:: JORDAN6 semantic presentation

REAL is non empty V36() V146() V147() V148() V152() V181() set
NAT is V146() V147() V148() V149() V150() V151() V152() V181() Element of K6(REAL)
K6(REAL) is set
COMPLEX is non empty V36() V146() V152() set
omega is V146() V147() V148() V149() V150() V151() V152() V181() set
K6(omega) is set
K6(NAT) is set
1 is non empty natural V11() real ext-real positive non negative V83() V84() V146() V147() V148() V149() V150() V151() Element of NAT
K7(1,1) is set
K6(K7(1,1)) is set
K7(K7(1,1),1) is set
K6(K7(K7(1,1),1)) is set
K7(K7(1,1),REAL) is set
K6(K7(K7(1,1),REAL)) is set
K7(REAL,REAL) is set
K7(K7(REAL,REAL),REAL) is set
K6(K7(K7(REAL,REAL),REAL)) is set
2 is non empty natural V11() real ext-real positive non negative V83() V84() V146() V147() V148() V149() V150() V151() Element of NAT
K7(2,2) is set
K7(K7(2,2),REAL) is set
K6(K7(K7(2,2),REAL)) is set
RAT is non empty V36() V146() V147() V148() V149() V152() set
INT is non empty V36() V146() V147() V148() V149() V150() V152() set
K6(K7(REAL,REAL)) is set
TOP-REAL 2 is non empty TopSpace-like T_0 T_1 T_2 V112() V158() V159() V160() V161() V162() V163() V164() strict V231() V232() RLTopStruct
the carrier of (TOP-REAL 2) is non empty functional set
K6( the carrier of (TOP-REAL 2)) is set
I[01] is non empty strict TopSpace-like T_0 T_1 T_2 compact V200() TopStruct
the carrier of I[01] is non empty V146() V147() V148() set
RealSpace is non empty strict Reflexive discerning symmetric triangle Discerning V200() MetrStruct
R^1 is non empty strict TopSpace-like V200() TopStruct
0 is empty natural V11() real ext-real non positive non negative V83() V84() V146() V147() V148() V149() V150() V151() V152() Element of NAT
the empty V146() V147() V148() V149() V150() V151() V152() set is empty V146() V147() V148() V149() V150() V151() V152() set
Closed-Interval-TSpace (0,1) is non empty strict TopSpace-like V200() SubSpace of R^1
the carrier of (Closed-Interval-TSpace (0,1)) is non empty V146() V147() V148() set
K7( the carrier of (TOP-REAL 2),REAL) is set
K6(K7( the carrier of (TOP-REAL 2),REAL)) is set
K7(COMPLEX,COMPLEX) is set
K6(K7(COMPLEX,COMPLEX)) is set
K7(COMPLEX,REAL) is set
K6(K7(COMPLEX,REAL)) is set
K537() is non empty V114() L10()
the carrier of K537() is non empty set
K542() is non empty V114() V211() V212() V213() V215() V241() V242() V243() V244() V245() V246() L10()
K543() is non empty V114() V213() V215() V244() V245() V246() M23(K542())
K544() is non empty V114() V211() V213() V215() V244() V245() V246() V247() M26(K542(),K543())
K546() is non empty V114() V211() V213() V215() L10()
K547() is non empty V114() V211() V213() V215() V247() M23(K546())
K7(K7(COMPLEX,COMPLEX),COMPLEX) is set
K6(K7(K7(COMPLEX,COMPLEX),COMPLEX)) is set
K7(RAT,RAT) is set
K6(K7(RAT,RAT)) is set
K7(K7(RAT,RAT),RAT) is set
K6(K7(K7(RAT,RAT),RAT)) is set
K7(INT,INT) is set
K6(K7(INT,INT)) is set
K7(K7(INT,INT),INT) is set
K6(K7(K7(INT,INT),INT)) is set
K7(NAT,NAT) is set
K7(K7(NAT,NAT),NAT) is set
K6(K7(K7(NAT,NAT),NAT)) is set
{} is empty V146() V147() V148() V149() V150() V151() V152() set
K608(RealSpace) is TopStruct
the carrier of R^1 is non empty V146() V147() V148() set
K6( the carrier of R^1) is set
real_dist is V22() V25(K7(REAL,REAL)) V26( REAL ) Function-like total quasi_total Element of K6(K7(K7(REAL,REAL),REAL))
MetrStruct(# REAL,real_dist #) is strict MetrStruct
I[01] is non empty strict TopSpace-like T_0 T_1 T_2 compact V200() SubSpace of R^1
the carrier of I[01] is non empty V146() V147() V148() set
K7( the carrier of I[01], the carrier of R^1) is set
K6(K7( the carrier of I[01], the carrier of R^1)) is set
K7( the carrier of (TOP-REAL 2), the carrier of R^1) is set
K6(K7( the carrier of (TOP-REAL 2), the carrier of R^1)) is set
proj1 is non empty V22() V25( the carrier of (TOP-REAL 2)) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of (TOP-REAL 2),REAL))
0[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))
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 V146() V147() V148() Element of K6(REAL)
C is V11() real ext-real set
r is V11() real ext-real set
C + r is V11() real ext-real set
(C + r) / 2 is V11() real ext-real Element of REAL
C is non empty TopSpace-like TopStruct
the carrier of C is non empty set
K6( the carrier of C) is set
r is Element of K6( the carrier of C)
C | r is strict TopSpace-like SubSpace of C
the carrier of (C | r) is set
K6( the carrier of (C | r)) is set
x is Element of K6( the carrier of (C | r))
fs is Element of K6( the carrier of C)
fs /\ r is Element of K6( the carrier of C)
[#] (C | r) is non proper closed Element of K6( the carrier of (C | r))
r is non empty TopSpace-like TopStruct
the carrier of r is non empty set
K6( the carrier of r) is set
C is non empty TopSpace-like TopStruct
the carrier of C is non empty set
K7( the carrier of C, the carrier of r) is set
K6(K7( the carrier of C, the carrier of r)) is set
x is non empty Element of K6( the carrier of r)
r | x is non empty strict TopSpace-like SubSpace of r
the carrier of (r | x) is non empty set
K7( the carrier of C, the carrier of (r | x)) is set
K6(K7( the carrier of C, the carrier of (r | x))) is set
fs is non empty V22() V25( the carrier of C) V26( the carrier of (r | x)) Function-like total quasi_total Element of K6(K7( the carrier of C, the carrier of (r | x)))
[#] (r | x) is non empty non proper closed Element of K6( the carrier of (r | x))
K6( the carrier of (r | x)) is set
P29 is non empty V22() V25( the carrier of C) V26( the carrier of r) Function-like total quasi_total Element of K6(K7( the carrier of C, the carrier of r))
f is Element of K6( the carrier of r)
P29 " f is Element of K6( the carrier of C)
K6( the carrier of C) is set
f /\ x is Element of K6( the carrier of r)
f1 is Element of K6( the carrier of (r | x))
P29 " x is Element of K6( the carrier of C)
dom P29 is Element of K6( the carrier of C)
(P29 " f) /\ (P29 " x) is Element of K6( the carrier of C)
fs " f1 is Element of K6( the carrier of C)
C is V11() real ext-real set
{ b₁ where b₁ is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : C <= b₁ `1 } is set
r is Element of K6( the carrier of (TOP-REAL 2))
Seg 2 is V146() V147() V148() V149() V150() V151() Element of K6(NAT)
r ` is Element of K6( the carrier of (TOP-REAL 2))
{ b₁ where b₁ is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : not C <= b₁ `1 } is set
x is set
the carrier of (TOP-REAL 2) \ r is Element of K6( the carrier of (TOP-REAL 2))
fs is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
fs `1 is V11() real ext-real Element of REAL
x is set
fs is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
fs `1 is V11() real ext-real Element of REAL
P29 is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
P29 `1 is V11() real ext-real Element of REAL
the carrier of (TOP-REAL 2) \ r is Element of K6( the carrier of (TOP-REAL 2))
fs is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
fs `1 is V11() real ext-real Element of REAL
{ b<sub>1</sub> where b<sub>1</sub> is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : not C <= b<sub>1</sub> /. 1 } is set
x is set
fs is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
fs `1 is V11() real ext-real Element of REAL
fs /. 1 is V11() real ext-real Element of REAL
x is set
fs is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
fs /. 1 is V11() real ext-real Element of REAL
fs `1 is V11() real ext-real Element of REAL
x is Element of K6( the carrier of (TOP-REAL 2))
C is V11() real ext-real set
{ b<sub>1</sub> where b<sub>1</sub> is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : b<sub>1</sub> `1 <= C } is set
r is Element of K6( the carrier of (TOP-REAL 2))
Seg 2 is V146() V147() V148() V149() V150() V151() Element of K6(NAT)
r ` is Element of K6( the carrier of (TOP-REAL 2))
{ b<sub>1</sub> where b<sub>1</sub> is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : not b<sub>1</sub> `1 <= C } is set
x is set
the carrier of (TOP-REAL 2) \ r is Element of K6( the carrier of (TOP-REAL 2))
fs is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
fs `1 is V11() real ext-real Element of REAL
x is set
fs is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
fs `1 is V11() real ext-real Element of REAL
P29 is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
P29 `1 is V11() real ext-real Element of REAL
the carrier of (TOP-REAL 2) \ r is Element of K6( the carrier of (TOP-REAL 2))
fs is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
fs `1 is V11() real ext-real Element of REAL
{ b₁ where b₁ is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : not b₁ /. 1 <= C } is set
x is set
fs is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
fs `1 is V11() real ext-real Element of REAL
fs /. 1 is V11() real ext-real Element of REAL
x is set
fs is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
fs /. 1 is V11() real ext-real Element of REAL
fs `1 is V11() real ext-real Element of REAL
x is Element of K6( the carrier of (TOP-REAL 2))
C is V11() real ext-real set
{ b₁ where b₁ is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : b₁ `1 = C } is set
r is Element of K6( the carrier of (TOP-REAL 2))
{ b<sub>1</sub> where b<sub>1</sub> is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() 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 V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : C <= b<sub>1</sub> `1 } is set
x is Element of K6( the carrier of (TOP-REAL 2))
{ b₁ where b₁ is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : S₂[b₁] } is set
{ b₁ where b₁ is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : b₁ `1 <= C } is set
fs is Element of K6( the carrier of (TOP-REAL 2))
x /\ fs is Element of K6( the carrier of (TOP-REAL 2))
P29 is set
f is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
f `1 is V11() real ext-real Element of REAL
f is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
f `1 is V11() real ext-real Element of REAL
P29 is set
f is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
f `1 is V11() real ext-real Element of REAL
f1 is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
f1 `1 is V11() real ext-real Element of REAL
C is V11() real ext-real set
{ b<sub>1</sub> where b<sub>1</sub> is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : C <= b<sub>1</sub> `2 } is set
r is Element of K6( the carrier of (TOP-REAL 2))
Seg 2 is V146() V147() V148() V149() V150() V151() Element of K6(NAT)
r ` is Element of K6( the carrier of (TOP-REAL 2))
{ b<sub>1</sub> where b<sub>1</sub> is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : not C <= b<sub>1</sub> `2 } is set
x is set
the carrier of (TOP-REAL 2) \ r is Element of K6( the carrier of (TOP-REAL 2))
fs is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
fs `2 is V11() real ext-real Element of REAL
x is set
fs is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
fs `2 is V11() real ext-real Element of REAL
P29 is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
P29 `2 is V11() real ext-real Element of REAL
the carrier of (TOP-REAL 2) \ r is Element of K6( the carrier of (TOP-REAL 2))
fs is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
fs `2 is V11() real ext-real Element of REAL
{ b₁ where b₁ is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : not C <= b₁ /. 2 } is set
x is set
fs is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
fs `2 is V11() real ext-real Element of REAL
fs /. 2 is V11() real ext-real Element of REAL
x is set
fs is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
fs /. 2 is V11() real ext-real Element of REAL
fs `2 is V11() real ext-real Element of REAL
x is Element of K6( the carrier of (TOP-REAL 2))
C is V11() real ext-real set
{ b₁ where b₁ is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : b₁ `2 <= C } is set
r is Element of K6( the carrier of (TOP-REAL 2))
Seg 2 is V146() V147() V148() V149() V150() V151() Element of K6(NAT)
r ` is Element of K6( the carrier of (TOP-REAL 2))
{ b₁ where b₁ is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : not b₁ `2 <= C } is set
x is set
the carrier of (TOP-REAL 2) \ r is Element of K6( the carrier of (TOP-REAL 2))
fs is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
fs `2 is V11() real ext-real Element of REAL
x is set
fs is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
fs `2 is V11() real ext-real Element of REAL
P29 is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
P29 `2 is V11() real ext-real Element of REAL
the carrier of (TOP-REAL 2) \ r is Element of K6( the carrier of (TOP-REAL 2))
fs is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
