REAL
2 * (S2 `1) is V11() real ext-real Element of REAL
1 - (2 * (S2 `1)) is V11() real ext-real Element of REAL
S2 `2 is V11() real ext-real Element of REAL
K599(S2,2) is V11() real ext-real Element of REAL
(AffineMap (1,0,(1 / 2),(- (1 / 2)))) . S2 is Relation-like Function-like V39(2) FinSequence-like V195() Element of the carrier of (TOP-REAL 2)
(1 / 2) * (1 - (2 * (S2 `1))) is V11() real ext-real Element of REAL
(1 / 2) * (S2 `2) is V11() real ext-real Element of REAL
(1 / 2) - (S2 `1) is V11() real ext-real Element of REAL
((1 / 2) - (S2 `1)) + (- (1 / 2)) is V11() real ext-real Element of REAL
((1 / 2) * (S2 `2)) + (- (1 / 2)) is V11() real ext-real Element of REAL
1 * (S2 `1) is V11() real ext-real Element of REAL
(1 * (S2 `1)) + 0 is V11() real ext-real Element of REAL
|[((1 * (S2 `1)) + 0),(((1 / 2) * (S2 `2)) + (- (1 / 2)))]| is Relation-like Function-like V39(2) FinSequence-like V195() Element of the carrier of (TOP-REAL 2)
((AffineMap (1,0,(1 / 2),(- (1 / 2)))) . S2) `1 is V11() real ext-real Element of REAL
K599(((AffineMap (1,0,(1 / 2),(- (1 / 2)))) . S2),1) is V11() real ext-real Element of REAL
- (((AffineMap (1,0,(1 / 2),(- (1 / 2)))) . S2) `1) is V11() real ext-real Element of REAL
((AffineMap (1,0,(1 / 2),(- (1 / 2)))) . S2) `2 is V11() real ext-real Element of REAL
K599(((AffineMap (1,0,(1 / 2),(- (1 / 2)))) . S2),2) is V11() real ext-real Element of REAL
gg is set
rng (AffineMap (1,0,(1 / 2),(- (1 / 2)))) is non empty Element of bool the carrier of (TOP-REAL 2)
dom (AffineMap (1,0,(1 / 2),(- (1 / 2)))) is non empty Element of bool the carrier of (TOP-REAL 2)
gg is set
(AffineMap (1,0,(1 / 2),(- (1 / 2)))) . gg is set
S2 is Relation-like Function-like V39(2) FinSequence-like V195() Element of the carrier of (TOP-REAL 2)
(AffineMap (1,0,(1 / 2),(- (1 / 2)))) . S2 is Relation-like Function-like V39(2) FinSequence-like V195() Element of the carrier of (TOP-REAL 2)
S2 `1 is V11() real ext-real Element of REAL
K599(S2,1) is V11() real ext-real Element of REAL
1 * (S2 `1) is V11() real ext-real Element of REAL
(1 * (S2 `1)) + 0 is V11() real ext-real Element of REAL
S2 `2 is V11() real ext-real Element of REAL
K599(S2,2) is V11() real ext-real Element of REAL
(1 / 2) * (S2 `2) is V11() real ext-real Element of REAL
((1 / 2) * (S2 `2)) + (- (1 / 2)) is V11() real ext-real Element of REAL
|[((1 * (S2 `1)) + 0),(((1 / 2) * (S2 `2)) + (- (1 / 2)))]| is Relation-like Function-like V39(2) FinSequence-like V195() Element of the carrier of (TOP-REAL 2)
((AffineMap (1,0,(1 / 2),(- (1 / 2)))) . S2) `1 is V11() real ext-real Element of REAL
K599(((AffineMap (1,0,(1 / 2),(- (1 / 2)))) . S2),1) is V11() real ext-real Element of REAL
- (S2 `1) is V11() real ext-real Element of REAL
2 * (- (S2 `1)) is V11() real ext-real Element of REAL
((AffineMap (1,0,(1 / 2),(- (1 / 2)))) . S2) `2 is V11() real ext-real Element of REAL
K599(((AffineMap (1,0,(1 / 2),(- (1 / 2)))) . S2),2) is V11() real ext-real Element of REAL
2 * (((AffineMap (1,0,(1 / 2),(- (1 / 2)))) . S2) `2) is V11() real ext-real Element of REAL
g is Relation-like Function-like V39(2) FinSequence-like V195() Element of the carrier of (TOP-REAL 2)
g `1 is V11() real ext-real Element of REAL
K599(g,1) is V11() real ext-real Element of REAL
- (g `1) is V11() real ext-real Element of REAL
g `2 is V11() real ext-real Element of REAL
K599(g,2) is V11() real ext-real Element of REAL
(2 * (- (S2 `1))) + 1 is V11() real ext-real Element of REAL
(2 * (((AffineMap (1,0,(1 / 2),(- (1 / 2)))) . S2) `2)) + 1 is V11() real ext-real Element of REAL
2 * (S2 `1) is V11() real ext-real Element of REAL
1 - (2 * (S2 `1)) is V11() real ext-real Element of REAL
{ b₁ where b₁ is Relation-like Function-like V39(2) FinSequence-like V195() Element of the carrier of (TOP-REAL 2) : b₁ `2 <= 1 - (2 * (b<sub>1</sub> `1)) } is set
Q is Element of bool the carrier of (TOP-REAL 2)
e2 is Element of bool the carrier of (TOP-REAL 2)
(AffineMap (1,0,(1 / 2),(- (1 / 2)))) .: Q is Element of bool the carrier of (TOP-REAL 2)
gg is set
dom (AffineMap (1,0,(1 / 2),(- (1 / 2)))) is non empty Element of bool the carrier of (TOP-REAL 2)
gg is set
(AffineMap (1,0,(1 / 2),(- (1 / 2)))) . gg is set
S2 is Relation-like Function-like V39(2) FinSequence-like V195() Element of the carrier of (TOP-REAL 2)
S2 `2 is V11() real ext-real Element of REAL
K599(S2,2) is V11() real ext-real Element of REAL
S2 `1 is V11() real ext-real Element of REAL
K599(S2,1) is V11() real ext-real Element of REAL
2 * (S2 `1) is V11() real ext-real Element of REAL
1 - (2 * (S2 `1)) is V11() real ext-real Element of REAL
(AffineMap (1,0,(1 / 2),(- (1 / 2)))) . S2 is Relation-like Function-like V39(2) FinSequence-like V195() Element of the carrier of (TOP-REAL 2)
(1 / 2) * (S2 `2) is V11() real ext-real Element of REAL
(1 / 2) * (1 - (2 * (S2 `1))) is V11() real ext-real Element of REAL
((1 / 2) * (S2 `2)) + (- (1 / 2)) is V11() real ext-real Element of REAL
(1 / 2) - (S2 `1) is V11() real ext-real Element of REAL
((1 / 2) - (S2 `1)) + (- (1 / 2)) is V11() real ext-real Element of REAL
1 * (S2 `1) is V11() real ext-real Element of REAL
(1 * (S2 `1)) + 0 is V11() real ext-real Element of REAL
|[((1 * (S2 `1)) + 0),(((1 / 2) * (S2 `2)) + (- (1 / 2)))]| is Relation-like Function-like V39(2) FinSequence-like V195() Element of the carrier of (TOP-REAL 2)
((AffineMap (1,0,(1 / 2),(- (1 / 2)))) . S2) `1 is V11() real ext-real Element of REAL
K599(((AffineMap (1,0,(1 / 2),(- (1 / 2)))) . S2),1) is V11() real ext-real Element of REAL
((AffineMap (1,0,(1 / 2),(- (1 / 2)))) . S2) `2 is V11() real ext-real Element of REAL
K599(((AffineMap (1,0,(1 / 2),(- (1 / 2)))) . S2),2) is V11() real ext-real Element of REAL
- (((AffineMap (1,0,(1 / 2),(- (1 / 2)))) . S2) `1) is V11() real ext-real Element of REAL
gg is set
rng (AffineMap (1,0,(1 / 2),(- (1 / 2)))) is non empty Element of bool the carrier of (TOP-REAL 2)
dom (AffineMap (1,0,(1 / 2),(- (1 / 2)))) is non empty Element of bool the carrier of (TOP-REAL 2)
gg is set
(AffineMap (1,0,(1 / 2),(- (1 / 2)))) . gg is set
S2 is Relation-like Function-like V39(2) FinSequence-like V195() Element of the carrier of (TOP-REAL 2)
(AffineMap (1,0,(1 / 2),(- (1 / 2)))) . S2 is Relation-like Function-like V39(2) FinSequence-like V195() Element of the carrier of (TOP-REAL 2)
S2 `1 is V11() real ext-real Element of REAL
K599(S2,1) is V11() real ext-real Element of REAL
1 * (S2 `1) is V11() real ext-real Element of REAL
(1 * (S2 `1)) + 0 is V11() real ext-real Element of REAL
S2 `2 is V11() real ext-real Element of REAL
K599(S2,2) is V11() real ext-real Element of REAL
(1 / 2) * (S2 `2) is V11() real ext-real Element of REAL
((1 / 2) * (S2 `2)) + (- (1 / 2)) is V11() real ext-real Element of REAL
|[((1 * (S2 `1)) + 0),(((1 / 2) * (S2 `2)) + (- (1 / 2)))]| is Relation-like Function-like V39(2) FinSequence-like V195() Element of the carrier of (TOP-REAL 2)
((AffineMap (1,0,(1 / 2),(- (1 / 2)))) . S2) `1 is V11() real ext-real Element of REAL
K599(((AffineMap (1,0,(1 / 2),(- (1 / 2)))) . S2),1) is V11() real ext-real Element of REAL
((AffineMap (1,0,(1 / 2),(- (1 / 2)))) . S2) `2 is V11() real ext-real Element of REAL
K599(((AffineMap (1,0,(1 / 2),(- (1 / 2)))) . S2),2) is V11() real ext-real Element of REAL
2 * (((AffineMap (1,0,(1 / 2),(- (1 / 2)))) . S2) `2) is V11() real ext-real Element of REAL
- (S2 `1) is V11() real ext-real Element of REAL
2 * (- (S2 `1)) is V11() real ext-real Element of REAL
g is Relation-like Function-like V39(2) FinSequence-like V195() Element of the carrier of (TOP-REAL 2)
g `2 is V11() real ext-real Element of REAL
K599(g,2) is V11() real ext-real Element of REAL
g `1 is V11() real ext-real Element of REAL
K599(g,1) is V11() real ext-real Element of REAL
- (g `1) is V11() real ext-real Element of REAL
(2 * (((AffineMap (1,0,(1 / 2),(- (1 / 2)))) . S2) `2)) + 1 is V11() real ext-real Element of REAL
(2 * (- (S2 `1))) + 1 is V11() real ext-real Element of REAL
2 * (S2 `1) is V11() real ext-real Element of REAL
1 - (2 * (S2 `1)) is V11() real ext-real Element of REAL
T is non empty 1-sorted
the carrier of T is non empty set
a is Element of the carrier of T
a is set
T is real-membered 1-sorted
the carrier of T is complex-membered ext-real-membered real-membered set
a is V11() real ext-real Element of the carrier of T
T is real-membered TopStruct
a is real-membered SubSpace of T
T is non empty TopSpace-like real-membered TopStruct
a is non empty TopSpace-like real-membered TopStruct
[:T,a:] is non empty strict TopSpace-like TopStruct
the carrier of [:T,a:] is non empty set
b is Element of the carrier of [:T,a:]
b `1 is set
the carrier of T is non empty complex-membered ext-real-membered real-membered set
the carrier of a is non empty complex-membered ext-real-membered real-membered set
[: the carrier of T, the carrier of a:] is non empty Relation-like set
b `2 is set
the carrier of T is non empty complex-membered ext-real-membered real-membered set
the carrier of a is non empty complex-membered ext-real-membered real-membered set
[: the carrier of T, the carrier of a:] is non empty Relation-like set
T is non empty TopSpace-like T_0 T_1 T_2 SubSpace of [:I[01],I[01]:]
the carrier of T is non empty set
a is Element of the carrier of T
a `1 is set
b is Element of the carrier of [:I[01],I[01]:]
b `1 is V11() real ext-real set
a `2 is set
b is Element of the carrier of [:I[01],I[01]:]
b `2 is V11() real ext-real set
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V39(2) FinSequence-like V195() Element of the carrier of (TOP-REAL 2) : S<sub>1</sub>[b<sub>1</sub>] } is set
b is Element of bool the carrier of (TOP-REAL 2)
dom (AffineMap (1,0,(1 / 2),(1 / 2))) is non empty Element of bool the carrier of (TOP-REAL 2)
(AffineMap (1,0,(1 / 2),(1 / 2))) .: b is Element of bool the carrier of (TOP-REAL 2)
T is closed Element of bool the carrier of (TOP-REAL 2)
(AffineMap (1,0,(1 / 2),(1 / 2))) " ((AffineMap (1,0,(1 / 2),(1 / 2))) .: b) is Element of bool the carrier of (TOP-REAL 2)
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V39(2) FinSequence-like V195() Element of the carrier of (TOP-REAL 2) : S<sub>1</sub>[b<sub>1</sub>] } is set
b is Element of bool the carrier of (TOP-REAL 2)
dom (AffineMap (1,0,(1 / 2),(1 / 2))) is non empty Element of bool the carrier of (TOP-REAL 2)
(AffineMap (1,0,(1 / 2),(1 / 2))) .: b is Element of bool the carrier of (TOP-REAL 2)
T is closed Element of bool the carrier of (TOP-REAL 2)
(AffineMap (1,0,(1 / 2),(1 / 2))) " ((AffineMap (1,0,(1 / 2),(1 / 2))) .: b) is Element of bool the carrier of (TOP-REAL 2)
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V39(2) FinSequence-like V195() Element of the carrier of (TOP-REAL 2) : S<sub>1</sub>[b<sub>1</sub>] } is set
b is Element of bool the carrier of (TOP-REAL 2)
dom (AffineMap (1,0,(1 / 2),(- (1 / 2)))) is non empty Element of bool the carrier of (TOP-REAL 2)
(AffineMap (1,0,(1 / 2),(- (1 / 2)))) .: b is Element of bool the carrier of (TOP-REAL 2)
T is closed Element of bool the carrier of (TOP-REAL 2)
(AffineMap (1,0,(1 / 2),(- (1 / 2)))) " ((AffineMap (1,0,(1 / 2),(- (1 / 2)))) .: b) is Element of bool the carrier of (TOP-REAL 2)
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V39(2) FinSequence-like V195() Element of the carrier of (TOP-REAL 2) : S<sub>1</sub>[b<sub>1</sub>] } is set
b is Element of bool the carrier of (TOP-REAL 2)
dom (AffineMap (1,0,(1 / 2),(- (1 / 2)))) is non empty Element of bool the carrier of (TOP-REAL 2)
(AffineMap (1,0,(1 / 2),(- (1 / 2)))) .: b is Element of bool the carrier of (TOP-REAL 2)
T is closed Element of bool the carrier of (TOP-REAL 2)
(AffineMap (1,0,(1 / 2),(- (1 / 2)))) " ((AffineMap (1,0,(1 / 2),(- (1 / 2)))) .: b) is Element of bool the carrier of (TOP-REAL 2)
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V39(2) FinSequence-like V195() Element of the carrier of (TOP-REAL 2) : ( 1 - (2 * (b<sub>1</sub> `1)) <= b₁ `2 & (2 * (b<sub>1</sub> `1)) - 1 <= b₁ `2 ) } is set
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V39(2) FinSequence-like V195() Element of the carrier of (TOP-REAL 2) : S<sub>1</sub>[b<sub>1</sub>] } is set
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V39(2) FinSequence-like V195() Element of the carrier of (TOP-REAL 2) : S<sub>2</sub>[b<sub>1</sub>] } is set
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V39(2) FinSequence-like V195() Element of the carrier of (TOP-REAL 2) : ( S<sub>2</sub>[b<sub>1</sub>] & S<sub>1</sub>[b<sub>1</sub>] ) } is set
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V39(2) FinSequence-like V195() Element of the carrier of (TOP-REAL 2) : S<sub>2</sub>[b<sub>1</sub>] } /\ { b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V39(2) FinSequence-like V195() Element of the carrier of (TOP-REAL 2) : S<sub>1</sub>[b<sub>1</sub>] } is set
a is closed Element of bool the carrier of (TOP-REAL 2)
T is closed Element of bool the carrier of (TOP-REAL 2)
a /\ T is closed Element of bool the carrier of (TOP-REAL 2)
REAL 2 is non empty FinSequence-membered FinSequenceSet of REAL
2 -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
T is V11() real ext-real Element of REAL
a is V11() real ext-real Element of REAL
<*T,a*> is set
[:NAT,REAL:] is Relation-like set
bool [:NAT,REAL:] is non empty set
[:[:REAL,REAL:],(REAL 2):] is non empty Relation-like set
bool [:[:REAL,REAL:],(REAL 2):] is non empty set
T is non empty Relation-like [:REAL,REAL:] -defined REAL 2 -valued Function-like V43([:REAL,REAL:]) quasi_total Element of bool [:[:REAL,REAL:],(REAL 2):]
[: the carrier of R^1, the carrier of R^1:] is non empty Relation-like set
a is non empty Relation-like the carrier of [:R^1,R^1:] -defined the carrier of (TOP-REAL 2) -valued Function-like V43( the carrier of [:R^1,R^1:]) quasi_total Element of bool [: the carrier of [:R^1,R^1:], the carrier of (TOP-REAL 2):]
b is V11() real ext-real Element of REAL
P is V11() real ext-real Element of REAL
[b,P] is non empty V29() set
{b,P} is non empty complex-membered ext-real-membered real-membered set
{b} is non empty trivial complex-membered ext-real-membered real-membered set
{{b,P},{b}} is non empty set
a . [b,P] is set
<*b,P*> is set
a . (b,P) is set
Q is Relation-like NAT -defined REAL -valued Function-like V39(2) FinSequence-like Element of REAL 2
b is V11() real ext-real Element of REAL
P is V11() real ext-real Element of REAL
[b,P] is non empty V29() set
{b,P} is non empty complex-membered ext-real-membered real-membered set
{b} is non empty trivial complex-membered ext-real-membered real-membered set
{{b,P},{b}} is non empty set
a . [b,P] is set
<*b,P*> is set
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier of [:R^1,R^1:] : b<sub>1</sub> `2 <= 1 - (2 * (b₁ `1)) } is set
bool the carrier of [:R^1,R^1:] is non empty set
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier of [:R^1,R^1:] : S<sub>1</sub>[b<sub>1</sub>] } is set
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V39(2) FinSequence-like V195() Element of the carrier of (TOP-REAL 2) : S<sub>2</sub>[b<sub>1</sub>] } is set
Q is non empty Relation-like the carrier of [:R^1,R^1:] -defined the carrier of (TOP-REAL 2) -valued Function-like V43( the carrier of [:R^1,R^1:]) quasi_total Element of bool [: the carrier of [:R^1,R^1:], the carrier of (TOP-REAL 2):]
Q is non empty Relation-like the carrier of [:R^1,R^1:] -defined the carrier of (TOP-REAL 2) -valued Function-like V43( the carrier of [:R^1,R^1:]) quasi_total Element of bool [: the carrier of [:R^1,R^1:], the carrier of (TOP-REAL 2):]
P is Element of bool the carrier of (TOP-REAL 2)
b is Element of bool the carrier of [:R^1,R^1:]
Q .: b is Element of bool the carrier of (TOP-REAL 2)
Q is set
e2 is Relation-like Function-like V39(2) FinSequence-like V195() Element of the carrier of (TOP-REAL 2)
e2 `2 is V11() real ext-real Element of REAL
K599(e2,2) is V11() real ext-real Element of REAL
e2 `1 is V11() real ext-real Element of REAL
K599(e2,1) is V11() real ext-real Element of REAL
2 * (e2 `1) is V11() real ext-real Element of REAL
1 - (2 * (e2 `1)) is V11() real ext-real Element of REAL
REAL 2 is non empty FinSequence-membered FinSequenceSet of REAL
2 -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
gg is V11() real ext-real Element of REAL
gg is V11() real ext-real Element of REAL
<*gg,gg*> is set
2 * gg is V11() real ext-real Element of REAL
1 - (2 * gg) is V11() real ext-real Element of REAL
[gg,gg] is non empty V29() set
{gg,gg} is non empty complex-membered ext-real-membered real-membered set
{gg} is non empty trivial complex-membered ext-real-membered real-membered set
{{gg,gg},{gg}} is non empty set
g is Element of the carrier of [:R^1,R^1:]
dom Q is non empty Element of bool the carrier of [:R^1,R^1:]
g `1 is V11() real ext-real set
g `2 is V11() real ext-real set
Q . g is Relation-like Function-like V39(2) FinSequence-like V195() Element of the carrier of (TOP-REAL 2)
Q is set
dom Q is non empty Element of bool the carrier of [:R^1,R^1:]
e2 is set
Q . e2 is set
gg is Element of the carrier of [:R^1,R^1:]
gg `2 is V11() real ext-real set
gg `1 is V11() real ext-real set
2 * (gg `1) is V11() real ext-real Element of REAL
1 - (2 * (gg `1)) is V11() real ext-real Element of REAL
[: the carrier of R^1, the carrier of R^1:] is non empty Relation-like set
gg is set
S2 is set
[gg,S2] is non empty V29() set
{gg,S2} is non empty set
{gg} is non empty trivial set
{{gg,S2},{gg}} is non empty set
g is V11() real ext-real Element of REAL
g is V11() real ext-real Element of REAL
|[g,g]| is Relation-like Function-like V39(2) FinSequence-like V195() Element of the carrier of (TOP-REAL 2)
S3 is Relation-like Function-like V39(2) FinSequence-like V195() Element of the carrier of (TOP-REAL 2)
S3 `1 is V11() real ext-real Element of REAL
K599(S3,1) is V11() real ext-real Element of REAL
S3 `2 is V11() real ext-real Element of REAL
K599(S3,2) is V11() real ext-real Element of REAL
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier of [:R^1,R^1:] : b<sub>1</sub> `2 <= (2 * (b₁ `1)) - 1 } is set
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier of [:R^1,R^1:] : S<sub>1</sub>[b<sub>1</sub>] } is set
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V39(2) FinSequence-like V195() Element of the carrier of (TOP-REAL 2) : S<sub>2</sub>[b<sub>1</sub>] } is set
Q is non empty Relation-like the carrier of [:R^1,R^1:] -defined the carrier of (TOP-REAL 2) -valued Function-like V43( the carrier of [:R^1,R^1:]) quasi_total Element of bool [: the carrier of [:R^1,R^1:], the carrier of (TOP-REAL 2):]
Q is non empty Relation-like the carrier of [:R^1,R^1:] -defined the carrier of (TOP-REAL 2) -valued Function-like V43( the carrier of [:R^1,R^1:]) quasi_total Element of bool [: the carrier of [:R^1,R^1:], the carrier of (TOP-REAL 2):]
P is Element of bool the carrier of (TOP-REAL 2)
b is Element of bool the carrier of [:R^1,R^1:]
Q .: b is Element of bool the carrier of (TOP-REAL 2)
Q is set
e2 is Relation-like Function-like V39(2) FinSequence-like V195() Element of the carrier of (TOP-REAL 2)
e2 `2 is V11() real ext-real Element of REAL
K599(e2,2) is V11() real ext-real Element of REAL
e2 `1 is V11() real ext-real Element of REAL
K599(e2,1) is V11() real ext-real Element of REAL
2 * (e2 `1) is V11() real ext-real Element of REAL
(2 * (e2 `1)) - 1 is V11() real ext-real Element of REAL
REAL 2 is non empty FinSequence-membered FinSequenceSet of REAL
2 -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
gg is V11() real ext-real Element of REAL
gg is V11() real ext-real Element of REAL
<*gg,gg*> is set
2 * gg is V11() real ext-real Element of REAL
(2 * gg) - 1 is V11() real ext-real Element of REAL
[gg,gg] is non empty V29() set
{gg,gg} is non empty complex-membered ext-real-membered real-membered set
{gg} is non empty trivial complex-membered ext-real-membered real-membered set
{{gg,gg},{gg}} is non empty set
[: the carrier of R^1, the carrier of R^1:] is non empty Relation-like set
g is Element of the carrier of [:R^1,R^1:]
dom Q is non empty Element of bool the carrier of [:R^1,R^1:]
g `1 is V11() real ext-real set
g `2 is V11() real ext-real set
Q . g is Relation-like Function-like V39(2) FinSequence-like V195() Element of the carrier of (TOP-REAL 2)
Q is set
dom Q is non empty Element of bool the carrier of [:R^1,R^1:]
e2 is set
Q . e2 is set
gg is Element of the carrier of [:R^1,R^1:]
gg `2 is V11() real ext-real set
gg `1 is V11() real ext-real set
2 * (gg `1) is V11() real ext-real Element of REAL
(2 * (gg `1)) - 1 is V11() real ext-real Element of REAL
[: the carrier of R^1, the carrier of R^1:] is non empty Relation-like set
gg is set
S2 is set
[gg,S2] is non empty V29() set
{gg,S2} is non empty set
{gg} is non empty trivial set
{{gg,S2},{gg}} is non empty set
g is V11() real ext-real Element of REAL
g is V11() real ext-real Element of REAL
|[g,g]| is Relation-like Function-like V39(2) FinSequence-like V195() Element of the carrier of (TOP-REAL 2)
S3 is Relation-like Function-like V39(2) FinSequence-like V195() Element of the carrier of (TOP-REAL 2)
S3 `1 is V11() real ext-real Element of REAL
K599(S3,1) is V11() real ext-real Element of REAL
S3 `2 is V11() real ext-real Element of REAL
K599(S3,2) is V11() real ext-real Element of REAL
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier of [:R^1,R^1:] : ( 1 - (2 * (b<sub>1</sub> `1)) <= b₁ `2 & (2 * (b<sub>1</sub> `1)) - 1 <= b₁ `2 ) } is set
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier of [:R^1,R^1:] : S<sub>1</sub>[b<sub>1</sub>] } is set
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V39(2) FinSequence-like V195() Element of the carrier of (TOP-REAL 2) : S<sub>2</sub>[b<sub>1</sub>] } is set
Q is non empty Relation-like the carrier of [:R^1,R^1:] -defined the carrier of (TOP-REAL 2) -valued Function-like V43( the carrier of [:R^1,R^1:]) quasi_total Element of bool [: the carrier of [:R^1,R^1:], the carrier of (TOP-REAL 2):]
Q is non empty Relation-like the carrier of [:R^1,R^1:] -defined the carrier of (TOP-REAL 2) -valued Function-like V43( the carrier of [:R^1,R^1:]) quasi_total Element of bool [: the carrier of [:R^1,R^1:], the carrier of (TOP-REAL 2):]
P is Element of bool the carrier of (TOP-REAL 2)
b is Element of bool the carrier of [:R^1,R^1:]
Q .: b is Element of bool the carrier of (TOP-REAL 2)
Q is set
e2 is Relation-like Function-like V39(2) FinSequence-like V195() Element of the carrier of (TOP-REAL 2)
e2 `1 is V11() real ext-real Element of REAL
K599(e2,1) is V11() real ext-real Element of REAL
2 * (e2 `1) is V11() real ext-real Element of REAL
1 - (2 * (e2 `1)) is V11() real ext-real Element of REAL
e2 `2 is V11() real ext-real Element of REAL
K599(e2,2) is V11() real ext-real Element of REAL
(2 * (e2 `1)) - 1 is V11() real ext-real Element of REAL
REAL 2 is non empty FinSequence-membered FinSequenceSet of REAL
2 -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
gg is V11() real ext-real Element of REAL
gg is V11() real ext-real Element of REAL
<*gg,gg*> is set
2 * gg is V11() real ext-real Element of REAL
1 - (2 * gg) is V11() real ext-real Element of REAL
(2 * gg) - 1 is V11() real ext-real Element of REAL
[gg,gg] is non empty V29() set
{gg,gg} is non empty complex-membered ext-real-membered real-membered set
{gg} is non empty trivial complex-membered ext-real-membered real-membered set
{{gg,gg},{gg}} is non empty set
[: the carrier of R^1, the carrier of R^1:] is non empty Relation-like set
g is Element of the carrier of [:R^1,R^1:]
dom Q is non empty Element of bool the carrier of [:R^1,R^1:]
g `1 is V11() real ext-real set
g `2 is V11() real ext-real set
Q . g is Relation-like Function-like V39(2) FinSequence-like V195() Element of the carrier of (TOP-REAL 2)
Q is set
dom Q is non empty Element of bool the carrier of [:R^1,R^1:]
e2 is set
Q . e2 is set
gg is Element of the carrier of [:R^1,R^1:]
gg `1 is V11() real ext-real set
2 * (gg `1) is V11() real ext-real Element of REAL
1 - (2 * (gg `1)) is V11() real ext-real Element of REAL
gg `2 is V11() real ext-real set
(2 * (gg `1)) - 1 is V11() real ext-real Element of REAL
[: the carrier of R^1, the carrier of R^1:] is non empty Relation-like set
gg is set
S2 is set
[gg,S2] is non empty V29() set
{gg,S2} is non empty set
{gg} is non empty trivial set
{{gg,S2},{gg}} is non empty set
g is V11() real ext-real Element of REAL
g is V11() real ext-real Element of REAL
|[g,g]| is Relation-like Function-like V39(2) FinSequence-like V195() Element of the carrier of (TOP-REAL 2)
S3 is Relation-like Function-like V39(2) FinSequence-like V195() Element of the carrier of (TOP-REAL 2)
S3 `1 is V11() real ext-real Element of REAL
K599(S3,1) is V11() real ext-real Element of REAL
S3 `2 is V11() real ext-real Element of REAL
K599(S3,2) is V11() real ext-real Element of REAL
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier of [:I[01],I[01]:] : b<sub>1</sub> `2 <= 1 - (2 * (b₁ `1)) } is set
[0,0] is non empty V29() set
{0,0} is non empty complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered set
{0} is non empty trivial complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered set
{{0,0},{0}} is non empty set
P is closed Element of bool the carrier of [:R^1,R^1:]
[#] [:I[01],I[01]:] is non empty non proper open closed Element of bool the carrier of [:I[01],I[01]:]
P /\ ([#] [:I[01],I[01]:]) is Element of bool the carrier of [:I[01],I[01]:]
Q is set
e2 is Element of the carrier of [:I[01],I[01]:]
e2 `2 is V11() real ext-real set
e2 `1 is V11() real ext-real set
2 * (e2 `1) is V11() real ext-real Element of REAL
1 - (2 * (e2 `1)) is V11() real ext-real Element of REAL
e2 is Element of the carrier of [:R^1,R^1:]
e2 `2 is V11() real ext-real set
e2 `1 is V11() real ext-real set
2 * (e2 `1) is V11() real ext-real Element of REAL
1 - (2 * (e2 `1)) is V11() real ext-real Element of REAL
gg is Element of the carrier of [:I[01],I[01]:]
gg `2 is V11() real ext-real set
gg `1 is V11() real ext-real set
2 * (gg `1) is V11() real ext-real Element of REAL
1 - (2 * (gg `1)) is V11() real ext-real Element of REAL
gg is Element of the carrier of [:I[01],I[01]:]
gg `2 is V11() real ext-real set
gg `1 is V11() real ext-real set
2 * (gg `1) is V11() real ext-real Element of REAL
1 - (2 * (gg `1)) is V11() real ext-real Element of REAL
Q is set
e2 is Element of the carrier of [:R^1,R^1:]
e2 `2 is V11() real ext-real set
e2 `1 is V11() real ext-real set
2 * (e2 `1) is V11() real ext-real Element of REAL
1 - (2 * (e2 `1)) is V11() real ext-real Element of REAL
b is Element of the carrier of [:I[01],I[01]:]
b `1 is V11() real ext-real set
b `2 is V11() real ext-real set
2 * (b `1) is V11() real ext-real Element of REAL
1 - (2 * (b `1)) is V11() real ext-real Element of REAL
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier of [:I[01],I[01]:] : ( 1 - (2 * (b<sub>1</sub> `1)) <= b₁ `2 & (2 * (b<sub>1</sub> `1)) - 1 <= b₁ `2 ) } is set
[1,1] is non empty V29() set
{1,1} is non empty complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered set
{1} is non empty trivial complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered set
{{1,1},{1}} is non empty set
b is Element of the carrier of [:I[01],I[01]:]
b `1 is V11() real ext-real set
2 * (b `1) is V11() real ext-real Element of REAL
(2 * (b `1)) - 1 is V11() real ext-real Element of REAL
b `2 is V11() real ext-real set
P is closed Element of bool the carrier of [:R^1,R^1:]
[#] [:I[01],I[01]:] is non empty non proper open closed Element of bool the carrier of [:I[01],I[01]:]
P /\ ([#] [:I[01],I[01]:]) is Element of bool the carrier of [:I[01],I[01]:]
Q is set
e2 is Element of the carrier of [:I[01],I[01]:]
e2 `1 is V11() real ext-real set
2 * (e2 `1) is V11() real ext-real Element of REAL
1 - (2 * (e2 `1)) is V11() real ext-real Element of REAL
e2 `2 is V11() real ext-real set
(2 * (e2 `1)) - 1 is V11() real ext-real Element of REAL
e2 is Element of the carrier of [:R^1,R^1:]
e2 `1 is V11() real ext-real set
2 * (e2 `1) is V11() real ext-real Element of REAL
1 - (2 * (e2 `1)) is V11() real ext-real Element of REAL
e2 `2 is V11() real ext-real set
gg is Element of the carrier of [:I[01],I[01]:]
gg `1 is V11() real ext-real set
2 * (gg `1) is V11() real ext-real Element of REAL
1 - (2 * (gg `1)) is V11() real ext-real Element of REAL
gg `2 is V11() real ext-real set
(2 * (gg `1)) - 1 is V11() real ext-real Element of REAL
gg is Element of the carrier of [:I[01],I[01]:]
gg `1 is V11() real ext-real set
2 * (gg `1) is V11() real ext-real Element of REAL
1 - (2 * (gg `1)) is V11() real ext-real Element of REAL
gg `2 is V11() real ext-real set
(2 * (gg `1)) - 1 is V11() real ext-real Element of REAL
gg is Element of the carrier of [:I[01],I[01]:]
gg `1 is V11() real ext-real set
2 * (gg `1) is V11() real ext-real Element of REAL
1 - (2 * (gg `1)) is V11() real ext-real Element of REAL
gg `2 is V11() real ext-real set
(2 * (gg `1)) - 1 is V11() real ext-real Element of REAL
Q is set
e2 is Element of the carrier of [:R^1,R^1:]
e2 `1 is V11() real ext-real set
2 * (e2 `1) is V11() real ext-real Element of REAL
1 - (2 * (e2 `1)) is V11() real ext-real Element of REAL
e2 `2 is V11() real ext-real set
(2 * (e2 `1)) - 1 is V11() real ext-real Element of REAL
1 - (2 * (b `1)) is V11() real ext-real Element of REAL
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier of [:I[01],I[01]:] : b<sub>1</sub> `2 <= (2 * (b₁ `1)) - 1 } is set
[1,0] is non empty V29() set
{1,0} is non empty complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered set
{1} is non empty trivial complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered set
{{1,0},{1}} is non empty set
P is closed Element of bool the carrier of [:R^1,R^1:]
[#] [:I[01],I[01]:] is non empty non proper open closed Element of bool the carrier of [:I[01],I[01]:]
P /\ ([#] [:I[01],I[01]:]) is Element of bool the carrier of [:I[01],I[01]:]
Q is set
e2 is Element of the carrier of [:I[01],I[01]:]
e2 `2 is V11() real ext-real set
e2 `1 is V11() real ext-real set
2 * (e2 `1) is V11() real ext-real Element of REAL
(2 * (e2 `1)) - 1 is V11() real ext-real Element of REAL
e2 is Element of the carrier of [:R^1,R^1:]
e2 `2 is V11() real ext-real set
e2 `1 is V11() real ext-real set
2 * (e2 `1) is V11() real ext-real Element of REAL
(2 * (e2 `1)) - 1 is V11() real ext-real Element of REAL
gg is Element of the carrier of [:I[01],I[01]:]
gg `2 is V11() real ext-real set
gg `1 is V11() real ext-real set
2 * (gg `1) is V11() real ext-real Element of REAL
(2 * (gg `1)) - 1 is V11() real ext-real Element of REAL
gg is Element of the carrier of [:I[01],I[01]:]
gg `2 is V11() real ext-real set
gg `1 is V11() real ext-real set
2 * (gg `1) is V11() real ext-real Element of REAL
(2 * (gg `1)) - 1 is V11() real ext-real Element of REAL
Q is set
e2 is Element of the carrier of [:R^1,R^1:]
e2 `2 is V11() real ext-real set
e2 `1 is V11() real ext-real set
2 * (e2 `1) is V11() real ext-real Element of REAL
(2 * (e2 `1)) - 1 is V11() real ext-real Element of REAL
b is Element of the carrier of [:I[01],I[01]:]
b `1 is V11() real ext-real set
b `2 is V11() real ext-real set
2 * (b `1) is V11() real ext-real Element of REAL
(2 * (b `1)) - 1 is V11() real ext-real Element of REAL
T is non empty TopSpace-like TopStruct
a is non empty TopSpace-like TopStruct
[:T,a:] is non empty strict TopSpace-like TopStruct
the carrier of [:T,a:] is non empty set
the carrier of T is non empty set
the carrier of a is non empty set
b is Element of the carrier of [:T,a:]
b `1 is set
b `2 is set
[: the carrier of T, the carrier of a:] is non empty Relation-like set
[.0,(1 / 2).] is complex-membered ext-real-membered real-membered Element of bool REAL
[:[.0,(1 / 2).],[.0,1.]:] is Relation-like REAL -defined REAL -valued Element of bool [:REAL,REAL:]