fs `2 is V11() real ext-real Element of REAL
{ b<sub>1</sub> where b<sub>1</sub> is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : not b<sub>1</sub> /. 2 <= C } is set
x is set
fs is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
fs `2 is V11() real ext-real Element of REAL
fs /. 2 is V11() real ext-real Element of REAL
x is set
fs is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
fs /. 2 is V11() real ext-real Element of REAL
fs `2 is V11() real ext-real Element of REAL
x is Element of K6( the carrier of (TOP-REAL 2))
C is V11() real ext-real set
{ b<sub>1</sub> where b<sub>1</sub> is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : b<sub>1</sub> `2 = C } is set
r is Element of K6( the carrier of (TOP-REAL 2))
{ b₁ where b₁ is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : S₁[b₁] } is set
{ b₁ where b₁ is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : C <= b₁ `2 } is set
x is Element of K6( the carrier of (TOP-REAL 2))
{ b<sub>1</sub> where b<sub>1</sub> is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() 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 V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : b<sub>1</sub> `2 <= C } is set
fs is Element of K6( the carrier of (TOP-REAL 2))
x /\ fs is Element of K6( the carrier of (TOP-REAL 2))
P29 is set
f is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
f `2 is V11() real ext-real Element of REAL
f is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
f `2 is V11() real ext-real Element of REAL
P29 is set
f is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
f `2 is V11() real ext-real Element of REAL
f1 is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
f1 `2 is V11() real ext-real Element of REAL
C is natural V11() real ext-real V83() V84() V146() V147() V148() V149() V150() V151() Element of NAT
TOP-REAL C is non empty TopSpace-like T_0 T_1 T_2 V112() V158() V159() V160() V161() V162() V163() V164() strict V231() V232() RLTopStruct
the carrier of (TOP-REAL C) is non empty functional set
K6( the carrier of (TOP-REAL C)) is set
r is Element of K6( the carrier of (TOP-REAL C))
x is V22() V26( REAL ) Function-like V43(C) FinSequence-like V138() Element of the carrier of (TOP-REAL C)
fs is V22() V26( REAL ) Function-like V43(C) FinSequence-like V138() Element of the carrier of (TOP-REAL C)
(TOP-REAL C) | r is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL C
the carrier of ((TOP-REAL C) | r) is set
K7( the carrier of I[01], the carrier of ((TOP-REAL C) | r)) is set
K6(K7( the carrier of I[01], the carrier of ((TOP-REAL C) | r))) is set
P29 is V22() V25( the carrier of I[01]) V26( the carrier of ((TOP-REAL C) | r)) Function-like quasi_total Element of K6(K7( the carrier of I[01], the carrier of ((TOP-REAL C) | r)))
P29 . 0 is set
P29 . 1 is set
f is non empty Element of K6( the carrier of (TOP-REAL C))
(TOP-REAL C) | f is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL C
the carrier of ((TOP-REAL C) | f) is non empty set
K7( the carrier of I[01], the carrier of ((TOP-REAL C) | f)) is set
K6(K7( the carrier of I[01], the carrier of ((TOP-REAL C) | f))) is set
[#] I[01] is non empty non proper closed V146() V147() V148() Element of K6( the carrier of I[01])
K6( the carrier of I[01]) is set
rng P29 is Element of K6( the carrier of ((TOP-REAL C) | r))
K6( the carrier of ((TOP-REAL C) | r)) is set
[#] ((TOP-REAL C) | r) is non proper closed Element of K6( the carrier of ((TOP-REAL C) | r))
dom P29 is V146() V147() V148() Element of K6( the carrier of I[01])
P29 .: ([#] I[01]) is Element of K6( the carrier of ((TOP-REAL C) | r))
r is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
x is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
C is Element of K6( the carrier of (TOP-REAL 2))
C is Element of K6( the carrier of (TOP-REAL 2))
r is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
x is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
r `1 is V11() real ext-real Element of REAL
x `1 is V11() real ext-real Element of REAL
(r `1) + (x `1) is V11() real ext-real Element of REAL
((r `1) + (x `1)) / 2 is V11() real ext-real Element of REAL
fs is non empty Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | fs is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | fs) is non empty set
K7( the carrier of I[01], the carrier of ((TOP-REAL 2) | fs)) is set
K6(K7( the carrier of I[01], the carrier of ((TOP-REAL 2) | fs))) is set
P29 is non empty V22() V25( the carrier of I[01]) V26( the carrier of ((TOP-REAL 2) | fs)) Function-like total quasi_total Element of K6(K7( the carrier of I[01], the carrier of ((TOP-REAL 2) | fs)))
P29 . 0 is set
P29 . 1 is set
f is non empty V22() V25( the carrier of (TOP-REAL 2)) V26( the carrier of R^1) Function-like total quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of R^1))
Seg 2 is V146() V147() V148() V149() V150() V151() Element of K6(NAT)
(TOP-REAL 2) | C is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | C) is set
[#] ((TOP-REAL 2) | C) is non proper closed Element of K6( the carrier of ((TOP-REAL 2) | C))
K6( the carrier of ((TOP-REAL 2) | C)) is set
K7( the carrier of I[01], the carrier of (TOP-REAL 2)) is set
K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2))) is set
f1 is non empty V22() V25( the carrier of I[01]) V26( the carrier of (TOP-REAL 2)) Function-like total quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
K7( the carrier of I[01], the carrier of R^1) is set
K6(K7( the carrier of I[01], the carrier of R^1)) is set
f * P29 is V22() V25( the carrier of I[01]) V26( the carrier of R^1) Function-like Element of K6(K7( the carrier of I[01], the carrier of R^1))
dom P29 is V146() V147() V148() Element of K6( the carrier of I[01])
K6( the carrier of I[01]) is set
f2 is non empty V22() V25( the carrier of I[01]) V26( the carrier of R^1) Function-like total quasi_total Element of K6(K7( the carrier of I[01], the carrier of R^1))
f2 . 0 is set
f . (P29 . 0) is set
r /. 1 is V11() real ext-real Element of REAL
f2 . 1 is set
f . (P29 . 1) is set
x /. 1 is V11() real ext-real Element of REAL
proj11 is V11() real ext-real Element of REAL
f2 . proj11 is set
P29 . proj11 is set
f . (P29 . proj11) is set
proj12 is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
proj12 /. 1 is V11() real ext-real Element of REAL
proj12 `1 is V11() real ext-real Element of REAL
C is Element of K6( the carrier of (TOP-REAL 2))
r is Element of K6( the carrier of (TOP-REAL 2))
C /\ r is Element of K6( the carrier of (TOP-REAL 2))
x is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
fs is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
x `1 is V11() real ext-real Element of REAL
fs `1 is V11() real ext-real Element of REAL
(x `1) + (fs `1) is V11() real ext-real Element of REAL
((x `1) + (fs `1)) / 2 is V11() real ext-real Element of REAL
{ b<sub>1</sub> where b<sub>1</sub> is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : b<sub>1</sub> `1 = ((x `1) + (fs `1)) / 2 } is set
f is non empty V22() V25( the carrier of (TOP-REAL 2)) V26( the carrier of R^1) Function-like total quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of R^1))
Seg 2 is V146() V147() V148() V149() V150() V151() Element of K6(NAT)
dom f is Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | C is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
[#] ((TOP-REAL 2) | C) is non proper closed Element of K6( the carrier of ((TOP-REAL 2) | C))
the carrier of ((TOP-REAL 2) | C) is set
K6( the carrier of ((TOP-REAL 2) | C)) is set
f1 is non empty Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | f1 is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | f1) is non empty set
f | C is V22() V25( the carrier of (TOP-REAL 2)) V26( the carrier of R^1) Function-like Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of R^1))
dom (f | C) is Element of K6( the carrier of (TOP-REAL 2))
the carrier of (TOP-REAL 2) /\ C is Element of K6( the carrier of (TOP-REAL 2))
rng (f | C) is V146() V147() V148() Element of K6( the carrier of R^1)
K7( the carrier of ((TOP-REAL 2) | C), the carrier of R^1) is set
K6(K7( the carrier of ((TOP-REAL 2) | C), the carrier of R^1)) is set
K7( the carrier of ((TOP-REAL 2) | f1), the carrier of R^1) is set
K6(K7( the carrier of ((TOP-REAL 2) | f1), the carrier of R^1)) is set
f2 is V22() V25( the carrier of ((TOP-REAL 2) | C)) V26( the carrier of R^1) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | C), the carrier of R^1))
proj11 is non empty V22() V25( the carrier of ((TOP-REAL 2) | f1)) V26( the carrier of R^1) Function-like total quasi_total continuous Element of K6(K7( the carrier of ((TOP-REAL 2) | f1), the carrier of R^1))
proj12 is Element of the carrier of ((TOP-REAL 2) | C)
proj11 . proj12 is set
f . x is V11() real ext-real Element of the carrier of R^1
x /. 1 is V11() real ext-real Element of REAL
g1 is Element of the carrier of ((TOP-REAL 2) | C)
proj11 . g1 is set
f . fs is V11() real ext-real Element of the carrier of R^1
fs /. 1 is V11() real ext-real Element of REAL
P29 is Element of K6( the carrier of (TOP-REAL 2))
g is Element of the carrier of ((TOP-REAL 2) | C)
proj11 . g is set
f . g is set
P19 is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
P19 /. 1 is V11() real ext-real Element of REAL
P19 `1 is V11() real ext-real Element of REAL
g is Element of the carrier of ((TOP-REAL 2) | C)
proj11 . g is set
f . g is set
P19 is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
P19 /. 1 is V11() real ext-real Element of REAL
P19 `1 is V11() real ext-real Element of REAL
g is Element of K6( the carrier of (TOP-REAL 2))
P19 is Element of K6( the carrier of (TOP-REAL 2))
C is Element of K6( the carrier of (TOP-REAL 2))
r is Element of K6( the carrier of (TOP-REAL 2))
C /\ r is Element of K6( the carrier of (TOP-REAL 2))
x is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
fs is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
x `2 is V11() real ext-real Element of REAL
fs `2 is V11() real ext-real Element of REAL
(x `2) + (fs `2) is V11() real ext-real Element of REAL
((x `2) + (fs `2)) / 2 is V11() real ext-real Element of REAL
{ b₁ where b₁ is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : b₁ `2 = ((x `2) + (fs `2)) / 2 } is set
P29 is non empty V22() V25( the carrier of (TOP-REAL 2)) V26( the carrier of R^1) Function-like total quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of R^1))
Seg 2 is V146() V147() V148() V149() V150() V151() Element of K6(NAT)
dom P29 is Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | C is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
[#] ((TOP-REAL 2) | C) is non proper closed Element of K6( the carrier of ((TOP-REAL 2) | C))
the carrier of ((TOP-REAL 2) | C) is set
K6( the carrier of ((TOP-REAL 2) | C)) is set
f is non empty Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | f is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | f) is non empty set
P29 | C is V22() V25( the carrier of (TOP-REAL 2)) V26( the carrier of R^1) Function-like Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of R^1))
dom (P29 | C) is Element of K6( the carrier of (TOP-REAL 2))
the carrier of (TOP-REAL 2) /\ C is Element of K6( the carrier of (TOP-REAL 2))
rng (P29 | C) is V146() V147() V148() Element of K6( the carrier of R^1)
K7( the carrier of ((TOP-REAL 2) | C), the carrier of R^1) is set
K6(K7( the carrier of ((TOP-REAL 2) | C), the carrier of R^1)) is set
K7( the carrier of ((TOP-REAL 2) | f), the carrier of R^1) is set
K6(K7( the carrier of ((TOP-REAL 2) | f), the carrier of R^1)) is set
f1 is V22() V25( the carrier of ((TOP-REAL 2) | C)) V26( the carrier of R^1) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | C), the carrier of R^1))
f2 is non empty V22() V25( the carrier of ((TOP-REAL 2) | f)) V26( the carrier of R^1) Function-like total quasi_total continuous Element of K6(K7( the carrier of ((TOP-REAL 2) | f), the carrier of R^1))
proj11 is Element of the carrier of ((TOP-REAL 2) | C)
f2 . proj11 is set
P29 . x is V11() real ext-real Element of the carrier of R^1
x /. 2 is V11() real ext-real Element of REAL
proj12 is Element of the carrier of ((TOP-REAL 2) | C)
f2 . proj12 is set
P29 . fs is V11() real ext-real Element of the carrier of R^1
fs /. 2 is V11() real ext-real Element of REAL
g1 is Element of K6( the carrier of (TOP-REAL 2))
g is Element of the carrier of ((TOP-REAL 2) | C)
f2 . g is set
P29 . g is set
P19 is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
P19 /. 2 is V11() real ext-real Element of REAL
P19 `2 is V11() real ext-real Element of REAL
g is Element of the carrier of ((TOP-REAL 2) | C)
f2 . g is set
P29 . g is set
P19 is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
P19 /. 2 is V11() real ext-real Element of REAL
P19 `2 is V11() real ext-real Element of REAL
g is Element of K6( the carrier of (TOP-REAL 2))
P19 is Element of K6( the carrier of (TOP-REAL 2))
r is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
r `1 is V11() real ext-real Element of REAL
x is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
x `1 is V11() real ext-real Element of REAL
(r `1) + (x `1) is V11() real ext-real Element of REAL
((r `1) + (x `1)) / 2 is V11() real ext-real Element of REAL
{ b<sub>1</sub> where b<sub>1</sub> is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : b<sub>1</sub> `1 = ((r `1) + (x `1)) / 2 } is set
C is Element of K6( the carrier of (TOP-REAL 2))
fs is set
P29 is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
P29 `1 is V11() real ext-real Element of REAL
fs is Element of K6( the carrier of (TOP-REAL 2))
First_Point (C,r,x,fs) is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
P29 is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
f is Element of K6( the carrier of (TOP-REAL 2))
First_Point (C,r,x,f) is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
fs is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
P29 is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
f is set
f1 is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
f1 `1 is V11() real ext-real Element of REAL
f is Element of K6( the carrier of (TOP-REAL 2))
First_Point (C,r,x,f) is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
r is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
r `2 is V11() real ext-real Element of REAL
x is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
x `2 is V11() real ext-real Element of REAL
(r `2) + (x `2) is V11() real ext-real Element of REAL
((r `2) + (x `2)) / 2 is V11() real ext-real Element of REAL
{ b₁ where b₁ is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : b₁ `2 = ((r `2) + (x `2)) / 2 } is set
C is Element of K6( the carrier of (TOP-REAL 2))
fs is set
P29 is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
P29 `2 is V11() real ext-real Element of REAL
fs is Element of K6( the carrier of (TOP-REAL 2))
First_Point (C,r,x,fs) is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
P29 is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
f is Element of K6( the carrier of (TOP-REAL 2))
First_Point (C,r,x,f) is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
fs is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
P29 is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
f is set
f1 is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
f1 `2 is V11() real ext-real Element of REAL
f is Element of K6( the carrier of (TOP-REAL 2))
First_Point (C,r,x,f) is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
C is Element of K6( the carrier of (TOP-REAL 2))
r is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
x is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(C,r,x) is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(C,r,x) is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
r `1 is V11() real ext-real Element of REAL
x `1 is V11() real ext-real Element of REAL
(r `1) + (x `1) is V11() real ext-real Element of REAL
((r `1) + (x `1)) / 2 is V11() real ext-real Element of REAL
{ H<sub>1</sub>(b<sub>1</sub>) where b<sub>1</sub> is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : S<sub>1</sub>[b<sub>1</sub>] } is set
fs is Element of K6( the carrier of (TOP-REAL 2))
First_Point (C,r,x,fs) is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
C /\ fs is Element of K6( the carrier of (TOP-REAL 2))
r `2 is V11() real ext-real Element of REAL
x `2 is V11() real ext-real Element of REAL
(r `2) + (x `2) is V11() real ext-real Element of REAL
((r `2) + (x `2)) / 2 is V11() real ext-real Element of REAL
{ H<sub>1</sub>(b<sub>1</sub>) where b<sub>1</sub> is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : S<sub>2</sub>[b<sub>1</sub>] } is set
P29 is Element of K6( the carrier of (TOP-REAL 2))
First_Point (C,r,x,P29) is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
C /\ P29 is Element of K6( the carrier of (TOP-REAL 2))
C is Element of K6( the carrier of (TOP-REAL 2))
r is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
x is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(C,r,x) is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
r `1 is V11() real ext-real Element of REAL
x `1 is V11() real ext-real Element of REAL
(r `1) + (x `1) is V11() real ext-real Element of REAL
((r `1) + (x `1)) / 2 is V11() real ext-real Element of REAL
{ H<sub>1</sub>(b<sub>1</sub>) where b<sub>1</sub> is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : S<sub>1</sub>[b<sub>1</sub>] } is set
fs is Element of K6( the carrier of (TOP-REAL 2))
C /\ fs is Element of K6( the carrier of (TOP-REAL 2))
First_Point (C,r,x,fs) is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
P29 is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
P29 `1 is V11() real ext-real Element of REAL
{ b₁ where b₁ is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : b₁ `1 = ((r `1) + (x `1)) / 2 } is set
fs is Element of K6( the carrier of (TOP-REAL 2))
First_Point (C,r,x,fs) is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
C /\ fs is Element of K6( the carrier of (TOP-REAL 2))
C is Element of K6( the carrier of (TOP-REAL 2))
r is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
x is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(C,r,x) is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
r `2 is V11() real ext-real Element of REAL
x `2 is V11() real ext-real Element of REAL
(r `2) + (x `2) is V11() real ext-real Element of REAL
((r `2) + (x `2)) / 2 is V11() real ext-real Element of REAL
{ H<sub>1</sub>(b<sub>1</sub>) where b<sub>1</sub> is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : S<sub>1</sub>[b<sub>1</sub>] } is set
fs is Element of K6( the carrier of (TOP-REAL 2))
C /\ fs is Element of K6( the carrier of (TOP-REAL 2))
First_Point (C,r,x,fs) is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
P29 is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
P29 `2 is V11() real ext-real Element of REAL
{ b₁ where b₁ is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : b₁ `2 = ((r `2) + (x `2)) / 2 } is set
fs is Element of K6( the carrier of (TOP-REAL 2))
First_Point (C,r,x,fs) is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
C /\ fs is Element of K6( the carrier of (TOP-REAL 2))
C is Element of K6( the carrier of (TOP-REAL 2))
r is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
x is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
fs is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
P29 is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(TOP-REAL 2) | C is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | C) is set
K7( the carrier of I[01], the carrier of ((TOP-REAL 2) | C)) is set
K6(K7( the carrier of I[01], the carrier of ((TOP-REAL 2) | C))) is set
K7( the carrier of I[01], the carrier of ((TOP-REAL 2) | C)) is set
K6(K7( the carrier of I[01], the carrier of ((TOP-REAL 2) | C))) is set
f1 is V22() V25( the carrier of I[01]) V26( the carrier of ((TOP-REAL 2) | C)) Function-like quasi_total Element of K6(K7( the carrier of I[01], the carrier of ((TOP-REAL 2) | C)))
f1 . 0 is set
f1 . 1 is set
f2 is V11() real ext-real Element of REAL
f1 . f2 is set
proj11 is V11() real ext-real Element of REAL
f1 . proj11 is set
1 - f2 is V11() real ext-real Element of REAL
1 - 0 is non empty V11() real ext-real positive non negative Element of REAL
1 - proj11 is V11() real ext-real Element of REAL
1 - 1 is V11() real ext-real Element of REAL
L[01] (((0,1) (#)),((#) (0,1))) is non empty V22() V25( the carrier of (Closed-Interval-TSpace (0,1))) V26( the carrier of (Closed-Interval-TSpace (0,1))) Function-like total quasi_total Element of K6(K7( the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace (0,1))))
K7( the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace (0,1))) is set
K6(K7( the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace (0,1)))) is set
f1 * (L[01] (((0,1) (#)),((#) (0,1)))) is V22() V25( the carrier of (Closed-Interval-TSpace (0,1))) V26( the carrier of ((TOP-REAL 2) | C)) Function-like Element of K6(K7( the carrier of (Closed-Interval-TSpace (0,1)), the carrier of ((TOP-REAL 2) | C)))
K7( the carrier of (Closed-Interval-TSpace (0,1)), the carrier of ((TOP-REAL 2) | C)) is set
K6(K7( the carrier of (Closed-Interval-TSpace (0,1)), the carrier of ((TOP-REAL 2) | C))) 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)))) . ((#) (0,1)) is V11() real ext-real Element of the carrier of (Closed-Interval-TSpace (0,1))
dom f1 is V146() V147() V148() Element of K6( the carrier of I[01])
K6( the carrier of I[01]) is set
[#] I[01] is non empty non proper closed V146() V147() V148() Element of K6( the carrier of I[01])
rng (L[01] (((0,1) (#)),((#) (0,1)))) is V146() V147() V148() Element of K6( the carrier of (Closed-Interval-TSpace (0,1)))
K6( the carrier of (Closed-Interval-TSpace (0,1))) is set
dom (f1 * (L[01] (((0,1) (#)),((#) (0,1))))) is V146() V147() V148() Element of K6( the carrier of (Closed-Interval-TSpace (0,1)))
dom (L[01] (((0,1) (#)),((#) (0,1)))) is V146() V147() V148() Element of K6( the carrier of (Closed-Interval-TSpace (0,1)))
f is non empty Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | f is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | f) is non empty set
K7( the carrier of I[01], the carrier of ((TOP-REAL 2) | f)) is set
K6(K7( the carrier of I[01], the carrier of ((TOP-REAL 2) | f))) is set
g is non empty V22() V25( the carrier of I[01]) V26( the carrier of ((TOP-REAL 2) | f)) Function-like total quasi_total Element of K6(K7( the carrier of I[01], the carrier of ((TOP-REAL 2) | f)))
dom g is V146() V147() V148() Element of K6( the carrier of I[01])
g . 0 is set
g . 1 is set
P19 is V11() real ext-real Element of the carrier of (Closed-Interval-TSpace (0,1))
(L[01] (((0,1) (#)),((#) (0,1)))) . P19 is V11() real ext-real Element of the carrier of (Closed-Interval-TSpace (0,1))
1 - (1 - f2) is V11() real ext-real Element of REAL
(1 - (1 - f2)) * 1 is V11() real ext-real Element of REAL
(1 - f2) * 0 is V11() real ext-real Element of REAL
((1 - (1 - f2)) * 1) + ((1 - f2) * 0) is V11() real ext-real Element of REAL
r1 is V11() real ext-real Element of the carrier of (Closed-Interval-TSpace (0,1))
(L[01] (((0,1) (#)),((#) (0,1)))) . r1 is V11() real ext-real Element of the carrier of (Closed-Interval-TSpace (0,1))
1 - (1 - proj11) is V11() real ext-real Element of REAL
(1 - (1 - proj11)) * 1 is V11() real ext-real Element of REAL
(1 - proj11) * 0 is V11() real ext-real Element of REAL
((1 - (1 - proj11)) * 1) + ((1 - proj11) * 0) is V11() real ext-real Element of REAL
g . (1 - f2) is set
g . (1 - proj11) is set
C is Element of K6( the carrier of (TOP-REAL 2))
r is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
x is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
fs is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
{ b<sub>1</sub> where b<sub>1</sub> is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : LE b<sub>1</sub>,fs,C,r,x } is set
P29 is set
f is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
C is Element of K6( the carrier of (TOP-REAL 2))
r is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
x is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
fs is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
{ b<sub>1</sub> where b<sub>1</sub> is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : LE fs,b<sub>1</sub>,C,r,x } is set
P29 is set
f is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
C is Element of K6( the carrier of (TOP-REAL 2))
r is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
x is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
fs is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(C,r,x,fs) is Element of K6( the carrier of (TOP-REAL 2))
{ b<sub>1</sub> where b<sub>1</sub> is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : LE b<sub>1</sub>,fs,C,r,x } is set
P29 is set
f is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
C is Element of K6( the carrier of (TOP-REAL 2))
r is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
x is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
fs is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(C,r,x,fs) is Element of K6( the carrier of (TOP-REAL 2))
{ b<sub>1</sub> where b<sub>1</sub> is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : LE fs,b<sub>1</sub>,C,r,x } is set