[.(1 / 2),1.] is complex-membered ext-real-membered real-membered Element of bool REAL
[:[.(1 / 2),1.],[.0,1.]:] is Relation-like REAL -defined REAL -valued Element of bool [:REAL,REAL:]
[#] [:I[01],I[01]:] is non empty non proper open closed Element of bool the carrier of [:I[01],I[01]:]
T is Element of bool the carrier of [:I[01],I[01]:]
a is Element of bool the carrier of [:I[01],I[01]:]
[:I[01],I[01]:] | T is strict TopSpace-like T_0 T_1 T_2 SubSpace of [:I[01],I[01]:]
[#] ([:I[01],I[01]:] | T) is non proper open closed Element of bool the carrier of ([:I[01],I[01]:] | T)
the carrier of ([:I[01],I[01]:] | T) is set
bool the carrier of ([:I[01],I[01]:] | T) is non empty set
[:I[01],I[01]:] | a is strict TopSpace-like T_0 T_1 T_2 SubSpace of [:I[01],I[01]:]
[#] ([:I[01],I[01]:] | a) is non proper open closed Element of bool the carrier of ([:I[01],I[01]:] | a)
the carrier of ([:I[01],I[01]:] | a) is set
bool the carrier of ([:I[01],I[01]:] | a) is non empty set
([#] ([:I[01],I[01]:] | T)) \/ ([#] ([:I[01],I[01]:] | a)) is set
T \/ ([#] ([:I[01],I[01]:] | a)) is set
T \/ a is Element of bool the carrier of [:I[01],I[01]:]
[.0,(1 / 2).] \/ [.(1 / 2),1.] is complex-membered ext-real-membered real-membered Element of bool REAL
[:([.0,(1 / 2).] \/ [.(1 / 2),1.]),[.0,1.]:] is Relation-like REAL -defined REAL -valued Element of bool [:REAL,REAL:]
{(1 / 2)} is non empty trivial complex-membered ext-real-membered real-membered set
[:{(1 / 2)},[.0,1.]:] is Relation-like set
T is Element of bool the carrier of [:I[01],I[01]:]
a is Element of bool the carrier of [:I[01],I[01]:]
[:I[01],I[01]:] | a is strict TopSpace-like T_0 T_1 T_2 SubSpace of [:I[01],I[01]:]
the carrier of ([:I[01],I[01]:] | a) is set
[:I[01],I[01]:] | T is strict TopSpace-like T_0 T_1 T_2 SubSpace of [:I[01],I[01]:]
[#] ([:I[01],I[01]:] | T) is non proper open closed Element of bool the carrier of ([:I[01],I[01]:] | T)
the carrier of ([:I[01],I[01]:] | T) is set
bool the carrier of ([:I[01],I[01]:] | T) is non empty set
[#] ([:I[01],I[01]:] | a) is non proper open closed Element of bool the carrier of ([:I[01],I[01]:] | a)
bool the carrier of ([:I[01],I[01]:] | a) is non empty set
([#] ([:I[01],I[01]:] | T)) /\ ([#] ([:I[01],I[01]:] | a)) is Element of bool the carrier of ([:I[01],I[01]:] | a)
T /\ ([#] ([:I[01],I[01]:] | a)) is Element of bool the carrier of ([:I[01],I[01]:] | a)
T /\ a is Element of bool the carrier of [:I[01],I[01]:]
[.0,(1 / 2).] /\ [.(1 / 2),1.] is complex-membered ext-real-membered real-membered Element of bool REAL
[:([.0,(1 / 2).] /\ [.(1 / 2),1.]),[.0,1.]:] is Relation-like REAL -defined REAL -valued Element of bool [:REAL,REAL:]
T is TopStruct
the carrier of T is set
bool the carrier of T is non empty set
{} T is empty trivial Relation-like non-empty empty-yielding compact complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V209() Element of bool the carrier of T
T is TopStruct
the carrier of T is set
bool the carrier of T is non empty set
{} T is empty trivial Relation-like non-empty empty-yielding compact complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V209() Element of bool the carrier of T
T is TopStruct
the carrier of T is set
bool the carrier of T is non empty set
a is V11() real ext-real set
b is V11() real ext-real set
[.a,b.] is complex-membered ext-real-membered real-membered Element of bool REAL
{} T is empty trivial Relation-like non-empty empty-yielding compact complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V209() Element of bool the carrier of T
T is V11() real ext-real Element of the carrier of I[01]
a is V11() real ext-real Element of the carrier of I[01]
[.T,a.] is complex-membered ext-real-membered real-membered Element of bool REAL
b is V11() real ext-real Element of the carrier of I[01]
P is V11() real ext-real Element of the carrier of I[01]
[.b,P.] is complex-membered ext-real-membered real-membered Element of bool REAL
[:[.T,a.],[.b,P.]:] is Relation-like REAL -defined REAL -valued Element of bool [:REAL,REAL:]
Q is empty trivial proper Relation-like non-empty empty-yielding open closed compact complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V209() Element of bool the carrier of I[01]
[:Q,[.b,P.]:] is empty trivial proper Relation-like non-empty empty-yielding the carrier of I[01] -defined REAL -valued complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V209() Element of bool [: the carrier of I[01],REAL:]
[: the carrier of I[01],REAL:] is non empty Relation-like set
bool [: the carrier of I[01],REAL:] is non empty set
Q is empty trivial proper Relation-like non-empty empty-yielding open closed compact complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V209() Element of bool the carrier of I[01]
[:[.T,a.],Q:] is empty trivial proper Relation-like non-empty empty-yielding REAL -defined the carrier of I[01] -valued complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V209() Element of bool [:REAL, the carrier of I[01]:]
[:REAL, the carrier of I[01]:] is non empty Relation-like set
bool [:REAL, the carrier of I[01]:] is non empty set
Q is empty trivial proper Relation-like non-empty empty-yielding open closed compact complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V209() Element of bool the carrier of I[01]
[:[.T,a.],Q:] is empty trivial proper Relation-like non-empty empty-yielding REAL -defined the carrier of I[01] -valued complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V209() Element of bool [:REAL, the carrier of I[01]:]
[:REAL, the carrier of I[01]:] is non empty Relation-like set
bool [:REAL, the carrier of I[01]:] is non empty set
T is V11() real ext-real set
a is V11() real ext-real set
Closed-Interval-TSpace (T,a) is non empty strict TopSpace-like real-membered SubSpace of R^1
the carrier of (Closed-Interval-TSpace (T,a)) is non empty complex-membered ext-real-membered real-membered set
b is V11() real ext-real set
P is V11() real ext-real set
Closed-Interval-TSpace (b,P) is non empty strict TopSpace-like real-membered SubSpace of R^1
the carrier of (Closed-Interval-TSpace (b,P)) is non empty complex-membered ext-real-membered real-membered set
P[01] (T,a,((#) (0,1)),((0,1) (#))) is non empty Relation-like the carrier of (Closed-Interval-TSpace (T,a)) -defined the carrier of (Closed-Interval-TSpace (0,1)) -valued Function-like V43( the carrier of (Closed-Interval-TSpace (T,a))) quasi_total Element of bool [: the carrier of (Closed-Interval-TSpace (T,a)), the carrier of (Closed-Interval-TSpace (0,1)):]
[: the carrier of (Closed-Interval-TSpace (T,a)), the carrier of (Closed-Interval-TSpace (0,1)):] is non empty Relation-like set
bool [: the carrier of (Closed-Interval-TSpace (T,a)), the carrier of (Closed-Interval-TSpace (0,1)):] is non empty set
(#) (b,P) is V11() real ext-real Element of the carrier of (Closed-Interval-TSpace (b,P))
(b,P) (#) is V11() real ext-real Element of the carrier of (Closed-Interval-TSpace (b,P))
L[01] (((#) (b,P)),((b,P) (#))) is non empty Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined the carrier of (Closed-Interval-TSpace (b,P)) -valued Function-like V43( the carrier of (Closed-Interval-TSpace (0,1))) quasi_total Element of bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace (b,P)):]
[: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace (b,P)):] is non empty Relation-like set
bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace (b,P)):] is non empty set
(L[01] (((#) (b,P)),((b,P) (#)))) * (P[01] (T,a,((#) (0,1)),((0,1) (#)))) is non empty Relation-like the carrier of (Closed-Interval-TSpace (T,a)) -defined the carrier of (Closed-Interval-TSpace (b,P)) -valued Function-like V43( the carrier of (Closed-Interval-TSpace (T,a))) quasi_total Element of bool [: the carrier of (Closed-Interval-TSpace (T,a)), the carrier of (Closed-Interval-TSpace (b,P)):]
[: the carrier of (Closed-Interval-TSpace (T,a)), the carrier of (Closed-Interval-TSpace (b,P)):] is non empty Relation-like set
bool [: the carrier of (Closed-Interval-TSpace (T,a)), the carrier of (Closed-Interval-TSpace (b,P)):] is non empty set
a is V11() real ext-real set
T is V11() real ext-real set
P is V11() real ext-real set
b is V11() real ext-real set
(T,a,b,P) is non empty Relation-like the carrier of (Closed-Interval-TSpace (T,a)) -defined the carrier of (Closed-Interval-TSpace (b,P)) -valued Function-like V43( the carrier of (Closed-Interval-TSpace (T,a))) quasi_total Element of bool [: the carrier of (Closed-Interval-TSpace (T,a)), the carrier of (Closed-Interval-TSpace (b,P)):]
Closed-Interval-TSpace (T,a) is non empty strict TopSpace-like real-membered SubSpace of R^1
the carrier of (Closed-Interval-TSpace (T,a)) is non empty complex-membered ext-real-membered real-membered set
Closed-Interval-TSpace (b,P) is non empty strict TopSpace-like real-membered SubSpace of R^1
the carrier of (Closed-Interval-TSpace (b,P)) is non empty complex-membered ext-real-membered real-membered set
[: the carrier of (Closed-Interval-TSpace (T,a)), the carrier of (Closed-Interval-TSpace (b,P)):] is non empty Relation-like set
bool [: the carrier of (Closed-Interval-TSpace (T,a)), the carrier of (Closed-Interval-TSpace (b,P)):] is non empty set
P[01] (T,a,((#) (0,1)),((0,1) (#))) is non empty Relation-like the carrier of (Closed-Interval-TSpace (T,a)) -defined the carrier of (Closed-Interval-TSpace (0,1)) -valued Function-like V43( the carrier of (Closed-Interval-TSpace (T,a))) quasi_total Element of bool [: the carrier of (Closed-Interval-TSpace (T,a)), the carrier of (Closed-Interval-TSpace (0,1)):]
[: the carrier of (Closed-Interval-TSpace (T,a)), the carrier of (Closed-Interval-TSpace (0,1)):] is non empty Relation-like set
bool [: the carrier of (Closed-Interval-TSpace (T,a)), the carrier of (Closed-Interval-TSpace (0,1)):] is non empty set
(#) (b,P) is V11() real ext-real Element of the carrier of (Closed-Interval-TSpace (b,P))
(b,P) (#) is V11() real ext-real Element of the carrier of (Closed-Interval-TSpace (b,P))
L[01] (((#) (b,P)),((b,P) (#))) is non empty Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined the carrier of (Closed-Interval-TSpace (b,P)) -valued Function-like V43( the carrier of (Closed-Interval-TSpace (0,1))) quasi_total Element of bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace (b,P)):]
[: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace (b,P)):] is non empty Relation-like set
bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace (b,P)):] is non empty set
(L[01] (((#) (b,P)),((b,P) (#)))) * (P[01] (T,a,((#) (0,1)),((0,1) (#)))) is non empty Relation-like the carrier of (Closed-Interval-TSpace (T,a)) -defined the carrier of (Closed-Interval-TSpace (b,P)) -valued Function-like V43( the carrier of (Closed-Interval-TSpace (T,a))) quasi_total Element of bool [: the carrier of (Closed-Interval-TSpace (T,a)), the carrier of (Closed-Interval-TSpace (b,P)):]
(T,a,b,P) . T is set
(T,a,b,P) . a is set
[.T,a.] is complex-membered ext-real-membered real-membered Element of bool REAL
dom (P[01] (T,a,((#) (0,1)),((0,1) (#)))) is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of (Closed-Interval-TSpace (T,a))
bool the carrier of (Closed-Interval-TSpace (T,a)) is non empty set
(P[01] (T,a,((#) (0,1)),((0,1) (#)))) . T is set
(L[01] (((#) (b,P)),((b,P) (#)))) . ((P[01] (T,a,((#) (0,1)),((0,1) (#)))) . T) is set
(#) (T,a) is V11() real ext-real Element of the carrier of (Closed-Interval-TSpace (T,a))
(P[01] (T,a,((#) (0,1)),((0,1) (#)))) . ((#) (T,a)) is V11() real ext-real Element of the carrier of (Closed-Interval-TSpace (0,1))
(L[01] (((#) (b,P)),((b,P) (#)))) . ((P[01] (T,a,((#) (0,1)),((0,1) (#)))) . ((#) (T,a))) is V11() real ext-real Element of the carrier of (Closed-Interval-TSpace (b,P))
(L[01] (((#) (b,P)),((b,P) (#)))) . ((#) (0,1)) is V11() real ext-real Element of the carrier of (Closed-Interval-TSpace (b,P))
(P[01] (T,a,((#) (0,1)),((0,1) (#)))) . a is set
(L[01] (((#) (b,P)),((b,P) (#)))) . ((P[01] (T,a,((#) (0,1)),((0,1) (#)))) . a) is set
(T,a) (#) is V11() real ext-real Element of the carrier of (Closed-Interval-TSpace (T,a))
(P[01] (T,a,((#) (0,1)),((0,1) (#)))) . ((T,a) (#)) is V11() real ext-real Element of the carrier of (Closed-Interval-TSpace (0,1))
(L[01] (((#) (b,P)),((b,P) (#)))) . ((P[01] (T,a,((#) (0,1)),((0,1) (#)))) . ((T,a) (#))) is V11() real ext-real Element of the carrier of (Closed-Interval-TSpace (b,P))
(L[01] (((#) (b,P)),((b,P) (#)))) . ((0,1) (#)) is V11() real ext-real Element of the carrier of (Closed-Interval-TSpace (b,P))
a is V11() real ext-real set
T is V11() real ext-real set
b is V11() real ext-real set
P is V11() real ext-real set
(T,a,b,P) is non empty Relation-like the carrier of (Closed-Interval-TSpace (T,a)) -defined the carrier of (Closed-Interval-TSpace (b,P)) -valued Function-like V43( the carrier of (Closed-Interval-TSpace (T,a))) quasi_total Element of bool [: the carrier of (Closed-Interval-TSpace (T,a)), the carrier of (Closed-Interval-TSpace (b,P)):]
Closed-Interval-TSpace (T,a) is non empty strict TopSpace-like real-membered SubSpace of R^1
the carrier of (Closed-Interval-TSpace (T,a)) is non empty complex-membered ext-real-membered real-membered set
Closed-Interval-TSpace (b,P) is non empty strict TopSpace-like real-membered SubSpace of R^1
the carrier of (Closed-Interval-TSpace (b,P)) is non empty complex-membered ext-real-membered real-membered set
[: the carrier of (Closed-Interval-TSpace (T,a)), the carrier of (Closed-Interval-TSpace (b,P)):] is non empty Relation-like set
bool [: the carrier of (Closed-Interval-TSpace (T,a)), the carrier of (Closed-Interval-TSpace (b,P)):] is non empty set
P[01] (T,a,((#) (0,1)),((0,1) (#))) is non empty Relation-like the carrier of (Closed-Interval-TSpace (T,a)) -defined the carrier of (Closed-Interval-TSpace (0,1)) -valued Function-like V43( the carrier of (Closed-Interval-TSpace (T,a))) quasi_total Element of bool [: the carrier of (Closed-Interval-TSpace (T,a)), the carrier of (Closed-Interval-TSpace (0,1)):]
[: the carrier of (Closed-Interval-TSpace (T,a)), the carrier of (Closed-Interval-TSpace (0,1)):] is non empty Relation-like set
bool [: the carrier of (Closed-Interval-TSpace (T,a)), the carrier of (Closed-Interval-TSpace (0,1)):] is non empty set
(#) (b,P) is V11() real ext-real Element of the carrier of (Closed-Interval-TSpace (b,P))
(b,P) (#) is V11() real ext-real Element of the carrier of (Closed-Interval-TSpace (b,P))
L[01] (((#) (b,P)),((b,P) (#))) is non empty Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined the carrier of (Closed-Interval-TSpace (b,P)) -valued Function-like V43( the carrier of (Closed-Interval-TSpace (0,1))) quasi_total Element of bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace (b,P)):]
[: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace (b,P)):] is non empty Relation-like set
bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace (b,P)):] is non empty set
(L[01] (((#) (b,P)),((b,P) (#)))) * (P[01] (T,a,((#) (0,1)),((0,1) (#)))) is non empty Relation-like the carrier of (Closed-Interval-TSpace (T,a)) -defined the carrier of (Closed-Interval-TSpace (b,P)) -valued Function-like V43( the carrier of (Closed-Interval-TSpace (T,a))) quasi_total Element of bool [: the carrier of (Closed-Interval-TSpace (T,a)), the carrier of (Closed-Interval-TSpace (b,P)):]
a is V11() real ext-real set
T is V11() real ext-real set
b is V11() real ext-real set
P is V11() real ext-real set
(T,a,b,P) is non empty Relation-like the carrier of (Closed-Interval-TSpace (T,a)) -defined the carrier of (Closed-Interval-TSpace (b,P)) -valued Function-like V43( the carrier of (Closed-Interval-TSpace (T,a))) quasi_total Element of bool [: the carrier of (Closed-Interval-TSpace (T,a)), the carrier of (Closed-Interval-TSpace (b,P)):]
Closed-Interval-TSpace (T,a) is non empty strict TopSpace-like real-membered SubSpace of R^1
the carrier of (Closed-Interval-TSpace (T,a)) is non empty complex-membered ext-real-membered real-membered set
Closed-Interval-TSpace (b,P) is non empty strict TopSpace-like real-membered SubSpace of R^1
the carrier of (Closed-Interval-TSpace (b,P)) is non empty complex-membered ext-real-membered real-membered set
[: the carrier of (Closed-Interval-TSpace (T,a)), the carrier of (Closed-Interval-TSpace (b,P)):] is non empty Relation-like set
bool [: the carrier of (Closed-Interval-TSpace (T,a)), the carrier of (Closed-Interval-TSpace (b,P)):] is non empty set
P[01] (T,a,((#) (0,1)),((0,1) (#))) is non empty Relation-like the carrier of (Closed-Interval-TSpace (T,a)) -defined the carrier of (Closed-Interval-TSpace (0,1)) -valued Function-like V43( the carrier of (Closed-Interval-TSpace (T,a))) quasi_total Element of bool [: the carrier of (Closed-Interval-TSpace (T,a)), the carrier of (Closed-Interval-TSpace (0,1)):]
[: the carrier of (Closed-Interval-TSpace (T,a)), the carrier of (Closed-Interval-TSpace (0,1)):] is non empty Relation-like set
bool [: the carrier of (Closed-Interval-TSpace (T,a)), the carrier of (Closed-Interval-TSpace (0,1)):] is non empty set
(#) (b,P) is V11() real ext-real Element of the carrier of (Closed-Interval-TSpace (b,P))
(b,P) (#) is V11() real ext-real Element of the carrier of (Closed-Interval-TSpace (b,P))
L[01] (((#) (b,P)),((b,P) (#))) is non empty Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined the carrier of (Closed-Interval-TSpace (b,P)) -valued Function-like V43( the carrier of (Closed-Interval-TSpace (0,1))) quasi_total Element of bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace (b,P)):]
[: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace (b,P)):] is non empty Relation-like set
bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace (b,P)):] is non empty set
(L[01] (((#) (b,P)),((b,P) (#)))) * (P[01] (T,a,((#) (0,1)),((0,1) (#)))) is non empty Relation-like the carrier of (Closed-Interval-TSpace (T,a)) -defined the carrier of (Closed-Interval-TSpace (b,P)) -valued Function-like V43( the carrier of (Closed-Interval-TSpace (T,a))) quasi_total Element of bool [: the carrier of (Closed-Interval-TSpace (T,a)), the carrier of (Closed-Interval-TSpace (b,P)):]
P - b is V11() real ext-real set
a - T is V11() real ext-real set
(P - b) / (a - T) is V11() real ext-real set
gg is V11() real ext-real set
(T,a,b,P) . gg is set
gg - T is V11() real ext-real set
((P - b) / (a - T)) * (gg - T) is V11() real ext-real set
(((P - b) / (a - T)) * (gg - T)) + b is V11() real ext-real set
(gg - T) / (a - T) is V11() real ext-real set
[.T,a.] is complex-membered ext-real-membered real-membered Element of bool REAL
dom (P[01] (T,a,((#) (0,1)),((0,1) (#)))) is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of (Closed-Interval-TSpace (T,a))
bool the carrier of (Closed-Interval-TSpace (T,a)) is non empty set
(P[01] (T,a,((#) (0,1)),((0,1) (#)))) . gg is set
(L[01] (((#) (b,P)),((b,P) (#)))) . ((P[01] (T,a,((#) (0,1)),((0,1) (#)))) . gg) is set
a - gg is V11() real ext-real set
(a - gg) * 0 is V11() real ext-real Element of REAL
(gg - T) * 1 is V11() real ext-real Element of REAL
((a - gg) * 0) + ((gg - T) * 1) is V11() real ext-real Element of REAL
(((a - gg) * 0) + ((gg - T) * 1)) / (a - T) is V11() real ext-real Element of REAL
(L[01] (((#) (b,P)),((b,P) (#)))) . ((((a - gg) * 0) + ((gg - T) * 1)) / (a - T)) is set
1 - ((gg - T) / (a - T)) is V11() real ext-real Element of REAL
(1 - ((gg - T) / (a - T))) * b is V11() real ext-real Element of REAL
((gg - T) / (a - T)) * P is V11() real ext-real set
((1 - ((gg - T) / (a - T))) * b) + (((gg - T) / (a - T)) * P) is V11() real ext-real Element of REAL
[: the carrier of [:I[01],I[01]:], the carrier of I[01]:] is non empty Relation-like set
bool [: the carrier of [:I[01],I[01]:], the carrier of I[01]:] is non empty set
bool the carrier of R^1 is non empty set
b is non empty Relation-like the carrier of [:I[01],I[01]:] -defined the carrier of I[01] -valued Function-like V43( the carrier of [:I[01],I[01]:]) quasi_total Element of bool [: the carrier of [:I[01],I[01]:], the carrier of I[01]:]
P is non empty Relation-like the carrier of [:I[01],I[01]:] -defined the carrier of I[01] -valued Function-like V43( the carrier of [:I[01],I[01]:]) quasi_total Element of bool [: the carrier of [:I[01],I[01]:], the carrier of I[01]:]
[: the carrier of [:I[01],I[01]:], the carrier of R^1:] is non empty Relation-like set
bool [: the carrier of [:I[01],I[01]:], the carrier of R^1:] is non empty set
Q is non empty Relation-like the carrier of [:I[01],I[01]:] -defined the carrier of R^1 -valued Function-like V43( the carrier of [:I[01],I[01]:]) quasi_total Element of bool [: the carrier of [:I[01],I[01]:], the carrier of R^1:]
Q is non empty Relation-like the carrier of [:I[01],I[01]:] -defined the carrier of R^1 -valued Function-like V43( the carrier of [:I[01],I[01]:]) quasi_total Element of bool [: the carrier of [:I[01],I[01]:], the carrier of R^1:]
e2 is non empty Relation-like the carrier of [:I[01],I[01]:] -defined the carrier of R^1 -valued Function-like V43( the carrier of [:I[01],I[01]:]) quasi_total Element of bool [: the carrier of [:I[01],I[01]:], the carrier of R^1:]
rng e2 is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of R^1
gg is set
dom e2 is non empty Element of bool the carrier of [:I[01],I[01]:]
gg is set
e2 . gg is set
S2 is Element of the carrier of [:I[01],I[01]:]
e2 . S2 is V11() real ext-real Element of the carrier of R^1
b . S2 is V11() real ext-real Element of the carrier of I[01]
P . S2 is V11() real ext-real Element of the carrier of I[01]
(b . S2) * (P . S2) is V11() real ext-real set
T is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of R^1
R^1 | T is non empty strict TopSpace-like real-membered SubSpace of R^1
the carrier of (R^1 | T) is non empty complex-membered ext-real-membered real-membered set
dom e2 is non empty Element of bool the carrier of [:I[01],I[01]:]
[: the carrier of [:I[01],I[01]:], the carrier of (R^1 | T):] is non empty Relation-like set
bool [: the carrier of [:I[01],I[01]:], the carrier of (R^1 | T):] is non empty set
gg is non empty Relation-like the carrier of [:I[01],I[01]:] -defined the carrier of (R^1 | T) -valued Function-like V43( the carrier of [:I[01],I[01]:]) quasi_total Element of bool [: the carrier of [:I[01],I[01]:], the carrier of (R^1 | T):]
gg is non empty Relation-like the carrier of [:I[01],I[01]:] -defined the carrier of I[01] -valued Function-like V43( the carrier of [:I[01],I[01]:]) quasi_total continuous Element of bool [: the carrier of [:I[01],I[01]:], the carrier of I[01]:]
S2 is Element of the carrier of [:I[01],I[01]:]
b . S2 is V11() real ext-real Element of the carrier of I[01]
g is V11() real ext-real set
P . S2 is V11() real ext-real Element of the carrier of I[01]
g is V11() real ext-real set
gg . S2 is V11() real ext-real Element of the carrier of I[01]
g * g is V11() real ext-real set
bool the carrier of R^1 is non empty set
b is non empty Relation-like the carrier of [:I[01],I[01]:] -defined the carrier of I[01] -valued Function-like V43( the carrier of [:I[01],I[01]:]) quasi_total Element of bool [: the carrier of [:I[01],I[01]:], the carrier of I[01]:]
P is non empty Relation-like the carrier of [:I[01],I[01]:] -defined the carrier of I[01] -valued Function-like V43( the carrier of [:I[01],I[01]:]) quasi_total Element of bool [: the carrier of [:I[01],I[01]:], the carrier of I[01]:]
[: the carrier of [:I[01],I[01]:], the carrier of R^1:] is non empty Relation-like set
bool [: the carrier of [:I[01],I[01]:], the carrier of R^1:] is non empty set
Q is non empty Relation-like the carrier of [:I[01],I[01]:] -defined the carrier of R^1 -valued Function-like V43( the carrier of [:I[01],I[01]:]) quasi_total Element of bool [: the carrier of [:I[01],I[01]:], the carrier of R^1:]
Q is non empty Relation-like the carrier of [:I[01],I[01]:] -defined the carrier of R^1 -valued Function-like V43( the carrier of [:I[01],I[01]:]) quasi_total Element of bool [: the carrier of [:I[01],I[01]:], the carrier of R^1:]
e2 is non empty Relation-like the carrier of [:I[01],I[01]:] -defined the carrier of R^1 -valued Function-like V43( the carrier of [:I[01],I[01]:]) quasi_total Element of bool [: the carrier of [:I[01],I[01]:], the carrier of R^1:]
rng e2 is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of R^1
gg is set
dom e2 is non empty Element of bool the carrier of [:I[01],I[01]:]
gg is set
e2 . gg is set
S2 is Element of the carrier of [:I[01],I[01]:]
e2 . S2 is V11() real ext-real Element of the carrier of R^1
b . S2 is V11() real ext-real Element of the carrier of I[01]
P . S2 is V11() real ext-real Element of the carrier of I[01]
(b . S2) + (P . S2) is V11() real ext-real set
T is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of R^1
R^1 | T is non empty strict TopSpace-like real-membered SubSpace of R^1
the carrier of (R^1 | T) is non empty complex-membered ext-real-membered real-membered set
dom e2 is non empty Element of bool the carrier of [:I[01],I[01]:]
[: the carrier of [:I[01],I[01]:], the carrier of (R^1 | T):] is non empty Relation-like set
bool [: the carrier of [:I[01],I[01]:], the carrier of (R^1 | T):] is non empty set
gg is non empty Relation-like the carrier of [:I[01],I[01]:] -defined the carrier of (R^1 | T) -valued Function-like V43( the carrier of [:I[01],I[01]:]) quasi_total Element of bool [: the carrier of [:I[01],I[01]:], the carrier of (R^1 | T):]
gg is non empty Relation-like the carrier of [:I[01],I[01]:] -defined the carrier of I[01] -valued Function-like V43( the carrier of [:I[01],I[01]:]) quasi_total continuous Element of bool [: the carrier of [:I[01],I[01]:], the carrier of I[01]:]
S2 is Element of the carrier of [:I[01],I[01]:]
b . S2 is V11() real ext-real Element of the carrier of I[01]
g is V11() real ext-real set
P . S2 is V11() real ext-real Element of the carrier of I[01]
g is V11() real ext-real set
gg . S2 is V11() real ext-real Element of the carrier of I[01]
g + g is V11() real ext-real set
bool the carrier of R^1 is non empty set
b is non empty Relation-like the carrier of [:I[01],I[01]:] -defined the carrier of I[01] -valued Function-like V43( the carrier of [:I[01],I[01]:]) quasi_total Element of bool [: the carrier of [:I[01],I[01]:], the carrier of I[01]:]
P is non empty Relation-like the carrier of [:I[01],I[01]:] -defined the carrier of I[01] -valued Function-like V43( the carrier of [:I[01],I[01]:]) quasi_total Element of bool [: the carrier of [:I[01],I[01]:], the carrier of I[01]:]
[: the carrier of [:I[01],I[01]:], the carrier of R^1:] is non empty Relation-like set
bool [: the carrier of [:I[01],I[01]:], the carrier of R^1:] is non empty set
Q is non empty Relation-like the carrier of [:I[01],I[01]:] -defined the carrier of R^1 -valued Function-like V43( the carrier of [:I[01],I[01]:]) quasi_total Element of bool [: the carrier of [:I[01],I[01]:], the carrier of R^1:]
Q is non empty Relation-like the carrier of [:I[01],I[01]:] -defined the carrier of R^1 -valued Function-like V43( the carrier of [:I[01],I[01]:]) quasi_total Element of bool [: the carrier of [:I[01],I[01]:], the carrier of R^1:]
e2 is non empty Relation-like the carrier of [:I[01],I[01]:] -defined the carrier of R^1 -valued Function-like V43( the carrier of [:I[01],I[01]:]) quasi_total Element of bool [: the carrier of [:I[01],I[01]:], the carrier of R^1:]
rng e2 is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of R^1
gg is set
dom e2 is non empty Element of bool the carrier of [:I[01],I[01]:]
gg is set
e2 . gg is set
S2 is Element of the carrier of [:I[01],I[01]:]
e2 . S2 is V11() real ext-real Element of the carrier of R^1
b . S2 is V11() real ext-real Element of the carrier of I[01]
P . S2 is V11() real ext-real Element of the carrier of I[01]
(b . S2) - (P . S2) is V11() real ext-real set
T is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of R^1
R^1 | T is non empty strict TopSpace-like real-membered SubSpace of R^1
the carrier of (R^1 | T) is non empty complex-membered ext-real-membered real-membered set
dom e2 is non empty Element of bool the carrier of [:I[01],I[01]:]
[: the carrier of [:I[01],I[01]:], the carrier of (R^1 | T):] is non empty Relation-like set
bool [: the carrier of [:I[01],I[01]:], the carrier of (R^1 | T):] is non empty set
gg is non empty Relation-like the carrier of [:I[01],I[01]:] -defined the carrier of (R^1 | T) -valued Function-like V43( the carrier of [:I[01],I[01]:]) quasi_total Element of bool [: the carrier of [:I[01],I[01]:], the carrier of (R^1 | T):]
gg is non empty Relation-like the carrier of [:I[01],I[01]:] -defined the carrier of I[01] -valued Function-like V43( the carrier of [:I[01],I[01]:]) quasi_total continuous Element of bool [: the carrier of [:I[01],I[01]:], the carrier of I[01]:]
S2 is Element of the carrier of [:I[01],I[01]:]
b . S2 is V11() real ext-real Element of the carrier of I[01]
g is V11() real ext-real set
P . S2 is V11() real ext-real Element of the carrier of I[01]
g is V11() real ext-real set
gg . S2 is V11() real ext-real Element of the carrier of I[01]
g - g is V11() real ext-real set
L[01] (((0,1) (#)),((#) (0,1))) is non empty Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined the carrier of (Closed-Interval-TSpace (0,1)) -valued Function-like V43( the carrier of (Closed-Interval-TSpace (0,1))) quasi_total Element of bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace (0,1)):]
[: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace (0,1)):] is non empty Relation-like set
bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace (0,1)):] is non empty set
T is non empty TopSpace-like TopStruct
the carrier of T is non empty set
[: the carrier of I[01], the carrier of T:] is non empty Relation-like set
bool [: the carrier of I[01], the carrier of T:] is non empty set
a is Element of the carrier of T
b is Element of the carrier of T
Q is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of a,b
Q * (L[01] (((0,1) (#)),((#) (0,1)))) is Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined the carrier of T -valued Function-like Element of bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of T:]
[: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of T:] is non empty Relation-like set
bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of T:] is non empty set
P is non empty Relation-like the carrier of I[01] -defined the carrier of I[01] -valued Function-like V43( the carrier of I[01]) quasi_total Element of bool [: the carrier of I[01], the carrier of I[01]:]
Q * P is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Element of bool [: the carrier of I[01], the carrier of T:]
Q is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Element of bool [: the carrier of I[01], the carrier of T:]
a is non empty TopStruct
the carrier of a is non empty set
b is Element of the carrier of a
P is Element of the carrier of a
Q is non empty Relation-like the carrier of I[01] -defined the carrier of a -valued Function-like V43( the carrier of I[01]) quasi_total Path of b,P
Q . 0 is set
Q . 1 is set
Q * (L[01] (((0,1) (#)),((#) (0,1)))) is Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined the carrier of a -valued Function-like Element of bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of a:]
[: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of a:] is non empty Relation-like set
bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of a:] is non empty set
(Q * (L[01] (((0,1) (#)),((#) (0,1))))) . 0 is set
(Q * (L[01] (((0,1) (#)),((#) (0,1))))) . 1 is set
(L[01] (((0,1) (#)),((#) (0,1)))) . 0 is set
(L[01] (((0,1) (#)),((#) (0,1)))) . ((#) (0,1)) is V11() real ext-real Element of the carrier of (Closed-Interval-TSpace (0,1))