P29 is set
f is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
C is Element of K6( the carrier of (TOP-REAL 2))
r is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
x is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(C,r,x,r) is Element of K6( the carrier of (TOP-REAL 2))
{ b<sub>1</sub> where b<sub>1</sub> is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : LE b<sub>1</sub>,r,C,r,x } is set
{r} is non empty set
fs is set
P29 is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
fs is set
C is Element of K6( the carrier of (TOP-REAL 2))
r is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
x is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(C,r,x,x) is Element of K6( the carrier of (TOP-REAL 2))
{ b<sub>1</sub> where b<sub>1</sub> is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : LE b<sub>1</sub>,x,C,r,x } is set
fs is set
P29 is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
C is Element of K6( the carrier of (TOP-REAL 2))
r is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
x is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(C,r,x,x) is Element of K6( the carrier of (TOP-REAL 2))
{ b<sub>1</sub> where b<sub>1</sub> is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : LE x,b<sub>1</sub>,C,r,x } is set
{x} is non empty set
fs is set
P29 is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
fs is set
C is Element of K6( the carrier of (TOP-REAL 2))
r is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
x is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(C,r,x,r) is Element of K6( the carrier of (TOP-REAL 2))
{ b<sub>1</sub> where b<sub>1</sub> is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : LE r,b<sub>1</sub>,C,r,x } is set
fs is set
P29 is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
C is Element of K6( the carrier of (TOP-REAL 2))
r is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
x is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
fs is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(C,r,x,fs) is Element of K6( the carrier of (TOP-REAL 2))
{ b<sub>1</sub> where b<sub>1</sub> is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : LE fs,b<sub>1</sub>,C,r,x } is set
(C,x,r,fs) is Element of K6( the carrier of (TOP-REAL 2))
{ b<sub>1</sub> where b<sub>1</sub> is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : LE b<sub>1</sub>,fs,C,x,r } is set
P29 is set
f is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
P29 is set
f is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
C is Element of K6( the carrier of (TOP-REAL 2))
r is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
x is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
fs is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(C,r,x,fs) is Element of K6( the carrier of (TOP-REAL 2))
{ b<sub>1</sub> where b<sub>1</sub> is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : LE fs,b<sub>1</sub>,C,r,x } is set
P29 is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(C,r,x,P29) is Element of K6( the carrier of (TOP-REAL 2))
{ b<sub>1</sub> where b<sub>1</sub> is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : LE b<sub>1</sub>,P29,C,r,x } is set
(C,r,x,fs) /\ (C,r,x,P29) is Element of K6( the carrier of (TOP-REAL 2))
C is Element of K6( the carrier of (TOP-REAL 2))
r is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
x is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
fs is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
P29 is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(C,r,x,fs,P29) is Element of K6( the carrier of (TOP-REAL 2))
(C,r,x,fs) is Element of K6( the carrier of (TOP-REAL 2))
{ b<sub>1</sub> where b<sub>1</sub> is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : LE fs,b<sub>1</sub>,C,r,x } is set
(C,r,x,P29) is Element of K6( the carrier of (TOP-REAL 2))
{ b<sub>1</sub> where b<sub>1</sub> is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : LE b<sub>1</sub>,P29,C,r,x } is set
(C,r,x,fs) /\ (C,r,x,P29) is Element of K6( the carrier of (TOP-REAL 2))
{ b<sub>1</sub> where b<sub>1</sub> is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : ( LE fs,b<sub>1</sub>,C,r,x & LE b<sub>1</sub>,P29,C,r,x ) } is set
f is set
f1 is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
f2 is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
f is set
f1 is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
f1 is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
r is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
x is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
C is Element of K6( the carrier of (TOP-REAL 2))
P29 is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
fs is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
C is Element of K6( the carrier of (TOP-REAL 2))
r is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
x is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
fs is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(C,r,x,fs) is Element of K6( the carrier of (TOP-REAL 2))
{ b<sub>1</sub> where b<sub>1</sub> is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : LE b<sub>1</sub>,fs,C,r,x } is set
(C,x,r,fs) is Element of K6( the carrier of (TOP-REAL 2))
{ b<sub>1</sub> where b<sub>1</sub> is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : LE fs,b<sub>1</sub>,C,x,r } is set
P29 is set
f is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
P29 is set
f is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
C is Element of K6( the carrier of (TOP-REAL 2))
r is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
x is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
fs is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
P29 is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(C,r,x,fs,P29) is Element of K6( the carrier of (TOP-REAL 2))
(C,r,x,fs) is Element of K6( the carrier of (TOP-REAL 2))
{ b<sub>1</sub> where b<sub>1</sub> is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : LE fs,b<sub>1</sub>,C,r,x } is set
(C,r,x,P29) is Element of K6( the carrier of (TOP-REAL 2))
{ b<sub>1</sub> where b<sub>1</sub> is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : LE b<sub>1</sub>,P29,C,r,x } is set
(C,r,x,fs) /\ (C,r,x,P29) is Element of K6( the carrier of (TOP-REAL 2))
(C,x,r,P29,fs) is Element of K6( the carrier of (TOP-REAL 2))
(C,x,r,P29) is Element of K6( the carrier of (TOP-REAL 2))
{ b<sub>1</sub> where b<sub>1</sub> is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : LE P29,b<sub>1</sub>,C,x,r } is set
(C,x,r,fs) is Element of K6( the carrier of (TOP-REAL 2))
{ b<sub>1</sub> where b<sub>1</sub> is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : LE b<sub>1</sub>,fs,C,x,r } is set
(C,x,r,P29) /\ (C,x,r,fs) is Element of K6( the carrier of (TOP-REAL 2))
C is V11() real ext-real set
{ b<sub>1</sub> where b<sub>1</sub> is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : b<sub>1</sub> `1 = C } is set
r is set
x is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
x `1 is V11() real ext-real Element of REAL
{ b<sub>1</sub> where b<sub>1</sub> is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : b<sub>1</sub> `2 = C } is set
r is set
x is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
x `2 is V11() real ext-real Element of REAL
C is V11() real ext-real set
(C) is Element of K6( the carrier of (TOP-REAL 2))
{ b<sub>1</sub> where b<sub>1</sub> is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : b<sub>1</sub> `1 = C } is set
r is V11() real ext-real set
(r) is Element of K6( the carrier of (TOP-REAL 2))
{ b₁ where b₁ is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : b₁ `2 = r } is set
C is V11() real ext-real set
(C) is Element of K6( the carrier of (TOP-REAL 2))
{ b<sub>1</sub> where b<sub>1</sub> is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : b<sub>1</sub> `1 = C } is set
r is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
r `1 is V11() real ext-real Element of REAL
x is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
x `1 is V11() real ext-real Element of REAL
C is V11() real ext-real set
(C) is Element of K6( the carrier of (TOP-REAL 2))
{ b₁ where b₁ is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : b₁ `2 = C } is set
r is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
r `2 is V11() real ext-real Element of REAL
x is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
x `2 is V11() real ext-real Element of REAL
C is Element of K6( the carrier of (TOP-REAL 2))
W-min C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
W-bound C is V11() real ext-real Element of REAL
(TOP-REAL 2) | C is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj1 | C is V22() V25( the carrier of ((TOP-REAL 2) | C)) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | C),REAL))
the carrier of ((TOP-REAL 2) | C) is set
K7( the carrier of ((TOP-REAL 2) | C),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | C),REAL)) is set
lower_bound (proj1 | C) is V11() real ext-real Element of REAL
(proj1 | C) .: the carrier of ((TOP-REAL 2) | C) is V146() V147() V148() Element of K6(REAL)
lower_bound ((proj1 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
W-most C is Element of K6( the carrier of (TOP-REAL 2))
SW-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
S-bound C is V11() real ext-real Element of REAL
proj2 is non empty V22() V25( the carrier of (TOP-REAL 2)) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of (TOP-REAL 2),REAL))
proj2 | C is V22() V25( the carrier of ((TOP-REAL 2) | C)) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | C),REAL))
lower_bound (proj2 | C) is V11() real ext-real Element of REAL
(proj2 | C) .: the carrier of ((TOP-REAL 2) | C) is V146() V147() V148() Element of K6(REAL)
lower_bound ((proj2 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
|[(W-bound C),(S-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
NW-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
N-bound C is V11() real ext-real Element of REAL
upper_bound (proj2 | C) is V11() real ext-real Element of REAL
upper_bound ((proj2 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
|[(W-bound C),(N-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner C),(NW-corner C)) is Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner C),(NW-corner C))) /\ C is Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (W-most C) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj2 | (W-most C) is V22() V25( the carrier of ((TOP-REAL 2) | (W-most C))) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL))
the carrier of ((TOP-REAL 2) | (W-most C)) is set
K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL)) is set
lower_bound (proj2 | (W-most C)) is V11() real ext-real Element of REAL
(proj2 | (W-most C)) .: the carrier of ((TOP-REAL 2) | (W-most C)) is V146() V147() V148() Element of K6(REAL)
lower_bound ((proj2 | (W-most C)) .: the carrier of ((TOP-REAL 2) | (W-most C))) is V11() real ext-real Element of REAL
|[(W-bound C),(lower_bound (proj2 | (W-most C)))]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
E-max C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
E-bound C is V11() real ext-real Element of REAL
upper_bound (proj1 | C) is V11() real ext-real Element of REAL
upper_bound ((proj1 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
E-most C is Element of K6( the carrier of (TOP-REAL 2))
SE-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
|[(E-bound C),(S-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
NE-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
|[(E-bound C),(N-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner C),(NE-corner C)) is Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SE-corner C),(NE-corner C))) /\ C is Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (E-most C) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj2 | (E-most C) is V22() V25( the carrier of ((TOP-REAL 2) | (E-most C))) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL))
the carrier of ((TOP-REAL 2) | (E-most C)) is set
K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL)) is set
upper_bound (proj2 | (E-most C)) is V11() real ext-real Element of REAL
(proj2 | (E-most C)) .: the carrier of ((TOP-REAL 2) | (E-most C)) is V146() V147() V148() Element of K6(REAL)
upper_bound ((proj2 | (E-most C)) .: the carrier of ((TOP-REAL 2) | (E-most C))) is V11() real ext-real Element of REAL
|[(E-bound C),(upper_bound (proj2 | (E-most C)))]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
{(W-min C),(E-max C)} is non empty set
(W-bound C) + (E-bound C) is V11() real ext-real Element of REAL
((W-bound C) + (E-bound C)) / 2 is V11() real ext-real Element of REAL
((((W-bound C) + (E-bound C)) / 2)) is Element of K6( the carrier of (TOP-REAL 2))
{ b<sub>1</sub> where b<sub>1</sub> is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : b<sub>1</sub> `1 = ((W-bound C) + (E-bound C)) / 2 } is set
r is non empty closed compact being_simple_closed_curve Element of K6( the carrier of (TOP-REAL 2))
W-min r is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
W-bound r is V11() real ext-real Element of REAL
(TOP-REAL 2) | r is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj1 | r is non empty V22() V25( the carrier of ((TOP-REAL 2) | r)) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | r),REAL))
the carrier of ((TOP-REAL 2) | r) is non empty set
K7( the carrier of ((TOP-REAL 2) | r),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | r),REAL)) is set
lower_bound (proj1 | r) is V11() real ext-real Element of REAL
(proj1 | r) .: the carrier of ((TOP-REAL 2) | r) is non empty V146() V147() V148() Element of K6(REAL)
lower_bound ((proj1 | r) .: the carrier of ((TOP-REAL 2) | r)) is V11() real ext-real Element of REAL
W-most r is Element of K6( the carrier of (TOP-REAL 2))
SW-corner r is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
S-bound r is V11() real ext-real Element of REAL
proj2 | r is non empty V22() V25( the carrier of ((TOP-REAL 2) | r)) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | r),REAL))
lower_bound (proj2 | r) is V11() real ext-real Element of REAL
(proj2 | r) .: the carrier of ((TOP-REAL 2) | r) is non empty V146() V147() V148() Element of K6(REAL)
lower_bound ((proj2 | r) .: the carrier of ((TOP-REAL 2) | r)) is V11() real ext-real Element of REAL
|[(W-bound r),(S-bound r)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
NW-corner r is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
N-bound r is V11() real ext-real Element of REAL
upper_bound (proj2 | r) is V11() real ext-real Element of REAL
upper_bound ((proj2 | r) .: the carrier of ((TOP-REAL 2) | r)) is V11() real ext-real Element of REAL
|[(W-bound r),(N-bound r)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner r),(NW-corner r)) is Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner r),(NW-corner r))) /\ r is Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (W-most r) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj2 | (W-most r) is V22() V25( the carrier of ((TOP-REAL 2) | (W-most r))) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | (W-most r)),REAL))
the carrier of ((TOP-REAL 2) | (W-most r)) is set
K7( the carrier of ((TOP-REAL 2) | (W-most r)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (W-most r)),REAL)) is set
lower_bound (proj2 | (W-most r)) is V11() real ext-real Element of REAL
(proj2 | (W-most r)) .: the carrier of ((TOP-REAL 2) | (W-most r)) is V146() V147() V148() Element of K6(REAL)
lower_bound ((proj2 | (W-most r)) .: the carrier of ((TOP-REAL 2) | (W-most r))) is V11() real ext-real Element of REAL
|[(W-bound r),(lower_bound (proj2 | (W-most r)))]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
E-max r is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
E-bound r is V11() real ext-real Element of REAL
upper_bound (proj1 | r) is V11() real ext-real Element of REAL
upper_bound ((proj1 | r) .: the carrier of ((TOP-REAL 2) | r)) is V11() real ext-real Element of REAL
E-most r is Element of K6( the carrier of (TOP-REAL 2))
SE-corner r is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
|[(E-bound r),(S-bound r)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
NE-corner r is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
|[(E-bound r),(N-bound r)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner r),(NE-corner r)) is Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SE-corner r),(NE-corner r))) /\ r is Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (E-most r) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj2 | (E-most r) is V22() V25( the carrier of ((TOP-REAL 2) | (E-most r))) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | (E-most r)),REAL))
the carrier of ((TOP-REAL 2) | (E-most r)) is set
K7( the carrier of ((TOP-REAL 2) | (E-most r)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (E-most r)),REAL)) is set
upper_bound (proj2 | (E-most r)) is V11() real ext-real Element of REAL
(proj2 | (E-most r)) .: the carrier of ((TOP-REAL 2) | (E-most r)) is V146() V147() V148() Element of K6(REAL)
upper_bound ((proj2 | (E-most r)) .: the carrier of ((TOP-REAL 2) | (E-most r))) is V11() real ext-real Element of REAL
|[(E-bound r),(upper_bound (proj2 | (E-most r)))]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
{(W-min r),(E-max r)} is non empty set
x is non empty Element of K6( the carrier of (TOP-REAL 2))
fs is non empty Element of K6( the carrier of (TOP-REAL 2))
x \/ fs is non empty Element of K6( the carrier of (TOP-REAL 2))
x /\ fs is Element of K6( the carrier of (TOP-REAL 2))
P29 is non empty Element of K6( the carrier of (TOP-REAL 2))
f is non empty Element of K6( the carrier of (TOP-REAL 2))
(E-max r) `1 is V11() real ext-real Element of REAL
(W-bound r) + (E-bound r) is V11() real ext-real Element of REAL
((W-bound r) + (E-bound r)) / 2 is V11() real ext-real Element of REAL
((((W-bound r) + (E-bound r)) / 2)) is Element of K6( the carrier of (TOP-REAL 2))
{ b<sub>1</sub> where b<sub>1</sub> is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : b<sub>1</sub> `1 = ((W-bound r) + (E-bound r)) / 2 } is set
P29 /\ ((((W-bound r) + (E-bound r)) / 2)) is Element of K6( the carrier of (TOP-REAL 2))
f /\ ((((W-bound r) + (E-bound r)) / 2)) is Element of K6( the carrier of (TOP-REAL 2))
f1 is non empty Element of K6( the carrier of (TOP-REAL 2))
(W-min r) `1 is V11() real ext-real Element of REAL
((W-min r) `1) + ((E-max r) `1) is V11() real ext-real Element of REAL
(((W-min r) `1) + ((E-max r) `1)) / 2 is V11() real ext-real Element of REAL
proj11 is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
proj11 `1 is V11() real ext-real Element of REAL
f2 is non empty Element of K6( the carrier of (TOP-REAL 2))
proj12 is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
proj12 `1 is V11() real ext-real Element of REAL
First_Point (P29,(W-min r),(E-max r),((((W-bound r) + (E-bound r)) / 2))) is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(First_Point (P29,(W-min r),(E-max r),((((W-bound r) + (E-bound r)) / 2)))) `2 is V11() real ext-real Element of REAL
Last_Point (f,(E-max r),(W-min r),((((W-bound r) + (E-bound r)) / 2))) is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(Last_Point (f,(E-max r),(W-min r),((((W-bound r) + (E-bound r)) / 2)))) `2 is V11() real ext-real Element of REAL
First_Point (P29,(W-min r),(E-max r),((((W-bound r) + (E-bound r)) / 2))) is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(First_Point (P29,(W-min r),(E-max r),((((W-bound r) + (E-bound r)) / 2)))) `2 is V11() real ext-real Element of REAL
Last_Point (f,(E-max r),(W-min r),((((W-bound r) + (E-bound r)) / 2))) is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(Last_Point (f,(E-max r),(W-min r),((((W-bound r) + (E-bound r)) / 2)))) `2 is V11() real ext-real Element of REAL
Last_Point (P29,(E-max r),(W-min r),((((W-bound r) + (E-bound r)) / 2))) is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
First_Point (f,(W-min r),(E-max r),((((W-bound r) + (E-bound r)) / 2))) is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(First_Point (P29,(W-min r),(E-max r),((((W-bound r) + (E-bound r)) / 2)))) `1 is V11() real ext-real Element of REAL
(Last_Point (f,(E-max r),(W-min r),((((W-bound r) + (E-bound r)) / 2)))) `1 is V11() real ext-real Element of REAL
P29 /\ f is Element of K6( the carrier of (TOP-REAL 2))
g1 is non empty Element of K6( the carrier of (TOP-REAL 2))
g is non empty Element of K6( the carrier of (TOP-REAL 2))
g1 /\ g is Element of K6( the carrier of (TOP-REAL 2))
g1 \/ g is non empty Element of K6( the carrier of (TOP-REAL 2))
First_Point (g1,(W-min r),(E-max r),((((W-bound r) + (E-bound r)) / 2))) is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(First_Point (g1,(W-min r),(E-max r),((((W-bound r) + (E-bound r)) / 2)))) `2 is V11() real ext-real Element of REAL
Last_Point (g,(E-max r),(W-min r),((((W-bound r) + (E-bound r)) / 2))) is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(Last_Point (g,(E-max r),(W-min r),((((W-bound r) + (E-bound r)) / 2)))) `2 is V11() real ext-real Element of REAL
g1 is non empty Element of K6( the carrier of (TOP-REAL 2))
g is non empty Element of K6( the carrier of (TOP-REAL 2))
g1 /\ g is Element of K6( the carrier of (TOP-REAL 2))
g1 \/ g is non empty Element of K6( the carrier of (TOP-REAL 2))
First_Point (g1,(W-min r),(E-max r),((((W-bound r) + (E-bound r)) / 2))) is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(First_Point (g1,(W-min r),(E-max r),((((W-bound r) + (E-bound r)) / 2)))) `2 is V11() real ext-real Element of REAL
Last_Point (g,(E-max r),(W-min r),((((W-bound r) + (E-bound r)) / 2))) is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(Last_Point (g,(E-max r),(W-min r),((((W-bound r) + (E-bound r)) / 2)))) `2 is V11() real ext-real Element of REAL
P19 is non empty Element of K6( the carrier of (TOP-REAL 2))
First_Point (P19,(W-min C),(E-max C),((((W-bound C) + (E-bound C)) / 2))) is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(First_Point (P19,(W-min C),(E-max C),((((W-bound C) + (E-bound C)) / 2)))) `2 is V11() real ext-real Element of REAL
r1 is non empty Element of K6( the carrier of (TOP-REAL 2))
P19 /\ r1 is Element of K6( the carrier of (TOP-REAL 2))
P19 \/ r1 is non empty Element of K6( the carrier of (TOP-REAL 2))
Last_Point (r1,(E-max C),(W-min C),((((W-bound C) + (E-bound C)) / 2))) is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(Last_Point (r1,(E-max C),(W-min C),((((W-bound C) + (E-bound C)) / 2)))) `2 is V11() real ext-real Element of REAL
First_Point (P29,(W-min r),(E-max r),((((W-bound r) + (E-bound r)) / 2))) is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(First_Point (P29,(W-min r),(E-max r),((((W-bound r) + (E-bound r)) / 2)))) `2 is V11() real ext-real Element of REAL
Last_Point (f,(E-max r),(W-min r),((((W-bound r) + (E-bound r)) / 2))) is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(Last_Point (f,(E-max r),(W-min r),((((W-bound r) + (E-bound r)) / 2)))) `2 is V11() real ext-real Element of REAL
K6( the carrier of I[01]) is set
{0,1} is non empty V146() V147() V148() V149() V150() V151() set
the carrier of I[01] \ {0,1} is V146() V147() V148() Element of K6( the carrier of I[01])
C is V146() V147() V148() Element of K6( the carrier of I[01])
{0} is non empty V146() V147() V148() V149() V150() V151() Element of K6(REAL)
{1} is non empty V146() V147() V148() V149() V150() V151() Element of K6(REAL)
r is V146() V147() V148() Element of K6( the carrier of I[01])
x is V146() V147() V148() Element of K6( the carrier of I[01])
r \/ x is V146() V147() V148() Element of K6( the carrier of I[01])
[#] I[01] is non empty non proper closed V146() V147() V148() Element of K6( the carrier of I[01])
([#] I[01]) \ (r \/ x) is V146() V147() V148() Element of K6( the carrier of I[01])
C is V146() V147() V148() Element of K6( the carrier of R^1)
r is V11() real ext-real set
x is V11() real ext-real set
].r,x.[ is V146() V147() V148() Element of K6(REAL)
{ b<sub>1</sub> where b<sub>1</sub> is V11() real ext-real Element of REAL : not b<sub>1</sub> <= r } is set
fs is set
P29 is V11() real ext-real Element of REAL
{ b<sub>1</sub> where b<sub>1</sub> is V11() real ext-real Element of REAL : not x <= b<sub>1</sub> } is set
P29 is set
f is V11() real ext-real Element of REAL
fs is V146() V147() V148() Element of K6( the carrier of R^1)
P29 is V146() V147() V148() Element of K6( the carrier of R^1)
fs /\ P29 is V146() V147() V148() Element of K6( the carrier of R^1)
f is set
f1 is V11() real ext-real Element of REAL
f is set
f1 is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
C is V146() V147() V148() Element of K6( the carrier of I[01])
1 / 2 is V11() real ext-real non negative Element of REAL
I[01] | C is strict TopSpace-like T_0 T_1 T_2 V200() SubSpace of I[01]
[#] (I[01] | C) is non proper closed V146() V147() V148() Element of K6( the carrier of (I[01] | C))
the carrier of (I[01] | C) is V146() V147() V148() set
K6( the carrier of (I[01] | C)) is set
{} (I[01] | C) is empty closed compact V146() V147() V148() V149() V150() V151() V152() Element of K6( the carrier of (I[01] | C))