(L[01] (((0,1) (#)),((#) (0,1)))) . 1 is set
(L[01] (((0,1) (#)),((#) (0,1)))) . ((0,1) (#)) is V11() real ext-real Element of the carrier of (Closed-Interval-TSpace (0,1))
T is non empty TopSpace-like TopStruct
the carrier of T is non empty set
a is Element of the carrier of T
b is Element of the carrier of T
P is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of a,b
P . 0 is set
P . 1 is set
- P is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of b,a
(- P) . 0 is set
(- P) . 1 is set
P * (L[01] (((0,1) (#)),((#) (0,1)))) is Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined the carrier of T -valued Function-like Element of bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of T:]
[: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of T:] is non empty Relation-like set
bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of T:] is non empty set
(P * (L[01] (((0,1) (#)),((#) (0,1))))) . 1 is set
[: the carrier of I[01], the carrier of T:] is non empty Relation-like set
bool [: the carrier of I[01], the carrier of T:] is non empty set
(P * (L[01] (((0,1) (#)),((#) (0,1))))) . 0 is set
T is non empty TopSpace-like TopStruct
the carrier of T is non empty set
P is Element of the carrier of T
P is Element of the carrier of T
Q is Element of the carrier of T
the non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of P,Q is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of P,Q
the non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of P,Q . 1 is set
- the non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of P,Q is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of Q,P
(- the non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of P,Q) . 0 is set
(- the non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of P,Q) . 1 is set
the non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of P,Q . 0 is set
T is non empty TopSpace-like TopStruct
the carrier of T is non empty set
a is Element of the carrier of T
b is Element of the carrier of T
P is Element of the carrier of T
the non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of a,b is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of a,b
the non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of b,P is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of b,P
the non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of a,b . 0 is set
the non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of a,b + the non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of b,P is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of a,P
( the non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of a,b + the non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of b,P) . 0 is set
( the non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of a,b + the non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of b,P) . 1 is set
the non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of b,P . 0 is set
the non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of b,P . 1 is set
the non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of a,b . 1 is set
T is non empty TopSpace-like TopStruct
the carrier of T is non empty set
a is Element of the carrier of T
b is Element of the carrier of T
Q is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of a,b
- Q is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of b,a
- (- Q) is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of a,b
Q is V11() real ext-real Element of the carrier of I[01]
Q . Q is Element of the carrier of T
(- (- Q)) . Q is Element of the carrier of T
1 - Q is V11() real ext-real Element of REAL
(- Q) . (1 - Q) is set
e2 is V11() real ext-real Element of the carrier of I[01]
1 - e2 is V11() real ext-real Element of REAL
Q . (1 - e2) is set
T is non empty TopSpace-like V74() pathwise_connected TopStruct
the carrier of T is non empty set
a is Element of the carrier of T
b is Element of the carrier of T
P is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total continuous Path of a,b
- P is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total continuous Path of b,a
- (- P) is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total continuous Path of a,b
T is non empty TopSpace-like V74() pathwise_connected TopStruct
the carrier of T is non empty set
a is Element of the carrier of T
b is Element of the carrier of T
P is Element of the carrier of T
Q is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total continuous Path of a,b
Q is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total continuous Path of b,P
Q + Q is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total continuous Path of a,P
e2 is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total continuous Path of a,P
gg is V11() real ext-real Element of the carrier of I[01]
e2 . gg is Element of the carrier of T
2 * gg is V11() real ext-real Element of REAL
Q . (2 * gg) is set
gg is V11() real ext-real Element of the carrier of I[01]
e2 . gg is Element of the carrier of T
2 * gg is V11() real ext-real Element of REAL
(2 * gg) - 1 is V11() real ext-real Element of REAL
Q . ((2 * gg) - 1) is set
T is non empty TopSpace-like V74() pathwise_connected TopStruct
the carrier of T is non empty set
a is Element of the carrier of T
b is Element of the carrier of T
P is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total continuous Path of a,b
- P is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total continuous Path of b,a
Q is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total continuous Path of b,a
Q is V11() real ext-real Element of the carrier of I[01]
Q . Q is Element of the carrier of T
1 - Q is V11() real ext-real Element of REAL
P . (1 - Q) is set
T is non empty TopSpace-like TopStruct
the carrier of T is non empty set
a is Element of the carrier of T
b is Element of the carrier of T
Q is non empty Relation-like the carrier of I[01] -defined the carrier of I[01] -valued Function-like V43( the carrier of I[01]) quasi_total continuous Element of bool [: the carrier of I[01], the carrier of I[01]:]
Q . 0 is set
Q . 1 is set
P is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of a,b
P * Q is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Element of bool [: the carrier of I[01], the carrier of T:]
[: the carrier of I[01], the carrier of T:] is non empty Relation-like set
bool [: the carrier of I[01], the carrier of T:] is non empty set
dom Q is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of I[01]
(P * Q) . 0 is set
P . (Q . 0) is set
(P * Q) . 1 is set
P . (Q . 1) is set
T is non empty TopSpace-like TopStruct
the carrier of T is non empty set
a is Element of the carrier of T
b is Element of the carrier of T
pr2 ( the carrier of I[01], the carrier of I[01]) is non empty Relation-like [: the carrier of I[01], the carrier of I[01]:] -defined the carrier of I[01] -valued Function-like V43([: the carrier of I[01], the carrier of I[01]:]) quasi_total Element of bool [:[: the carrier of I[01], the carrier of I[01]:], the carrier of I[01]:]
[:[: the carrier of I[01], the carrier of I[01]:], the carrier of I[01]:] is non empty Relation-like set
bool [:[: the carrier of I[01], the carrier of I[01]:], the carrier of I[01]:] is non empty set
pr1 ( the carrier of I[01], the carrier of I[01]) is non empty Relation-like [: the carrier of I[01], the carrier of I[01]:] -defined the carrier of I[01] -valued Function-like V43([: the carrier of I[01], the carrier of I[01]:]) quasi_total Element of bool [:[: the carrier of I[01], the carrier of I[01]:], the carrier of I[01]:]
S2 is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of a,b
g is non empty Relation-like the carrier of I[01] -defined the carrier of I[01] -valued Function-like V43( the carrier of I[01]) quasi_total continuous Element of bool [: the carrier of I[01], the carrier of I[01]:]
g . 0 is set
g . 1 is set
(T,a,b,S2,g) is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of a,b
Q is non empty Relation-like the carrier of [:I[01],I[01]:] -defined the carrier of I[01] -valued Function-like V43( the carrier of [:I[01],I[01]:]) quasi_total continuous Element of bool [: the carrier of [:I[01],I[01]:], the carrier of I[01]:]
g * Q is non empty Relation-like the carrier of [:I[01],I[01]:] -defined the carrier of [:I[01],I[01]:] -defined the carrier of I[01] -valued the carrier of I[01] -valued Function-like V43( the carrier of [:I[01],I[01]:]) V43( the carrier of [:I[01],I[01]:]) quasi_total quasi_total continuous Element of bool [: the carrier of [:I[01],I[01]:], the carrier of I[01]:]
gg is non empty Relation-like the carrier of I[01] -defined the carrier of I[01] -valued Function-like V43( the carrier of I[01]) quasi_total continuous Path of 0[01] , 1[01]
- gg is non empty Relation-like the carrier of I[01] -defined the carrier of I[01] -valued Function-like V43( the carrier of I[01]) quasi_total continuous Path of 1[01] , 0[01]
Q is non empty Relation-like the carrier of [:I[01],I[01]:] -defined the carrier of I[01] -valued Function-like V43( the carrier of [:I[01],I[01]:]) quasi_total continuous Element of bool [: the carrier of [:I[01],I[01]:], the carrier of I[01]:]
(- gg) * Q is non empty Relation-like the carrier of [:I[01],I[01]:] -defined the carrier of [:I[01],I[01]:] -defined the carrier of I[01] -valued the carrier of I[01] -valued the carrier of I[01] -valued Function-like V43( the carrier of [:I[01],I[01]:]) V43( the carrier of [:I[01],I[01]:]) quasi_total quasi_total quasi_total continuous Element of bool [: the carrier of [:I[01],I[01]:], the carrier of I[01]:]
[: the carrier of [:I[01],I[01]:], the carrier of I[01]:] is non empty Relation-like set
bool [: the carrier of [:I[01],I[01]:], the carrier of I[01]:] is non empty set
S1 is non empty Relation-like the carrier of [:I[01],I[01]:] -defined the carrier of I[01] -valued Function-like V43( the carrier of [:I[01],I[01]:]) quasi_total continuous Element of bool [: the carrier of [:I[01],I[01]:], the carrier of I[01]:]
e1 is V11() real ext-real Element of the carrier of I[01]
PP is V11() real ext-real Element of the carrier of I[01]
[e1,PP] is non empty V29() Element of the carrier of [:I[01],I[01]:]
{e1,PP} is non empty complex-membered ext-real-membered real-membered set
{e1} is non empty trivial complex-membered ext-real-membered real-membered set
{{e1,PP},{e1}} is non empty set
S1 . [e1,PP] is V11() real ext-real Element of the carrier of I[01]
1 - PP is V11() real ext-real Element of REAL
dom Q is non empty Element of bool the carrier of [:I[01],I[01]:]
Q . (e1,PP) is set
[e1,PP] is non empty V29() set
Q . [e1,PP] is set
(- gg) . (Q . (e1,PP)) is set
(- gg) . PP is V11() real ext-real Element of the carrier of I[01]
gg . (1 - PP) is set
e2 is non empty Relation-like the carrier of [:I[01],I[01]:] -defined the carrier of I[01] -valued Function-like V43( the carrier of [:I[01],I[01]:]) quasi_total continuous Element of bool [: the carrier of [:I[01],I[01]:], the carrier of I[01]:]
gg is non empty Relation-like the carrier of [:I[01],I[01]:] -defined the carrier of I[01] -valued Function-like V43( the carrier of [:I[01],I[01]:]) quasi_total continuous Element of bool [: the carrier of [:I[01],I[01]:], the carrier of I[01]:]
e1 is Element of the carrier of [:I[01],I[01]:]
e2 . e1 is V11() real ext-real Element of the carrier of I[01]
gg . e1 is V11() real ext-real Element of the carrier of I[01]
(e2 . e1) * (gg . e1) is V11() real ext-real set
e1 is non empty Relation-like the carrier of [:I[01],I[01]:] -defined the carrier of I[01] -valued Function-like V43( the carrier of [:I[01],I[01]:]) quasi_total Element of bool [: the carrier of [:I[01],I[01]:], the carrier of I[01]:]
g is non empty Relation-like the carrier of [:I[01],I[01]:] -defined the carrier of I[01] -valued Function-like V43( the carrier of [:I[01],I[01]:]) quasi_total continuous Element of bool [: the carrier of [:I[01],I[01]:], the carrier of I[01]:]
PP is Element of the carrier of [:I[01],I[01]:]
S1 . PP is V11() real ext-real Element of the carrier of I[01]
g . PP is V11() real ext-real Element of the carrier of I[01]
(S1 . PP) * (g . PP) is V11() real ext-real set
PP is non empty Relation-like the carrier of [:I[01],I[01]:] -defined the carrier of I[01] -valued Function-like V43( the carrier of [:I[01],I[01]:]) quasi_total Element of bool [: the carrier of [:I[01],I[01]:], the carrier of I[01]:]
ff is V11() real ext-real Element of the carrier of I[01]
f is V11() real ext-real Element of the carrier of I[01]
g . (ff,f) is set
[ff,f] is non empty V29() set
{ff,f} is non empty complex-membered ext-real-membered real-membered set
{ff} is non empty trivial complex-membered ext-real-membered real-membered set
{{ff,f},{ff}} is non empty set
g . [ff,f] is set
g . ff is V11() real ext-real Element of the carrier of I[01]
[ff,f] is non empty V29() Element of the carrier of [:I[01],I[01]:]
dom Q is non empty Element of bool the carrier of [:I[01],I[01]:]
Q . (ff,f) is set
Q . [ff,f] is set
g . (Q . (ff,f)) is set
f is V11() real ext-real Element of the carrier of I[01]
ff is V11() real ext-real Element of the carrier of I[01]
[f,ff] is non empty V29() Element of the carrier of [:I[01],I[01]:]
{f,ff} is non empty complex-membered ext-real-membered real-membered set
{f} is non empty trivial complex-membered ext-real-membered real-membered set
{{f,ff},{f}} is non empty set
PP . [f,ff] is V11() real ext-real Element of the carrier of I[01]
1 - ff is V11() real ext-real Element of REAL
g . f is V11() real ext-real Element of the carrier of I[01]
(1 - ff) * (g . f) is V11() real ext-real Element of REAL
S1 . (f,ff) is set
[f,ff] is non empty V29() set
S1 . [f,ff] is set
g . (f,ff) is set
g . [f,ff] is set
f is V11() real ext-real Element of the carrier of I[01]
ff is V11() real ext-real Element of the carrier of I[01]
[f,ff] is non empty V29() Element of the carrier of [:I[01],I[01]:]
{f,ff} is non empty complex-membered ext-real-membered real-membered set
{f} is non empty trivial complex-membered ext-real-membered real-membered set
{{f,ff},{f}} is non empty set
e1 . [f,ff] is V11() real ext-real Element of the carrier of I[01]
ff * f is V11() real ext-real set
e2 . (f,ff) is set
[f,ff] is non empty V29() set
e2 . [f,ff] is set
gg . (f,ff) is set
gg . [f,ff] is set
ff is Element of the carrier of [:I[01],I[01]:]
PP . ff is V11() real ext-real Element of the carrier of I[01]
e1 . ff is V11() real ext-real Element of the carrier of I[01]
(PP . ff) + (e1 . ff) is V11() real ext-real set
f is set
f is set
[f,f] is non empty V29() set
{f,f} is non empty set
{f} is non empty trivial set
{{f,f},{f}} is non empty set
S12 is V11() real ext-real Element of the carrier of I[01]
g . S12 is V11() real ext-real Element of the carrier of I[01]
S12 is V11() real ext-real Element of the carrier of I[01]
1 - S12 is V11() real ext-real Element of REAL
(1 - S12) * (g . S12) is V11() real ext-real Element of REAL
S12 * S12 is V11() real ext-real set
((1 - S12) * (g . S12)) + (S12 * S12) is V11() real ext-real Element of REAL
((1 - S12) * (g . S12)) + (e1 . ff) is V11() real ext-real Element of REAL
S12 is V11() real ext-real Element of the carrier of I[01]
1 - S12 is V11() real ext-real Element of REAL
1 - (1 - S12) is V11() real ext-real Element of REAL
(1 - (1 - S12)) * S12 is V11() real ext-real Element of REAL
(1 - S12) * (g . S12) is V11() real ext-real Element of REAL
((1 - (1 - S12)) * S12) + ((1 - S12) * (g . S12)) is V11() real ext-real Element of REAL
S12 * S12 is V11() real ext-real set
((1 - S12) * (g . S12)) + (S12 * S12) is V11() real ext-real Element of REAL
((1 - S12) * (g . S12)) + (e1 . ff) is V11() real ext-real Element of REAL
ff is non empty Relation-like the carrier of [:I[01],I[01]:] -defined the carrier of I[01] -valued Function-like V43( the carrier of [:I[01],I[01]:]) quasi_total Element of bool [: the carrier of [:I[01],I[01]:], the carrier of I[01]:]
f is V11() real ext-real Element of the carrier of I[01]
f is V11() real ext-real Element of the carrier of I[01]
[f,f] is non empty V29() Element of the carrier of [:I[01],I[01]:]
{f,f} is non empty complex-membered ext-real-membered real-membered set
{f} is non empty trivial complex-membered ext-real-membered real-membered set
{{f,f},{f}} is non empty set
ff . [f,f] is V11() real ext-real Element of the carrier of I[01]
1 - f is V11() real ext-real Element of REAL
g . f is V11() real ext-real Element of the carrier of I[01]
(1 - f) * (g . f) is V11() real ext-real Element of REAL
f * f is V11() real ext-real set
((1 - f) * (g . f)) + (f * f) is V11() real ext-real Element of REAL
PP . [f,f] is V11() real ext-real Element of the carrier of I[01]
e1 . [f,f] is V11() real ext-real Element of the carrier of I[01]
f is V11() real ext-real Element of the carrier of I[01]
[1,f] is non empty V29() set
{1,f} is non empty complex-membered ext-real-membered real-membered set
{1} is non empty trivial complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered set
{{1,f},{1}} is non empty set
ff . [1,f] is set
1 - f is V11() real ext-real Element of REAL
f is V11() real ext-real Element of the carrier of I[01]
g . f is V11() real ext-real Element of the carrier of I[01]
(1 - f) * (g . f) is V11() real ext-real Element of REAL
f * 1 is V11() real ext-real Element of REAL
((1 - f) * (g . f)) + (f * 1) is V11() real ext-real Element of REAL
S2 * ff is non empty Relation-like the carrier of [:I[01],I[01]:] -defined the carrier of T -valued Function-like V43( the carrier of [:I[01],I[01]:]) quasi_total Element of bool [: the carrier of [:I[01],I[01]:], the carrier of T:]
[: the carrier of [:I[01],I[01]:], the carrier of T:] is non empty Relation-like set
bool [: the carrier of [:I[01],I[01]:], the carrier of T:] is non empty set
dom ff is non empty Element of bool the carrier of [:I[01],I[01]:]
S12 is V11() real ext-real Element of the carrier of I[01]
[S12,1] is non empty V29() set
{S12,1} is non empty complex-membered ext-real-membered real-membered set
{S12} is non empty trivial complex-membered ext-real-membered real-membered set
{{S12,1},{S12}} is non empty set
ff . [S12,1] is set
1 - 1 is V11() real ext-real Element of REAL
g . S12 is V11() real ext-real Element of the carrier of I[01]
(1 - 1) * (g . S12) is V11() real ext-real Element of REAL
1 * S12 is V11() real ext-real Element of REAL
((1 - 1) * (g . S12)) + (1 * S12) is V11() real ext-real Element of REAL
S12 is V11() real ext-real Element of the carrier of I[01]
[S12,0] is non empty V29() set
{S12,0} is non empty complex-membered ext-real-membered real-membered set
{S12} is non empty trivial complex-membered ext-real-membered real-membered set
{{S12,0},{S12}} is non empty set
ff . [S12,0] is set
g . S12 is V11() real ext-real Element of the carrier of I[01]
1 - 0 is non empty V11() real ext-real positive non negative Element of REAL
(1 - 0) * (g . S12) is V11() real ext-real Element of REAL
0 * S12 is V11() real ext-real Element of REAL
((1 - 0) * (g . S12)) + (0 * S12) is V11() real ext-real Element of REAL
S12 is V11() real ext-real Element of the carrier of I[01]
(S2 * ff) . (S12,0) is set
[S12,0] is non empty V29() set
{S12,0} is non empty complex-membered ext-real-membered real-membered set
{S12} is non empty trivial complex-membered ext-real-membered real-membered set
{{S12,0},{S12}} is non empty set
(S2 * ff) . [S12,0] is set
(T,a,b,S2,g) . S12 is Element of the carrier of T
(S2 * ff) . (S12,1) is set
[S12,1] is non empty V29() set
{S12,1} is non empty complex-membered ext-real-membered real-membered set
{{S12,1},{S12}} is non empty set
(S2 * ff) . [S12,1] is set
S2 . S12 is Element of the carrier of T
dom g is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of I[01]
ff . [S12,0] is set
S2 . (ff . [S12,0]) is set
g . S12 is V11() real ext-real Element of the carrier of I[01]
S2 . (g . S12) is Element of the carrier of T
S2 * g is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Element of bool [: the carrier of I[01], the carrier of T:]
[: the carrier of I[01], the carrier of T:] is non empty Relation-like set
bool [: the carrier of I[01], the carrier of T:] is non empty set
(S2 * g) . S12 is Element of the carrier of T
ff . [S12,1] is set
S2 . (ff . [S12,1]) is set
S12 is V11() real ext-real Element of the carrier of I[01]
[0,S12] is non empty V29() set
{0,S12} is non empty complex-membered ext-real-membered real-membered set
{0} is non empty trivial complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered set
{{0,S12},{0}} is non empty set
ff . [0,S12] is set
1 - S12 is V11() real ext-real Element of REAL
S12 is V11() real ext-real Element of the carrier of I[01]
g . S12 is V11() real ext-real Element of the carrier of I[01]
(1 - S12) * (g . S12) is V11() real ext-real Element of REAL
S12 * 0 is V11() real ext-real Element of REAL
((1 - S12) * (g . S12)) + (S12 * 0) is V11() real ext-real Element of REAL
S12 is V11() real ext-real Element of the carrier of I[01]
(S2 * ff) . (0,S12) is set
[0,S12] is non empty V29() set
{0,S12} is non empty complex-membered ext-real-membered real-membered set
{0} is non empty trivial complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered set
{{0,S12},{0}} is non empty set
(S2 * ff) . [0,S12] is set
(S2 * ff) . (1,S12) is set
[1,S12] is non empty V29() set
{1,S12} is non empty complex-membered ext-real-membered real-membered set
{1} is non empty trivial complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered set
{{1,S12},{1}} is non empty set
(S2 * ff) . [1,S12] is set
ff . [0,S12] is set
S2 . (ff . [0,S12]) is set
S2 . 0 is set
ff . [1,S12] is set
S2 . (ff . [1,S12]) is set
S2 . 1 is set
T is non empty TopSpace-like V74() pathwise_connected TopStruct
the carrier of T is non empty set
a is Element of the carrier of T
b is Element of the carrier of T
P is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total continuous Path of a,b
Q is non empty Relation-like the carrier of I[01] -defined the carrier of I[01] -valued Function-like V43( the carrier of I[01]) quasi_total continuous Element of bool [: the carrier of I[01], the carrier of I[01]:]
Q . 0 is set
Q . 1 is set
(T,a,b,P,Q) is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total continuous Path of a,b
T is Relation-like Function-like set
proj1 T is set
a is set
T . a is set
b is V11() real ext-real Element of the carrier of I[01]
T . b is set
2 * b is V11() real ext-real Element of REAL
b is V11() real ext-real Element of the carrier of I[01]
T . b is set
b is V11() real ext-real Element of the carrier of I[01]
a is non empty Relation-like the carrier of I[01] -defined the carrier of I[01] -valued Function-like V43( the carrier of I[01]) quasi_total Element of bool [: the carrier of I[01], the carrier of I[01]:]
b is V11() real ext-real Element of the carrier of I[01]
a . b is V11() real ext-real Element of the carrier of I[01]
2 * b is V11() real ext-real Element of REAL
P is V11() real ext-real Element of the carrier of I[01]
a . P is V11() real ext-real Element of the carrier of I[01]
T is non empty Relation-like the carrier of I[01] -defined the carrier of I[01] -valued Function-like V43( the carrier of I[01]) quasi_total Element of bool [: the carrier of I[01], the carrier of I[01]:]
a is non empty Relation-like the carrier of I[01] -defined the carrier of I[01] -valued Function-like V43( the carrier of I[01]) quasi_total Element of bool [: the carrier of I[01], the carrier of I[01]:]
b is V11() real ext-real Element of the carrier of I[01]
T . b is V11() real ext-real Element of the carrier of I[01]
a . b is V11() real ext-real Element of the carrier of I[01]
2 * b is V11() real ext-real Element of REAL
() is non empty Relation-like the carrier of I[01] -defined the carrier of I[01] -valued Function-like V43( the carrier of I[01]) quasi_total Element of bool [: the carrier of I[01], the carrier of I[01]:]
a is non empty closed compact complex-membered ext-real-membered real-membered Element of bool the carrier of I[01]
I[01] | a is non empty strict TopSpace-like T_0 T_1 T_2 compact real-membered SubSpace of I[01]
T is non empty closed compact complex-membered ext-real-membered real-membered Element of bool the carrier of I[01]
I[01] | T is non empty strict TopSpace-like T_0 T_1 T_2 compact real-membered SubSpace of I[01]
the carrier of (I[01] | T) is non empty complex-membered ext-real-membered real-membered set
[: the carrier of (I[01] | T), the carrier of I[01]:] is non empty Relation-like set
bool [: the carrier of (I[01] | T), the carrier of I[01]:] is non empty set
(I[01] | T) --> 1[01] is non empty Relation-like the carrier of (I[01] | T) -defined the carrier of I[01] -valued Function-like V43( the carrier of (I[01] | T)) quasi_total continuous Element of bool [: the carrier of (I[01] | T), the carrier of I[01]:]
[: the carrier of (I[01] | T), the carrier of I[01]:] is non empty Relation-like set
bool [: the carrier of (I[01] | T), the carrier of I[01]:] is non empty set
K607( the carrier of I[01], the carrier of (I[01] | T),1[01]) is non empty Relation-like the carrier of (I[01] | T) -defined the carrier of I[01] -valued Function-like V43( the carrier of (I[01] | T)) quasi_total Element of bool [: the carrier of (I[01] | T), the carrier of I[01]:]
Closed-Interval-TSpace (0,(1 / 2)) is non empty strict TopSpace-like real-membered SubSpace of R^1
the carrier of (I[01] | a) is non empty complex-membered ext-real-membered real-membered set
[: the carrier of (I[01] | a), the carrier of I[01]:] is non empty Relation-like set
bool [: the carrier of (I[01] | a), the carrier of I[01]:] is non empty set
(0,(1 / 2),0,1) is non empty Relation-like the carrier of (Closed-Interval-TSpace (0,(1 / 2))) -defined the carrier of (Closed-Interval-TSpace (0,1)) -valued Function-like V43( the carrier of (Closed-Interval-TSpace (0,(1 / 2)))) quasi_total Element of bool [: the carrier of (Closed-Interval-TSpace (0,(1 / 2))), the carrier of (Closed-Interval-TSpace (0,1)):]
the carrier of (Closed-Interval-TSpace (0,(1 / 2))) is non empty complex-membered ext-real-membered real-membered set
[: the carrier of (Closed-Interval-TSpace (0,(1 / 2))), the carrier of (Closed-Interval-TSpace (0,1)):] is non empty Relation-like set
bool [: the carrier of (Closed-Interval-TSpace (0,(1 / 2))), the carrier of (Closed-Interval-TSpace (0,1)):] is non empty set
P[01] (0,(1 / 2),((#) (0,1)),((0,1) (#))) is non empty Relation-like the carrier of (Closed-Interval-TSpace (0,(1 / 2))) -defined the carrier of (Closed-Interval-TSpace (0,1)) -valued Function-like V43( the carrier of (Closed-Interval-TSpace (0,(1 / 2)))) quasi_total Element of bool [: the carrier of (Closed-Interval-TSpace (0,(1 / 2))), the carrier of (Closed-Interval-TSpace (0,1)):]
L[01] (((#) (0,1)),((0,1) (#))) is non empty Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined the carrier of (Closed-Interval-TSpace (0,1)) -valued Function-like V43( the carrier of (Closed-Interval-TSpace (0,1))) quasi_total Element of bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace (0,1)):]
(L[01] (((#) (0,1)),((0,1) (#)))) * (P[01] (0,(1 / 2),((#) (0,1)),((0,1) (#)))) is non empty Relation-like the carrier of (Closed-Interval-TSpace (0,(1 / 2))) -defined the carrier of (Closed-Interval-TSpace (0,1)) -valued Function-like V43( the carrier of (Closed-Interval-TSpace (0,(1 / 2)))) quasi_total Element of bool [: the carrier of (Closed-Interval-TSpace (0,(1 / 2))), the carrier of (Closed-Interval-TSpace (0,1)):]
[#] (I[01] | a) is non empty non proper open closed complex-membered ext-real-membered real-membered Element of bool the carrier of (I[01] | a)
bool the carrier of (I[01] | a) is non empty set
[#] (I[01] | T) is non empty non proper open closed complex-membered ext-real-membered real-membered Element of bool the carrier of (I[01] | T)
bool the carrier of (I[01] | T) is non empty set
([#] (I[01] | a)) /\ ([#] (I[01] | T)) is complex-membered ext-real-membered real-membered Element of bool the carrier of (I[01] | T)
e2 is non empty Relation-like the carrier of (I[01] | a) -defined the carrier of I[01] -valued Function-like V43( the carrier of (I[01] | a)) quasi_total continuous Element of bool [: the carrier of (I[01] | a), the carrier of I[01]:]
Q is non empty Relation-like the carrier of (I[01] | T) -defined the carrier of I[01] -valued Function-like V43( the carrier of (I[01] | T)) quasi_total continuous Element of bool [: the carrier of (I[01] | T), the carrier of I[01]:]
gg is set
e2 . gg is set
Q . gg is set
[.0,(1 / 2).] /\ ([#] (I[01] | T)) is complex-membered ext-real-membered real-membered Element of bool the carrier of (I[01] | T)
[.0,(1 / 2).] /\ [.(1 / 2),1.] is complex-membered ext-real-membered real-membered Element of bool REAL
1 - 0 is non empty V11() real ext-real positive non negative Element of REAL
(1 / 2) - 0 is V11() real ext-real non negative Element of REAL
(1 - 0) / ((1 / 2) - 0) is V11() real ext-real non negative Element of REAL
((1 - 0) / ((1 / 2) - 0)) * ((1 / 2) - 0) is V11() real ext-real non negative Element of REAL
(((1 - 0) / ((1 / 2) - 0)) * ((1 / 2) - 0)) + 0 is V11() real ext-real non negative Element of REAL
e2 +* Q is Relation-like Function-like set
gg is V11() real ext-real Element of the carrier of I[01]
() . gg is V11() real ext-real Element of the carrier of I[01]
(e2 +* Q) . gg is set
dom Q is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of (I[01] | T)
e2 . gg is set
1 - 0 is non empty V11() real ext-real positive non negative Element of REAL
(1 / 2) - 0 is V11() real ext-real non negative Element of REAL
(1 - 0) / ((1 / 2) - 0) is V11() real ext-real non negative Element of REAL
gg - 0 is V11() real ext-real Element of REAL
((1 - 0) / ((1 / 2) - 0)) * (gg - 0) is V11() real ext-real Element of REAL
(((1 - 0) / ((1 / 2) - 0)) * (gg - 0)) + 0 is V11() real ext-real Element of REAL
1 / (1 / 2) is V11() real ext-real non negative Element of REAL
(1 / (1 / 2)) * gg is V11() real ext-real Element of REAL
2 * gg is V11() real ext-real Element of REAL
2 * (1 / 2) is V11() real ext-real non negative Element of REAL
Q . gg is set
Q . gg is set
([#] (I[01] | a)) \/ ([#] (I[01] | T)) is non empty complex-membered ext-real-membered real-membered set
[.0,(1 / 2).] \/ ([#] (I[01] | T)) is non empty complex-membered ext-real-membered real-membered set
[.0,(1 / 2).] \/ [.(1 / 2),1.] is complex-membered ext-real-membered real-membered Element of bool REAL
[#] I[01] is non empty non proper open closed complex-membered ext-real-membered real-membered Element of bool the carrier of I[01]
gg is non empty Relation-like the carrier of I[01] -defined the carrier of I[01] -valued Function-like V43( the carrier of I[01]) quasi_total Element of bool [: the carrier of I[01], the carrier of I[01]:]
() . 0 is set
() . 1 is set
T is V11() real ext-real Element of the carrier of I[01]
2 * T is V11() real ext-real Element of REAL
a is V11() real ext-real Element of the carrier of I[01]
() . a is V11() real ext-real Element of the carrier of I[01]
T is Relation-like Function-like set
proj1 T is set
a is set
T . a is set
b is V11() real ext-real Element of the carrier of I[01]
T . b is set
b is V11() real ext-real Element of the carrier of I[01]
T . b is set
2 * b is V11() real ext-real Element of REAL
(2 * b) - 1 is V11() real ext-real Element of REAL
b is V11() real ext-real Element of the carrier of I[01]
a is non empty Relation-like the carrier of I[01] -defined the carrier of I[01] -valued Function-like V43( the carrier of I[01]) quasi_total Element of bool [: the carrier of I[01], the carrier of I[01]:]
b is V11() real ext-real Element of the carrier of I[01]
a . b is V11() real ext-real Element of the carrier of I[01]
P is V11() real ext-real Element of the carrier of I[01]
a . P is V11() real ext-real Element of the carrier of I[01]
2 * P is V11() real ext-real Element of REAL
(2 * P) - 1 is V11() real ext-real Element of REAL
T is non empty Relation-like the carrier of I[01] -defined the carrier of I[01] -valued Function-like V43( the carrier of I[01]) quasi_total Element of bool [: the carrier of I[01], the carrier of I[01]:]
a is non empty Relation-like the carrier of I[01] -defined the carrier of I[01] -valued Function-like V43( the carrier of I[01]) quasi_total Element of bool [: the carrier of I[01], the carrier of I[01]:]
b is V11() real ext-real Element of the carrier of I[01]
T . b is V11() real ext-real Element of the carrier of I[01]
a . b is V11() real ext-real Element of the carrier of I[01]
2 * b is V11() real ext-real Element of REAL
(2 * b) - 1 is V11() real ext-real Element of REAL
() is non empty Relation-like the carrier of I[01] -defined the carrier of I[01] -valued Function-like V43( the carrier of I[01]) quasi_total Element of bool [: the carrier of I[01], the carrier of I[01]:]
a is non empty closed compact complex-membered ext-real-membered real-membered Element of bool the carrier of I[01]
I[01] | a is non empty strict TopSpace-like T_0 T_1 T_2 compact real-membered SubSpace of I[01]
T is non empty closed compact complex-membered ext-real-membered real-membered Element of bool the carrier of I[01]
I[01] | T is non empty strict TopSpace-like T_0 T_1 T_2 compact real-membered SubSpace of I[01]
the carrier of (I[01] | a) is non empty complex-membered ext-real-membered real-membered set
[: the carrier of (I[01] | a), the carrier of I[01]:] is non empty Relation-like set
bool [: the carrier of (I[01] | a), the carrier of I[01]:] is non empty set
(I[01] | a) --> 0[01] is non empty Relation-like the carrier of (I[01] | a) -defined the carrier of I[01] -valued Function-like V43( the carrier of (I[01] | a)) quasi_total continuous Element of bool [: the carrier of (I[01] | a), the carrier of I[01]:]
[: the carrier of (I[01] | a), the carrier of I[01]:] is non empty Relation-like set
bool [: the carrier of (I[01] | a), the carrier of I[01]:] is non empty set
K607( the carrier of I[01], the carrier of (I[01] | a),0[01]) is non empty Relation-like the carrier of (I[01] | a) -defined the carrier of I[01] -valued Function-like V43( the carrier of (I[01] | a)) quasi_total Element of bool [: the carrier of (I[01] | a), the carrier of I[01]:]
Closed-Interval-TSpace ((1 / 2),1) is non empty strict TopSpace-like real-membered SubSpace of R^1
the carrier of (I[01] | T) is non empty complex-membered ext-real-membered real-membered set
[: the carrier of (I[01] | T), the carrier of I[01]:] is non empty Relation-like set
bool [: the carrier of (I[01] | T), the carrier of I[01]:] is non empty set
((1 / 2),1,0,1) is non empty Relation-like the carrier of (Closed-Interval-TSpace ((1 / 2),1)) -defined the carrier of (Closed-Interval-TSpace (0,1)) -valued Function-like V43( the carrier of (Closed-Interval-TSpace ((1 / 2),1))) quasi_total Element of bool [: the carrier of (Closed-Interval-TSpace ((1 / 2),1)), the carrier of (Closed-Interval-TSpace (0,1)):]
the carrier of (Closed-Interval-TSpace ((1 / 2),1)) is non empty complex-membered ext-real-membered real-membered set
[: the carrier of (Closed-Interval-TSpace ((1 / 2),1)), the carrier of (Closed-Interval-TSpace (0,1)):] is non empty Relation-like set
bool [: the carrier of (Closed-Interval-TSpace ((1 / 2),1)), the carrier of (Closed-Interval-TSpace (0,1)):] is non empty set
P[01] ((1 / 2),1,((#) (0,1)),((0,1) (#))) is non empty Relation-like the carrier of (Closed-Interval-TSpace ((1 / 2),1)) -defined the carrier of (Closed-Interval-TSpace (0,1)) -valued Function-like V43( the carrier of (Closed-Interval-TSpace ((1 / 2),1))) quasi_total Element of bool [: the carrier of (Closed-Interval-TSpace ((1 / 2),1)), the carrier of (Closed-Interval-TSpace (0,1)):]
L[01] (((#) (0,1)),((0,1) (#))) is non empty Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined the carrier of (Closed-Interval-TSpace (0,1)) -valued Function-like V43( the carrier of (Closed-Interval-TSpace (0,1))) quasi_total Element of bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace (0,1)):]
(L[01] (((#) (0,1)),((0,1) (#)))) * (P[01] ((1 / 2),1,((#) (0,1)),((0,1) (#)))) is non empty Relation-like the carrier of (Closed-Interval-TSpace ((1 / 2),1)) -defined the carrier of (Closed-Interval-TSpace (0,1)) -valued Function-like V43( the carrier of (Closed-Interval-TSpace ((1 / 2),1))) quasi_total Element of bool [: the carrier of (Closed-Interval-TSpace ((1 / 2),1)), the carrier of (Closed-Interval-TSpace (0,1)):]
[#] (I[01] | T) is non empty non proper open closed complex-membered ext-real-membered real-membered Element of bool the carrier of (I[01] | T)
bool the carrier of (I[01] | T) is non empty set
[#] (I[01] | a) is non empty non proper open closed complex-membered ext-real-membered real-membered Element of bool the carrier of (I[01] | a)
bool the carrier of (I[01] | a) is non empty set
([#] (I[01] | T)) /\ ([#] (I[01] | a)) is complex-membered ext-real-membered real-membered Element of bool the carrier of (I[01] | a)
e2 is non empty Relation-like the carrier of (I[01] | T) -defined the carrier of I[01] -valued Function-like V43( the carrier of (I[01] | T)) quasi_total continuous Element of bool [: the carrier of (I[01] | T), the carrier of I[01]:]
Q is non empty Relation-like the carrier of (I[01] | a) -defined the carrier of I[01] -valued Function-like V43( the carrier of (I[01] | a)) quasi_total continuous Element of bool [: the carrier of (I[01] | a), the carrier of I[01]:]
gg is set
e2 . gg is set
Q . gg is set
[.0,(1 / 2).] /\ ([#] (I[01] | T)) is complex-membered ext-real-membered real-membered Element of bool the carrier of (I[01] | T)
[.0,(1 / 2).] /\ [.(1 / 2),1.] is complex-membered ext-real-membered real-membered Element of bool REAL
1 - 0 is non empty V11() real ext-real positive non negative Element of REAL
1 - (1 / 2) is V11() real ext-real Element of REAL
(1 - 0) / (1 - (1 / 2)) is V11() real ext-real Element of REAL
(1 / 2) - (1 / 2) is V11() real ext-real Element of REAL
((1 - 0) / (1 - (1 / 2))) * ((1 / 2) - (1 / 2)) is V11() real ext-real Element of REAL
(((1 - 0) / (1 - (1 / 2))) * ((1 / 2) - (1 / 2))) + 0 is V11() real ext-real Element of REAL
Q +* e2 is Relation-like Function-like set
gg is V11() real ext-real Element of the carrier of I[01]
() . gg is V11() real ext-real Element of the carrier of I[01]
(Q +* e2) . gg is set
dom e2 is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of (I[01] | T)
e2 . gg is set
1 - 0 is non empty V11() real ext-real positive non negative Element of REAL
1 - (1 / 2) is V11() real ext-real Element of REAL
(1 - 0) / (1 - (1 / 2)) is V11() real ext-real Element of REAL
gg - (1 / 2) is V11() real ext-real Element of REAL
((1 - 0) / (1 - (1 / 2))) * (gg - (1 / 2)) is V11() real ext-real Element of REAL
(((1 - 0) / (1 - (1 / 2))) * (gg - (1 / 2))) + 0 is V11() real ext-real Element of REAL
2 * gg is V11() real ext-real Element of REAL
(2 * gg) - 1 is V11() real ext-real Element of REAL
1 - 0 is non empty V11() real ext-real positive non negative Element of REAL
1 - (1 / 2) is V11() real ext-real Element of REAL
(1 - 0) / (1 - (1 / 2)) is V11() real ext-real Element of REAL
(1 / 2) - (1 / 2) is V11() real ext-real Element of REAL
((1 - 0) / (1 - (1 / 2))) * ((1 / 2) - (1 / 2)) is V11() real ext-real Element of REAL
(((1 - 0) / (1 - (1 / 2))) * ((1 / 2) - (1 / 2))) + 0 is V11() real ext-real Element of REAL
e2 . gg is set
Q . gg is set
([#] (I[01] | T)) \/ ([#] (I[01] | a)) is non empty complex-membered ext-real-membered real-membered set
[.0,(1 / 2).] \/ ([#] (I[01] | T)) is non empty complex-membered ext-real-membered real-membered set
[.0,(1 / 2).] \/ [.(1 / 2),1.] is complex-membered ext-real-membered real-membered Element of bool REAL
[#] I[01] is non empty non proper open closed complex-membered ext-real-membered real-membered Element of bool the carrier of I[01]
gg is non empty Relation-like the carrier of I[01] -defined the carrier of I[01] -valued Function-like V43( the carrier of I[01]) quasi_total Element of bool [: the carrier of I[01], the carrier of I[01]:]
() . 0 is set
() . 1 is set
T is V11() real ext-real Element of the carrier of I[01]
() . T is V11() real ext-real Element of the carrier of I[01]
a is V11() real ext-real Element of the carrier of I[01]
2 * a is V11() real ext-real Element of REAL
(2 * a) - 1 is V11() real ext-real Element of REAL
3 is non empty natural V11() real ext-real positive non negative V172() V173() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered Element of NAT
3 / 4 is V11() real ext-real non negative Element of REAL
T is V11() real ext-real Element of the carrier of I[01]
T is V11() real ext-real Element of the carrier of I[01]
a is V11() real ext-real Element of the carrier of I[01]
b is V11() real ext-real Element of the carrier of I[01]
T is Relation-like Function-like set
proj1 T is set
a is set
T . a is set
b is V11() real ext-real Element of the carrier of I[01]
T . b is set
(1 / 2) * b is V11() real ext-real Element of REAL
b is V11() real ext-real Element of the carrier of I[01]
T . b is set
b - (1 / 4) is V11() real ext-real Element of REAL
b is V11() real ext-real Element of the carrier of I[01]
T . b is set
2 * b is V11() real ext-real Element of REAL
(2 * b) - 1 is V11() real ext-real Element of REAL
b is V11() real ext-real Element of the carrier of I[01]
a is non empty Relation-like the carrier of I[01] -defined the carrier of I[01] -valued Function-like V43( the carrier of I[01]) quasi_total Element of bool [: the carrier of I[01], the carrier of I[01]:]
b is V11() real ext-real Element of the carrier of I[01]
a . b is V11() real ext-real Element of the carrier of I[01]
(1 / 2) * b is V11() real ext-real Element of REAL
P is V11() real ext-real Element of the carrier of I[01]
a . P is V11() real ext-real Element of the carrier of I[01]
P - (1 / 4) is V11() real ext-real Element of REAL
Q is V11() real ext-real Element of the carrier of I[01]
a . Q is V11() real ext-real Element of the carrier of I[01]
2 * Q is V11() real ext-real Element of REAL
(2 * Q) - 1 is V11() real ext-real Element of REAL
T is non empty Relation-like the carrier of I[01] -defined the carrier of I[01] -valued Function-like V43( the carrier of I[01]) quasi_total Element of bool [: the carrier of I[01], the carrier of I[01]:]
a is non empty Relation-like the carrier of I[01] -defined the carrier of I[01] -valued Function-like V43( the carrier of I[01]) quasi_total Element of bool [: the carrier of I[01], the carrier of I[01]:]
b is V11() real ext-real Element of the carrier of I[01]
T . b is V11() real ext-real Element of the carrier of I[01]
a . b is V11() real ext-real Element of the carrier of I[01]
(1 / 2) * b is V11() real ext-real Element of REAL
b - (1 / 4) is V11() real ext-real Element of REAL
2 * b is V11() real ext-real Element of REAL
(2 * b) - 1 is V11() real ext-real Element of REAL
() is non empty Relation-like the carrier of I[01] -defined the carrier of I[01] -valued Function-like V43( the carrier of I[01]) quasi_total Element of bool [: the carrier of I[01], the carrier of I[01]:]
[.(1 / 2),(3 / 4).] is complex-membered ext-real-membered real-membered Element of bool REAL
[.0,(3 / 4).] is complex-membered ext-real-membered real-membered Element of bool REAL
[.(1 / 4),(1 / 2).] is complex-membered ext-real-membered real-membered Element of bool REAL
[.0,(1 / 4).] is complex-membered ext-real-membered real-membered Element of bool REAL
[.(3 / 4),1.] is complex-membered ext-real-membered real-membered Element of bool REAL
a is non empty closed compact complex-membered ext-real-membered real-membered Element of bool the carrier of I[01]
I[01] | a is non empty strict TopSpace-like T_0 T_1 T_2 compact real-membered SubSpace of I[01]
T is non empty closed compact complex-membered ext-real-membered real-membered Element of bool the carrier of I[01]
I[01] | T is non empty strict TopSpace-like T_0 T_1 T_2 compact real-membered SubSpace of I[01]
Q is non empty closed compact complex-membered ext-real-membered real-membered Element of bool the carrier of I[01]
I[01] | Q is non empty strict TopSpace-like T_0 T_1 T_2 compact real-membered SubSpace of I[01]
e2 is non empty closed compact complex-membered ext-real-membered real-membered Element of bool the carrier of I[01]
I[01] | e2 is non empty strict TopSpace-like T_0 T_1 T_2 compact real-membered SubSpace of I[01]
P is non empty closed compact complex-membered ext-real-membered real-membered Element of bool the carrier of I[01]
I[01] | P is non empty strict TopSpace-like T_0 T_1 T_2 compact real-membered SubSpace of I[01]
Q is non empty closed compact complex-membered ext-real-membered real-membered Element of bool the carrier of I[01]
I[01] | Q is non empty strict TopSpace-like T_0 T_1 T_2 compact real-membered SubSpace of I[01]
(0,(1 / 2),0,(1 / 4)) is non empty Relation-like the carrier of (Closed-Interval-TSpace (0,(1 / 2))) -defined the carrier of (Closed-Interval-TSpace (0,(1 / 4))) -valued Function-like V43( the carrier of (Closed-Interval-TSpace (0,(1 / 2)))) quasi_total Element of bool [: the carrier of (Closed-Interval-TSpace (0,(1 / 2))), the carrier of (Closed-Interval-TSpace (0,(1 / 4))):]
Closed-Interval-TSpace (0,(1 / 2)) is non empty strict TopSpace-like real-membered SubSpace of R^1
the carrier of (Closed-Interval-TSpace (0,(1 / 2))) is non empty complex-membered ext-real-membered real-membered set
Closed-Interval-TSpace (0,(1 / 4)) is non empty strict TopSpace-like real-membered SubSpace of R^1
the carrier of (Closed-Interval-TSpace (0,(1 / 4))) is non empty complex-membered ext-real-membered real-membered set
[: the carrier of (Closed-Interval-TSpace (0,(1 / 2))), the carrier of (Closed-Interval-TSpace (0,(1 / 4))):] is non empty Relation-like set
bool [: the carrier of (Closed-Interval-TSpace (0,(1 / 2))), the carrier of (Closed-Interval-TSpace (0,(1 / 4))):] is non empty set
P[01] (0,(1 / 2),((#) (0,1)),((0,1) (#))) is non empty Relation-like the carrier of (Closed-Interval-TSpace (0,(1 / 2))) -defined the carrier of (Closed-Interval-TSpace (0,1)) -valued Function-like V43( the carrier of (Closed-Interval-TSpace (0,(1 / 2)))) quasi_total Element of bool [: the carrier of (Closed-Interval-TSpace (0,(1 / 2))), the carrier of (Closed-Interval-TSpace (0,1)):]
[: the carrier of (Closed-Interval-TSpace (0,(1 / 2))), the carrier of (Closed-Interval-TSpace (0,1)):] is non empty Relation-like set
bool [: the carrier of (Closed-Interval-TSpace (0,(1 / 2))), the carrier of (Closed-Interval-TSpace (0,1)):] is non empty set
(#) (0,(1 / 4)) is V11() real ext-real Element of the carrier of (Closed-Interval-TSpace (0,(1 / 4)))
(0,(1 / 4)) (#) is V11() real ext-real Element of the carrier of (Closed-Interval-TSpace (0,(1 / 4)))
L[01] (((#) (0,(1 / 4))),((0,(1 / 4)) (#))) is non empty Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined the carrier of (Closed-Interval-TSpace (0,(1 / 4))) -valued Function-like V43( the carrier of (Closed-Interval-TSpace (0,1))) quasi_total Element of bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace (0,(1 / 4))):]
[: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace (0,(1 / 4))):] is non empty Relation-like set
bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace (0,(1 / 4))):] is non empty set
(L[01] (((#) (0,(1 / 4))),((0,(1 / 4)) (#)))) * (P[01] (0,(1 / 2),((#) (0,1)),((0,1) (#)))) is non empty Relation-like the carrier of (Closed-Interval-TSpace (0,(1 / 2))) -defined the carrier of (Closed-Interval-TSpace (0,(1 / 4))) -valued Function-like V43( the carrier of (Closed-Interval-TSpace (0,(1 / 2)))) quasi_total Element of bool [: the carrier of (Closed-Interval-TSpace (0,(1 / 2))), the carrier of (Closed-Interval-TSpace (0,(1 / 4))):]
((1 / 2),(3 / 4),(1 / 4),(1 / 2)) is non empty Relation-like the carrier of (Closed-Interval-TSpace ((1 / 2),(3 / 4))) -defined the carrier of (Closed-Interval-TSpace ((1 / 4),(1 / 2))) -valued Function-like V43( the carrier of (Closed-Interval-TSpace ((1 / 2),(3 / 4)))) quasi_total Element of bool [: the carrier of (Closed-Interval-TSpace ((1 / 2),(3 / 4))), the carrier of (Closed-Interval-TSpace ((1 / 4),(1 / 2))):]
Closed-Interval-TSpace ((1 / 2),(3 / 4)) is non empty strict TopSpace-like real-membered SubSpace of R^1
the carrier of (Closed-Interval-TSpace ((1 / 2),(3 / 4))) is non empty complex-membered ext-real-membered real-membered set
Closed-Interval-TSpace ((1 / 4),(1 / 2)) is non empty strict TopSpace-like real-membered SubSpace of R^1
the carrier of (Closed-Interval-TSpace ((1 / 4),(1 / 2))) is non empty complex-membered ext-real-membered real-membered set
[: the carrier of (Closed-Interval-TSpace ((1 / 2),(3 / 4))), the carrier of (Closed-Interval-TSpace ((1 / 4),(1 / 2))):] is non empty Relation-like set
bool [: the carrier of (Closed-Interval-TSpace ((1 / 2),(3 / 4))), the carrier of (Closed-Interval-TSpace ((1 / 4),(1 / 2))):] is non empty set
P[01] ((1 / 2),(3 / 4),((#) (0,1)),((0,1) (#))) is non empty Relation-like the carrier of (Closed-Interval-TSpace ((1 / 2),(3 / 4))) -defined the carrier of (Closed-Interval-TSpace (0,1)) -valued Function-like V43( the carrier of (Closed-Interval-TSpace ((1 / 2),(3 / 4)))) quasi_total Element of bool [: the carrier of (Closed-Interval-TSpace ((1 / 2),(3 / 4))), the carrier of (Closed-Interval-TSpace (0,1)):]
[: the carrier of (Closed-Interval-TSpace ((1 / 2),(3 / 4))), the carrier of (Closed-Interval-TSpace (0,1)):] is non empty Relation-like set
bool [: the carrier of (Closed-Interval-TSpace ((1 / 2),(3 / 4))), the carrier of (Closed-Interval-TSpace (0,1)):] is non empty set
(#) ((1 / 4),(1 / 2)) is V11() real ext-real Element of the carrier of (Closed-Interval-TSpace ((1 / 4),(1 / 2)))
((1 / 4),(1 / 2)) (#) is V11() real ext-real Element of the carrier of (Closed-Interval-TSpace ((1 / 4),(1 / 2)))
L[01] (((#) ((1 / 4),(1 / 2))),(((1 / 4),(1 / 2)) (#))) is non empty Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined the carrier of (Closed-Interval-TSpace ((1 / 4),(1 / 2))) -valued Function-like V43( the carrier of (Closed-Interval-TSpace (0,1))) quasi_total Element of bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((1 / 4),(1 / 2))):]
[: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((1 / 4),(1 / 2))):] is non empty Relation-like set
bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((1 / 4),(1 / 2))):] is non empty set
(L[01] (((#) ((1 / 4),(1 / 2))),(((1 / 4),(1 / 2)) (#)))) * (P[01] ((1 / 2),(3 / 4),((#) (0,1)),((0,1) (#)))) is non empty Relation-like the carrier of (Closed-Interval-TSpace ((1 / 2),(3 / 4))) -defined the carrier of (Closed-Interval-TSpace ((1 / 4),(1 / 2))) -valued Function-like V43( the carrier of (Closed-Interval-TSpace ((1 / 2),(3 / 4)))) quasi_total Element of bool [: the carrier of (Closed-Interval-TSpace ((1 / 2),(3 / 4))), the carrier of (Closed-Interval-TSpace ((1 / 4),(1 / 2))):]
((3 / 4),1,(1 / 2),1) is non empty Relation-like the carrier of (Closed-Interval-TSpace ((3 / 4),1)) -defined the carrier of (Closed-Interval-TSpace ((1 / 2),1)) -valued Function-like V43( the carrier of (Closed-Interval-TSpace ((3 / 4),1))) quasi_total Element of bool [: the carrier of (Closed-Interval-TSpace ((3 / 4),1)), the carrier of (Closed-Interval-TSpace ((1 / 2),1)):]
Closed-Interval-TSpace ((3 / 4),1) is non empty strict TopSpace-like real-membered SubSpace of R^1
the carrier of (Closed-Interval-TSpace ((3 / 4),1)) is non empty complex-membered ext-real-membered real-membered set
Closed-Interval-TSpace ((1 / 2),1) is non empty strict TopSpace-like real-membered SubSpace of R^1
the carrier of (Closed-Interval-TSpace ((1 / 2),1)) is non empty complex-membered ext-real-membered real-membered set
[: the carrier of (Closed-Interval-TSpace ((3 / 4),1)), the carrier of (Closed-Interval-TSpace ((1 / 2),1)):] is non empty Relation-like set
bool [: the carrier of (Closed-Interval-TSpace ((3 / 4),1)), the carrier of (Closed-Interval-TSpace ((1 / 2),1)):] is non empty set
P[01] ((3 / 4),1,((#) (0,1)),((0,1) (#))) is non empty Relation-like the carrier of (Closed-Interval-TSpace ((3 / 4),1)) -defined the carrier of (Closed-Interval-TSpace (0,1)) -valued Function-like V43( the carrier of (Closed-Interval-TSpace ((3 / 4),1))) quasi_total Element of bool [: the carrier of (Closed-Interval-TSpace ((3 / 4),1)), the carrier of (Closed-Interval-TSpace (0,1)):]
[: the carrier of (Closed-Interval-TSpace ((3 / 4),1)), the carrier of (Closed-Interval-TSpace (0,1)):] is non empty Relation-like set
bool [: the carrier of (Closed-Interval-TSpace ((3 / 4),1)), the carrier of (Closed-Interval-TSpace (0,1)):] is non empty set
(#) ((1 / 2),1) is V11() real ext-real Element of the carrier of (Closed-Interval-TSpace ((1 / 2),1))
((1 / 2),1) (#) is V11() real ext-real Element of the carrier of (Closed-Interval-TSpace ((1 / 2),1))
L[01] (((#) ((1 / 2),1)),(((1 / 2),1) (#))) is non empty Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined the carrier of (Closed-Interval-TSpace ((1 / 2),1)) -valued Function-like V43( the carrier of (Closed-Interval-TSpace (0,1))) quasi_total Element of bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((1 / 2),1)):]
[: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((1 / 2),1)):] is non empty Relation-like set
bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((1 / 2),1)):] is non empty set
(L[01] (((#) ((1 / 2),1)),(((1 / 2),1) (#)))) * (P[01] ((3 / 4),1,((#) (0,1)),((0,1) (#)))) is non empty Relation-like the carrier of (Closed-Interval-TSpace ((3 / 4),1)) -defined the carrier of (Closed-Interval-TSpace ((1 / 2),1)) -valued Function-like V43( the carrier of (Closed-Interval-TSpace ((3 / 4),1))) quasi_total Element of bool [: the carrier of (Closed-Interval-TSpace ((3 / 4),1)), the carrier of (Closed-Interval-TSpace ((1 / 2),1)):]
b is non empty closed compact complex-membered ext-real-membered real-membered Element of bool the carrier of I[01]
I[01] | b is non empty strict TopSpace-like T_0 T_1 T_2 compact real-membered SubSpace of I[01]
the carrier of (I[01] | Q) is non empty complex-membered ext-real-membered real-membered set
the carrier of (I[01] | e2) is non empty complex-membered ext-real-membered real-membered set
[: the carrier of (I[01] | Q), the carrier of (I[01] | e2):] is non empty Relation-like set
bool [: the carrier of (I[01] | Q), the carrier of (I[01] | e2):] is non empty set
[: the carrier of (I[01] | Q), the carrier of I[01]:] is non empty Relation-like set
bool [: the carrier of (I[01] | Q), the carrier of I[01]:] is non empty set
S12 is non empty Relation-like the carrier of (I[01] | Q) -defined the carrier of (I[01] | e2) -valued Function-like V43( the carrier of (I[01] | Q)) quasi_total continuous Element of bool [: the carrier of (I[01] | Q), the carrier of (I[01] | e2):]
S12 is non empty Relation-like the carrier of (I[01] | Q) -defined the carrier of I[01] -valued Function-like V43( the carrier of (I[01] | Q)) quasi_total continuous Element of bool [: the carrier of (I[01] | Q), the carrier of I[01]:]
hh is V11() real ext-real Element of the carrier of (I[01] | Q)
S12 . hh is V11() real ext-real Element of the carrier of I[01]
2 * hh is V11() real ext-real Element of REAL
(2 * hh) - 1 is V11() real ext-real Element of REAL
1 - (1 / 2) is V11() real ext-real Element of REAL
1 - (3 / 4) is V11() real ext-real Element of REAL
(1 - (1 / 2)) / (1 - (3 / 4)) is V11() real ext-real Element of REAL
hh - (3 / 4) is V11() real ext-real Element of REAL
((1 - (1 / 2)) / (1 - (3 / 4))) * (hh - (3 / 4)) is V11() real ext-real Element of REAL
(((1 - (1 / 2)) / (1 - (3 / 4))) * (hh - (3 / 4))) + (1 / 2) is V11() real ext-real Element of REAL
the carrier of (I[01] | a) is non empty complex-membered ext-real-membered real-membered set
the carrier of (I[01] | Q) is non empty complex-membered ext-real-membered real-membered set
[: the carrier of (I[01] | a), the carrier of (I[01] | Q):] is non empty Relation-like set
bool [: the carrier of (I[01] | a), the carrier of (I[01] | Q):] is non empty set
the carrier of (I[01] | T) is non empty complex-membered ext-real-membered real-membered set
the carrier of (I[01] | P) is non empty complex-membered ext-real-membered real-membered set
[: the carrier of (I[01] | T), the carrier of (I[01] | P):] is non empty Relation-like set
bool [: the carrier of (I[01] | T), the carrier of (I[01] | P):] is non empty set
[: the carrier of (I[01] | T), the carrier of I[01]:] is non empty Relation-like set
bool [: the carrier of (I[01] | T), the carrier of I[01]:] is non empty set
h is non empty Relation-like the carrier of (I[01] | T) -defined the carrier of (I[01] | P) -valued Function-like V43( the carrier of (I[01] | T)) quasi_total continuous Element of bool [: the carrier of (I[01] | T), the carrier of (I[01] | P):]
[: the carrier of (I[01] | a), the carrier of I[01]:] is non empty Relation-like set
bool [: the carrier of (I[01] | a), the carrier of I[01]:] is non empty set
hh is non empty Relation-like the carrier of (I[01] | a) -defined the carrier of (I[01] | Q) -valued Function-like V43( the carrier of (I[01] | a)) quasi_total continuous Element of bool [: the carrier of (I[01] | a), the carrier of (I[01] | Q):]
s3 is non empty Relation-like the carrier of (I[01] | a) -defined the carrier of I[01] -valued Function-like V43( the carrier of (I[01] | a)) quasi_total continuous Element of bool [: the carrier of (I[01] | a), the carrier of I[01]:]
h is non empty Relation-like the carrier of (I[01] | T) -defined the carrier of I[01] -valued Function-like V43( the carrier of (I[01] | T)) quasi_total continuous Element of bool [: the carrier of (I[01] | T), the carrier of I[01]:]
fg is V11() real ext-real Element of the carrier of (I[01] | T)
h . fg is V11() real ext-real Element of the carrier of I[01]
fg - (1 / 4) is V11() real ext-real Element of REAL
(1 / 2) - (1 / 4) is V11() real ext-real Element of REAL
(3 / 4) - (1 / 2) is V11() real ext-real Element of REAL
((1 / 2) - (1 / 4)) / ((3 / 4) - (1 / 2)) is V11() real ext-real Element of REAL
fg - (1 / 2) is V11() real ext-real Element of REAL
(((1 / 2) - (1 / 4)) / ((3 / 4) - (1 / 2))) * (fg - (1 / 2)) is V11() real ext-real Element of REAL
((((1 / 2) - (1 / 4)) / ((3 / 4) - (1 / 2))) * (fg - (1 / 2))) + (1 / 4) is V11() real ext-real Element of REAL
f is TopSpace-like T_0 T_1 T_2 real-membered SubSpace of I[01] | b
the carrier of f is complex-membered ext-real-membered real-membered set
f is TopSpace-like T_0 T_1 T_2 real-membered SubSpace of I[01] | b
[#] f is non proper open closed complex-membered ext-real-membered real-membered Element of bool the carrier of f
the carrier of f is complex-membered ext-real-membered real-membered set
bool the carrier of f is non empty set
[#] f is non proper open closed complex-membered ext-real-membered real-membered Element of bool the carrier of f
bool the carrier of f is non empty set
([#] f) /\ ([#] f) is complex-membered ext-real-membered real-membered Element of bool the carrier of f
a /\ ([#] f) is complex-membered ext-real-membered real-membered Element of bool the carrier of f
a /\ T is closed complex-membered ext-real-membered real-membered Element of bool the carrier of I[01]
fg is set
s3 . fg is set
h . fg is set
H is V11() real ext-real Element of the carrier of I[01]
s3 . H is set
(1 / 4) - 0 is V11() real ext-real non negative Element of REAL
(1 / 2) - 0 is V11() real ext-real non negative Element of REAL
((1 / 4) - 0) / ((1 / 2) - 0) is V11() real ext-real non negative Element of REAL
H - 0 is V11() real ext-real Element of REAL
(((1 / 4) - 0) / ((1 / 2) - 0)) * (H - 0) is V11() real ext-real Element of REAL
((((1 / 4) - 0) / ((1 / 2) - 0)) * (H - 0)) + 0 is V11() real ext-real Element of REAL
(1 / 2) - (1 / 4) is V11() real ext-real Element of REAL
(3 / 4) - (1 / 2) is V11() real ext-real Element of REAL
((1 / 2) - (1 / 4)) / ((3 / 4) - (1 / 2)) is V11() real ext-real Element of REAL
H - (1 / 2) is V11() real ext-real Element of REAL
(((1 / 2) - (1 / 4)) / ((3 / 4) - (1 / 2))) * (H - (1 / 2)) is V11() real ext-real Element of REAL
((((1 / 2) - (1 / 4)) / ((3 / 4) - (1 / 2))) * (H - (1 / 2))) + (1 / 4) is V11() real ext-real Element of REAL
h . H is set
([#] f) \/ ([#] f) is complex-membered ext-real-membered real-membered set
a \/ ([#] f) is non empty complex-membered ext-real-membered real-membered set
a \/ T is non empty closed complex-membered ext-real-membered real-membered Element of bool the carrier of I[01]
[#] (I[01] | b) is non empty non proper open closed complex-membered ext-real-membered real-membered Element of bool the carrier of (I[01] | b)
the carrier of (I[01] | b) is non empty complex-membered ext-real-membered real-membered set
bool the carrier of (I[01] | b) is non empty set
[: the carrier of (I[01] | b), the carrier of I[01]:] is non empty Relation-like set
bool [: the carrier of (I[01] | b), the carrier of I[01]:] is non empty set
s3 +* h is Relation-like Function-like set
fg is non empty Relation-like the carrier of (I[01] | b) -defined the carrier of I[01] -valued Function-like V43( the carrier of (I[01] | b)) quasi_total Element of bool [: the carrier of (I[01] | b), the carrier of I[01]:]
[#] (I[01] | Q) is non empty non proper open closed complex-membered ext-real-membered real-membered Element of bool the carrier of (I[01] | Q)
bool the carrier of (I[01] | Q) is non empty set
([#] (I[01] | b)) /\ ([#] (I[01] | Q)) is complex-membered ext-real-membered real-membered Element of bool the carrier of (I[01] | Q)
b /\ ([#] (I[01] | Q)) is complex-membered ext-real-membered real-membered Element of bool the carrier of (I[01] | Q)
b /\ Q is closed complex-membered ext-real-membered real-membered Element of bool the carrier of I[01]
{(3 / 4)} is non empty trivial complex-membered ext-real-membered real-membered set
H is set
fg . H is set
S12 . H is set
t is V11() real ext-real Element of the carrier of I[01]
dom h is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of (I[01] | T)
bool the carrier of (I[01] | T) is non empty set
fg . t is set
h . t is set
S12 . t is set
([#] (I[01] | b)) \/ ([#] (I[01] | Q)) is non empty complex-membered ext-real-membered real-membered set
b \/ ([#] (I[01] | Q)) is non empty complex-membered ext-real-membered real-membered set
b \/ Q is non empty closed complex-membered ext-real-membered real-membered Element of bool the carrier of I[01]
[#] I[01] is non empty non proper open closed complex-membered ext-real-membered real-membered Element of bool the carrier of I[01]
fg +* S12 is Relation-like Function-like set
H is non empty Relation-like the carrier of I[01] -defined the carrier of I[01] -valued Function-like V43( the carrier of I[01]) quasi_total Element of bool [: the carrier of I[01], the carrier of I[01]:]
t is V11() real ext-real Element of the carrier of (I[01] | a)
s3 . t is V11() real ext-real Element of the carrier of I[01]
(1 / 2) * t is V11() real ext-real Element of REAL
(1 / 4) - 0 is V11() real ext-real non negative Element of REAL
(1 / 2) - 0 is V11() real ext-real non negative Element of REAL
((1 / 4) - 0) / ((1 / 2) - 0) is V11() real ext-real non negative Element of REAL
t - 0 is V11() real ext-real Element of REAL
(((1 / 4) - 0) / ((1 / 2) - 0)) * (t - 0) is V11() real ext-real Element of REAL
((((1 / 4) - 0) / ((1 / 2) - 0)) * (t - 0)) + 0 is V11() real ext-real Element of REAL
t is V11() real ext-real Element of the carrier of I[01]
H . t is V11() real ext-real Element of the carrier of I[01]
() . t is V11() real ext-real Element of the carrier of I[01]
dom h is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of (I[01] | T)