r is V146() V147() V148() Element of K6( the carrier of (I[01] | C))
x is V146() V147() V148() Element of K6( the carrier of (I[01] | C))
r \/ x is V146() V147() V148() Element of K6( the carrier of (I[01] | C))
].0,1.[ is V146() V147() V148() Element of K6(REAL)
].0,1.[ \/ {0,1} is non empty V146() V147() V148() set
(].0,1.[ \/ {0,1}) \ {0,1} is V146() V147() V148() Element of K6((].0,1.[ \/ {0,1}))
K6((].0,1.[ \/ {0,1})) is set
].0,1.[ \ {0,1} is V146() V147() V148() Element of K6(REAL)
fs is V146() V147() V148() Element of K6( the carrier of R^1)
R^1 | fs is strict TopSpace-like V200() SubSpace of R^1
P29 is V146() V147() V148() Element of K6( the carrier of R^1)
R^1 | P29 is strict TopSpace-like V200() SubSpace of R^1
{ b<sub>1</sub> where b<sub>1</sub> is V11() real ext-real Element of REAL : ( not b<sub>1</sub> <= 0 & not 1 <= b<sub>1</sub> ) } is set
f is non empty V146() V147() V148() Element of K6(REAL)
f1 is non empty V146() V147() V148() Element of K6(REAL)
f2 is non empty V146() V147() V148() Element of K6( the carrier of R^1)
proj11 is non empty V146() V147() V148() Element of K6( the carrier of R^1)
the V11() real ext-real Element of f is V11() real ext-real Element of f
g1 is V11() real ext-real Element of REAL
g is ext-real set
P19 is V11() real ext-real Element of REAL
g is ext-real set
P19 is V11() real ext-real Element of REAL
lower_bound f1 is V11() real ext-real Element of REAL
the carrier of RealSpace is non empty V146() V147() V148() set
g is V11() real ext-real Element of REAL
P19 is V11() real ext-real Element of the carrier of RealSpace
p is V11() real ext-real set
Ball (P19,p) is V146() V147() V148() Element of K6( the carrier of RealSpace)
K6( the carrier of RealSpace) is set
R29 is V11() real ext-real Element of REAL
R29 / 2 is V11() real ext-real Element of REAL
g - (R29 / 2) is V11() real ext-real Element of REAL
g - (g - (R29 / 2)) is V11() real ext-real Element of REAL
abs (g - (g - (R29 / 2))) is V11() real ext-real Element of REAL
the distance of RealSpace is V22() V25(K7( the carrier of RealSpace, the carrier of RealSpace)) V26( REAL ) Function-like total quasi_total Element of K6(K7(K7( the carrier of RealSpace, the carrier of RealSpace),REAL))
K7( the carrier of RealSpace, the carrier of RealSpace) is set
K7(K7( the carrier of RealSpace, the carrier of RealSpace),REAL) is set
K6(K7(K7( the carrier of RealSpace, the carrier of RealSpace),REAL)) is set
y is V11() real ext-real Element of the carrier of RealSpace
the distance of RealSpace . (P19,y) is V11() real ext-real Element of REAL
dist (P19,y) is V11() real ext-real Element of REAL
{ b<sub>1</sub> where b<sub>1</sub> is V11() real ext-real Element of the carrier of RealSpace : not R29 <= dist (P19,b<sub>1</sub>) } is set
Ball (P19,R29) is V146() V147() V148() Element of K6( the carrier of RealSpace)
g + (R29 / 2) is V11() real ext-real Element of REAL
(g + (R29 / 2)) - g is V11() real ext-real Element of REAL
g - g is V11() real ext-real Element of REAL
g1 - g is V11() real ext-real Element of REAL
g + (g1 - g) is V11() real ext-real Element of REAL
p is V11() real ext-real set
R29 is V11() real ext-real Element of REAL
{ b<sub>1</sub> where b<sub>1</sub> is V11() real ext-real Element of REAL : ( b<sub>1</sub> in f & not b<sub>1</sub> <= R29 ) } is set
y is set
x is V11() real ext-real Element of REAL
y is V146() V147() V148() Element of K6(REAL)
lower_bound y is V11() real ext-real Element of REAL
x is V11() real ext-real Element of REAL
R29 - x is V11() real ext-real Element of REAL
x + (R29 - x) is V11() real ext-real Element of REAL
s3 is V11() real ext-real set
e1 is V11() real ext-real Element of REAL
r2 is V11() real ext-real Element of the carrier of RealSpace
s3 is V11() real ext-real set
Ball (r2,s3) is V146() V147() V148() Element of K6( the carrier of RealSpace)
K6( the carrier of RealSpace) is set
x + s3 is V11() real ext-real Element of REAL
e1 is V11() real ext-real set
s1 is V11() real ext-real Element of REAL
s1 - x is V11() real ext-real Element of REAL
(x + s3) - x is V11() real ext-real Element of REAL
abs (s1 - x) is V11() real ext-real Element of REAL
the distance of RealSpace is V22() V25(K7( the carrier of RealSpace, the carrier of RealSpace)) V26( REAL ) Function-like total quasi_total Element of K6(K7(K7( the carrier of RealSpace, the carrier of RealSpace),REAL))
K7( the carrier of RealSpace, the carrier of RealSpace) is set
K7(K7( the carrier of RealSpace, the carrier of RealSpace),REAL) is set
K6(K7(K7( the carrier of RealSpace, the carrier of RealSpace),REAL)) is set
r2 is V11() real ext-real Element of the carrier of RealSpace
the distance of RealSpace . (r2,r2) is V11() real ext-real Element of REAL
dist (r2,r2) is V11() real ext-real Element of REAL
{ b<sub>1</sub> where b<sub>1</sub> is V11() real ext-real Element of the carrier of RealSpace : not s3 <= dist (r2,b<sub>1</sub>) } is set
x - R29 is V11() real ext-real Element of REAL
the V11() real ext-real Element of y is V11() real ext-real Element of y
e1 is V11() real ext-real Element of REAL
s1 is V11() real ext-real set
Ball (r2,s1) is V146() V147() V148() Element of K6( the carrier of RealSpace)
r2 is V11() real ext-real Element of REAL
min (r2,(x - R29)) is V11() real ext-real set
(min (r2,(x - R29))) / 2 is V11() real ext-real Element of REAL
(x - R29) + R29 is V11() real ext-real Element of REAL
((min (r2,(x - R29))) / 2) + R29 is V11() real ext-real Element of REAL
x - ((min (r2,(x - R29))) / 2) is V11() real ext-real Element of REAL
(((min (r2,(x - R29))) / 2) + R29) - ((min (r2,(x - R29))) / 2) is V11() real ext-real Element of REAL
x - (x - ((min (r2,(x - R29))) / 2)) is V11() real ext-real Element of REAL
abs (x - (x - ((min (r2,(x - R29))) / 2))) is V11() real ext-real Element of REAL
real_dist . (x,(x - ((min (r2,(x - R29))) / 2))) is V11() real ext-real Element of REAL
s3 is V11() real ext-real Element of the carrier of RealSpace
dist (r2,s3) is V11() real ext-real Element of REAL
{ b<sub>1</sub> where b<sub>1</sub> is V11() real ext-real Element of the carrier of RealSpace : not r2 <= dist (r2,b<sub>1</sub>) } is set
Ball (r2,r2) is V146() V147() V148() Element of K6( the carrier of RealSpace)
x + ((min (r2,(x - R29))) / 2) is V11() real ext-real Element of REAL
(x + ((min (r2,(x - R29))) / 2)) - ((min (r2,(x - R29))) / 2) is V11() real ext-real Element of REAL
s1 is V11() real ext-real set
Ball (r2,s1) is V146() V147() V148() Element of K6( the carrier of RealSpace)
s1 / 2 is V11() real ext-real Element of REAL
x + (s1 / 2) is V11() real ext-real Element of REAL
r2 is V11() real ext-real set
r2 is V11() real ext-real Element of REAL
r2 - x is V11() real ext-real Element of REAL
s3 is V11() real ext-real Element of REAL
x + s3 is V11() real ext-real Element of REAL
(x + (s1 / 2)) - x is V11() real ext-real Element of REAL
(x + s3) - x is V11() real ext-real Element of REAL
abs ((x + s3) - x) is V11() real ext-real Element of REAL
real_dist . ((x + s3),x) is V11() real ext-real Element of REAL
e1 is V11() real ext-real Element of the carrier of RealSpace
dist (e1,r2) is V11() real ext-real Element of REAL
{ b<sub>1</sub> where b<sub>1</sub> is V11() real ext-real Element of the carrier of RealSpace : not s1 <= dist (r2,b<sub>1</sub>) } is set
y /\ f1 is V146() V147() V148() Element of K6(REAL)
f /\ f1 is V146() V147() V148() Element of K6(REAL)
the V11() real ext-real Element of f1 is V11() real ext-real Element of f1
R29 is V11() real ext-real Element of REAL
r1 is V11() real ext-real Element of the carrier of R^1
y is V11() real ext-real set
Ball (P19,y) is V146() V147() V148() Element of K6( the carrier of RealSpace)
y / 2 is V11() real ext-real Element of REAL
g + (y / 2) is V11() real ext-real Element of REAL
x is V11() real ext-real set
r2 is V11() real ext-real Element of REAL
r2 - g is V11() real ext-real Element of REAL
g + (r2 - g) is V11() real ext-real Element of REAL
(g + (y / 2)) - g is V11() real ext-real Element of REAL
(g + (r2 - g)) - g is V11() real ext-real Element of REAL
abs ((g + (r2 - g)) - g) is V11() real ext-real Element of REAL
real_dist . ((g + (r2 - g)),g) is V11() real ext-real Element of REAL
e1 is V11() real ext-real Element of the carrier of RealSpace
dist (e1,P19) is V11() real ext-real Element of REAL
{ b<sub>1</sub> where b<sub>1</sub> is V11() real ext-real Element of the carrier of RealSpace : not y <= dist (P19,b<sub>1</sub>) } is set
C is natural V11() real ext-real V83() V84() V146() V147() V148() V149() V150() V151() Element of NAT
TOP-REAL C is non empty TopSpace-like T_0 T_1 T_2 V112() V158() V159() V160() V161() V162() V163() V164() strict V231() V232() RLTopStruct
the carrier of (TOP-REAL C) is non empty functional set
K6( the carrier of (TOP-REAL C)) is set
r is Element of K6( the carrier of (TOP-REAL C))
x is V22() V26( REAL ) Function-like V43(C) FinSequence-like V138() Element of the carrier of (TOP-REAL C)
fs is V22() V26( REAL ) Function-like V43(C) FinSequence-like V138() Element of the carrier of (TOP-REAL C)
(TOP-REAL C) | r is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL C
the carrier of ((TOP-REAL C) | r) is set
K7( the carrier of I[01], the carrier of ((TOP-REAL C) | r)) is set
K6(K7( the carrier of I[01], the carrier of ((TOP-REAL C) | r))) is set
P29 is V22() V25( the carrier of I[01]) V26( the carrier of ((TOP-REAL C) | r)) Function-like quasi_total Element of K6(K7( the carrier of I[01], the carrier of ((TOP-REAL C) | r)))
P29 . 0 is set
P29 . 1 is set
[#] I[01] is non empty non proper closed V146() V147() V148() Element of K6( the carrier of I[01])
dom P29 is V146() V147() V148() Element of K6( the carrier of I[01])
C is natural V11() real ext-real V83() V84() V146() V147() V148() V149() V150() V151() Element of NAT
TOP-REAL C is non empty TopSpace-like T_0 T_1 T_2 V112() V158() V159() V160() V161() V162() V163() V164() strict V231() V232() RLTopStruct
the carrier of (TOP-REAL C) is non empty functional set
K6( the carrier of (TOP-REAL C)) is set
r is Element of K6( the carrier of (TOP-REAL C))
(TOP-REAL C) | r is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL C
the carrier of ((TOP-REAL C) | r) is set
K6( the carrier of ((TOP-REAL C) | r)) is set
x is Element of K6( the carrier of ((TOP-REAL C) | r))
fs is V22() V26( REAL ) Function-like V43(C) FinSequence-like V138() Element of the carrier of (TOP-REAL C)
P29 is V22() V26( REAL ) Function-like V43(C) FinSequence-like V138() Element of the carrier of (TOP-REAL C)
{fs,P29} is non empty set
r \ {fs,P29} is Element of K6( the carrier of (TOP-REAL C))
f is non empty Element of K6( the carrier of (TOP-REAL C))
(TOP-REAL C) | f is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL C
the carrier of ((TOP-REAL C) | f) is non empty set
K7( the carrier of I[01], the carrier of ((TOP-REAL C) | f)) is set
K6(K7( the carrier of I[01], the carrier of ((TOP-REAL C) | f))) is set
f1 is non empty V22() V25( the carrier of I[01]) V26( the carrier of ((TOP-REAL C) | f)) Function-like total quasi_total Element of K6(K7( the carrier of I[01], the carrier of ((TOP-REAL C) | f)))
f1 . 0 is set
f1 . 1 is set
f1 /" is non empty V22() V25( the carrier of ((TOP-REAL C) | f)) V26( the carrier of I[01]) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL C) | f), the carrier of I[01]))
K7( the carrier of ((TOP-REAL C) | f), the carrier of I[01]) is set
K6(K7( the carrier of ((TOP-REAL C) | f), the carrier of I[01])) is set
K7( the carrier of ((TOP-REAL C) | r), the carrier of I[01]) is set
K6(K7( the carrier of ((TOP-REAL C) | r), the carrier of I[01])) is set
proj11 is V22() V25( the carrier of ((TOP-REAL C) | r)) V26( the carrier of I[01]) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL C) | r), the carrier of I[01]))
[#] I[01] is non empty non proper closed V146() V147() V148() Element of K6( the carrier of I[01])
g1 is V146() V147() V148() Element of K6( the carrier of I[01])
dom f1 is V146() V147() V148() Element of K6( the carrier of I[01])
rng f1 is Element of K6( the carrier of ((TOP-REAL C) | f))
K6( the carrier of ((TOP-REAL C) | f)) is set
[#] ((TOP-REAL C) | r) is non proper closed Element of K6( the carrier of ((TOP-REAL C) | r))
(f1 /") /" is non empty V22() V25( the carrier of I[01]) V26( the carrier of ((TOP-REAL C) | f)) Function-like total quasi_total Element of K6(K7( the carrier of I[01], the carrier of ((TOP-REAL C) | f)))
rng proj11 is V146() V147() V148() Element of K6( the carrier of I[01])
proj12 is V22() Function-like set
proj12 " is V22() Function-like set
f2 is V22() Function-like set
proj11 " g1 is Element of K6( the carrier of ((TOP-REAL C) | r))