bool the carrier of (I[01] | T) is non empty set
dom S12 is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of (I[01] | Q)
fg . t is set
s3 . t is set
(1 / 2) * t is V11() real ext-real Element of REAL
dom h is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of (I[01] | T)
bool the carrier of (I[01] | T) is non empty set
dom S12 is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of (I[01] | Q)
fg . t is set
h . t is set
(1 / 2) * t is V11() real ext-real Element of REAL
dom h is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of (I[01] | T)
bool the carrier of (I[01] | T) is non empty set
dom S12 is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of (I[01] | Q)
fg . t is set
h . t is set
t - (1 / 4) is V11() real ext-real Element of REAL
dom S12 is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of (I[01] | Q)
S12 . t is set
t - (1 / 4) is V11() real ext-real Element of REAL
dom S12 is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of (I[01] | Q)
S12 . t is set
2 * t is V11() real ext-real Element of REAL
(2 * t) - 1 is V11() real ext-real Element of REAL
() . 0 is set
() . 1 is set
(1 / 2) * 0 is empty trivial V11() real ext-real non positive non negative Relation-like non-empty empty-yielding complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V209() Element of REAL
2 * 1 is V11() real ext-real non negative Element of REAL
(2 * 1) - 1 is V11() real ext-real Element of REAL
T is non empty TopSpace-like TopStruct
the carrier of T is non empty set
a is Element of the carrier of T
b is Element of the carrier of T
P is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of a,b
(T,a,b,P,()) is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of a,b
Q is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like constant V43( the carrier of I[01]) quasi_total Path of b,b
P + Q is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of a,b
dom Q is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of I[01]
gg is V11() real ext-real Element of the carrier of I[01]
(T,a,b,P,()) . gg is Element of the carrier of T
(P + Q) . gg is Element of the carrier of T
dom () is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of I[01]
P * () is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Element of bool [: the carrier of I[01], the carrier of T:]
[: the carrier of I[01], the carrier of T:] is non empty Relation-like set
bool [: the carrier of I[01], the carrier of T:] is non empty set
(P * ()) . gg is Element of the carrier of T
() . gg is V11() real ext-real Element of the carrier of I[01]
P . (() . gg) is Element of the carrier of T
2 * gg is V11() real ext-real Element of REAL
P . (2 * gg) is set
2 * gg is V11() real ext-real Element of REAL
(2 * gg) - 1 is V11() real ext-real Element of REAL
P . 1 is set
Q . 0 is set
Q . ((2 * gg) - 1) is set
T is non empty TopSpace-like TopStruct
the carrier of T is non empty set
a is Element of the carrier of T
b is Element of the carrier of T
P is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of a,b
(T,a,b,P,()) is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of a,b
Q is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like constant V43( the carrier of I[01]) quasi_total Path of a,a
Q + P is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of a,b
dom Q is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of I[01]
gg is V11() real ext-real Element of the carrier of I[01]
(T,a,b,P,()) . gg is Element of the carrier of T
(Q + P) . gg is Element of the carrier of T
dom () is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of I[01]
P * () is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Element of bool [: the carrier of I[01], the carrier of T:]
[: the carrier of I[01], the carrier of T:] is non empty Relation-like set
bool [: the carrier of I[01], the carrier of T:] is non empty set
(P * ()) . gg is Element of the carrier of T
() . gg is V11() real ext-real Element of the carrier of I[01]
P . (() . gg) is Element of the carrier of T
2 * gg is V11() real ext-real Element of REAL
P . 0 is set
Q . 0 is set
Q . (2 * gg) is set
2 * gg is V11() real ext-real Element of REAL
(2 * gg) - 1 is V11() real ext-real Element of REAL
P . ((2 * gg) - 1) is set
T is non empty TopSpace-like TopStruct
the carrier of T is non empty set
a is Element of the carrier of T
b is Element of the carrier of T
P is Element of the carrier of T
Q is Element of the carrier of T
Q is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of a,b
e2 is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of b,P
Q + e2 is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of a,P
gg is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of P,Q
(Q + e2) + gg is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of a,Q
(T,a,Q,((Q + e2) + gg),()) is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of a,Q
e2 + gg is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of b,Q
Q + (e2 + gg) is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of a,Q
g is V11() real ext-real Element of the carrier of I[01]
(T,a,Q,((Q + e2) + gg),()) . g is Element of the carrier of T
(Q + (e2 + gg)) . g is Element of the carrier of T
dom () is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of I[01]
((Q + e2) + gg) * () is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Element of bool [: the carrier of I[01], the carrier of T:]
[: the carrier of I[01], the carrier of T:] is non empty Relation-like set
bool [: the carrier of I[01], the carrier of T:] is non empty set
(((Q + e2) + gg) * ()) . g is Element of the carrier of T
() . g is V11() real ext-real Element of the carrier of I[01]
((Q + e2) + gg) . (() . g) is Element of the carrier of T
(1 / 2) * g is V11() real ext-real Element of REAL
(1 / 2) * (1 / 2) is V11() real ext-real non negative Element of REAL
S3 is V11() real ext-real Element of the carrier of I[01]
2 * S3 is V11() real ext-real Element of REAL
((Q + e2) + gg) . S3 is Element of the carrier of T
S1 is V11() real ext-real Element of the carrier of I[01]
(Q + e2) . S1 is Element of the carrier of T
2 * g is V11() real ext-real Element of REAL
Q . (2 * g) is set
(1 / 2) - (1 / 4) is V11() real ext-real Element of REAL
g - (1 / 4) is V11() real ext-real Element of REAL
(3 / 4) - (1 / 4) is V11() real ext-real Element of REAL
S3 is V11() real ext-real Element of the carrier of I[01]
2 * S3 is V11() real ext-real Element of REAL
2 * (1 / 4) is V11() real ext-real non negative Element of REAL
2 * g is V11() real ext-real Element of REAL
(2 * g) - 1 is V11() real ext-real Element of REAL
2 * (3 / 4) is V11() real ext-real non negative Element of REAL
3 / 2 is V11() real ext-real non negative Element of REAL
(3 / 2) - 1 is V11() real ext-real Element of REAL
((Q + e2) + gg) . S3 is Element of the carrier of T
S1 is V11() real ext-real Element of the carrier of I[01]
(Q + e2) . S1 is Element of the carrier of T
2 * S1 is V11() real ext-real Element of REAL
(2 * S1) - 1 is V11() real ext-real Element of REAL
e2 . ((2 * S1) - 1) is set
e1 is V11() real ext-real Element of the carrier of I[01]
2 * e1 is V11() real ext-real Element of REAL
e2 . (2 * e1) is set
(e2 + gg) . e1 is Element of the carrier of T
2 * g is V11() real ext-real Element of REAL
(2 * g) - 1 is V11() real ext-real Element of REAL
2 * (3 / 4) is V11() real ext-real non negative Element of REAL
(2 * (3 / 4)) - 1 is V11() real ext-real Element of REAL
S1 is V11() real ext-real Element of the carrier of I[01]
((Q + e2) + gg) . S1 is Element of the carrier of T
2 * S1 is V11() real ext-real Element of REAL
(2 * S1) - 1 is V11() real ext-real Element of REAL
gg . ((2 * S1) - 1) is set
S3 is V11() real ext-real Element of the carrier of I[01]
(e2 + gg) . S3 is Element of the carrier of T
T is set
a is set
a is Element of bool the carrier of [:I[01],I[01]:]
b is set
P is set
Q is V11() real ext-real Element of the carrier of I[01]
Q is V11() real ext-real Element of the carrier of I[01]
[Q,Q] is non empty V29() Element of the carrier of [:I[01],I[01]:]
{Q,Q} is non empty complex-membered ext-real-membered real-membered set
{Q} is non empty trivial complex-membered ext-real-membered real-membered set
{{Q,Q},{Q}} is non empty set
2 * Q is V11() real ext-real Element of REAL
1 - (2 * Q) is V11() real ext-real Element of REAL
T is Element of bool the carrier of [:I[01],I[01]:]
a is Element of bool the carrier of [:I[01],I[01]:]
b is set
P is V11() real ext-real Element of the carrier of I[01]
Q is V11() real ext-real Element of the carrier of I[01]
[P,Q] is non empty V29() Element of the carrier of [:I[01],I[01]:]
{P,Q} is non empty complex-membered ext-real-membered real-membered set
{P} is non empty trivial complex-membered ext-real-membered real-membered set
{{P,Q},{P}} is non empty set
2 * P is V11() real ext-real Element of REAL
1 - (2 * P) is V11() real ext-real Element of REAL
b is set
P is V11() real ext-real Element of the carrier of I[01]
Q is V11() real ext-real Element of the carrier of I[01]
[P,Q] is non empty V29() Element of the carrier of [:I[01],I[01]:]
{P,Q} is non empty complex-membered ext-real-membered real-membered set
{P} is non empty trivial complex-membered ext-real-membered real-membered set
{{P,Q},{P}} is non empty set
2 * P is V11() real ext-real Element of REAL
1 - (2 * P) is V11() real ext-real Element of REAL
() is Element of bool the carrier of [:I[01],I[01]:]
T is set
a is set
a is Element of bool the carrier of [:I[01],I[01]:]
b is set
P is set
Q is V11() real ext-real Element of the carrier of I[01]
Q is V11() real ext-real Element of the carrier of I[01]
[Q,Q] is non empty V29() Element of the carrier of [:I[01],I[01]:]
{Q,Q} is non empty complex-membered ext-real-membered real-membered set
{Q} is non empty trivial complex-membered ext-real-membered real-membered set
{{Q,Q},{Q}} is non empty set
2 * Q is V11() real ext-real Element of REAL
1 - (2 * Q) is V11() real ext-real Element of REAL
(2 * Q) - 1 is V11() real ext-real Element of REAL
T is Element of bool the carrier of [:I[01],I[01]:]
a is Element of bool the carrier of [:I[01],I[01]:]
b is set
P is V11() real ext-real Element of the carrier of I[01]
Q is V11() real ext-real Element of the carrier of I[01]
[P,Q] is non empty V29() Element of the carrier of [:I[01],I[01]:]
{P,Q} is non empty complex-membered ext-real-membered real-membered set
{P} is non empty trivial complex-membered ext-real-membered real-membered set
{{P,Q},{P}} is non empty set
2 * P is V11() real ext-real Element of REAL
1 - (2 * P) is V11() real ext-real Element of REAL
(2 * P) - 1 is V11() real ext-real Element of REAL
b is set
P is V11() real ext-real Element of the carrier of I[01]
Q is V11() real ext-real Element of the carrier of I[01]
[P,Q] is non empty V29() Element of the carrier of [:I[01],I[01]:]
{P,Q} is non empty complex-membered ext-real-membered real-membered set
{P} is non empty trivial complex-membered ext-real-membered real-membered set
{{P,Q},{P}} is non empty set
2 * P is V11() real ext-real Element of REAL
1 - (2 * P) is V11() real ext-real Element of REAL
(2 * P) - 1 is V11() real ext-real Element of REAL
() is Element of bool the carrier of [:I[01],I[01]:]
T is set
a is set
a is Element of bool the carrier of [:I[01],I[01]:]
b is set
P is set
Q is V11() real ext-real Element of the carrier of I[01]
Q is V11() real ext-real Element of the carrier of I[01]
[Q,Q] is non empty V29() Element of the carrier of [:I[01],I[01]:]
{Q,Q} is non empty complex-membered ext-real-membered real-membered set
{Q} is non empty trivial complex-membered ext-real-membered real-membered set
{{Q,Q},{Q}} is non empty set
2 * Q is V11() real ext-real Element of REAL
(2 * Q) - 1 is V11() real ext-real Element of REAL
T is Element of bool the carrier of [:I[01],I[01]:]
a is Element of bool the carrier of [:I[01],I[01]:]
b is set
P is V11() real ext-real Element of the carrier of I[01]
Q is V11() real ext-real Element of the carrier of I[01]
[P,Q] is non empty V29() Element of the carrier of [:I[01],I[01]:]
{P,Q} is non empty complex-membered ext-real-membered real-membered set
{P} is non empty trivial complex-membered ext-real-membered real-membered set
{{P,Q},{P}} is non empty set
2 * P is V11() real ext-real Element of REAL
(2 * P) - 1 is V11() real ext-real Element of REAL
b is set
P is V11() real ext-real Element of the carrier of I[01]
Q is V11() real ext-real Element of the carrier of I[01]
[P,Q] is non empty V29() Element of the carrier of [:I[01],I[01]:]
{P,Q} is non empty complex-membered ext-real-membered real-membered set
{P} is non empty trivial complex-membered ext-real-membered real-membered set
{{P,Q},{P}} is non empty set
2 * P is V11() real ext-real Element of REAL
(2 * P) - 1 is V11() real ext-real Element of REAL
() is Element of bool the carrier of [:I[01],I[01]:]
a is set
P is V11() real ext-real Element of the carrier of I[01]
Q is V11() real ext-real Element of the carrier of I[01]
[P,Q] is non empty V29() Element of the carrier of [:I[01],I[01]:]
{P,Q} is non empty complex-membered ext-real-membered real-membered set
{P} is non empty trivial complex-membered ext-real-membered real-membered set
{{P,Q},{P}} is non empty set
2 * P is V11() real ext-real Element of REAL
1 - (2 * P) is V11() real ext-real Element of REAL
b is Element of the carrier of [:I[01],I[01]:]
b `1 is V11() real ext-real set
b `2 is V11() real ext-real set
a is set
b is Element of the carrier of [:I[01],I[01]:]
b `2 is V11() real ext-real set
b `1 is V11() real ext-real set
2 * (b `1) is V11() real ext-real Element of REAL
1 - (2 * (b `1)) is V11() real ext-real Element of REAL
a `1 is set
a `2 is set
[(a `1),(a `2)] is non empty V29() set
{(a `1),(a `2)} is non empty set
{(a `1)} is non empty trivial set
{{(a `1),(a `2)},{(a `1)}} is non empty set
a is set
P is V11() real ext-real Element of the carrier of I[01]
Q is V11() real ext-real Element of the carrier of I[01]
[P,Q] is non empty V29() Element of the carrier of [:I[01],I[01]:]
{P,Q} is non empty complex-membered ext-real-membered real-membered set
{P} is non empty trivial complex-membered ext-real-membered real-membered set
{{P,Q},{P}} is non empty set
2 * P is V11() real ext-real Element of REAL
1 - (2 * P) is V11() real ext-real Element of REAL
(2 * P) - 1 is V11() real ext-real Element of REAL
b is Element of the carrier of [:I[01],I[01]:]
b `1 is V11() real ext-real set
b `2 is V11() real ext-real set
a is set
b is Element of the carrier of [:I[01],I[01]:]
b `1 is V11() real ext-real set
2 * (b `1) is V11() real ext-real Element of REAL
1 - (2 * (b `1)) is V11() real ext-real Element of REAL
b `2 is V11() real ext-real set
(2 * (b `1)) - 1 is V11() real ext-real Element of REAL
a `1 is set
a `2 is set
[(a `1),(a `2)] is non empty V29() set
{(a `1),(a `2)} is non empty set
{(a `1)} is non empty trivial set
{{(a `1),(a `2)},{(a `1)}} is non empty set
a is set
P is V11() real ext-real Element of the carrier of I[01]
Q is V11() real ext-real Element of the carrier of I[01]
[P,Q] is non empty V29() Element of the carrier of [:I[01],I[01]:]
{P,Q} is non empty complex-membered ext-real-membered real-membered set
{P} is non empty trivial complex-membered ext-real-membered real-membered set
{{P,Q},{P}} is non empty set
2 * P is V11() real ext-real Element of REAL
(2 * P) - 1 is V11() real ext-real Element of REAL
b is Element of the carrier of [:I[01],I[01]:]
b `1 is V11() real ext-real set
b `2 is V11() real ext-real set
a is set
b is Element of the carrier of [:I[01],I[01]:]
b `2 is V11() real ext-real set
b `1 is V11() real ext-real set
2 * (b `1) is V11() real ext-real Element of REAL
(2 * (b `1)) - 1 is V11() real ext-real Element of REAL
a `1 is set
a `2 is set
[(a `1),(a `2)] is non empty V29() set
{(a `1),(a `2)} is non empty set
{(a `1)} is non empty trivial set
{{(a `1),(a `2)},{(a `1)}} is non empty set
() \/ () is non empty closed Element of bool the carrier of [:I[01],I[01]:]
(() \/ ()) \/ () is non empty closed Element of bool the carrier of [:I[01],I[01]:]
T is set
T `1 is set
T `2 is set
a is V11() real ext-real Element of the carrier of I[01]
b is V11() real ext-real Element of the carrier of I[01]
[a,b] is non empty V29() Element of the carrier of [:I[01],I[01]:]
{a,b} is non empty complex-membered ext-real-membered real-membered set
{a} is non empty trivial complex-membered ext-real-membered real-membered set
{{a,b},{a}} is non empty set
2 * a is V11() real ext-real Element of REAL
1 - (2 * a) is V11() real ext-real Element of REAL
(2 * a) - 1 is V11() real ext-real Element of REAL
(2 * a) - 1 is V11() real ext-real Element of REAL
(2 * a) - 1 is V11() real ext-real Element of REAL
2 * a is V11() real ext-real Element of REAL
1 - (2 * a) is V11() real ext-real Element of REAL
2 * a is V11() real ext-real Element of REAL
1 - (2 * a) is V11() real ext-real Element of REAL
() /\ () is closed Element of bool the carrier of [:I[01],I[01]:]
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier of [:I[01],I[01]:] : b<sub>1</sub> `2 = 1 - (2 * (b₁ `1)) } is set
a is set
b is Element of the carrier of [:I[01],I[01]:]
b `2 is V11() real ext-real set
b `1 is V11() real ext-real set
2 * (b `1) is V11() real ext-real Element of REAL
1 - (2 * (b `1)) is V11() real ext-real Element of REAL
P is Element of the carrier of [:I[01],I[01]:]
P `1 is V11() real ext-real set
2 * (P `1) is V11() real ext-real Element of REAL
1 - (2 * (P `1)) is V11() real ext-real Element of REAL
P `2 is V11() real ext-real set
(2 * (P `1)) - 1 is V11() real ext-real Element of REAL
a is set
b is Element of the carrier of [:I[01],I[01]:]
b `2 is V11() real ext-real set
b `1 is V11() real ext-real set
2 * (b `1) is V11() real ext-real Element of REAL
1 - (2 * (b `1)) is V11() real ext-real Element of REAL
[(b `1),(b `2)] is non empty V29() set
{(b `1),(b `2)} is non empty complex-membered ext-real-membered real-membered set
{(b `1)} is non empty trivial complex-membered ext-real-membered real-membered set
{{(b `1),(b `2)},{(b `1)}} is non empty set
0 + (2 * (b `1)) is V11() real ext-real Element of REAL
(2 * (b `1)) / 2 is V11() real ext-real Element of REAL
(2 * (b `1)) - 1 is V11() real ext-real Element of REAL
() /\ () is closed Element of bool the carrier of [:I[01],I[01]:]
{ b<sub>1</sub> where b<sub>1</sub> is Element of the carrier of [:I[01],I[01]:] : b<sub>1</sub> `2 = (2 * (b₁ `1)) - 1 } is set
a is set
b is Element of the carrier of [:I[01],I[01]:]
b `2 is V11() real ext-real set
b `1 is V11() real ext-real set
2 * (b `1) is V11() real ext-real Element of REAL
(2 * (b `1)) - 1 is V11() real ext-real Element of REAL
P is Element of the carrier of [:I[01],I[01]:]
P `1 is V11() real ext-real set
2 * (P `1) is V11() real ext-real Element of REAL
1 - (2 * (P `1)) is V11() real ext-real Element of REAL
P `2 is V11() real ext-real set
(2 * (P `1)) - 1 is V11() real ext-real Element of REAL
a is set
b is Element of the carrier of [:I[01],I[01]:]
b `2 is V11() real ext-real set
b `1 is V11() real ext-real set
2 * (b `1) is V11() real ext-real Element of REAL
(2 * (b `1)) - 1 is V11() real ext-real Element of REAL
[(b `1),(b `2)] is non empty V29() set
{(b `1),(b `2)} is non empty complex-membered ext-real-membered real-membered set
{(b `1)} is non empty trivial complex-membered ext-real-membered real-membered set
{{(b `1),(b `2)},{(b `1)}} is non empty set
0 + 1 is non empty V11() real ext-real positive non negative Element of REAL
(2 * (b `1)) / 2 is V11() real ext-real Element of REAL
1 - (2 * (b `1)) is V11() real ext-real Element of REAL
a is Element of the carrier of [:I[01],I[01]:]
a `1 is V11() real ext-real set
b is V11() real ext-real Element of the carrier of I[01]
P is V11() real ext-real Element of the carrier of I[01]
[b,P] is non empty V29() Element of the carrier of [:I[01],I[01]:]
{b,P} is non empty complex-membered ext-real-membered real-membered set
{b} is non empty trivial complex-membered ext-real-membered real-membered set
{{b,P},{b}} is non empty set
2 * b is V11() real ext-real Element of REAL
1 - (2 * b) is V11() real ext-real Element of REAL
0 + (2 * b) is V11() real ext-real Element of REAL
(2 * b) / 2 is V11() real ext-real Element of REAL
a `2 is V11() real ext-real set
[(a `1),(a `2)] is non empty V29() set
{(a `1),(a `2)} is non empty complex-membered ext-real-membered real-membered set
{(a `1)} is non empty trivial complex-membered ext-real-membered real-membered set
{{(a `1),(a `2)},{(a `1)}} is non empty set
a is Element of the carrier of [:I[01],I[01]:]
a `1 is V11() real ext-real set
b is V11() real ext-real Element of the carrier of I[01]
P is V11() real ext-real Element of the carrier of I[01]
[b,P] is non empty V29() Element of the carrier of [:I[01],I[01]:]
{b,P} is non empty complex-membered ext-real-membered real-membered set
{b} is non empty trivial complex-membered ext-real-membered real-membered set
{{b,P},{b}} is non empty set
2 * b is V11() real ext-real Element of REAL
(2 * b) - 1 is V11() real ext-real Element of REAL
0 + 1 is non empty V11() real ext-real positive non negative Element of REAL
(2 * b) / 2 is V11() real ext-real Element of REAL
a `2 is V11() real ext-real set
[(a `1),(a `2)] is non empty V29() set
{(a `1),(a `2)} is non empty complex-membered ext-real-membered real-membered set
{(a `1)} is non empty trivial complex-membered ext-real-membered real-membered set
{{(a `1),(a `2)},{(a `1)}} is non empty set
T is V11() real ext-real Element of the carrier of I[01]
[0,T] is non empty V29() set
{0,T} is non empty complex-membered ext-real-membered real-membered set
{0} is non empty trivial complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered set
{{0,T},{0}} is non empty set
2 * 0 is empty trivial V11() real ext-real non positive non negative Relation-like non-empty empty-yielding complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V209() Element of REAL
1 - (2 * 0) is non empty V11() real ext-real positive non negative Element of REAL
T is set
[0,T] is non empty V29() set
{0,T} is non empty set
{0} is non empty trivial complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered set
{{0,T},{0}} is non empty set
a is V11() real ext-real Element of the carrier of I[01]
b is V11() real ext-real Element of the carrier of I[01]
[a,b] is non empty V29() Element of the carrier of [:I[01],I[01]:]
{a,b} is non empty complex-membered ext-real-membered real-membered set
{a} is non empty trivial complex-membered ext-real-membered real-membered set
{{a,b},{a}} is non empty set
2 * a is V11() real ext-real Element of REAL
1 - (2 * a) is V11() real ext-real Element of REAL
(2 * a) - 1 is V11() real ext-real Element of REAL
T is set
[T,1] is non empty V29() set
{T,1} is non empty set
{T} is non empty trivial set
{{T,1},{T}} is non empty set
a is V11() real ext-real Element of the carrier of I[01]
b is V11() real ext-real Element of the carrier of I[01]
[a,b] is non empty V29() Element of the carrier of [:I[01],I[01]:]
{a,b} is non empty complex-membered ext-real-membered real-membered set
{a} is non empty trivial complex-membered ext-real-membered real-membered set
{{a,b},{a}} is non empty set
2 * a is V11() real ext-real Element of REAL
(2 * a) - 1 is V11() real ext-real Element of REAL
1 + 1 is non empty V11() real ext-real positive non negative Element of REAL
2 / 2 is V11() real ext-real non negative Element of REAL
(2 * a) / 2 is V11() real ext-real Element of REAL
[0,1] is non empty V29() set
{0,1} is non empty complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered set
{0} is non empty trivial complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered set
{{0,1},{0}} is non empty set
2 * 0 is empty trivial V11() real ext-real non positive non negative Relation-like non-empty empty-yielding complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V209() Element of REAL
1 - (2 * 0) is non empty V11() real ext-real positive non negative Element of REAL
(2 * 0) - 1 is non empty V11() real ext-real non positive negative Element of REAL
T is V11() real ext-real Element of the carrier of I[01]
[T,1] is non empty V29() set
{T,1} is non empty complex-membered ext-real-membered real-membered set
{T} is non empty trivial complex-membered ext-real-membered real-membered set
{{T,1},{T}} is non empty set
2 * T is V11() real ext-real Element of REAL
2 * 1 is V11() real ext-real non negative Element of REAL
(2 * T) - 1 is V11() real ext-real Element of REAL
(2 * 1) - 1 is V11() real ext-real Element of REAL
1 - (2 * T) is V11() real ext-real Element of REAL
2 * 0 is empty trivial V11() real ext-real non positive non negative Relation-like non-empty empty-yielding complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V209() Element of REAL
1 - (2 * 0) is non empty V11() real ext-real positive non negative Element of REAL
[(1 / 2),0] is non empty V29() set
{(1 / 2),0} is non empty complex-membered ext-real-membered real-membered set
{{(1 / 2),0},{(1 / 2)}} is non empty set
[1,1] is non empty V29() set
{1,1} is non empty complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered set
{1} is non empty trivial complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered set
{{1,1},{1}} is non empty set
2 * (1 / 2) is V11() real ext-real non negative Element of REAL
(2 * (1 / 2)) - 1 is V11() real ext-real Element of REAL
2 * 1 is V11() real ext-real non negative Element of REAL
(2 * 1) - 1 is V11() real ext-real Element of REAL
2 * (1 / 2) is V11() real ext-real non negative Element of REAL
1 - (2 * (1 / 2)) is V11() real ext-real Element of REAL
T is V11() real ext-real Element of the carrier of I[01]
[1,T] is non empty V29() set
{1,T} is non empty complex-membered ext-real-membered real-membered set
{{1,T},{1}} is non empty set
2 * 1 is V11() real ext-real non negative Element of REAL
(2 * 1) - 1 is V11() real ext-real Element of REAL
T is V11() real ext-real Element of the carrier of I[01]
[T,0] is non empty V29() set
{T,0} is non empty complex-membered ext-real-membered real-membered set
{T} is non empty trivial complex-membered ext-real-membered real-membered set
{{T,0},{T}} is non empty set
2 * (1 / 2) is V11() real ext-real non negative Element of REAL
2 * T is V11() real ext-real Element of REAL
(2 * (1 / 2)) - 1 is V11() real ext-real Element of REAL
(2 * T) - 1 is V11() real ext-real Element of REAL
T is V11() real ext-real Element of the carrier of I[01]
[T,0] is non empty V29() set
{T,0} is non empty complex-membered ext-real-membered real-membered set
{T} is non empty trivial complex-membered ext-real-membered real-membered set
{{T,0},{T}} is non empty set
2 * T is V11() real ext-real Element of REAL
2 * (1 / 2) is V11() real ext-real non negative Element of REAL
1 - (2 * (1 / 2)) is V11() real ext-real Element of REAL
1 - (2 * T) is V11() real ext-real Element of REAL
T is V11() real ext-real Element of the carrier of I[01]
[T,0] is non empty V29() set
{T,0} is non empty complex-membered ext-real-membered real-membered set
{T} is non empty trivial complex-membered ext-real-membered real-membered set
{{T,0},{T}} is non empty set
a is V11() real ext-real Element of the carrier of I[01]
b is V11() real ext-real Element of the carrier of I[01]
[a,b] is non empty V29() Element of the carrier of [:I[01],I[01]:]
{a,b} is non empty complex-membered ext-real-membered real-membered set
{a} is non empty trivial complex-membered ext-real-membered real-membered set
{{a,b},{a}} is non empty set
2 * a is V11() real ext-real Element of REAL
1 - (2 * a) is V11() real ext-real Element of REAL
(2 * a) - 1 is V11() real ext-real Element of REAL
2 * T is V11() real ext-real Element of REAL
0 + (2 * T) is V11() real ext-real Element of REAL
(2 * T) / 2 is V11() real ext-real Element of REAL
a is V11() real ext-real Element of the carrier of I[01]
b is V11() real ext-real Element of the carrier of I[01]
[a,b] is non empty V29() Element of the carrier of [:I[01],I[01]:]
{a,b} is non empty complex-membered ext-real-membered real-membered set
{a} is non empty trivial complex-membered ext-real-membered real-membered set
{{a,b},{a}} is non empty set
2 * a is V11() real ext-real Element of REAL
(2 * a) - 1 is V11() real ext-real Element of REAL
0 + 1 is non empty V11() real ext-real positive non negative Element of REAL
2 * T is V11() real ext-real Element of REAL
(2 * T) / 2 is V11() real ext-real Element of REAL
() /\ () is closed Element of bool the carrier of [:I[01],I[01]:]
{[(1 / 2),0]} is non empty trivial Relation-like set
T is set
a is Element of the carrier of [:I[01],I[01]:]
a `1 is V11() real ext-real set
a `2 is V11() real ext-real set
b is Element of the carrier of [:I[01],I[01]:]
b `2 is V11() real ext-real set
b `1 is V11() real ext-real set
2 * (b `1) is V11() real ext-real Element of REAL
(2 * (b `1)) - 1 is V11() real ext-real Element of REAL
T is V11() real ext-real Element of the carrier of I[01]
a is V11() real ext-real Element of the carrier of I[01]
[T,a] is non empty V29() Element of the carrier of [:I[01],I[01]:]
{T,a} is non empty complex-membered ext-real-membered real-membered set
{T} is non empty trivial complex-membered ext-real-membered real-membered set
{{T,a},{T}} is non empty set
T is non empty TopSpace-like TopStruct
the carrier of T is non empty set
a is Element of the carrier of T
b is Element of the carrier of T
P is Element of the carrier of T
Q is Element of the carrier of T
Q is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of a,b
e2 is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of b,P
Q + e2 is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of a,P
gg is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of P,Q
(Q + e2) + gg is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of a,Q
e2 + gg is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of b,Q
Q + (e2 + gg) is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of a,Q
(T,a,Q,((Q + e2) + gg),()) is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of a,Q
T is non empty TopSpace-like V74() pathwise_connected TopStruct
the carrier of T is non empty set
a is Element of the carrier of T
b is Element of the carrier of T
P is Element of the carrier of T
Q is Element of the carrier of T
Q is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total continuous Path of a,b
e2 is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total continuous Path of b,P
Q + e2 is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total continuous Path of a,P
gg is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total continuous Path of P,Q
(Q + e2) + gg is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total continuous Path of a,Q
e2 + gg is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total continuous Path of b,Q
Q + (e2 + gg) is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total continuous Path of a,Q
T is non empty TopSpace-like TopStruct
the carrier of T is non empty set
a is Element of the carrier of T
b is Element of the carrier of T
P is Element of the carrier of T
Closed-Interval-TSpace (0,(1 / 2)) is non empty strict TopSpace-like real-membered SubSpace of R^1
the carrier of (Closed-Interval-TSpace (0,(1 / 2))) is non empty complex-membered ext-real-membered real-membered set
[: the carrier of (Closed-Interval-TSpace (0,(1 / 2))), the carrier of I[01]:] is non empty Relation-like set
bool [: the carrier of (Closed-Interval-TSpace (0,(1 / 2))), the carrier of I[01]:] is non empty set
(0,(1 / 2),0,1) is non empty Relation-like the carrier of (Closed-Interval-TSpace (0,(1 / 2))) -defined the carrier of (Closed-Interval-TSpace (0,1)) -valued Function-like V43( the carrier of (Closed-Interval-TSpace (0,(1 / 2)))) quasi_total Element of bool [: the carrier of (Closed-Interval-TSpace (0,(1 / 2))), the carrier of (Closed-Interval-TSpace (0,1)):]
[: the carrier of (Closed-Interval-TSpace (0,(1 / 2))), the carrier of (Closed-Interval-TSpace (0,1)):] is non empty Relation-like set
bool [: the carrier of (Closed-Interval-TSpace (0,(1 / 2))), the carrier of (Closed-Interval-TSpace (0,1)):] is non empty set
P[01] (0,(1 / 2),((#) (0,1)),((0,1) (#))) is non empty Relation-like the carrier of (Closed-Interval-TSpace (0,(1 / 2))) -defined the carrier of (Closed-Interval-TSpace (0,1)) -valued Function-like V43( the carrier of (Closed-Interval-TSpace (0,(1 / 2)))) quasi_total Element of bool [: the carrier of (Closed-Interval-TSpace (0,(1 / 2))), the carrier of (Closed-Interval-TSpace (0,1)):]
L[01] (((#) (0,1)),((0,1) (#))) is non empty Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined the carrier of (Closed-Interval-TSpace (0,1)) -valued Function-like V43( the carrier of (Closed-Interval-TSpace (0,1))) quasi_total Element of bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace (0,1)):]
(L[01] (((#) (0,1)),((0,1) (#)))) * (P[01] (0,(1 / 2),((#) (0,1)),((0,1) (#)))) is non empty Relation-like the carrier of (Closed-Interval-TSpace (0,(1 / 2))) -defined the carrier of (Closed-Interval-TSpace (0,1)) -valued Function-like V43( the carrier of (Closed-Interval-TSpace (0,(1 / 2)))) quasi_total Element of bool [: the carrier of (Closed-Interval-TSpace (0,(1 / 2))), the carrier of (Closed-Interval-TSpace (0,1)):]
e2 is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of a,b
gg is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of a,b
gg is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of b,P
S2 is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of b,P
e2 + gg is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of a,P
gg + S2 is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of a,P
Closed-Interval-TSpace ((1 / 2),1) is non empty strict TopSpace-like real-membered SubSpace of R^1
the carrier of (Closed-Interval-TSpace ((1 / 2),1)) is non empty complex-membered ext-real-membered real-membered set
[: the carrier of (Closed-Interval-TSpace ((1 / 2),1)), the carrier of I[01]:] is non empty Relation-like set
bool [: the carrier of (Closed-Interval-TSpace ((1 / 2),1)), the carrier of I[01]:] is non empty set
((1 / 2),1,0,1) is non empty Relation-like the carrier of (Closed-Interval-TSpace ((1 / 2),1)) -defined the carrier of (Closed-Interval-TSpace (0,1)) -valued Function-like V43( the carrier of (Closed-Interval-TSpace ((1 / 2),1))) quasi_total Element of bool [: the carrier of (Closed-Interval-TSpace ((1 / 2),1)), the carrier of (Closed-Interval-TSpace (0,1)):]
[: the carrier of (Closed-Interval-TSpace ((1 / 2),1)), the carrier of (Closed-Interval-TSpace (0,1)):] is non empty Relation-like set
bool [: the carrier of (Closed-Interval-TSpace ((1 / 2),1)), the carrier of (Closed-Interval-TSpace (0,1)):] is non empty set
P[01] ((1 / 2),1,((#) (0,1)),((0,1) (#))) is non empty Relation-like the carrier of (Closed-Interval-TSpace ((1 / 2),1)) -defined the carrier of (Closed-Interval-TSpace (0,1)) -valued Function-like V43( the carrier of (Closed-Interval-TSpace ((1 / 2),1))) quasi_total Element of bool [: the carrier of (Closed-Interval-TSpace ((1 / 2),1)), the carrier of (Closed-Interval-TSpace (0,1)):]
(L[01] (((#) (0,1)),((0,1) (#)))) * (P[01] ((1 / 2),1,((#) (0,1)),((0,1) (#)))) is non empty Relation-like the carrier of (Closed-Interval-TSpace ((1 / 2),1)) -defined the carrier of (Closed-Interval-TSpace (0,1)) -valued Function-like V43( the carrier of (Closed-Interval-TSpace ((1 / 2),1))) quasi_total Element of bool [: the carrier of (Closed-Interval-TSpace ((1 / 2),1)), the carrier of (Closed-Interval-TSpace (0,1)):]
e1 is non empty closed compact Element of bool the carrier of [:I[01],I[01]:]
[:I[01],I[01]:] | e1 is non empty strict TopSpace-like T_0 T_1 T_2 compact SubSpace of [:I[01],I[01]:]
S1 is non empty closed compact Element of bool the carrier of [:I[01],I[01]:]
[:I[01],I[01]:] | S1 is non empty strict TopSpace-like T_0 T_1 T_2 compact SubSpace of [:I[01],I[01]:]
g is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of I[01]
[#] I[01] is non empty non proper open closed complex-membered ext-real-membered real-membered Element of bool the carrier of I[01]
I[01] | g is non empty strict TopSpace-like T_0 T_1 T_2 real-membered SubSpace of I[01]
Q is non empty Relation-like the carrier of (Closed-Interval-TSpace (0,(1 / 2))) -defined the carrier of I[01] -valued Function-like V43( the carrier of (Closed-Interval-TSpace (0,(1 / 2)))) quasi_total continuous Element of bool [: the carrier of (Closed-Interval-TSpace (0,(1 / 2))), the carrier of I[01]:]
[:Q,(id I[01]):] is non empty Relation-like the carrier of [:(Closed-Interval-TSpace (0,(1 / 2))),I[01]:] -defined the carrier of [:I[01],I[01]:] -valued Function-like V43( the carrier of [:(Closed-Interval-TSpace (0,(1 / 2))),I[01]:]) quasi_total continuous Element of bool [: the carrier of [:(Closed-Interval-TSpace (0,(1 / 2))),I[01]:], the carrier of [:I[01],I[01]:]:]
[:(Closed-Interval-TSpace (0,(1 / 2))),I[01]:] is non empty strict TopSpace-like TopStruct
the carrier of [:(Closed-Interval-TSpace (0,(1 / 2))),I[01]:] is non empty set
[: the carrier of [:(Closed-Interval-TSpace (0,(1 / 2))),I[01]:], the carrier of [:I[01],I[01]:]:] is non empty Relation-like set
bool [: the carrier of [:(Closed-Interval-TSpace (0,(1 / 2))),I[01]:], the carrier of [:I[01],I[01]:]:] is non empty set
g is non empty Relation-like the carrier of (Closed-Interval-TSpace ((1 / 2),1)) -defined the carrier of I[01] -valued Function-like V43( the carrier of (Closed-Interval-TSpace ((1 / 2),1))) quasi_total continuous Element of bool [: the carrier of (Closed-Interval-TSpace ((1 / 2),1)), the carrier of I[01]:]
[:g,(id I[01]):] is non empty Relation-like the carrier of [:(Closed-Interval-TSpace ((1 / 2),1)),I[01]:] -defined the carrier of [:I[01],I[01]:] -valued Function-like V43( the carrier of [:(Closed-Interval-TSpace ((1 / 2),1)),I[01]:]) quasi_total continuous Element of bool [: the carrier of [:(Closed-Interval-TSpace ((1 / 2),1)),I[01]:], the carrier of [:I[01],I[01]:]:]
[:(Closed-Interval-TSpace ((1 / 2),1)),I[01]:] is non empty strict TopSpace-like TopStruct
the carrier of [:(Closed-Interval-TSpace ((1 / 2),1)),I[01]:] is non empty set
[: the carrier of [:(Closed-Interval-TSpace ((1 / 2),1)),I[01]:], the carrier of [:I[01],I[01]:]:] is non empty Relation-like set
bool [: the carrier of [:(Closed-Interval-TSpace ((1 / 2),1)),I[01]:], the carrier of [:I[01],I[01]:]:] is non empty set
S12 is non empty Relation-like the carrier of [:(Closed-Interval-TSpace ((1 / 2),1)),I[01]:] -defined the carrier of [:I[01],I[01]:] -valued Function-like V43( the carrier of [:(Closed-Interval-TSpace ((1 / 2),1)),I[01]:]) quasi_total continuous Element of bool [: the carrier of [:(Closed-Interval-TSpace ((1 / 2),1)),I[01]:], the carrier of [:I[01],I[01]:]:]
dom S12 is non empty Element of bool the carrier of [:(Closed-Interval-TSpace ((1 / 2),1)),I[01]:]
bool the carrier of [:(Closed-Interval-TSpace ((1 / 2),1)),I[01]:] is non empty set
[: the carrier of [:I[01],I[01]:], the carrier of T:] is non empty Relation-like set
bool [: the carrier of [:I[01],I[01]:], the carrier of T:] is non empty set
h is non empty Relation-like the carrier of [:I[01],I[01]:] -defined the carrier of T -valued Function-like V43( the carrier of [:I[01],I[01]:]) quasi_total Element of bool [: the carrier of [:I[01],I[01]:], the carrier of T:]
S3 is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of I[01]
I[01] | S3 is non empty strict TopSpace-like T_0 T_1 T_2 real-membered SubSpace of I[01]
the carrier of ([:I[01],I[01]:] | e1) is non empty set
[: the carrier of ([:I[01],I[01]:] | e1), the carrier of T:] is non empty Relation-like set
bool [: the carrier of ([:I[01],I[01]:] | e1), the carrier of T:] is non empty set
S12 is non empty Relation-like the carrier of [:(Closed-Interval-TSpace (0,(1 / 2))),I[01]:] -defined the carrier of [:I[01],I[01]:] -valued Function-like V43( the carrier of [:(Closed-Interval-TSpace (0,(1 / 2))),I[01]:]) quasi_total continuous Element of bool [: the carrier of [:(Closed-Interval-TSpace (0,(1 / 2))),I[01]:], the carrier of [:I[01],I[01]:]:]
h * S12 is non empty Relation-like the carrier of [:(Closed-Interval-TSpace (0,(1 / 2))),I[01]:] -defined the carrier of T -valued Function-like V43( the carrier of [:(Closed-Interval-TSpace (0,(1 / 2))),I[01]:]) quasi_total Element of bool [: the carrier of [:(Closed-Interval-TSpace (0,(1 / 2))),I[01]:], the carrier of T:]
[: the carrier of [:(Closed-Interval-TSpace (0,(1 / 2))),I[01]:], the carrier of T:] is non empty Relation-like set
bool [: the carrier of [:(Closed-Interval-TSpace (0,(1 / 2))),I[01]:], the carrier of T:] is non empty set
s3 is non empty Relation-like the carrier of [:I[01],I[01]:] -defined the carrier of T -valued Function-like V43( the carrier of [:I[01],I[01]:]) quasi_total Element of bool [: the carrier of [:I[01],I[01]:], the carrier of T:]
hh is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of I[01]
I[01] | hh is non empty strict TopSpace-like T_0 T_1 T_2 real-membered SubSpace of I[01]
the carrier of ([:I[01],I[01]:] | S1) is non empty set
[: the carrier of ([:I[01],I[01]:] | S1), the carrier of T:] is non empty Relation-like set
bool [: the carrier of ([:I[01],I[01]:] | S1), the carrier of T:] is non empty set
s3 * S12 is non empty Relation-like the carrier of [:(Closed-Interval-TSpace ((1 / 2),1)),I[01]:] -defined the carrier of T -valued Function-like V43( the carrier of [:(Closed-Interval-TSpace ((1 / 2),1)),I[01]:]) quasi_total Element of bool [: the carrier of [:(Closed-Interval-TSpace ((1 / 2),1)),I[01]:], the carrier of T:]
[: the carrier of [:(Closed-Interval-TSpace ((1 / 2),1)),I[01]:], the carrier of T:] is non empty Relation-like set
bool [: the carrier of [:(Closed-Interval-TSpace ((1 / 2),1)),I[01]:], the carrier of T:] is non empty set
s1 is non empty Relation-like the carrier of ([:I[01],I[01]:] | S1) -defined the carrier of T -valued Function-like V43( the carrier of ([:I[01],I[01]:] | S1)) quasi_total continuous Element of bool [: the carrier of ([:I[01],I[01]:] | S1), the carrier of T:]
dom s1 is non empty Element of bool the carrier of ([:I[01],I[01]:] | S1)
bool the carrier of ([:I[01],I[01]:] | S1) is non empty set
[#] ([:I[01],I[01]:] | e1) is non empty non proper open closed Element of bool the carrier of ([:I[01],I[01]:] | e1)
bool the carrier of ([:I[01],I[01]:] | e1) is non empty set
[#] ([:I[01],I[01]:] | S1) is non empty non proper open closed Element of bool the carrier of ([:I[01],I[01]:] | S1)
([#] ([:I[01],I[01]:] | e1)) /\ ([#] ([:I[01],I[01]:] | S1)) is Element of bool the carrier of ([:I[01],I[01]:] | S1)
h is non empty Relation-like the carrier of ([:I[01],I[01]:] | e1) -defined the carrier of T -valued Function-like V43( the carrier of ([:I[01],I[01]:] | e1)) quasi_total continuous Element of bool [: the carrier of ([:I[01],I[01]:] | e1), the carrier of T:]
g . (1 / 2) is set
s2 is set
h . s2 is set
s1 . s2 is set
Q . (1 / 2) is set
fg is set
H is set
[fg,H] is non empty V29() set
{fg,H} is non empty set
{fg} is non empty trivial set
{{fg,H},{fg}} is non empty set
t is V11() real ext-real Element of the carrier of I[01]
dom (id I[01]) is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of I[01]
dom Q is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of (Closed-Interval-TSpace (0,(1 / 2)))
bool the carrier of (Closed-Interval-TSpace (0,(1 / 2))) is non empty set
[fg,t] is non empty V29() set
{fg,t} is non empty set
{{fg,t},{fg}} is non empty set
[:(dom Q),(dom (id I[01])):] is non empty Relation-like Element of bool the carrier of [:(Closed-Interval-TSpace (0,(1 / 2))),I[01]:]
bool the carrier of [:(Closed-Interval-TSpace (0,(1 / 2))),I[01]:] is non empty set
dom g is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of (Closed-Interval-TSpace ((1 / 2),1))
bool the carrier of (Closed-Interval-TSpace ((1 / 2),1)) is non empty set
[:(dom g),(dom (id I[01])):] is non empty Relation-like Element of bool the carrier of [:(Closed-Interval-TSpace ((1 / 2),1)),I[01]:]
dom S12 is non empty Element of bool the carrier of [:(Closed-Interval-TSpace (0,(1 / 2))),I[01]:]
S12 . (fg,t) is set
S12 . [fg,t] is set
h . (S12 . (fg,t)) is set
Q . fg is set
(id I[01]) . t is V11() real ext-real Element of the carrier of I[01]
h . ((Q . fg),((id I[01]) . t)) is set
[(Q . fg),((id I[01]) . t)] is non empty V29() set
{(Q . fg),((id I[01]) . t)} is non empty set
{(Q . fg)} is non empty trivial set
{{(Q . fg),((id I[01]) . t)},{(Q . fg)}} is non empty set
h . [(Q . fg),((id I[01]) . t)] is set
g . fg is set
s3 . ((g . fg),((id I[01]) . t)) is set
[(g . fg),((id I[01]) . t)] is non empty V29() set
{(g . fg),((id I[01]) . t)} is non empty set
{(g . fg)} is non empty trivial set
{{(g . fg),((id I[01]) . t)},{(g . fg)}} is non empty set
s3 . [(g . fg),((id I[01]) . t)] is set
S12 . (fg,t) is set
S12 . [fg,t] is set
s3 . (S12 . (fg,t)) is set
([#] ([:I[01],I[01]:] | e1)) \/ ([#] ([:I[01],I[01]:] | S1)) is non empty set
h +* s1 is Relation-like Function-like set
s2 is non empty Relation-like the carrier of [:I[01],I[01]:] -defined the carrier of T -valued Function-like V43( the carrier of [:I[01],I[01]:]) quasi_total Element of bool [: the carrier of [:I[01],I[01]:], the carrier of T:]
dom S12 is non empty Element of bool the carrier of [:(Closed-Interval-TSpace (0,(1 / 2))),I[01]:]
bool the carrier of [:(Closed-Interval-TSpace (0,(1 / 2))),I[01]:] is non empty set
fg is V11() real ext-real Element of the carrier of I[01]
s2 . (fg,0) is set
[fg,0] is non empty V29() set
{fg,0} is non empty complex-membered ext-real-membered real-membered set
{fg} is non empty trivial complex-membered ext-real-membered real-membered set
{{fg,0},{fg}} is non empty set
s2 . [fg,0] is set
(e2 + gg) . fg is Element of the carrier of T
s2 . (fg,1) is set
[fg,1] is non empty V29() set
{fg,1} is non empty complex-membered ext-real-membered real-membered set
{{fg,1},{fg}} is non empty set
s2 . [fg,1] is set
(gg + S2) . fg is Element of the carrier of T
2 * fg is V11() real ext-real Element of REAL
dom (id I[01]) is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of I[01]
Q . fg is set
1 - 0 is non empty V11() real ext-real positive non negative Element of REAL
(1 / 2) - 0 is V11() real ext-real non negative Element of REAL
(1 - 0) / ((1 / 2) - 0) is V11() real ext-real non negative Element of REAL
fg - 0 is V11() real ext-real Element of REAL
((1 - 0) / ((1 / 2) - 0)) * (fg - 0) is V11() real ext-real Element of REAL
(((1 - 0) / ((1 / 2) - 0)) * (fg - 0)) + 0 is V11() real ext-real Element of REAL
dom Q is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of (Closed-Interval-TSpace (0,(1 / 2)))
bool the carrier of (Closed-Interval-TSpace (0,(1 / 2))) is non empty set
[:(dom Q),(dom (id I[01])):] is non empty Relation-like Element of bool the carrier of [:(Closed-Interval-TSpace (0,(1 / 2))),I[01]:]
h . (fg,1) is set
h . [fg,1] is set
S12 . (fg,1) is set
S12 . [fg,1] is set
h . (S12 . (fg,1)) is set
(id I[01]) . 1 is set
h . ((Q . fg),((id I[01]) . 1)) is set
[(Q . fg),((id I[01]) . 1)] is non empty V29() set
{(Q . fg),((id I[01]) . 1)} is non empty set
{(Q . fg)} is non empty trivial set
{{(Q . fg),((id I[01]) . 1)},{(Q . fg)}} is non empty set
h . [(Q . fg),((id I[01]) . 1)] is set
h . ((2 * fg),1) is set
[(2 * fg),1] is non empty V29() set
{(2 * fg),1} is non empty complex-membered ext-real-membered real-membered set
{(2 * fg)} is non empty trivial complex-membered ext-real-membered real-membered set
{{(2 * fg),1},{(2 * fg)}} is non empty set
h . [(2 * fg),1] is set
gg . (2 * fg) is set
g . fg is set
1 - 0 is non empty V11() real ext-real positive non negative Element of REAL
1 - (1 / 2) is V11() real ext-real Element of REAL
(1 - 0) / (1 - (1 / 2)) is V11() real ext-real Element of REAL
fg - (1 / 2) is V11() real ext-real Element of REAL
((1 - 0) / (1 - (1 / 2))) * (fg - (1 / 2)) is V11() real ext-real Element of REAL
(((1 - 0) / (1 - (1 / 2))) * (fg - (1 / 2))) + 0 is V11() real ext-real Element of REAL
2 * fg is V11() real ext-real Element of REAL
(2 * fg) - 1 is V11() real ext-real Element of REAL
dom (id I[01]) is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of I[01]
dom g is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of (Closed-Interval-TSpace ((1 / 2),1))
bool the carrier of (Closed-Interval-TSpace ((1 / 2),1)) is non empty set
[:(dom g),(dom (id I[01])):] is non empty Relation-like Element of bool the carrier of [:(Closed-Interval-TSpace ((1 / 2),1)),I[01]:]
s1 . (fg,1) is set
s1 . [fg,1] is set
S12 . (fg,1) is set
S12 . [fg,1] is set
s3 . (S12 . (fg,1)) is set
(id I[01]) . 1 is set
s3 . ((g . fg),((id I[01]) . 1)) is set
[(g . fg),((id I[01]) . 1)] is non empty V29() set
{(g . fg),((id I[01]) . 1)} is non empty set
{(g . fg)} is non empty trivial set
{{(g . fg),((id I[01]) . 1)},{(g . fg)}} is non empty set
s3 . [(g . fg),((id I[01]) . 1)] is set
s3 . (((2 * fg) - 1),1) is set
[((2 * fg) - 1),1] is non empty V29() set
{((2 * fg) - 1),1} is non empty complex-membered ext-real-membered real-membered set
{((2 * fg) - 1)} is non empty trivial complex-membered ext-real-membered real-membered set
{{((2 * fg) - 1),1},{((2 * fg) - 1)}} is non empty set
s3 . [((2 * fg) - 1),1] is set
S2 . ((2 * fg) - 1) is set
2 * fg is V11() real ext-real Element of REAL
dom (id I[01]) is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of I[01]
Q . fg is set
1 - 0 is non empty V11() real ext-real positive non negative Element of REAL
(1 / 2) - 0 is V11() real ext-real non negative Element of REAL
(1 - 0) / ((1 / 2) - 0) is V11() real ext-real non negative Element of REAL
fg - 0 is V11() real ext-real Element of REAL
((1 - 0) / ((1 / 2) - 0)) * (fg - 0) is V11() real ext-real Element of REAL
(((1 - 0) / ((1 / 2) - 0)) * (fg - 0)) + 0 is V11() real ext-real Element of REAL
dom Q is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of (Closed-Interval-TSpace (0,(1 / 2)))
bool the carrier of (Closed-Interval-TSpace (0,(1 / 2))) is non empty set
[:(dom Q),(dom (id I[01])):] is non empty Relation-like Element of bool the carrier of [:(Closed-Interval-TSpace (0,(1 / 2))),I[01]:]
h . (fg,0) is set
h . [fg,0] is set
S12 . (fg,0) is set
S12 . [fg,0] is set
h . (S12 . (fg,0)) is set
(id I[01]) . 0 is set
h . ((Q . fg),((id I[01]) . 0)) is set
[(Q . fg),((id I[01]) . 0)] is non empty V29() set
{(Q . fg),((id I[01]) . 0)} is non empty set
{(Q . fg)} is non empty trivial set
{{(Q . fg),((id I[01]) . 0)},{(Q . fg)}} is non empty set
h . [(Q . fg),((id I[01]) . 0)] is set
h . ((2 * fg),0) is set
[(2 * fg),0] is non empty V29() set
{(2 * fg),0} is non empty complex-membered ext-real-membered real-membered set
{(2 * fg)} is non empty trivial complex-membered ext-real-membered real-membered set
{{(2 * fg),0},{(2 * fg)}} is non empty set
h . [(2 * fg),0] is set
e2 . (2 * fg) is set
g . fg is set
1 - 0 is non empty V11() real ext-real positive non negative Element of REAL
1 - (1 / 2) is V11() real ext-real Element of REAL
(1 - 0) / (1 - (1 / 2)) is V11() real ext-real Element of REAL
fg - (1 / 2) is V11() real ext-real Element of REAL
((1 - 0) / (1 - (1 / 2))) * (fg - (1 / 2)) is V11() real ext-real Element of REAL
(((1 - 0) / (1 - (1 / 2))) * (fg - (1 / 2))) + 0 is V11() real ext-real Element of REAL
2 * fg is V11() real ext-real Element of REAL
(2 * fg) - 1 is V11() real ext-real Element of REAL
dom (id I[01]) is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of I[01]
dom g is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of (Closed-Interval-TSpace ((1 / 2),1))
bool the carrier of (Closed-Interval-TSpace ((1 / 2),1)) is non empty set
[:(dom g),(dom (id I[01])):] is non empty Relation-like Element of bool the carrier of [:(Closed-Interval-TSpace ((1 / 2),1)),I[01]:]
s1 . (fg,0) is set
s1 . [fg,0] is set
S12 . (fg,0) is set
S12 . [fg,0] is set
s3 . (S12 . (fg,0)) is set
(id I[01]) . 0 is set
s3 . ((g . fg),((id I[01]) . 0)) is set
[(g . fg),((id I[01]) . 0)] is non empty V29() set
{(g . fg),((id I[01]) . 0)} is non empty set
{(g . fg)} is non empty trivial set
{{(g . fg),((id I[01]) . 0)},{(g . fg)}} is non empty set
s3 . [(g . fg),((id I[01]) . 0)] is set
s3 . (((2 * fg) - 1),0) is set
[((2 * fg) - 1),0] is non empty V29() set
{((2 * fg) - 1),0} is non empty complex-membered ext-real-membered real-membered set
{((2 * fg) - 1)} is non empty trivial complex-membered ext-real-membered real-membered set
{{((2 * fg) - 1),0},{((2 * fg) - 1)}} is non empty set
s3 . [((2 * fg) - 1),0] is set
gg . ((2 * fg) - 1) is set
fg is V11() real ext-real Element of the carrier of I[01]
s2 . (0,fg) is set
[0,fg] is non empty V29() set
{0,fg} is non empty complex-membered ext-real-membered real-membered set
{{0,fg},{0}} is non empty set
s2 . [0,fg] is set
s2 . (1,fg) is set
[1,fg] is non empty V29() set
{1,fg} is non empty complex-membered ext-real-membered real-membered set
{{1,fg},{1}} is non empty set
s2 . [1,fg] is set
dom (id I[01]) is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of I[01]
dom Q is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of (Closed-Interval-TSpace (0,(1 / 2)))
bool the carrier of (Closed-Interval-TSpace (0,(1 / 2))) is non empty set
[:(dom Q),(dom (id I[01])):] is non empty Relation-like Element of bool the carrier of [:(Closed-Interval-TSpace (0,(1 / 2))),I[01]:]
h . (0,fg) is set
h . [0,fg] is set
S12 . (0,fg) is set
S12 . [0,fg] is set
h . (S12 . (0,fg)) is set
Q . 0 is set
(id I[01]) . fg is V11() real ext-real Element of the carrier of I[01]
h . ((Q . 0),((id I[01]) . fg)) is set
[(Q . 0),((id I[01]) . fg)] is non empty V29() set
{(Q . 0),((id I[01]) . fg)} is non empty set
{(Q . 0)} is non empty trivial set
{{(Q . 0),((id I[01]) . fg)},{(Q . 0)}} is non empty set
h . [(Q . 0),((id I[01]) . fg)] is set
h . ((Q . 0),fg) is set
[(Q . 0),fg] is non empty V29() set
{(Q . 0),fg} is non empty set
{{(Q . 0),fg},{(Q . 0)}} is non empty set
h . [(Q . 0),fg] is set
h . (0,fg) is set
h . [0,fg] is set
dom g is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of (Closed-Interval-TSpace ((1 / 2),1))
bool the carrier of (Closed-Interval-TSpace ((1 / 2),1)) is non empty set
[:(dom g),(dom (id I[01])):] is non empty Relation-like Element of bool the carrier of [:(Closed-Interval-TSpace ((1 / 2),1)),I[01]:]
s1 . (1,fg) is set
s1 . [1,fg] is set
S12 . (1,fg) is set
S12 . [1,fg] is set
s3 . (S12 . (1,fg)) is set
g . 1 is set
s3 . ((g . 1),((id I[01]) . fg)) is set
[(g . 1),((id I[01]) . fg)] is non empty V29() set
{(g . 1),((id I[01]) . fg)} is non empty set
{(g . 1)} is non empty trivial set
{{(g . 1),((id I[01]) . fg)},{(g . 1)}} is non empty set
s3 . [(g . 1),((id I[01]) . fg)] is set
s3 . ((g . 1),fg) is set
[(g . 1),fg] is non empty V29() set
{(g . 1),fg} is non empty set
{{(g . 1),fg},{(g . 1)}} is non empty set
s3 . [(g . 1),fg] is set
s3 . (1,fg) is set
s3 . [1,fg] is set
fg is V11() real ext-real Element of the carrier of I[01]
s2 . (fg,0) is set
[fg,0] is non empty V29() set
{fg,0} is non empty complex-membered ext-real-membered real-membered set
{fg} is non empty trivial complex-membered ext-real-membered real-membered set
{{fg,0},{fg}} is non empty set
s2 . [fg,0] is set
(e2 + gg) . fg is Element of the carrier of T
H is V11() real ext-real Element of the carrier of I[01]
s2 . (H,1) is set
[H,1] is non empty V29() set
{H,1} is non empty complex-membered ext-real-membered real-membered set
{H} is non empty trivial complex-membered ext-real-membered real-membered set
{{H,1},{H}} is non empty set
s2 . [H,1] is set
(gg + S2) . H is Element of the carrier of T
t is V11() real ext-real Element of the carrier of I[01]
s2 . (0,t) is set
[0,t] is non empty V29() set
{0,t} is non empty complex-membered ext-real-membered real-membered set
{{0,t},{0}} is non empty set
s2 . [0,t] is set
x is V11() real ext-real Element of the carrier of I[01]
s2 . (1,x) is set
[1,x] is non empty V29() set
{1,x} is non empty complex-membered ext-real-membered real-membered set
{{1,x},{1}} is non empty set
s2 . [1,x] is set
T is non empty TopSpace-like V74() pathwise_connected TopStruct
the carrier of T is non empty set
a is Element of the carrier of T
b is Element of the carrier of T
P is Element of the carrier of T
Q is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total continuous Path of a,b
Q is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total continuous Path of a,b
e2 is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total continuous Path of b,P
gg is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total continuous Path of b,P
Q + e2 is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total continuous Path of a,P
Q + gg is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total continuous Path of a,P
T is non empty TopSpace-like TopStruct
the carrier of T is non empty set
a is Element of the carrier of T
b is Element of the carrier of T
Q is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of a,b
e2 is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of a,b
- Q is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of b,a
- e2 is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of b,a
Q is non empty Relation-like the carrier of I[01] -defined the carrier of I[01] -valued Function-like V43( the carrier of I[01]) quasi_total continuous Element of bool [: the carrier of I[01], the carrier of I[01]:]
P is non empty Relation-like the carrier of I[01] -defined the carrier of I[01] -valued Function-like V43( the carrier of I[01]) quasi_total continuous Element of bool [: the carrier of I[01], the carrier of I[01]:]
[:Q,P:] is non empty Relation-like the carrier of [:I[01],I[01]:] -defined the carrier of [:I[01],I[01]:] -valued Function-like V43( the carrier of [:I[01],I[01]:]) quasi_total continuous Element of bool [: the carrier of [:I[01],I[01]:], the carrier of [:I[01],I[01]:]:]
[: the carrier of [:I[01],I[01]:], the carrier of [:I[01],I[01]:]:] is non empty Relation-like set
bool [: the carrier of [:I[01],I[01]:], the carrier of [:I[01],I[01]:]:] is non empty set
dom Q is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of I[01]
[: the carrier of [:I[01],I[01]:], the carrier of T:] is non empty Relation-like set
bool [: the carrier of [:I[01],I[01]:], the carrier of T:] is non empty set
gg is non empty Relation-like the carrier of [:I[01],I[01]:] -defined the carrier of T -valued Function-like V43( the carrier of [:I[01],I[01]:]) quasi_total Element of bool [: the carrier of [:I[01],I[01]:], the carrier of T:]
gg * [:Q,P:] is non empty Relation-like the carrier of [:I[01],I[01]:] -defined the carrier of T -valued Function-like V43( the carrier of [:I[01],I[01]:]) quasi_total Element of bool [: the carrier of [:I[01],I[01]:], the carrier of T:]
S2 is non empty Relation-like the carrier of [:I[01],I[01]:] -defined the carrier of T -valued Function-like V43( the carrier of [:I[01],I[01]:]) quasi_total Element of bool [: the carrier of [:I[01],I[01]:], the carrier of T:]
g is V11() real ext-real Element of the carrier of I[01]
Q . g is V11() real ext-real Element of the carrier of I[01]
g is V11() real ext-real Element of REAL
1 - g is V11() real ext-real Element of REAL
S3 is V11() real ext-real Element of the carrier of (Closed-Interval-TSpace (0,1))
Q . S3 is set
0 - 1 is non empty V11() real ext-real non positive negative Element of REAL
(0 - 1) * g is V11() real ext-real Element of REAL
((0 - 1) * g) + 1 is V11() real ext-real Element of REAL
1 * g is V11() real ext-real Element of REAL
1 - (1 * g) is V11() real ext-real Element of REAL
Q . 0 is set
1 - 0 is non empty V11() real ext-real positive non negative Element of REAL
Q . 1 is set
1 - 1 is V11() real ext-real Element of REAL
g is V11() real ext-real Element of the carrier of I[01]
S2 . (0,g) is set
[0,g] is non empty V29() set
{0,g} is non empty complex-membered ext-real-membered real-membered set
{{0,g},{0}} is non empty set
S2 . [0,g] is set
S2 . (1,g) is set
[1,g] is non empty V29() set
{1,g} is non empty complex-membered ext-real-membered real-membered set
{{1,g},{1}} is non empty set
S2 . [1,g] is set
dom P is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of I[01]
dom [:Q,P:] is non empty Element of bool the carrier of [:I[01],I[01]:]
[:(dom Q),(dom P):] is non empty Relation-like Element of bool the carrier of [:I[01],I[01]:]
[:Q,P:] . (1,g) is set
[:Q,P:] . [1,g] is set
P . g is V11() real ext-real Element of the carrier of I[01]
[(Q . 1),(P . g)] is non empty V29() set
{(Q . 1),(P . g)} is non empty set
{(Q . 1)} is non empty trivial set
{{(Q . 1),(P . g)},{(Q . 1)}} is non empty set
g is V11() real ext-real Element of REAL
[0,g] is non empty V29() set
{0,g} is non empty complex-membered ext-real-membered real-membered set
{{0,g},{0}} is non empty set
gg . (0,g) is set
gg . [0,g] is set
[:Q,P:] . (0,g) is set
[:Q,P:] . [0,g] is set
[(Q . 0),(P . g)] is non empty V29() set
{(Q . 0),(P . g)} is non empty set
{(Q . 0)} is non empty trivial set
{{(Q . 0),(P . g)},{(Q . 0)}} is non empty set
[1,g] is non empty V29() set
{1,g} is non empty complex-membered ext-real-membered real-membered set
{{1,g},{1}} is non empty set
gg . (1,g) is set
gg . [1,g] is set
dom P is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of I[01]
g is V11() real ext-real Element of the carrier of I[01]
S2 . (g,0) is set
[g,0] is non empty V29() set
{g,0} is non empty complex-membered ext-real-membered real-membered set
{g} is non empty trivial complex-membered ext-real-membered real-membered set
{{g,0},{g}} is non empty set
S2 . [g,0] is set
(- Q) . g is Element of the carrier of T
S2 . (g,1) is set
[g,1] is non empty V29() set
{g,1} is non empty complex-membered ext-real-membered real-membered set
{{g,1},{g}} is non empty set
S2 . [g,1] is set
(- e2) . g is Element of the carrier of T
g is V11() real ext-real Element of the carrier of I[01]
Q . g is V11() real ext-real Element of the carrier of I[01]
S3 is V11() real ext-real Element of REAL
1 - S3 is V11() real ext-real Element of REAL
S1 is V11() real ext-real Element of the carrier of (Closed-Interval-TSpace (0,1))
Q . S1 is set
0 - 1 is non empty V11() real ext-real non positive negative Element of REAL
(0 - 1) * S3 is V11() real ext-real Element of REAL
((0 - 1) * S3) + 1 is V11() real ext-real Element of REAL
1 * S3 is V11() real ext-real Element of REAL
1 - (1 * S3) is V11() real ext-real Element of REAL
Q . g is V11() real ext-real Element of the carrier of I[01]
1 - g is V11() real ext-real Element of REAL
dom [:Q,P:] is non empty Element of bool the carrier of [:I[01],I[01]:]
[:(dom Q),(dom P):] is non empty Relation-like Element of bool the carrier of [:I[01],I[01]:]
[:Q,P:] . (g,1) is set
[:Q,P:] . [g,1] is set
P . 1 is set
[(Q . g),(P . 1)] is non empty V29() set
{(Q . g),(P . 1)} is non empty set
{(Q . g)} is non empty trivial complex-membered ext-real-membered real-membered set
{{(Q . g),(P . 1)},{(Q . g)}} is non empty set
[(1 - g),1] is non empty V29() set
{(1 - g),1} is non empty complex-membered ext-real-membered real-membered set
{(1 - g)} is non empty trivial complex-membered ext-real-membered real-membered set
{{(1 - g),1},{(1 - g)}} is non empty set
gg . ((1 - g),1) is set
gg . [(1 - g),1] is set
e2 . (1 - g) is set
[:Q,P:] . (g,0) is set
[:Q,P:] . [g,0] is set
P . 0 is set
[(Q . g),(P . 0)] is non empty V29() set
{(Q . g),(P . 0)} is non empty set
{{(Q . g),(P . 0)},{(Q . g)}} is non empty set
[(1 - g),0] is non empty V29() set
{(1 - g),0} is non empty complex-membered ext-real-membered real-membered set
{{(1 - g),0},{(1 - g)}} is non empty set
gg . ((1 - g),0) is set
gg . [(1 - g),0] is set
Q . (1 - g) is set
g is V11() real ext-real Element of the carrier of I[01]
S2 . (g,0) is set