proj12 " the carrier of I[01] is set
proj12 " {0,1} is set
(proj12 " the carrier of I[01]) \ (proj12 " {0,1}) is Element of K6((proj12 " the carrier of I[01]))
K6((proj12 " the carrier of I[01])) is set
(proj12 ") .: the carrier of I[01] is set
((proj12 ") .: the carrier of I[01]) \ (proj12 " {0,1}) is Element of K6(((proj12 ") .: the carrier of I[01]))
K6(((proj12 ") .: the carrier of I[01])) is set
f2 .: ([#] I[01]) is set
f2 .: {0,1} is set
(f2 .: ([#] I[01])) \ (f2 .: {0,1}) is Element of K6((f2 .: ([#] I[01])))
K6((f2 .: ([#] I[01]))) is set
f1 .: {0,1} is Element of K6( the carrier of ((TOP-REAL C) | f))
(rng f1) \ (f1 .: {0,1}) is Element of K6( the carrier of ((TOP-REAL C) | f))
([#] ((TOP-REAL C) | r)) \ (f1 .: {0,1}) is Element of K6( the carrier of ((TOP-REAL C) | r))
r \ (f1 .: {0,1}) is Element of K6( the carrier of (TOP-REAL C))
C is natural V11() real ext-real V83() V84() V146() V147() V148() V149() V150() V151() Element of NAT
TOP-REAL C is non empty TopSpace-like T_0 T_1 T_2 V112() V158() V159() V160() V161() V162() V163() V164() strict V231() V232() RLTopStruct
the carrier of (TOP-REAL C) is non empty functional set
K6( the carrier of (TOP-REAL C)) is set
r is Element of K6( the carrier of (TOP-REAL C))
(TOP-REAL C) | r is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL C
the carrier of ((TOP-REAL C) | r) is set
K6( the carrier of ((TOP-REAL C) | r)) is set
fs is Element of K6( the carrier of (TOP-REAL C))
x is Element of K6( the carrier of (TOP-REAL C))
x \/ fs is Element of K6( the carrier of (TOP-REAL C))
x /\ fs is Element of K6( the carrier of (TOP-REAL C))
P29 is Element of K6( the carrier of ((TOP-REAL C) | r))
f is V22() V26( REAL ) Function-like V43(C) FinSequence-like V138() Element of the carrier of (TOP-REAL C)
f1 is V22() V26( REAL ) Function-like V43(C) FinSequence-like V138() Element of the carrier of (TOP-REAL C)
{f,f1} is non empty set
x \ {f,f1} is Element of K6( the carrier of (TOP-REAL C))
f2 is Element of K6( the carrier of (TOP-REAL C))
[#] ((TOP-REAL C) | r) is non proper closed Element of K6( the carrier of ((TOP-REAL C) | r))
proj11 is Element of K6( the carrier of ((TOP-REAL C) | r))
r \ fs is Element of K6( the carrier of (TOP-REAL C))
x \ fs is Element of K6( the carrier of (TOP-REAL C))
fs \ fs is Element of K6( the carrier of (TOP-REAL C))
(x \ fs) \/ (fs \ fs) is Element of K6( the carrier of (TOP-REAL C))
(x \ fs) \/ {} is set
proj12 is set
proj12 is set
proj11 ` is Element of K6( the carrier of ((TOP-REAL C) | r))
C is natural V11() real ext-real V83() V84() V146() V147() V148() V149() V150() V151() Element of NAT
TOP-REAL C is non empty TopSpace-like T_0 T_1 T_2 V112() V158() V159() V160() V161() V162() V163() V164() strict V231() V232() RLTopStruct
the carrier of (TOP-REAL C) is non empty functional set
K6( the carrier of (TOP-REAL C)) is set
r is Element of K6( the carrier of (TOP-REAL C))
(TOP-REAL C) | r is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL C
the carrier of ((TOP-REAL C) | r) is set
K6( the carrier of ((TOP-REAL C) | r)) is set
x is Element of K6( the carrier of ((TOP-REAL C) | r))
fs is V22() V26( REAL ) Function-like V43(C) FinSequence-like V138() Element of the carrier of (TOP-REAL C)
P29 is V22() V26( REAL ) Function-like V43(C) FinSequence-like V138() Element of the carrier of (TOP-REAL C)
{fs,P29} is non empty set
r \ {fs,P29} is Element of K6( the carrier of (TOP-REAL C))
f is non empty Element of K6( the carrier of (TOP-REAL C))
(TOP-REAL C) | f is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL C
the carrier of ((TOP-REAL C) | f) is non empty set
K7( the carrier of I[01], the carrier of ((TOP-REAL C) | f)) is set
K6(K7( the carrier of I[01], the carrier of ((TOP-REAL C) | f))) is set
f1 is non empty V22() V25( the carrier of I[01]) V26( the carrier of ((TOP-REAL C) | f)) Function-like total quasi_total Element of K6(K7( the carrier of I[01], the carrier of ((TOP-REAL C) | f)))
f1 . 0 is set
f1 . 1 is set
f2 is V146() V147() V148() Element of K6( the carrier of I[01])
f1 .: f2 is Element of K6( the carrier of ((TOP-REAL C) | f))
K6( the carrier of ((TOP-REAL C) | f)) is set
[#] ((TOP-REAL C) | r) is non proper closed Element of K6( the carrier of ((TOP-REAL C) | r))
rng f1 is Element of K6( the carrier of ((TOP-REAL C) | f))
proj11 is set
dom f1 is V146() V147() V148() Element of K6( the carrier of I[01])
proj12 is set
f1 . proj12 is set
proj11 is set
dom f1 is V146() V147() V148() Element of K6( the carrier of I[01])
proj12 is set
f1 . proj12 is set
g1 is non empty V22() V25( the carrier of I[01]) V26( the carrier of ((TOP-REAL C) | f)) Function-like total quasi_total Element of K6(K7( the carrier of I[01], the carrier of ((TOP-REAL C) | f)))
dom g1 is V146() V147() V148() Element of K6( the carrier of I[01])
g1 is non empty V22() V25( the carrier of I[01]) V26( the carrier of ((TOP-REAL C) | f)) Function-like total quasi_total Element of K6(K7( the carrier of I[01], the carrier of ((TOP-REAL C) | f)))
dom g1 is V146() V147() V148() Element of K6( the carrier of I[01])
C is TopSpace-like TopStruct
the carrier of C is set
K6( the carrier of C) is set
r is Element of K6( the carrier of C)
C | r is strict TopSpace-like SubSpace of C
the carrier of (C | r) is set
K6( the carrier of (C | r)) is set
x is Element of K6( the carrier of C)
C | x is strict TopSpace-like SubSpace of C
the carrier of (C | x) is set
K6( the carrier of (C | x)) is set
fs is Element of K6( the carrier of (C | r))
P29 is Element of K6( the carrier of (C | x))
[#] (C | x) is non proper closed Element of K6( the carrier of (C | x))
f is Element of K6( the carrier of (C | x))
(C | x) | f is strict TopSpace-like SubSpace of C | x
C is natural V11() real ext-real V83() V84() V146() V147() V148() V149() V150() V151() Element of NAT
TOP-REAL C is non empty TopSpace-like T_0 T_1 T_2 V112() V158() V159() V160() V161() V162() V163() V164() strict V231() V232() RLTopStruct
the carrier of (TOP-REAL C) is non empty functional set
K6( the carrier of (TOP-REAL C)) is set
r is Element of K6( the carrier of (TOP-REAL C))
x is V22() V26( REAL ) Function-like V43(C) FinSequence-like V138() Element of the carrier of (TOP-REAL C)
fs is V22() V26( REAL ) Function-like V43(C) FinSequence-like V138() Element of the carrier of (TOP-REAL C)
(TOP-REAL C) | r is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL C
the carrier of ((TOP-REAL C) | r) is set
K7( the carrier of I[01], the carrier of ((TOP-REAL C) | r)) is set
K6(K7( the carrier of I[01], the carrier of ((TOP-REAL C) | r))) is set
P29 is V22() V25( the carrier of I[01]) V26( the carrier of ((TOP-REAL C) | r)) Function-like quasi_total Element of K6(K7( the carrier of I[01], the carrier of ((TOP-REAL C) | r)))
P29 . 0 is set
P29 . 1 is set
1 / 2 is V11() real ext-real non negative Element of REAL
[#] I[01] is non empty non proper closed V146() V147() V148() Element of K6( the carrier of I[01])
dom P29 is V146() V147() V148() Element of K6( the carrier of I[01])
P29 . (1 / 2) is set
rng P29 is Element of K6( the carrier of ((TOP-REAL C) | r))
K6( the carrier of ((TOP-REAL C) | r)) is set
f is V22() V26( REAL ) Function-like V43(C) FinSequence-like V138() Element of the carrier of (TOP-REAL C)
C is natural V11() real ext-real V83() V84() V146() V147() V148() V149() V150() V151() Element of NAT
TOP-REAL C is non empty TopSpace-like T_0 T_1 T_2 V112() V158() V159() V160() V161() V162() V163() V164() strict V231() V232() RLTopStruct
the carrier of (TOP-REAL C) is non empty functional set
K6( the carrier of (TOP-REAL C)) is set
r is Element of K6( the carrier of (TOP-REAL C))
x is V22() V26( REAL ) Function-like V43(C) FinSequence-like V138() Element of the carrier of (TOP-REAL C)
fs is V22() V26( REAL ) Function-like V43(C) FinSequence-like V138() Element of the carrier of (TOP-REAL C)
{x,fs} is non empty set
r \ {x,fs} is Element of K6( the carrier of (TOP-REAL C))
P29 is V22() V26( REAL ) Function-like V43(C) FinSequence-like V138() Element of the carrier of (TOP-REAL C)
C is natural V11() real ext-real V83() V84() V146() V147() V148() V149() V150() V151() Element of NAT
TOP-REAL C is non empty TopSpace-like T_0 T_1 T_2 V112() V158() V159() V160() V161() V162() V163() V164() strict V231() V232() RLTopStruct
the carrier of (TOP-REAL C) is non empty functional set
K6( the carrier of (TOP-REAL C)) is set
r is Element of K6( the carrier of (TOP-REAL C))
x is Element of K6( the carrier of (TOP-REAL C))
(TOP-REAL C) | x is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL C
the carrier of ((TOP-REAL C) | x) is set
K6( the carrier of ((TOP-REAL C) | x)) is set
fs is Element of K6( the carrier of ((TOP-REAL C) | x))
P29 is V22() V26( REAL ) Function-like V43(C) FinSequence-like V138() Element of the carrier of (TOP-REAL C)
f is V22() V26( REAL ) Function-like V43(C) FinSequence-like V138() Element of the carrier of (TOP-REAL C)
{P29,f} is non empty set
r \ {P29,f} is Element of K6( the carrier of (TOP-REAL C))
(TOP-REAL C) | r is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL C
[#] ((TOP-REAL C) | r) is non proper closed Element of K6( the carrier of ((TOP-REAL C) | r))
the carrier of ((TOP-REAL C) | r) is set
K6( the carrier of ((TOP-REAL C) | r)) is set
f1 is Element of K6( the carrier of ((TOP-REAL C) | r))
r is non empty TopSpace-like TopStruct
the carrier of r is non empty set
K6( the carrier of r) is set
C is non empty TopSpace-like TopStruct
the carrier of C is non empty set
x is non empty TopSpace-like TopStruct
the carrier of x is non empty set
K7( the carrier of C, the carrier of x) is set
K6(K7( the carrier of C, the carrier of x)) is set
fs is non empty Element of K6( the carrier of r)
r | fs is non empty strict TopSpace-like SubSpace of r
the carrier of (r | fs) is non empty set
K7( the carrier of C, the carrier of (r | fs)) is set
K6(K7( the carrier of C, the carrier of (r | fs))) is set
P29 is Element of K6( the carrier of r)
r | P29 is strict TopSpace-like SubSpace of r
the carrier of (r | P29) is set
K7( the carrier of (r | P29), the carrier of x) is set
K6(K7( the carrier of (r | P29), the carrier of x)) is set
f is non empty V22() V25( the carrier of C) V26( the carrier of (r | fs)) Function-like total quasi_total Element of K6(K7( the carrier of C, the carrier of (r | fs)))
f1 is V22() V25( the carrier of (r | P29)) V26( the carrier of x) Function-like total quasi_total Element of K6(K7( the carrier of (r | P29), the carrier of x))
f1 * f is V22() V25( the carrier of C) V26( the carrier of x) Function-like Element of K6(K7( the carrier of C, the carrier of x))
[#] (r | fs) is non empty non proper closed Element of K6( the carrier of (r | fs))
K6( the carrier of (r | fs)) is set
[#] (r | P29) is non proper closed Element of K6( the carrier of (r | P29))
K6( the carrier of (r | P29)) is set
f2 is non empty Element of K6( the carrier of r)
r | f2 is non empty strict TopSpace-like SubSpace of r
the carrier of (r | f2) is non empty set
K7( the carrier of C, the carrier of (r | f2)) is set
K6(K7( the carrier of C, the carrier of (r | f2))) is set
proj11 is non empty V22() V25( the carrier of C) V26( the carrier of (r | f2)) Function-like total quasi_total Element of K6(K7( the carrier of C, the carrier of (r | f2)))
proj12 is Element of K6( the carrier of (r | P29))
proj11 " proj12 is Element of K6( the carrier of C)
K6( the carrier of C) is set
K6( the carrier of (r | f2)) is set
g1 is non empty Element of K6( the carrier of (r | f2))
(r | f2) | g1 is non empty strict TopSpace-like SubSpace of r | f2
the carrier of ((r | f2) | g1) is non empty set
K6( the carrier of ((r | f2) | g1)) is set
proj12 /\ g1 is Element of K6( the carrier of (r | f2))
g is Element of K6( the carrier of ((r | f2) | g1))
proj11 " fs is Element of K6( the carrier of C)
dom proj11 is Element of K6( the carrier of C)
(proj11 " proj12) /\ (proj11 " fs) is Element of K6( the carrier of C)
f " g is Element of K6( the carrier of C)
C is natural V11() real ext-real V83() V84() V146() V147() V148() V149() V150() V151() Element of NAT
TOP-REAL C is non empty TopSpace-like T_0 T_1 T_2 V112() V158() V159() V160() V161() V162() V163() V164() strict V231() V232() RLTopStruct
the carrier of (TOP-REAL C) is non empty functional set
K6( the carrier of (TOP-REAL C)) is set
r is Element of K6( the carrier of (TOP-REAL C))
x is Element of K6( the carrier of (TOP-REAL C))
fs is V22() V26( REAL ) Function-like V43(C) FinSequence-like V138() Element of the carrier of (TOP-REAL C)
P29 is V22() V26( REAL ) Function-like V43(C) FinSequence-like V138() Element of the carrier of (TOP-REAL C)
x \ r is Element of K6( the carrier of (TOP-REAL C))