[g,0] is non empty V29() set
{g,0} is non empty complex-membered ext-real-membered real-membered set
{g} is non empty trivial complex-membered ext-real-membered real-membered set
{{g,0},{g}} is non empty set
S2 . [g,0] is set
(- Q) . g is Element of the carrier of T
g is V11() real ext-real Element of the carrier of I[01]
S2 . (g,1) is set
[g,1] is non empty V29() set
{g,1} is non empty complex-membered ext-real-membered real-membered set
{g} is non empty trivial complex-membered ext-real-membered real-membered set
{{g,1},{g}} is non empty set
S2 . [g,1] is set
(- e2) . g is Element of the carrier of T
S3 is V11() real ext-real Element of the carrier of I[01]
S2 . (0,S3) is set
[0,S3] is non empty V29() set
{0,S3} is non empty complex-membered ext-real-membered real-membered set
{{0,S3},{0}} is non empty set
S2 . [0,S3] is set
S1 is V11() real ext-real Element of the carrier of I[01]
S2 . (1,S1) is set
[1,S1] is non empty V29() set
{1,S1} is non empty complex-membered ext-real-membered real-membered set
{{1,S1},{1}} is non empty set
S2 . [1,S1] is set
T is non empty TopSpace-like V74() pathwise_connected TopStruct
the carrier of T is non empty set
a is Element of the carrier of T
b is Element of the carrier of T
P is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total continuous Path of a,b
Q is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total continuous Path of a,b
- P is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total continuous Path of b,a
- Q is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total continuous Path of b,a
T is non empty TopSpace-like TopStruct
the carrier of T is non empty set
a is Element of the carrier of T
b is Element of the carrier of T
Closed-Interval-TSpace (0,(1 / 2)) is non empty strict TopSpace-like real-membered SubSpace of R^1
the carrier of (Closed-Interval-TSpace (0,(1 / 2))) is non empty complex-membered ext-real-membered real-membered set
Closed-Interval-TSpace ((1 / 2),1) is non empty strict TopSpace-like real-membered SubSpace of R^1
the carrier of (Closed-Interval-TSpace ((1 / 2),1)) is non empty complex-membered ext-real-membered real-membered set
[:[.0,1.],[.0,(1 / 2).]:] is Relation-like REAL -defined REAL -valued Element of bool [:REAL,REAL:]
Q is non empty Element of bool the carrier of [:I[01],I[01]:]
[:I[01],I[01]:] | Q is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of [:I[01],I[01]:]
[: the carrier of (Closed-Interval-TSpace ((1 / 2),1)), the carrier of I[01]:] is non empty Relation-like set
bool [: the carrier of (Closed-Interval-TSpace ((1 / 2),1)), the carrier of I[01]:] is non empty set
P[01] ((1 / 2),1,((#) (0,1)),((0,1) (#))) is non empty Relation-like the carrier of (Closed-Interval-TSpace ((1 / 2),1)) -defined the carrier of (Closed-Interval-TSpace (0,1)) -valued Function-like V43( the carrier of (Closed-Interval-TSpace ((1 / 2),1))) quasi_total Element of bool [: the carrier of (Closed-Interval-TSpace ((1 / 2),1)), the carrier of (Closed-Interval-TSpace (0,1)):]
[: the carrier of (Closed-Interval-TSpace ((1 / 2),1)), the carrier of (Closed-Interval-TSpace (0,1)):] is non empty Relation-like set
bool [: the carrier of (Closed-Interval-TSpace ((1 / 2),1)), the carrier of (Closed-Interval-TSpace (0,1)):] is non empty set
[: the carrier of (Closed-Interval-TSpace (0,(1 / 2))), the carrier of I[01]:] is non empty Relation-like set
bool [: the carrier of (Closed-Interval-TSpace (0,(1 / 2))), the carrier of I[01]:] is non empty set
P[01] (0,(1 / 2),((#) (0,1)),((0,1) (#))) is non empty Relation-like the carrier of (Closed-Interval-TSpace (0,(1 / 2))) -defined the carrier of (Closed-Interval-TSpace (0,1)) -valued Function-like V43( the carrier of (Closed-Interval-TSpace (0,(1 / 2)))) quasi_total Element of bool [: the carrier of (Closed-Interval-TSpace (0,(1 / 2))), the carrier of (Closed-Interval-TSpace (0,1)):]
[: the carrier of (Closed-Interval-TSpace (0,(1 / 2))), the carrier of (Closed-Interval-TSpace (0,1)):] is non empty Relation-like set
bool [: the carrier of (Closed-Interval-TSpace (0,(1 / 2))), the carrier of (Closed-Interval-TSpace (0,1)):] is non empty set
gg is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of a,b
S2 is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of a,b
g is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of a,b
[: the carrier of [:I[01],I[01]:], the carrier of T:] is non empty Relation-like set
bool [: the carrier of [:I[01],I[01]:], the carrier of T:] is non empty set
g is non empty Relation-like the carrier of [:I[01],I[01]:] -defined the carrier of T -valued Function-like V43( the carrier of [:I[01],I[01]:]) quasi_total Element of bool [: the carrier of [:I[01],I[01]:], the carrier of T:]
S3 is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of I[01]
[#] I[01] is non empty non proper open closed complex-membered ext-real-membered real-membered Element of bool the carrier of I[01]
I[01] | S3 is non empty strict TopSpace-like T_0 T_1 T_2 real-membered SubSpace of I[01]
[:[.0,1.],[.(1 / 2),1.]:] is Relation-like REAL -defined REAL -valued Element of bool [:REAL,REAL:]
e1 is non empty Element of bool the carrier of [:I[01],I[01]:]
[:I[01],I[01]:] | e1 is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of [:I[01],I[01]:]
gg is non empty Relation-like the carrier of (Closed-Interval-TSpace (0,(1 / 2))) -defined the carrier of I[01] -valued Function-like V43( the carrier of (Closed-Interval-TSpace (0,(1 / 2)))) quasi_total continuous Element of bool [: the carrier of (Closed-Interval-TSpace (0,(1 / 2))), the carrier of I[01]:]
[:(id I[01]),gg:] is non empty Relation-like the carrier of [:I[01],(Closed-Interval-TSpace (0,(1 / 2))):] -defined the carrier of [:I[01],I[01]:] -valued Function-like V43( the carrier of [:I[01],(Closed-Interval-TSpace (0,(1 / 2))):]) quasi_total continuous Element of bool [: the carrier of [:I[01],(Closed-Interval-TSpace (0,(1 / 2))):], the carrier of [:I[01],I[01]:]:]
[:I[01],(Closed-Interval-TSpace (0,(1 / 2))):] is non empty strict TopSpace-like TopStruct
the carrier of [:I[01],(Closed-Interval-TSpace (0,(1 / 2))):] is non empty set
[: the carrier of [:I[01],(Closed-Interval-TSpace (0,(1 / 2))):], the carrier of [:I[01],I[01]:]:] is non empty Relation-like set
bool [: the carrier of [:I[01],(Closed-Interval-TSpace (0,(1 / 2))):], the carrier of [:I[01],I[01]:]:] is non empty set
e2 is non empty Relation-like the carrier of (Closed-Interval-TSpace ((1 / 2),1)) -defined the carrier of I[01] -valued Function-like V43( the carrier of (Closed-Interval-TSpace ((1 / 2),1))) quasi_total continuous Element of bool [: the carrier of (Closed-Interval-TSpace ((1 / 2),1)), the carrier of I[01]:]
[:(id I[01]),e2:] is non empty Relation-like the carrier of [:I[01],(Closed-Interval-TSpace ((1 / 2),1)):] -defined the carrier of [:I[01],I[01]:] -valued Function-like V43( the carrier of [:I[01],(Closed-Interval-TSpace ((1 / 2),1)):]) quasi_total continuous Element of bool [: the carrier of [:I[01],(Closed-Interval-TSpace ((1 / 2),1)):], the carrier of [:I[01],I[01]:]:]
[:I[01],(Closed-Interval-TSpace ((1 / 2),1)):] is non empty strict TopSpace-like TopStruct
the carrier of [:I[01],(Closed-Interval-TSpace ((1 / 2),1)):] is non empty set
[: the carrier of [:I[01],(Closed-Interval-TSpace ((1 / 2),1)):], the carrier of [:I[01],I[01]:]:] is non empty Relation-like set
bool [: the carrier of [:I[01],(Closed-Interval-TSpace ((1 / 2),1)):], the carrier of [:I[01],I[01]:]:] is non empty set
dom (id I[01]) is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of I[01]
dom (P[01] ((1 / 2),1,((#) (0,1)),((0,1) (#)))) is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of (Closed-Interval-TSpace ((1 / 2),1))
bool the carrier of (Closed-Interval-TSpace ((1 / 2),1)) is non empty set
rng [:(id I[01]),e2:] is non empty Element of bool the carrier of [:I[01],I[01]:]
rng (id I[01]) is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of I[01]
rng (P[01] ((1 / 2),1,((#) (0,1)),((0,1) (#)))) is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of (Closed-Interval-TSpace (0,1))
bool the carrier of (Closed-Interval-TSpace (0,1)) is non empty set
[:(rng (id I[01])),(rng (P[01] ((1 / 2),1,((#) (0,1)),((0,1) (#))))):] is non empty Relation-like Element of bool the carrier of [:I[01],(Closed-Interval-TSpace (0,1)):]
[:I[01],(Closed-Interval-TSpace (0,1)):] is non empty strict TopSpace-like TopStruct
the carrier of [:I[01],(Closed-Interval-TSpace (0,1)):] is non empty set
bool the carrier of [:I[01],(Closed-Interval-TSpace (0,1)):] is non empty set
f is non empty Relation-like the carrier of [:I[01],I[01]:] -defined the carrier of T -valued Function-like V43( the carrier of [:I[01],I[01]:]) quasi_total Element of bool [: the carrier of [:I[01],I[01]:], the carrier of T:]
g * [:(id I[01]),gg:] is non empty Relation-like the carrier of [:I[01],(Closed-Interval-TSpace (0,(1 / 2))):] -defined the carrier of T -valued Function-like V43( the carrier of [:I[01],(Closed-Interval-TSpace (0,(1 / 2))):]) quasi_total Element of bool [: the carrier of [:I[01],(Closed-Interval-TSpace (0,(1 / 2))):], the carrier of T:]
[: the carrier of [:I[01],(Closed-Interval-TSpace (0,(1 / 2))):], the carrier of T:] is non empty Relation-like set
bool [: the carrier of [:I[01],(Closed-Interval-TSpace (0,(1 / 2))):], the carrier of T:] is non empty set
f * [:(id I[01]),e2:] is non empty Relation-like the carrier of [:I[01],(Closed-Interval-TSpace ((1 / 2),1)):] -defined the carrier of T -valued Function-like V43( the carrier of [:I[01],(Closed-Interval-TSpace ((1 / 2),1)):]) quasi_total Element of bool [: the carrier of [:I[01],(Closed-Interval-TSpace ((1 / 2),1)):], the carrier of T:]
[: the carrier of [:I[01],(Closed-Interval-TSpace ((1 / 2),1)):], the carrier of T:] is non empty Relation-like set
bool [: the carrier of [:I[01],(Closed-Interval-TSpace ((1 / 2),1)):], the carrier of T:] is non empty set
dom f is non empty Element of bool the carrier of [:I[01],I[01]:]
dom (f * [:(id I[01]),e2:]) is non empty Element of bool the carrier of [:I[01],(Closed-Interval-TSpace ((1 / 2),1)):]
bool the carrier of [:I[01],(Closed-Interval-TSpace ((1 / 2),1)):] is non empty set
dom [:(id I[01]),e2:] is non empty Element of bool the carrier of [:I[01],(Closed-Interval-TSpace ((1 / 2),1)):]
[: the carrier of I[01], the carrier of (Closed-Interval-TSpace ((1 / 2),1)):] is non empty Relation-like set
P is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of I[01]
I[01] | P is non empty strict TopSpace-like T_0 T_1 T_2 real-membered SubSpace of I[01]
the carrier of ([:I[01],I[01]:] | e1) is non empty set
[: the carrier of ([:I[01],I[01]:] | e1), the carrier of T:] is non empty Relation-like set
bool [: the carrier of ([:I[01],I[01]:] | e1), the carrier of T:] is non empty set
S1 is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of I[01]
I[01] | S1 is non empty strict TopSpace-like T_0 T_1 T_2 real-membered SubSpace of I[01]
the carrier of ([:I[01],I[01]:] | Q) is non empty set
[: the carrier of ([:I[01],I[01]:] | Q), the carrier of T:] is non empty Relation-like set
bool [: the carrier of ([:I[01],I[01]:] | Q), the carrier of T:] is non empty set
dom [:(id I[01]),gg:] is non empty Element of bool the carrier of [:I[01],(Closed-Interval-TSpace (0,(1 / 2))):]
bool the carrier of [:I[01],(Closed-Interval-TSpace (0,(1 / 2))):] is non empty set
[: the carrier of I[01], the carrier of (Closed-Interval-TSpace (0,(1 / 2))):] is non empty Relation-like set
dom e2 is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of (Closed-Interval-TSpace ((1 / 2),1))
[:(dom (id I[01])),(dom e2):] is non empty Relation-like Element of bool the carrier of [:I[01],(Closed-Interval-TSpace ((1 / 2),1)):]
dom gg is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of (Closed-Interval-TSpace (0,(1 / 2)))
bool the carrier of (Closed-Interval-TSpace (0,(1 / 2))) is non empty set
[:(dom (id I[01])),(dom gg):] is non empty Relation-like Element of bool the carrier of [:I[01],(Closed-Interval-TSpace (0,(1 / 2))):]
[#] ([:I[01],I[01]:] | Q) is non empty non proper open closed Element of bool the carrier of ([:I[01],I[01]:] | Q)
bool the carrier of ([:I[01],I[01]:] | Q) is non empty set
[#] ([:I[01],I[01]:] | e1) is non empty non proper open closed Element of bool the carrier of ([:I[01],I[01]:] | e1)
bool the carrier of ([:I[01],I[01]:] | e1) is non empty set
([#] ([:I[01],I[01]:] | Q)) /\ ([#] ([:I[01],I[01]:] | e1)) is Element of bool the carrier of ([:I[01],I[01]:] | e1)
[.0,(1 / 2).] /\ [.(1 / 2),1.] is complex-membered ext-real-membered real-membered Element of bool REAL
[:[.0,1.],([.0,(1 / 2).] /\ [.(1 / 2),1.]):] is Relation-like REAL -defined REAL -valued Element of bool [:REAL,REAL:]
[:[.0,1.],{(1 / 2)}:] is Relation-like set
h is non empty Relation-like the carrier of ([:I[01],I[01]:] | Q) -defined the carrier of T -valued Function-like V43( the carrier of ([:I[01],I[01]:] | Q)) quasi_total continuous Element of bool [: the carrier of ([:I[01],I[01]:] | Q), the carrier of T:]
hh is non empty Relation-like the carrier of ([:I[01],I[01]:] | e1) -defined the carrier of T -valued Function-like V43( the carrier of ([:I[01],I[01]:] | e1)) quasi_total continuous Element of bool [: the carrier of ([:I[01],I[01]:] | e1), the carrier of T:]
h is set
h . h is set
hh . h is set
s3 is set
s1 is set
[s3,s1] is non empty V29() set
{s3,s1} is non empty set
{s3} is non empty trivial set
{{s3,s1},{s3}} is non empty set
{ b₁ where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
fg is V11() real ext-real Element of REAL
fg is V11() real ext-real Element of the carrier of (Closed-Interval-TSpace (0,(1 / 2)))
gg . fg is V11() real ext-real Element of the carrier of I[01]
x is V11() real ext-real Element of REAL
t is V11() real ext-real Element of REAL
x - t is V11() real ext-real Element of REAL
(1 / 2) - 0 is V11() real ext-real non negative Element of REAL
(x - t) / ((1 / 2) - 0) is V11() real ext-real Element of REAL
((x - t) / ((1 / 2) - 0)) * (1 / 2) is V11() real ext-real Element of REAL
(1 / 2) * t is V11() real ext-real Element of REAL
0 * x is V11() real ext-real Element of REAL
((1 / 2) * t) - (0 * x) is V11() real ext-real Element of REAL
(((1 / 2) * t) - (0 * x)) / ((1 / 2) - 0) is V11() real ext-real Element of REAL
(((x - t) / ((1 / 2) - 0)) * (1 / 2)) + ((((1 / 2) * t) - (0 * x)) / ((1 / 2) - 0)) is V11() real ext-real Element of REAL
1 - t is V11() real ext-real Element of REAL
(1 - t) / ((1 / 2) - 0) is V11() real ext-real Element of REAL
((1 - t) / ((1 / 2) - 0)) * (1 / 2) is V11() real ext-real Element of REAL
(((1 - t) / ((1 / 2) - 0)) * (1 / 2)) + ((((1 / 2) * t) - (0 * x)) / ((1 / 2) - 0)) is V11() real ext-real Element of REAL
1 - 0 is non empty V11() real ext-real positive non negative Element of REAL
(1 - 0) / ((1 / 2) - 0) is V11() real ext-real non negative Element of REAL
((1 - 0) / ((1 / 2) - 0)) * (1 / 2) is V11() real ext-real non negative Element of REAL
(((1 - 0) / ((1 / 2) - 0)) * (1 / 2)) + ((((1 / 2) * t) - (0 * x)) / ((1 / 2) - 0)) is V11() real ext-real Element of REAL
(1 / 2) * 0 is empty trivial V11() real ext-real non positive non negative Relation-like non-empty empty-yielding complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V209() Element of REAL
0 * 1 is empty trivial V11() real ext-real non positive non negative Relation-like non-empty empty-yielding complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V209() Element of REAL
((1 / 2) * 0) - (0 * 1) is empty trivial V11() real ext-real non positive non negative Relation-like non-empty empty-yielding complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V209() Element of REAL
(((1 / 2) * 0) - (0 * 1)) / ((1 / 2) - 0) is empty trivial V11() real ext-real non positive non negative Relation-like non-empty empty-yielding complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V209() Element of REAL
(((1 - 0) / ((1 / 2) - 0)) * (1 / 2)) + ((((1 / 2) * 0) - (0 * 1)) / ((1 / 2) - 0)) is V11() real ext-real non negative Element of REAL
y9 is V11() real ext-real Element of the carrier of (Closed-Interval-TSpace ((1 / 2),1))
e2 . y9 is V11() real ext-real Element of the carrier of I[01]
1 - (1 / 2) is V11() real ext-real Element of REAL
(x - t) / (1 - (1 / 2)) is V11() real ext-real Element of REAL
((x - t) / (1 - (1 / 2))) * (1 / 2) is V11() real ext-real Element of REAL
1 * t is V11() real ext-real Element of REAL
(1 / 2) * x is V11() real ext-real Element of REAL
(1 * t) - ((1 / 2) * x) is V11() real ext-real Element of REAL
((1 * t) - ((1 / 2) * x)) / (1 - (1 / 2)) is V11() real ext-real Element of REAL
(((x - t) / (1 - (1 / 2))) * (1 / 2)) + (((1 * t) - ((1 / 2) * x)) / (1 - (1 / 2))) is V11() real ext-real Element of REAL
c₃₃ is V11() real ext-real Element of REAL
[:(id I[01]),gg:] . (s3,s1) is set
[:(id I[01]),gg:] . [s3,s1] is set
g . ([:(id I[01]),gg:] . (s3,s1)) is set
(id I[01]) . s3 is set
gg . s1 is set
g . (((id I[01]) . s3),(gg . s1)) is set
[((id I[01]) . s3),(gg . s1)] is non empty V29() set
{((id I[01]) . s3),(gg . s1)} is non empty set
{((id I[01]) . s3)} is non empty trivial set
{{((id I[01]) . s3),(gg . s1)},{((id I[01]) . s3)}} is non empty set
g . [((id I[01]) . s3),(gg . s1)] is set
s2 is V11() real ext-real Element of the carrier of I[01]
g . (s2,1) is set
[s2,1] is non empty V29() set
{s2,1} is non empty complex-membered ext-real-membered real-membered set
{s2} is non empty trivial complex-membered ext-real-membered real-membered set
{{s2,1},{s2}} is non empty set
g . [s2,1] is set
S2 . s2 is Element of the carrier of T
f . (s2,0) is set
[s2,0] is non empty V29() set
{s2,0} is non empty complex-membered ext-real-membered real-membered set
{{s2,0},{s2}} is non empty set
f . [s2,0] is set
(id I[01]) . s2 is V11() real ext-real Element of the carrier of I[01]
e2 . s1 is set
f . (((id I[01]) . s2),(e2 . s1)) is set
[((id I[01]) . s2),(e2 . s1)] is non empty V29() set
{((id I[01]) . s2),(e2 . s1)} is non empty set
{((id I[01]) . s2)} is non empty trivial complex-membered ext-real-membered real-membered set
{{((id I[01]) . s2),(e2 . s1)},{((id I[01]) . s2)}} is non empty set
f . [((id I[01]) . s2),(e2 . s1)] is set
[:(id I[01]),e2:] . (s3,s1) is set
[:(id I[01]),e2:] . [s3,s1] is set
f . ([:(id I[01]),e2:] . (s3,s1)) is set
([#] ([:I[01],I[01]:] | Q)) \/ ([#] ([:I[01],I[01]:] | e1)) is non empty set
[.0,(1 / 2).] \/ [.(1 / 2),1.] is complex-membered ext-real-membered real-membered Element of bool REAL
[:[.0,1.],([.0,(1 / 2).] \/ [.(1 / 2),1.]):] is Relation-like REAL -defined REAL -valued Element of bool [:REAL,REAL:]
h +* hh is Relation-like Function-like set
h is non empty Relation-like the carrier of [:I[01],I[01]:] -defined the carrier of T -valued Function-like V43( the carrier of [:I[01],I[01]:]) quasi_total Element of bool [: the carrier of [:I[01],I[01]:], the carrier of T:]
s3 is V11() real ext-real Element of the carrier of I[01]
h . (0,s3) is set
[0,s3] is non empty V29() set
{0,s3} is non empty complex-membered ext-real-membered real-membered set
{{0,s3},{0}} is non empty set
h . [0,s3] is set
h . (1,s3) is set
[1,s3] is non empty V29() set
{1,s3} is non empty complex-membered ext-real-membered real-membered set
{{1,s3},{1}} is non empty set
h . [1,s3] is set
gg . s3 is set
s2 is V11() real ext-real Element of REAL
s1 is V11() real ext-real Element of REAL
s2 - s1 is V11() real ext-real Element of REAL
(1 / 2) - 0 is V11() real ext-real non negative Element of REAL
(s2 - s1) / ((1 / 2) - 0) is V11() real ext-real Element of REAL
((s2 - s1) / ((1 / 2) - 0)) * s3 is V11() real ext-real Element of REAL
(1 / 2) * s1 is V11() real ext-real Element of REAL
0 * s2 is V11() real ext-real Element of REAL
((1 / 2) * s1) - (0 * s2) is V11() real ext-real Element of REAL
(((1 / 2) * s1) - (0 * s2)) / ((1 / 2) - 0) is V11() real ext-real Element of REAL
(((s2 - s1) / ((1 / 2) - 0)) * s3) + ((((1 / 2) * s1) - (0 * s2)) / ((1 / 2) - 0)) is V11() real ext-real Element of REAL
1 - s1 is V11() real ext-real Element of REAL
(1 - s1) / (1 / 2) is V11() real ext-real Element of REAL
((1 - s1) / (1 / 2)) * s3 is V11() real ext-real Element of REAL
((1 / 2) * s1) / (1 / 2) is V11() real ext-real Element of REAL
(((1 - s1) / (1 / 2)) * s3) + (((1 / 2) * s1) / (1 / 2)) is V11() real ext-real Element of REAL
1 - 0 is non empty V11() real ext-real positive non negative Element of REAL
(1 - 0) / (1 / 2) is V11() real ext-real non negative Element of REAL
((1 - 0) / (1 / 2)) * s3 is V11() real ext-real Element of REAL
(((1 - 0) / (1 / 2)) * s3) + (((1 / 2) * s1) / (1 / 2)) is V11() real ext-real Element of REAL
1 / (1 / 2) is V11() real ext-real non negative Element of REAL
(1 / (1 / 2)) * s3 is V11() real ext-real Element of REAL
(1 / 2) * 0 is empty trivial V11() real ext-real non positive non negative Relation-like non-empty empty-yielding complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V209() Element of REAL
((1 / 2) * 0) / (1 / 2) is empty trivial V11() real ext-real non positive non negative Relation-like non-empty empty-yielding complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V209() Element of REAL
((1 / (1 / 2)) * s3) + (((1 / 2) * 0) / (1 / 2)) is V11() real ext-real Element of REAL
2 * s3 is V11() real ext-real Element of REAL
dom hh is non empty Element of bool the carrier of ([:I[01],I[01]:] | e1)
h . (0,s3) is set
h . [0,s3] is set
[:(id I[01]),gg:] . (0,s3) is set
[:(id I[01]),gg:] . [0,s3] is set
g . ([:(id I[01]),gg:] . (0,s3)) is set
(id I[01]) . 0 is set
g . (((id I[01]) . 0),(gg . s3)) is set
[((id I[01]) . 0),(gg . s3)] is non empty V29() set
{((id I[01]) . 0),(gg . s3)} is non empty set
{((id I[01]) . 0)} is non empty trivial set
{{((id I[01]) . 0),(gg . s3)},{((id I[01]) . 0)}} is non empty set
g . [((id I[01]) . 0),(gg . s3)] is set
g . (0,(gg . s3)) is set
[0,(gg . s3)] is non empty V29() set
{0,(gg . s3)} is non empty set
{{0,(gg . s3)},{0}} is non empty set
g . [0,(gg . s3)] is set
h . (1,s3) is set
h . [1,s3] is set
[:(id I[01]),gg:] . (1,s3) is set
[:(id I[01]),gg:] . [1,s3] is set
g . ([:(id I[01]),gg:] . (1,s3)) is set
(id I[01]) . 1 is set
g . (((id I[01]) . 1),(gg . s3)) is set
[((id I[01]) . 1),(gg . s3)] is non empty V29() set
{((id I[01]) . 1),(gg . s3)} is non empty set
{((id I[01]) . 1)} is non empty trivial set
{{((id I[01]) . 1),(gg . s3)},{((id I[01]) . 1)}} is non empty set
g . [((id I[01]) . 1),(gg . s3)] is set
g . (1,(gg . s3)) is set
[1,(gg . s3)] is non empty V29() set
{1,(gg . s3)} is non empty set
{{1,(gg . s3)},{1}} is non empty set
g . [1,(gg . s3)] is set
e2 . s3 is set
s2 is V11() real ext-real Element of REAL
s1 is V11() real ext-real Element of REAL
s2 - s1 is V11() real ext-real Element of REAL
1 - (1 / 2) is V11() real ext-real Element of REAL
(s2 - s1) / (1 - (1 / 2)) is V11() real ext-real Element of REAL
((s2 - s1) / (1 - (1 / 2))) * s3 is V11() real ext-real Element of REAL
1 * s1 is V11() real ext-real Element of REAL
(1 / 2) * s2 is V11() real ext-real Element of REAL
(1 * s1) - ((1 / 2) * s2) is V11() real ext-real Element of REAL
((1 * s1) - ((1 / 2) * s2)) / (1 - (1 / 2)) is V11() real ext-real Element of REAL
(((s2 - s1) / (1 - (1 / 2))) * s3) + (((1 * s1) - ((1 / 2) * s2)) / (1 - (1 / 2))) is V11() real ext-real Element of REAL
1 - s1 is V11() real ext-real Element of REAL
(1 - s1) / (1 / 2) is V11() real ext-real Element of REAL
((1 - s1) / (1 / 2)) * s3 is V11() real ext-real Element of REAL
((1 * s1) - ((1 / 2) * s2)) / (1 / 2) is V11() real ext-real Element of REAL
(((1 - s1) / (1 / 2)) * s3) + (((1 * s1) - ((1 / 2) * s2)) / (1 / 2)) is V11() real ext-real Element of REAL
1 - 0 is non empty V11() real ext-real positive non negative Element of REAL
(1 - 0) / (1 / 2) is V11() real ext-real non negative Element of REAL
((1 - 0) / (1 / 2)) * s3 is V11() real ext-real Element of REAL
(((1 - 0) / (1 / 2)) * s3) + (((1 * s1) - ((1 / 2) * s2)) / (1 / 2)) is V11() real ext-real Element of REAL
2 * s3 is V11() real ext-real Element of REAL
1 * 0 is empty trivial V11() real ext-real non positive non negative Relation-like non-empty empty-yielding complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V209() Element of REAL
(1 * 0) - ((1 / 2) * s2) is V11() real ext-real Element of REAL
((1 * 0) - ((1 / 2) * s2)) / (1 / 2) is V11() real ext-real Element of REAL
(2 * s3) + (((1 * 0) - ((1 / 2) * s2)) / (1 / 2)) is V11() real ext-real Element of REAL
- ((1 / 2) * s2) is V11() real ext-real Element of REAL
(- ((1 / 2) * s2)) / (1 / 2) is V11() real ext-real Element of REAL
(2 * s3) + ((- ((1 / 2) * s2)) / (1 / 2)) is V11() real ext-real Element of REAL
(1 / 2) * 1 is V11() real ext-real non negative Element of REAL
- ((1 / 2) * 1) is V11() real ext-real non positive Element of REAL
(- ((1 / 2) * 1)) / (1 / 2) is V11() real ext-real non positive Element of REAL
(2 * s3) + ((- ((1 / 2) * 1)) / (1 / 2)) is V11() real ext-real Element of REAL
(2 * s3) - 1 is V11() real ext-real Element of REAL
1 / (1 / 2) is V11() real ext-real non negative Element of REAL
(1 / (1 / 2)) * s3 is V11() real ext-real Element of REAL
((1 / (1 / 2)) * s3) + (((1 * 0) - ((1 / 2) * s2)) / (1 / 2)) is V11() real ext-real Element of REAL
(1 * 0) - ((1 / 2) * 1) is V11() real ext-real non positive Element of REAL
((1 * 0) - ((1 / 2) * 1)) / (1 / 2) is V11() real ext-real non positive Element of REAL
((1 / (1 / 2)) * s3) + (((1 * 0) - ((1 / 2) * 1)) / (1 / 2)) is V11() real ext-real Element of REAL
dom hh is non empty Element of bool the carrier of ([:I[01],I[01]:] | e1)
hh . (0,s3) is set
hh . [0,s3] is set
[:(id I[01]),e2:] . (0,s3) is set
[:(id I[01]),e2:] . [0,s3] is set
f . ([:(id I[01]),e2:] . (0,s3)) is set
(id I[01]) . 0 is set
f . (((id I[01]) . 0),(e2 . s3)) is set
[((id I[01]) . 0),(e2 . s3)] is non empty V29() set
{((id I[01]) . 0),(e2 . s3)} is non empty set
{((id I[01]) . 0)} is non empty trivial set
{{((id I[01]) . 0),(e2 . s3)},{((id I[01]) . 0)}} is non empty set
f . [((id I[01]) . 0),(e2 . s3)] is set
f . (0,(e2 . s3)) is set
[0,(e2 . s3)] is non empty V29() set
{0,(e2 . s3)} is non empty set
{{0,(e2 . s3)},{0}} is non empty set
f . [0,(e2 . s3)] is set
hh . (1,s3) is set
hh . [1,s3] is set
[:(id I[01]),e2:] . (1,s3) is set
[:(id I[01]),e2:] . [1,s3] is set
f . ([:(id I[01]),e2:] . (1,s3)) is set
(id I[01]) . 1 is set
f . (((id I[01]) . 1),(e2 . s3)) is set
[((id I[01]) . 1),(e2 . s3)] is non empty V29() set
{((id I[01]) . 1),(e2 . s3)} is non empty set
{((id I[01]) . 1)} is non empty trivial set
{{((id I[01]) . 1),(e2 . s3)},{((id I[01]) . 1)}} is non empty set
f . [((id I[01]) . 1),(e2 . s3)] is set
f . (1,(e2 . s3)) is set
[1,(e2 . s3)] is non empty V29() set
{1,(e2 . s3)} is non empty set
{{1,(e2 . s3)},{1}} is non empty set
f . [1,(e2 . s3)] is set
s2 is V11() real ext-real Element of the carrier of I[01]
h . (s2,0) is set
[s2,0] is non empty V29() set
{s2,0} is non empty complex-membered ext-real-membered real-membered set
{s2} is non empty trivial complex-membered ext-real-membered real-membered set
{{s2,0},{s2}} is non empty set
h . [s2,0] is set
gg . s2 is Element of the carrier of T
h . (s2,1) is set
[s2,1] is non empty V29() set
{s2,1} is non empty complex-membered ext-real-membered real-membered set
{{s2,1},{s2}} is non empty set
h . [s2,1] is set
g . s2 is Element of the carrier of T
((1 / 2),1) (#) is V11() real ext-real Element of the carrier of (Closed-Interval-TSpace ((1 / 2),1))
e2 . 1 is set
dom hh is non empty Element of bool the carrier of ([:I[01],I[01]:] | e1)
hh . (s2,1) is set
hh . [s2,1] is set
[:(id I[01]),e2:] . (s2,1) is set
[:(id I[01]),e2:] . [s2,1] is set
f . ([:(id I[01]),e2:] . (s2,1)) is set
(id I[01]) . s2 is V11() real ext-real Element of the carrier of I[01]
f . (((id I[01]) . s2),(e2 . 1)) is set
[((id I[01]) . s2),(e2 . 1)] is non empty V29() set
{((id I[01]) . s2),(e2 . 1)} is non empty set
{((id I[01]) . s2)} is non empty trivial complex-membered ext-real-membered real-membered set
{{((id I[01]) . s2),(e2 . 1)},{((id I[01]) . s2)}} is non empty set
f . [((id I[01]) . s2),(e2 . 1)] is set
f . (s2,1) is set
f . [s2,1] is set
gg . 0 is set
s1 is V11() real ext-real Element of REAL
s3 is V11() real ext-real Element of REAL
s1 - s3 is V11() real ext-real Element of REAL
(1 / 2) - 0 is V11() real ext-real non negative Element of REAL
(s1 - s3) / ((1 / 2) - 0) is V11() real ext-real Element of REAL
((s1 - s3) / ((1 / 2) - 0)) * 0 is V11() real ext-real Element of REAL
(1 / 2) * s3 is V11() real ext-real Element of REAL
0 * s1 is V11() real ext-real Element of REAL
((1 / 2) * s3) - (0 * s1) is V11() real ext-real Element of REAL
(((1 / 2) * s3) - (0 * s1)) / ((1 / 2) - 0) is V11() real ext-real Element of REAL
(((s1 - s3) / ((1 / 2) - 0)) * 0) + ((((1 / 2) * s3) - (0 * s1)) / ((1 / 2) - 0)) is V11() real ext-real Element of REAL
(1 / 2) * 0 is empty trivial V11() real ext-real non positive non negative Relation-like non-empty empty-yielding complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V209() Element of REAL
((1 / 2) * 0) - (0 * s1) is V11() real ext-real Element of REAL
(((1 / 2) * 0) - (0 * s1)) / ((1 / 2) - 0) is V11() real ext-real Element of REAL
h . (s2,0) is set
h . [s2,0] is set
[:(id I[01]),gg:] . (s2,0) is set
[:(id I[01]),gg:] . [s2,0] is set
g . ([:(id I[01]),gg:] . (s2,0)) is set
g . (((id I[01]) . s2),(gg . 0)) is set
[((id I[01]) . s2),(gg . 0)] is non empty V29() set
{((id I[01]) . s2),(gg . 0)} is non empty set
{{((id I[01]) . s2),(gg . 0)},{((id I[01]) . s2)}} is non empty set
g . [((id I[01]) . s2),(gg . 0)] is set
g . (s2,0) is set
g . [s2,0] is set
T is non empty TopSpace-like TopStruct
the carrier of T is non empty set
a is Element of the carrier of T
b is Element of the carrier of T
P is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of a,b
Q is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like constant V43( the carrier of I[01]) quasi_total Path of b,b
P + Q is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of a,b
(T,a,b,P,()) is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of a,b
T is non empty TopSpace-like V74() pathwise_connected TopStruct
the carrier of T is non empty set
a is Element of the carrier of T
b is Element of the carrier of T
P is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total continuous Path of a,b
Q is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like constant V43( the carrier of I[01]) quasi_total continuous Path of b,b
P + Q is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total continuous Path of a,b
T is non empty TopSpace-like TopStruct
the carrier of T is non empty set
a is Element of the carrier of T
b is Element of the carrier of T
P is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of a,b
Q is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like constant V43( the carrier of I[01]) quasi_total Path of a,a
Q + P is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of a,b
(T,a,b,P,()) is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of a,b
T is non empty TopSpace-like V74() pathwise_connected TopStruct
the carrier of T is non empty set
a is Element of the carrier of T
b is Element of the carrier of T
P is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total continuous Path of a,b
Q is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like constant V43( the carrier of I[01]) quasi_total continuous Path of a,a
Q + P is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total continuous Path of a,b
T is non empty TopSpace-like TopStruct
the carrier of T is non empty set
a is Element of the carrier of T
b is Element of the carrier of T
Q is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of a,b
- Q is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of b,a
Q + (- Q) is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of a,a
Q is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like constant V43( the carrier of I[01]) quasi_total Path of a,a
pr2 ( the carrier of I[01], the carrier of I[01]) is non empty Relation-like [: the carrier of I[01], the carrier of I[01]:] -defined the carrier of I[01] -valued Function-like V43([: the carrier of I[01], the carrier of I[01]:]) quasi_total Element of bool [:[: the carrier of I[01], the carrier of I[01]:], the carrier of I[01]:]
[:[: the carrier of I[01], the carrier of I[01]:], the carrier of I[01]:] is non empty Relation-like set
bool [:[: the carrier of I[01], the carrier of I[01]:], the carrier of I[01]:] is non empty set
e2 is non empty Relation-like the carrier of [:I[01],I[01]:] -defined the carrier of I[01] -valued Function-like V43( the carrier of [:I[01],I[01]:]) quasi_total continuous Element of bool [: the carrier of [:I[01],I[01]:], the carrier of I[01]:]
(- Q) * e2 is non empty Relation-like the carrier of [:I[01],I[01]:] -defined the carrier of T -valued Function-like V43( the carrier of [:I[01],I[01]:]) quasi_total Element of bool [: the carrier of [:I[01],I[01]:], the carrier of T:]
[: the carrier of [:I[01],I[01]:], the carrier of T:] is non empty Relation-like set
bool [: the carrier of [:I[01],I[01]:], the carrier of T:] is non empty set
[:I[01],I[01]:] | () is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of [:I[01],I[01]:]
the carrier of ([:I[01],I[01]:] | ()) is non empty set
[: the carrier of ([:I[01],I[01]:] | ()), the carrier of T:] is non empty Relation-like set
bool [: the carrier of ([:I[01],I[01]:] | ()), the carrier of T:] is non empty set
gg is non empty Relation-like the carrier of [:I[01],I[01]:] -defined the carrier of T -valued Function-like V43( the carrier of [:I[01],I[01]:]) quasi_total continuous Element of bool [: the carrier of [:I[01],I[01]:], the carrier of T:]
gg | () is Relation-like the carrier of [:I[01],I[01]:] -defined () -defined the carrier of [:I[01],I[01]:] -defined the carrier of T -valued Function-like Element of bool [: the carrier of [:I[01],I[01]:], the carrier of T:]
g is non empty Relation-like the carrier of ([:I[01],I[01]:] | ()) -defined the carrier of T -valued Function-like V43( the carrier of ([:I[01],I[01]:] | ())) quasi_total Element of bool [: the carrier of ([:I[01],I[01]:] | ()), the carrier of T:]
g is non empty Relation-like the carrier of ([:I[01],I[01]:] | ()) -defined the carrier of T -valued Function-like V43( the carrier of ([:I[01],I[01]:] | ())) quasi_total continuous Element of bool [: the carrier of ([:I[01],I[01]:] | ()), the carrier of T:]
S3 is Element of the carrier of ([:I[01],I[01]:] | ())
g . S3 is Element of the carrier of T
S3 `2 is V11() real ext-real set
1 - (S3 `2) is V11() real ext-real Element of REAL
Q . (1 - (S3 `2)) is set
S3 `1 is V11() real ext-real set
[(S3 `1),(S3 `2)] is non empty V29() set
{(S3 `1),(S3 `2)} is non empty complex-membered ext-real-membered real-membered set
{(S3 `1)} is non empty trivial complex-membered ext-real-membered real-membered set
{{(S3 `1),(S3 `2)},{(S3 `1)}} is non empty set
e2 . ((S3 `1),(S3 `2)) is set
e2 . [(S3 `1),(S3 `2)] is set
dom e2 is non empty Element of bool the carrier of [:I[01],I[01]:]
gg . S3 is set
e2 . S3 is set
(- Q) . (e2 . S3) is set
[:I[01],I[01]:] | () is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of [:I[01],I[01]:]
[:I[01],I[01]:] | () is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of [:I[01],I[01]:]
pr1 ( the carrier of I[01], the carrier of I[01]) is non empty Relation-like [: the carrier of I[01], the carrier of I[01]:] -defined the carrier of I[01] -valued Function-like V43([: the carrier of I[01], the carrier of I[01]:]) quasi_total Element of bool [:[: the carrier of I[01], the carrier of I[01]:], the carrier of I[01]:]
e1 is non empty Relation-like the carrier of [:I[01],I[01]:] -defined the carrier of I[01] -valued Function-like V43( the carrier of [:I[01],I[01]:]) quasi_total continuous Element of bool [: the carrier of [:I[01],I[01]:], the carrier of I[01]:]
PP is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total continuous Path of a,a
PP * e1 is non empty Relation-like the carrier of [:I[01],I[01]:] -defined the carrier of [:I[01],I[01]:] -defined the carrier of T -valued the carrier of T -valued Function-like V43( the carrier of [:I[01],I[01]:]) V43( the carrier of [:I[01],I[01]:]) quasi_total quasi_total continuous Element of bool [: the carrier of [:I[01],I[01]:], the carrier of T:]
the carrier of ([:I[01],I[01]:] | ()) is non empty set
[: the carrier of ([:I[01],I[01]:] | ()), the carrier of T:] is non empty Relation-like set
bool [: the carrier of ([:I[01],I[01]:] | ()), the carrier of T:] is non empty set
(PP * e1) | () is Relation-like the carrier of [:I[01],I[01]:] -defined () -defined the carrier of [:I[01],I[01]:] -defined the carrier of T -valued Function-like Element of bool [: the carrier of [:I[01],I[01]:], the carrier of T:]
f is non empty Relation-like the carrier of ([:I[01],I[01]:] | ()) -defined the carrier of T -valued Function-like V43( the carrier of ([:I[01],I[01]:] | ())) quasi_total Element of bool [: the carrier of ([:I[01],I[01]:] | ()), the carrier of T:]
[:I[01],I[01]:] | (() \/ ()) is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of [:I[01],I[01]:]
S12 is non empty TopSpace-like T_0 T_1 T_2 SubSpace of [:I[01],I[01]:]
the carrier of S12 is non empty set
the carrier of ([:I[01],I[01]:] | ()) is non empty set
[: the carrier of ([:I[01],I[01]:] | ()), the carrier of T:] is non empty Relation-like set
bool [: the carrier of ([:I[01],I[01]:] | ()), the carrier of T:] is non empty set
(PP * e1) | () is Relation-like the carrier of [:I[01],I[01]:] -defined () -defined the carrier of [:I[01],I[01]:] -defined the carrier of T -valued Function-like Element of bool [: the carrier of [:I[01],I[01]:], the carrier of T:]
h is non empty Relation-like the carrier of ([:I[01],I[01]:] | ()) -defined the carrier of T -valued Function-like V43( the carrier of ([:I[01],I[01]:] | ())) quasi_total Element of bool [: the carrier of ([:I[01],I[01]:] | ()), the carrier of T:]
h is non empty Relation-like the carrier of ([:I[01],I[01]:] | ()) -defined the carrier of T -valued Function-like V43( the carrier of ([:I[01],I[01]:] | ())) quasi_total continuous Element of bool [: the carrier of ([:I[01],I[01]:] | ()), the carrier of T:]
s3 is Element of the carrier of ([:I[01],I[01]:] | ())
h . s3 is Element of the carrier of T
s3 `1 is V11() real ext-real set
2 * (s3 `1) is V11() real ext-real Element of REAL
(2 * (s3 `1)) - 1 is V11() real ext-real Element of REAL
(- Q) . ((2 * (s3 `1)) - 1) is set
s3 `2 is V11() real ext-real set
[(s3 `1),(s3 `2)] is non empty V29() set
{(s3 `1),(s3 `2)} is non empty complex-membered ext-real-membered real-membered set
{(s3 `1)} is non empty trivial complex-membered ext-real-membered real-membered set
{{(s3 `1),(s3 `2)},{(s3 `1)}} is non empty set
e1 . ((s3 `1),(s3 `2)) is set
e1 . [(s3 `1),(s3 `2)] is set
dom e1 is non empty Element of bool the carrier of [:I[01],I[01]:]
(PP * e1) . s3 is set
e1 . s3 is set
(Q + (- Q)) . (e1 . s3) is set
f is non empty Relation-like the carrier of ([:I[01],I[01]:] | ()) -defined the carrier of T -valued Function-like V43( the carrier of ([:I[01],I[01]:] | ())) quasi_total continuous Element of bool [: the carrier of ([:I[01],I[01]:] | ()), the carrier of T:]
s3 is Element of the carrier of ([:I[01],I[01]:] | ())
f . s3 is Element of the carrier of T
s3 `1 is V11() real ext-real set
2 * (s3 `1) is V11() real ext-real Element of REAL
Q . (2 * (s3 `1)) is set
s3 `2 is V11() real ext-real set
[(s3 `1),(s3 `2)] is non empty V29() set
{(s3 `1),(s3 `2)} is non empty complex-membered ext-real-membered real-membered set
{(s3 `1)} is non empty trivial complex-membered ext-real-membered real-membered set
{{(s3 `1),(s3 `2)},{(s3 `1)}} is non empty set
e1 . ((s3 `1),(s3 `2)) is set
e1 . [(s3 `1),(s3 `2)] is set
dom e1 is non empty Element of bool the carrier of [:I[01],I[01]:]
(PP * e1) . s3 is set
e1 . s3 is set
(Q + (- Q)) . (e1 . s3) is set
[#] ([:I[01],I[01]:] | ()) is non empty non proper open closed Element of bool the carrier of ([:I[01],I[01]:] | ())
bool the carrier of ([:I[01],I[01]:] | ()) is non empty set
[#] ([:I[01],I[01]:] | ()) is non empty non proper open closed Element of bool the carrier of ([:I[01],I[01]:] | ())
bool the carrier of ([:I[01],I[01]:] | ()) is non empty set
([#] ([:I[01],I[01]:] | ())) /\ ([#] ([:I[01],I[01]:] | ())) is Element of bool the carrier of ([:I[01],I[01]:] | ())
s3 is set
f . s3 is set
g . s3 is set
([#] ([:I[01],I[01]:] | ())) /\ () is Element of bool the carrier of [:I[01],I[01]:]
s1 is Element of the carrier of [:I[01],I[01]:]
s1 `2 is V11() real ext-real set
s1 `1 is V11() real ext-real set
2 * (s1 `1) is V11() real ext-real Element of REAL
1 - (2 * (s1 `1)) is V11() real ext-real Element of REAL
1 - (s1 `2) is V11() real ext-real Element of REAL
s2 is Element of the carrier of ([:I[01],I[01]:] | ())
s2 `1 is V11() real ext-real set
2 * (s2 `1) is V11() real ext-real Element of REAL
Q . (2 * (s2 `1)) is set
[#] ([:I[01],I[01]:] | ()) is non empty non proper open closed Element of bool the carrier of ([:I[01],I[01]:] | ())
bool the carrier of ([:I[01],I[01]:] | ()) is non empty set
s3 is Element of bool the carrier of [:I[01],I[01]:]
bool the carrier of S12 is non empty set
s1 is Element of bool the carrier of S12
s2 is Element of bool the carrier of S12
([#] ([:I[01],I[01]:] | ())) \/ ([#] ([:I[01],I[01]:] | ())) is non empty set
[#] S12 is non empty non proper open closed Element of bool the carrier of S12
[: the carrier of S12, the carrier of T:] is non empty Relation-like set
bool [: the carrier of S12, the carrier of T:] is non empty set
f +* g is Relation-like Function-like set
fg is non empty Relation-like the carrier of S12 -defined the carrier of T -valued Function-like V43( the carrier of S12) quasi_total Element of bool [: the carrier of S12, the carrier of T:]
([#] S12) /\ ([#] ([:I[01],I[01]:] | ())) is Element of bool the carrier of ([:I[01],I[01]:] | ())
H is set
fg . H is set
h . H is set
() /\ () is closed Element of bool the carrier of [:I[01],I[01]:]
{[(1 / 2),0]} \/ (() /\ ()) is non empty set
t is Element of the carrier of ([:I[01],I[01]:] | ())
t `1 is V11() real ext-real set
2 * (t `1) is V11() real ext-real Element of REAL
(2 * (t `1)) - 1 is V11() real ext-real Element of REAL
x is Element of the carrier of [:I[01],I[01]:]
x `2 is V11() real ext-real set
x `1 is V11() real ext-real set
2 * (x `1) is V11() real ext-real Element of REAL
(2 * (x `1)) - 1 is V11() real ext-real Element of REAL
dom g is non empty Element of bool the carrier of ([:I[01],I[01]:] | ())
g . H is set
t `2 is V11() real ext-real set
1 - (t `2) is V11() real ext-real Element of REAL
Q . (1 - (t `2)) is set
(- Q) . ((2 * (t `1)) - 1) is set
x is Element of the carrier of [:I[01],I[01]:]
x `2 is V11() real ext-real set
x `1 is V11() real ext-real set
2 * (x `1) is V11() real ext-real Element of REAL
(2 * (x `1)) - 1 is V11() real ext-real Element of REAL
([#] S12) \/ ([#] ([:I[01],I[01]:] | ())) is non empty set
fg +* h is Relation-like Function-like set
H is non empty Relation-like the carrier of [:I[01],I[01]:] -defined the carrier of T -valued Function-like V43( the carrier of [:I[01],I[01]:]) quasi_total Element of bool [: the carrier of [:I[01],I[01]:], the carrier of T:]
t is V11() real ext-real Element of the carrier of I[01]
H . (t,0) is set
[t,0] is non empty V29() set
{t,0} is non empty complex-membered ext-real-membered real-membered set
{t} is non empty trivial complex-membered ext-real-membered real-membered set
{{t,0},{t}} is non empty set
H . [t,0] is set
(Q + (- Q)) . t is Element of the carrier of T
H . (t,1) is set
[t,1] is non empty V29() set
{t,1} is non empty complex-membered ext-real-membered real-membered set
{{t,1},{t}} is non empty set
H . [t,1] is set
Q . t is Element of the carrier of T
[t,0] `1 is set
dom g is non empty Element of bool the carrier of ([:I[01],I[01]:] | ())
dom h is non empty Element of bool the carrier of ([:I[01],I[01]:] | ())
fg . [t,0] is set
f . [t,0] is set
2 * t is V11() real ext-real Element of REAL
Q . (2 * t) is set
dom h is non empty Element of bool the carrier of ([:I[01],I[01]:] | ())
h . [t,0] is set
2 * t is V11() real ext-real Element of REAL
(2 * t) - 1 is V11() real ext-real Element of REAL
(- Q) . ((2 * t) - 1) is set
2 * (1 / 2) is V11() real ext-real non negative Element of REAL
Q . (2 * (1 / 2)) is set
dom h is non empty Element of bool the carrier of ([:I[01],I[01]:] | ())
h . [t,0] is set
2 * t is V11() real ext-real Element of REAL
(2 * t) - 1 is V11() real ext-real Element of REAL
(- Q) . ((2 * t) - 1) is set
[t,1] `2 is set
[t,1] `1 is set
dom Q is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of I[01]
dom g is non empty Element of bool the carrier of ([:I[01],I[01]:] | ())
dom h is non empty Element of bool the carrier of ([:I[01],I[01]:] | ())
fg . [t,1] is set
g . [t,1] is set
1 - 1 is V11() real ext-real Element of REAL
Q . (1 - 1) is set
Q . 0 is set
dom h is non empty Element of bool the carrier of ([:I[01],I[01]:] | ())
h . [t,1] is set
2 * t is V11() real ext-real Element of REAL
(2 * t) - 1 is V11() real ext-real Element of REAL
(- Q) . ((2 * t) - 1) is set
Q . 0 is set
t is V11() real ext-real Element of the carrier of I[01]
H . (0,t) is set
[0,t] is non empty V29() set
{0,t} is non empty complex-membered ext-real-membered real-membered set
{{0,t},{0}} is non empty set
H . [0,t] is set
H . (1,t) is set
[1,t] is non empty V29() set
{1,t} is non empty complex-membered ext-real-membered real-membered set
{{1,t},{1}} is non empty set
H . [1,t] is set
x is Element of the carrier of [:I[01],I[01]:]
x `2 is V11() real ext-real set
x `1 is V11() real ext-real set
dom h is non empty Element of bool the carrier of ([:I[01],I[01]:] | ())
dom g is non empty Element of bool the carrier of ([:I[01],I[01]:] | ())
fg . [0,t] is set
f . [0,t] is set
2 * (x `1) is V11() real ext-real Element of REAL
Q . (2 * (x `1)) is set
dom g is non empty Element of bool the carrier of ([:I[01],I[01]:] | ())
fg . [0,t] is set
g . [0,1] is set
1 - (x `2) is V11() real ext-real Element of REAL
Q . (1 - (x `2)) is set
x is Element of the carrier of [:I[01],I[01]:]
x `1 is V11() real ext-real set
dom h is non empty Element of bool the carrier of ([:I[01],I[01]:] | ())
h . [1,t] is set
2 * (x `1) is V11() real ext-real Element of REAL
(2 * (x `1)) - 1 is V11() real ext-real Element of REAL
(- Q) . ((2 * (x `1)) - 1) is set
T is non empty TopSpace-like V74() pathwise_connected TopStruct
the carrier of T is non empty set
a is Element of the carrier of T
b is Element of the carrier of T
P is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total continuous Path of a,b
- P is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total continuous Path of b,a
P + (- P) is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total continuous Path of a,a
Q is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like constant V43( the carrier of I[01]) quasi_total continuous Path of a,a
T is non empty TopSpace-like TopStruct
the carrier of T is non empty set
a is Element of the carrier of T
b is Element of the carrier of T
Q is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of a,b
- Q is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of b,a
(- Q) + Q is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of b,b
Q is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like constant V43( the carrier of I[01]) quasi_total Path of b,b
pr2 ( the carrier of I[01], the carrier of I[01]) is non empty Relation-like [: the carrier of I[01], the carrier of I[01]:] -defined the carrier of I[01] -valued Function-like V43([: the carrier of I[01], the carrier of I[01]:]) quasi_total Element of bool [:[: the carrier of I[01], the carrier of I[01]:], the carrier of I[01]:]
[:[: the carrier of I[01], the carrier of I[01]:], the carrier of I[01]:] is non empty Relation-like set
bool [:[: the carrier of I[01], the carrier of I[01]:], the carrier of I[01]:] is non empty set
e2 is non empty Relation-like the carrier of [:I[01],I[01]:] -defined the carrier of I[01] -valued Function-like V43( the carrier of [:I[01],I[01]:]) quasi_total continuous Element of bool [: the carrier of [:I[01],I[01]:], the carrier of I[01]:]
Q * e2 is non empty Relation-like the carrier of [:I[01],I[01]:] -defined the carrier of T -valued Function-like V43( the carrier of [:I[01],I[01]:]) quasi_total Element of bool [: the carrier of [:I[01],I[01]:], the carrier of T:]
[: the carrier of [:I[01],I[01]:], the carrier of T:] is non empty Relation-like set
bool [: the carrier of [:I[01],I[01]:], the carrier of T:] is non empty set
[:I[01],I[01]:] | () is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of [:I[01],I[01]:]
the carrier of ([:I[01],I[01]:] | ()) is non empty set
[: the carrier of ([:I[01],I[01]:] | ()), the carrier of T:] is non empty Relation-like set
bool [: the carrier of ([:I[01],I[01]:] | ()), the carrier of T:] is non empty set
gg is non empty Relation-like the carrier of [:I[01],I[01]:] -defined the carrier of T -valued Function-like V43( the carrier of [:I[01],I[01]:]) quasi_total continuous Element of bool [: the carrier of [:I[01],I[01]:], the carrier of T:]
gg | () is Relation-like the carrier of [:I[01],I[01]:] -defined () -defined the carrier of [:I[01],I[01]:] -defined the carrier of T -valued Function-like Element of bool [: the carrier of [:I[01],I[01]:], the carrier of T:]
g is non empty Relation-like the carrier of ([:I[01],I[01]:] | ()) -defined the carrier of T -valued Function-like V43( the carrier of ([:I[01],I[01]:] | ())) quasi_total Element of bool [: the carrier of ([:I[01],I[01]:] | ()), the carrier of T:]
g is non empty Relation-like the carrier of ([:I[01],I[01]:] | ()) -defined the carrier of T -valued Function-like V43( the carrier of ([:I[01],I[01]:] | ())) quasi_total continuous Element of bool [: the carrier of ([:I[01],I[01]:] | ()), the carrier of T:]
S3 is Element of the carrier of ([:I[01],I[01]:] | ())
g . S3 is Element of the carrier of T
S3 `2 is V11() real ext-real set
1 - (S3 `2) is V11() real ext-real Element of REAL
(- Q) . (1 - (S3 `2)) is set
S3 `1 is V11() real ext-real set
[(S3 `1),(S3 `2)] is non empty V29() set
{(S3 `1),(S3 `2)} is non empty complex-membered ext-real-membered real-membered set
{(S3 `1)} is non empty trivial complex-membered ext-real-membered real-membered set
{{(S3 `1),(S3 `2)},{(S3 `1)}} is non empty set
e2 . ((S3 `1),(S3 `2)) is set
e2 . [(S3 `1),(S3 `2)] is set
dom e2 is non empty Element of bool the carrier of [:I[01],I[01]:]
gg . ((S3 `1),(S3 `2)) is set
gg . [(S3 `1),(S3 `2)] is set
1 - (1 - (S3 `2)) is V11() real ext-real Element of REAL
Q . (1 - (1 - (S3 `2))) is set
[:I[01],I[01]:] | () is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of [:I[01],I[01]:]
[:I[01],I[01]:] | () is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of [:I[01],I[01]:]
pr1 ( the carrier of I[01], the carrier of I[01]) is non empty Relation-like [: the carrier of I[01], the carrier of I[01]:] -defined the carrier of I[01] -valued Function-like V43([: the carrier of I[01], the carrier of I[01]:]) quasi_total Element of bool [:[: the carrier of I[01], the carrier of I[01]:], the carrier of I[01]:]
e1 is non empty Relation-like the carrier of [:I[01],I[01]:] -defined the carrier of I[01] -valued Function-like V43( the carrier of [:I[01],I[01]:]) quasi_total continuous Element of bool [: the carrier of [:I[01],I[01]:], the carrier of I[01]:]
PP is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total continuous Path of b,b
PP * e1 is non empty Relation-like the carrier of [:I[01],I[01]:] -defined the carrier of [:I[01],I[01]:] -defined the carrier of T -valued the carrier of T -valued Function-like V43( the carrier of [:I[01],I[01]:]) V43( the carrier of [:I[01],I[01]:]) quasi_total quasi_total continuous Element of bool [: the carrier of [:I[01],I[01]:], the carrier of T:]
the carrier of ([:I[01],I[01]:] | ()) is non empty set
[: the carrier of ([:I[01],I[01]:] | ()), the carrier of T:] is non empty Relation-like set
bool [: the carrier of ([:I[01],I[01]:] | ()), the carrier of T:] is non empty set
(PP * e1) | () is Relation-like the carrier of [:I[01],I[01]:] -defined () -defined the carrier of [:I[01],I[01]:] -defined the carrier of T -valued Function-like Element of bool [: the carrier of [:I[01],I[01]:], the carrier of T:]
f is non empty Relation-like the carrier of ([:I[01],I[01]:] | ()) -defined the carrier of T -valued Function-like V43( the carrier of ([:I[01],I[01]:] | ())) quasi_total Element of bool [: the carrier of ([:I[01],I[01]:] | ()), the carrier of T:]
[:I[01],I[01]:] | (() \/ ()) is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of [:I[01],I[01]:]
S12 is non empty TopSpace-like T_0 T_1 T_2 SubSpace of [:I[01],I[01]:]
the carrier of S12 is non empty set
the carrier of ([:I[01],I[01]:] | ()) is non empty set
[: the carrier of ([:I[01],I[01]:] | ()), the carrier of T:] is non empty Relation-like set
bool [: the carrier of ([:I[01],I[01]:] | ()), the carrier of T:] is non empty set
(PP * e1) | () is Relation-like the carrier of [:I[01],I[01]:] -defined () -defined the carrier of [:I[01],I[01]:] -defined the carrier of T -valued Function-like Element of bool [: the carrier of [:I[01],I[01]:], the carrier of T:]
h is non empty Relation-like the carrier of ([:I[01],I[01]:] | ()) -defined the carrier of T -valued Function-like V43( the carrier of ([:I[01],I[01]:] | ())) quasi_total Element of bool [: the carrier of ([:I[01],I[01]:] | ()), the carrier of T:]
h is non empty Relation-like the carrier of ([:I[01],I[01]:] | ()) -defined the carrier of T -valued Function-like V43( the carrier of ([:I[01],I[01]:] | ())) quasi_total continuous Element of bool [: the carrier of ([:I[01],I[01]:] | ()), the carrier of T:]
s3 is Element of the carrier of ([:I[01],I[01]:] | ())
h . s3 is Element of the carrier of T
s3 `1 is V11() real ext-real set
2 * (s3 `1) is V11() real ext-real Element of REAL
(2 * (s3 `1)) - 1 is V11() real ext-real Element of REAL
Q . ((2 * (s3 `1)) - 1) is set
s3 `2 is V11() real ext-real set
[(s3 `1),(s3 `2)] is non empty V29() set
{(s3 `1),(s3 `2)} is non empty complex-membered ext-real-membered real-membered set
{(s3 `1)} is non empty trivial complex-membered ext-real-membered real-membered set
{{(s3 `1),(s3 `2)},{(s3 `1)}} is non empty set
e1 . ((s3 `1),(s3 `2)) is set
e1 . [(s3 `1),(s3 `2)] is set
dom e1 is non empty Element of bool the carrier of [:I[01],I[01]:]
(PP * e1) . s3 is set
((- Q) + Q) . (e1 . ((s3 `1),(s3 `2))) is set
f is non empty Relation-like the carrier of ([:I[01],I[01]:] | ()) -defined the carrier of T -valued Function-like V43( the carrier of ([:I[01],I[01]:] | ())) quasi_total continuous Element of bool [: the carrier of ([:I[01],I[01]:] | ()), the carrier of T:]
s3 is Element of the carrier of ([:I[01],I[01]:] | ())
f . s3 is Element of the carrier of T
s3 `1 is V11() real ext-real set
2 * (s3 `1) is V11() real ext-real Element of REAL
(- Q) . (2 * (s3 `1)) is set
s3 `2 is V11() real ext-real set
[(s3 `1),(s3 `2)] is non empty V29() set
{(s3 `1),(s3 `2)} is non empty complex-membered ext-real-membered real-membered set
{(s3 `1)} is non empty trivial complex-membered ext-real-membered real-membered set
{{(s3 `1),(s3 `2)},{(s3 `1)}} is non empty set
e1 . ((s3 `1),(s3 `2)) is set
e1 . [(s3 `1),(s3 `2)] is set
dom e1 is non empty Element of bool the carrier of [:I[01],I[01]:]
(PP * e1) . s3 is set
e1 . s3 is set
((- Q) + Q) . (e1 . s3) is set
[#] ([:I[01],I[01]:] | ()) is non empty non proper open closed Element of bool the carrier of ([:I[01],I[01]:] | ())
bool the carrier of ([:I[01],I[01]:] | ()) is non empty set
[#] ([:I[01],I[01]:] | ()) is non empty non proper open closed Element of bool the carrier of ([:I[01],I[01]:] | ())
bool the carrier of ([:I[01],I[01]:] | ()) is non empty set
([#] ([:I[01],I[01]:] | ())) /\ ([#] ([:I[01],I[01]:] | ())) is Element of bool the carrier of ([:I[01],I[01]:] | ())
s3 is set
f . s3 is set
g . s3 is set
([#] ([:I[01],I[01]:] | ())) /\ () is Element of bool the carrier of [:I[01],I[01]:]
s1 is Element of the carrier of [:I[01],I[01]:]
s1 `2 is V11() real ext-real set
s1 `1 is V11() real ext-real set
2 * (s1 `1) is V11() real ext-real Element of REAL
1 - (2 * (s1 `1)) is V11() real ext-real Element of REAL
1 - (s1 `2) is V11() real ext-real Element of REAL
s2 is Element of the carrier of ([:I[01],I[01]:] | ())
s2 `1 is V11() real ext-real set
2 * (s2 `1) is V11() real ext-real Element of REAL
(- Q) . (2 * (s2 `1)) is set
[#] ([:I[01],I[01]:] | ()) is non empty non proper open closed Element of bool the carrier of ([:I[01],I[01]:] | ())
bool the carrier of ([:I[01],I[01]:] | ()) is non empty set
s3 is Element of bool the carrier of [:I[01],I[01]:]
bool the carrier of S12 is non empty set
s1 is Element of bool the carrier of S12
s2 is Element of bool the carrier of S12
([#] ([:I[01],I[01]:] | ())) \/ ([#] ([:I[01],I[01]:] | ())) is non empty set
[#] S12 is non empty non proper open closed Element of bool the carrier of S12
[: the carrier of S12, the carrier of T:] is non empty Relation-like set
bool [: the carrier of S12, the carrier of T:] is non empty set
f +* g is Relation-like Function-like set
fg is non empty Relation-like the carrier of S12 -defined the carrier of T -valued Function-like V43( the carrier of S12) quasi_total Element of bool [: the carrier of S12, the carrier of T:]
([#] S12) /\ ([#] ([:I[01],I[01]:] | ())) is Element of bool the carrier of ([:I[01],I[01]:] | ())
H is set
fg . H is set
h . H is set
() /\ () is closed Element of bool the carrier of [:I[01],I[01]:]
{[(1 / 2),0]} \/ (() /\ ()) is non empty set
t is Element of the carrier of ([:I[01],I[01]:] | ())
t `2 is V11() real ext-real set
1 - (t `2) is V11() real ext-real Element of REAL
dom g is non empty Element of bool the carrier of ([:I[01],I[01]:] | ())
g . H is set
(- Q) . (1 - (t `2)) is set
1 - (1 - (t `2)) is V11() real ext-real Element of REAL
Q . (1 - (1 - (t `2))) is set
x is Element of the carrier of [:I[01],I[01]:]
x `2 is V11() real ext-real set
x `1 is V11() real ext-real set
2 * (x `1) is V11() real ext-real Element of REAL
(2 * (x `1)) - 1 is V11() real ext-real Element of REAL
([#] S12) \/ ([#] ([:I[01],I[01]:] | ())) is non empty set
fg +* h is Relation-like Function-like set
H is non empty Relation-like the carrier of [:I[01],I[01]:] -defined the carrier of T -valued Function-like V43( the carrier of [:I[01],I[01]:]) quasi_total Element of bool [: the carrier of [:I[01],I[01]:], the carrier of T:]
t is V11() real ext-real Element of the carrier of I[01]
H . (t,0) is set
[t,0] is non empty V29() set
{t,0} is non empty complex-membered ext-real-membered real-membered set
{t} is non empty trivial complex-membered ext-real-membered real-membered set
{{t,0},{t}} is non empty set
H . [t,0] is set
((- Q) + Q) . t is Element of the carrier of T
H . (t,1) is set
[t,1] is non empty V29() set
{t,1} is non empty complex-membered ext-real-membered real-membered set
{{t,1},{t}} is non empty set
H . [t,1] is set
Q . t is Element of the carrier of T
[t,0] `1 is set
dom g is non empty Element of bool the carrier of ([:I[01],I[01]:] | ())
dom h is non empty Element of bool the carrier of ([:I[01],I[01]:] | ())
fg . [t,0] is set
f . [t,0] is set
2 * t is V11() real ext-real Element of REAL
(- Q) . (2 * t) is set
dom h is non empty Element of bool the carrier of ([:I[01],I[01]:] | ())
h . [t,0] is set
2 * t is V11() real ext-real Element of REAL
(2 * t) - 1 is V11() real ext-real Element of REAL
Q . ((2 * t) - 1) is set
2 * (1 / 2) is V11() real ext-real non negative Element of REAL
(- Q) . (2 * (1 / 2)) is set
dom h is non empty Element of bool the carrier of ([:I[01],I[01]:] | ())
h . [t,0] is set
2 * t is V11() real ext-real Element of REAL
(2 * t) - 1 is V11() real ext-real Element of REAL
Q . ((2 * t) - 1) is set
[t,1] `2 is set
[t,1] `1 is set
dom Q is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of I[01]
dom g is non empty Element of bool the carrier of ([:I[01],I[01]:] | ())
dom h is non empty Element of bool the carrier of ([:I[01],I[01]:] | ())
fg . [t,1] is set
g . [t,1] is set
1 - 1 is V11() real ext-real Element of REAL
(- Q) . (1 - 1) is set
Q . 0 is set
dom h is non empty Element of bool the carrier of ([:I[01],I[01]:] | ())
h . [t,1] is set
2 * t is V11() real ext-real Element of REAL
(2 * t) - 1 is V11() real ext-real Element of REAL
Q . ((2 * t) - 1) is set
Q . 0 is set
t is V11() real ext-real Element of the carrier of I[01]
H . (0,t) is set
[0,t] is non empty V29() set
{0,t} is non empty complex-membered ext-real-membered real-membered set
{{0,t},{0}} is non empty set
H . [0,t] is set
H . (1,t) is set
[1,t] is non empty V29() set
{1,t} is non empty complex-membered ext-real-membered real-membered set
{{1,t},{1}} is non empty set
H . [1,t] is set
x is Element of the carrier of [:I[01],I[01]:]
x `2 is V11() real ext-real set
x `1 is V11() real ext-real set
dom h is non empty Element of bool the carrier of ([:I[01],I[01]:] | ())
dom g is non empty Element of bool the carrier of ([:I[01],I[01]:] | ())
fg . [0,t] is set
f . [0,t] is set
2 * (x `1) is V11() real ext-real Element of REAL
(- Q) . (2 * (x `1)) is set
dom g is non empty Element of bool the carrier of ([:I[01],I[01]:] | ())
fg . [0,t] is set
g . [0,1] is set
1 - (x `2) is V11() real ext-real Element of REAL
(- Q) . (1 - (x `2)) is set
x is Element of the carrier of [:I[01],I[01]:]
x `1 is V11() real ext-real set
dom h is non empty Element of bool the carrier of ([:I[01],I[01]:] | ())
h . [1,t] is set
2 * (x `1) is V11() real ext-real Element of REAL
(2 * (x `1)) - 1 is V11() real ext-real Element of REAL
Q . ((2 * (x `1)) - 1) is set
T is non empty TopSpace-like V74() pathwise_connected TopStruct
the carrier of T is non empty set
a is Element of the carrier of T
b is Element of the carrier of T
P is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total continuous Path of a,b
- P is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total continuous Path of b,a
(- P) + P is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total continuous Path of b,b
Q is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like constant V43( the carrier of I[01]) quasi_total continuous Path of b,b
T is non empty TopSpace-like TopStruct
the carrier of T is non empty set
a is Element of the carrier of T
b is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like constant V43( the carrier of I[01]) quasi_total Path of a,a
P is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like constant V43( the carrier of I[01]) quasi_total Path of a,a
I[01] --> a is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total continuous Element of bool [: the carrier of I[01], the carrier of T:]
[: the carrier of I[01], the carrier of T:] is non empty Relation-like set
bool [: the carrier of I[01], the carrier of T:] is non empty set
K607( the carrier of T, the carrier of I[01],a) is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Element of bool [: the carrier of I[01], the carrier of T:]
T is non empty TopSpace-like TopStruct
the carrier of T is non empty set
a is Element of the carrier of T
b is Element of the carrier of T
P is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of a,b
Q is non empty Relation-like the carrier of I[01] -defined the carrier of T -valued Function-like V43( the carrier of I[01]) quasi_total Path of a,b
[: the carrier of [:I[01],I[01]:], the carrier of T:] is non empty Relation-like set
bool [: the carrier of [:I[01],I[01]:], the carrier of T:] is non empty set