the Element of x \ r is Element of x \ r
f is non empty Element of K6( the carrier of (TOP-REAL C))
(TOP-REAL C) | f is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL C
the carrier of ((TOP-REAL C) | f) is non empty set
K7( the carrier of I[01], the carrier of ((TOP-REAL C) | f)) is set
K6(K7( the carrier of I[01], the carrier of ((TOP-REAL C) | f))) is set
proj11 is non empty V22() V25( the carrier of I[01]) V26( the carrier of ((TOP-REAL C) | f)) Function-like total quasi_total Element of K6(K7( the carrier of I[01], the carrier of ((TOP-REAL C) | f)))
proj11 . 0 is set
proj11 . 1 is set
f1 is non empty Element of K6( the carrier of (TOP-REAL C))
(TOP-REAL C) | f1 is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL C
the carrier of ((TOP-REAL C) | f1) is non empty set
K7( the carrier of I[01], the carrier of ((TOP-REAL C) | f1)) is set
K6(K7( the carrier of I[01], the carrier of ((TOP-REAL C) | f1))) is set
proj12 is non empty V22() V25( the carrier of I[01]) V26( the carrier of ((TOP-REAL C) | f1)) Function-like total quasi_total Element of K6(K7( the carrier of I[01], the carrier of ((TOP-REAL C) | f1)))
proj12 . 0 is set
proj12 . 1 is set
rng proj12 is Element of K6( the carrier of ((TOP-REAL C) | f1))
K6( the carrier of ((TOP-REAL C) | f1)) is set
(TOP-REAL C) | x is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL C
[#] ((TOP-REAL C) | x) is non proper closed Element of K6( the carrier of ((TOP-REAL C) | x))
the carrier of ((TOP-REAL C) | x) is set
K6( the carrier of ((TOP-REAL C) | x)) is set
proj12 /" is non empty V22() V25( the carrier of ((TOP-REAL C) | f1)) V26( the carrier of I[01]) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL C) | f1), the carrier of I[01]))
K7( the carrier of ((TOP-REAL C) | f1), the carrier of I[01]) is set
K6(K7( the carrier of ((TOP-REAL C) | f1), the carrier of I[01])) is set
dom (proj12 /") is Element of K6( the carrier of ((TOP-REAL C) | f1))
K7( the carrier of I[01], the carrier of I[01]) is set
K6(K7( the carrier of I[01], the carrier of I[01])) is set
(proj12 /") * proj11 is V22() V25( the carrier of I[01]) V26( the carrier of I[01]) Function-like Element of K6(K7( the carrier of I[01], the carrier of I[01]))
g is non empty V22() V25( the carrier of I[01]) V26( the carrier of I[01]) Function-like total quasi_total Element of K6(K7( the carrier of I[01], the carrier of I[01]))
K7( the carrier of (Closed-Interval-TSpace (0,1)), the carrier of R^1) is set
K6(K7( the carrier of (Closed-Interval-TSpace (0,1)), the carrier of R^1)) is set
P19 is non empty V22() V25( the carrier of (Closed-Interval-TSpace (0,1))) V26( the carrier of R^1) Function-like total quasi_total Element of K6(K7( the carrier of (Closed-Interval-TSpace (0,1)), the carrier of R^1))
r1 is V146() V147() V148() Element of K6( the carrier of R^1)
P19 " r1 is V146() V147() V148() Element of K6( the carrier of (Closed-Interval-TSpace (0,1)))
K6( the carrier of (Closed-Interval-TSpace (0,1))) is set
p is V146() V147() V148() Element of K6( the carrier of R^1)
R^1 | p is strict TopSpace-like V200() SubSpace of R^1
the carrier of (R^1 | p) is V146() V147() V148() set
K6( the carrier of (R^1 | p)) is set
r1 /\ p is V146() V147() V148() Element of K6( the carrier of R^1)
R29 is V146() V147() V148() Element of K6( the carrier of (R^1 | p))
P19 " p is V146() V147() V148() Element of K6( the carrier of (Closed-Interval-TSpace (0,1)))
dom P19 is V146() V147() V148() Element of K6( the carrier of (Closed-Interval-TSpace (0,1)))
(P19 " r1) /\ (P19 " p) is V146() V147() V148() Element of K6( the carrier of (Closed-Interval-TSpace (0,1)))
g " R29 is V146() V147() V148() Element of K6( the carrier of I[01])
dom proj11 is V146() V147() V148() Element of K6( the carrier of I[01])
[#] I[01] is non empty non proper closed V146() V147() V148() Element of K6( the carrier of I[01])
r1 is non empty V22() V25( the carrier of (Closed-Interval-TSpace (0,1))) V26( the carrier of R^1) Function-like total quasi_total continuous Element of K6(K7( the carrier of (Closed-Interval-TSpace (0,1)), the carrier of R^1))
r1 . 0 is set
(proj12 /") . fs is set
r1 . 1 is set
(proj12 /") . P29 is set
dom proj12 is V146() V147() V148() Element of K6( the carrier of I[01])
g1 is V22() Function-like set
g1 " is V22() Function-like set
(g1 ") . fs is set
(g1 ") . P29 is set
(proj12 /") . the Element of x \ r is set
rng r1 is V146() V147() V148() Element of K6( the carrier of R^1)
dom r1 is V146() V147() V148() Element of K6( the carrier of (Closed-Interval-TSpace (0,1)))
K6( the carrier of (Closed-Interval-TSpace (0,1))) is set
p is set
r1 . p is set
proj11 . p is set
(proj12 /") . (proj11 . p) is set
rng proj11 is Element of K6( the carrier of ((TOP-REAL C) | f))
K6( the carrier of ((TOP-REAL C) | f)) is set
(TOP-REAL C) | r is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL C
[#] ((TOP-REAL C) | r) is non proper closed Element of K6( the carrier of ((TOP-REAL C) | r))
the carrier of ((TOP-REAL C) | r) is set
K6( the carrier of ((TOP-REAL C) | r)) is set
p is V11() real ext-real Element of REAL
proj12 . p is set
(g1 ") . the Element of x \ r is set
g1 . ((g1 ") . the Element of x \ r) is set
R29 is V11() real ext-real Element of REAL
r1 . R29 is set
C is Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | C is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | C) is set
K6( the carrier of ((TOP-REAL 2) | C)) is set
r is Element of K6( the carrier of ((TOP-REAL 2) | C))
x is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
fs is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
{x,fs} is non empty set
C \ {x,fs} is Element of K6( the carrier of (TOP-REAL 2))
P29 is non empty Element of K6( the carrier of (TOP-REAL 2))
f is non empty Element of K6( the carrier of (TOP-REAL 2))
P29 \/ f is non empty Element of K6( the carrier of (TOP-REAL 2))
P29 /\ f is Element of K6( the carrier of (TOP-REAL 2))
[#] ((TOP-REAL 2) | C) is non proper closed Element of K6( the carrier of ((TOP-REAL 2) | C))
f1 is non empty closed compact being_simple_closed_curve Element of K6( the carrier of (TOP-REAL 2))
P29 \ {x,fs} is Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | f1 is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | f1) is non empty set
K6( the carrier of ((TOP-REAL 2) | f1)) is set
f \ {x,fs} is Element of K6( the carrier of (TOP-REAL 2))
f2 is Element of K6( the carrier of ((TOP-REAL 2) | f1))
proj11 is Element of K6( the carrier of ((TOP-REAL 2) | f1))
f2 \/ proj11 is Element of K6( the carrier of ((TOP-REAL 2) | f1))
proj12 is set
proj12 is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
g1 is set
f2 /\ r is Element of K6( the carrier of ((TOP-REAL 2) | C))
g1 is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
g is set
proj11 /\ r is Element of K6( the carrier of ((TOP-REAL 2) | C))
g is set
C is Element of K6( the carrier of (TOP-REAL 2))
r is Element of K6( the carrier of (TOP-REAL 2))
x is Element of K6( the carrier of (TOP-REAL 2))
r \/ x is Element of K6( the carrier of (TOP-REAL 2))
fs is Element of K6( the carrier of (TOP-REAL 2))
P29 is Element of K6( the carrier of (TOP-REAL 2))
fs \/ P29 is Element of K6( the carrier of (TOP-REAL 2))
f is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
f1 is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
f2 is non empty closed compact being_simple_closed_curve Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | f2 is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
[#] ((TOP-REAL 2) | f2) is non empty non proper closed Element of K6( the carrier of ((TOP-REAL 2) | f2))
the carrier of ((TOP-REAL 2) | f2) is non empty set
K6( the carrier of ((TOP-REAL 2) | f2)) is set
{f,f1} is non empty set
r \ {f,f1} is Element of K6( the carrier of (TOP-REAL 2))
x \ {f,f1} is Element of K6( the carrier of (TOP-REAL 2))
fs \ {f,f1} is Element of K6( the carrier of (TOP-REAL 2))
P29 \ {f,f1} is Element of K6( the carrier of (TOP-REAL 2))
proj11 is Element of K6( the carrier of ((TOP-REAL 2) | f2))
proj12 is Element of K6( the carrier of ((TOP-REAL 2) | f2))
proj11 \/ proj12 is Element of K6( the carrier of ((TOP-REAL 2) | f2))
f2 \ {f,f1} is Element of K6( the carrier of (TOP-REAL 2))
g1 is Element of K6( the carrier of ((TOP-REAL 2) | f2))
g is Element of K6( the carrier of ((TOP-REAL 2) | f2))
g1 \/ g is Element of K6( the carrier of ((TOP-REAL 2) | f2))
g1 \/ (proj11 \/ proj12) is Element of K6( the carrier of ((TOP-REAL 2) | f2))
g \/ (proj11 \/ proj12) is Element of K6( the carrier of ((TOP-REAL 2) | f2))
proj11 \/ (g1 \/ g) is Element of K6( the carrier of ((TOP-REAL 2) | f2))
proj12 \/ (g1 \/ g) is Element of K6( the carrier of ((TOP-REAL 2) | f2))
(TOP-REAL 2) | r is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
[#] ((TOP-REAL 2) | r) is non proper closed Element of K6( the carrier of ((TOP-REAL 2) | r))
the carrier of ((TOP-REAL 2) | r) is set
K6( the carrier of ((TOP-REAL 2) | r)) is set
P19 is Element of K6( the carrier of ((TOP-REAL 2) | r))
(TOP-REAL 2) | x is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
[#] ((TOP-REAL 2) | x) is non proper closed Element of K6( the carrier of ((TOP-REAL 2) | x))
the carrier of ((TOP-REAL 2) | x) is set
K6( the carrier of ((TOP-REAL 2) | x)) is set
r1 is Element of K6( the carrier of ((TOP-REAL 2) | x))
(TOP-REAL 2) | fs is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
[#] ((TOP-REAL 2) | fs) is non proper closed Element of K6( the carrier of ((TOP-REAL 2) | fs))
the carrier of ((TOP-REAL 2) | fs) is set
K6( the carrier of ((TOP-REAL 2) | fs)) is set
p is Element of K6( the carrier of ((TOP-REAL 2) | fs))
(TOP-REAL 2) | P29 is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
[#] ((TOP-REAL 2) | P29) is non proper closed Element of K6( the carrier of ((TOP-REAL 2) | P29))
the carrier of ((TOP-REAL 2) | P29) is set
K6( the carrier of ((TOP-REAL 2) | P29)) is set
R29 is Element of K6( the carrier of ((TOP-REAL 2) | P29))
y is set
y is set
y is set
y is set
proj11 \/ {f,f1} is non empty set
proj12 \/ {f,f1} is non empty set
g1 \/ {f,f1} is non empty set
g \/ {f,f1} is non empty set
proj11 \ g is Element of K6( the carrier of ((TOP-REAL 2) | f2))
g \ proj11 is Element of K6( the carrier of ((TOP-REAL 2) | f2))
the Element of proj11 \ g is Element of proj11 \ g
proj11 /\ g1 is Element of K6( the carrier of ((TOP-REAL 2) | f2))
proj11 \/ g1 is Element of K6( the carrier of ((TOP-REAL 2) | f2))
(proj11 \/ g1) \/ proj12 is Element of K6( the carrier of ((TOP-REAL 2) | f2))
proj12 /\ g1 is Element of K6( the carrier of ((TOP-REAL 2) | f2))
x is set
x is set
the Element of g \ proj11 is Element of g \ proj11
proj12 \/ proj11 is Element of K6( the carrier of ((TOP-REAL 2) | f2))
g /\ proj12 is Element of K6( the carrier of ((TOP-REAL 2) | f2))
g \/ proj12 is Element of K6( the carrier of ((TOP-REAL 2) | f2))
(g \/ proj12) \/ g1 is Element of K6( the carrier of ((TOP-REAL 2) | f2))
g1 /\ proj12 is Element of K6( the carrier of ((TOP-REAL 2) | f2))
x is set
x is set
proj12 \ g1 is Element of K6( the carrier of ((TOP-REAL 2) | f2))
g1 \ proj12 is Element of K6( the carrier of ((TOP-REAL 2) | f2))
the Element of proj12 \ g1 is Element of proj12 \ g1
g \/ g1 is Element of K6( the carrier of ((TOP-REAL 2) | f2))
proj12 /\ g is Element of K6( the carrier of ((TOP-REAL 2) | f2))
proj12 \/ g is Element of K6( the carrier of ((TOP-REAL 2) | f2))
(proj12 \/ g) \/ proj11 is Element of K6( the carrier of ((TOP-REAL 2) | f2))
proj11 /\ g is Element of K6( the carrier of ((TOP-REAL 2) | f2))
x is set
proj12 \/ proj11 is Element of K6( the carrier of ((TOP-REAL 2) | f2))
x is set
proj12 \/ proj11 is Element of K6( the carrier of ((TOP-REAL 2) | f2))
the Element of g1 \ proj12 is Element of g1 \ proj12
g1 /\ proj11 is Element of K6( the carrier of ((TOP-REAL 2) | f2))
g1 \/ proj11 is Element of K6( the carrier of ((TOP-REAL 2) | f2))
(g1 \/ proj11) \/ g is Element of K6( the carrier of ((TOP-REAL 2) | f2))
g /\ proj11 is Element of K6( the carrier of ((TOP-REAL 2) | f2))
x is set
g \/ g1 is Element of K6( the carrier of ((TOP-REAL 2) | f2))
x is set
K7( the carrier of I[01], the carrier of R^1) is set
K6(K7( the carrier of I[01], the carrier of R^1)) is set
C is non empty V22() V25( the carrier of I[01]) V26( the carrier of R^1) Function-like total quasi_total Element of K6(K7( the carrier of I[01], the carrier of R^1))
C . 0[01] is V11() real ext-real Element of the carrier of R^1
C . 1[01] is V11() real ext-real Element of the carrier of R^1
fs is V11() real ext-real set
P29 is V11() real ext-real Element of REAL
C . P29 is set
C is Element of K6( the carrier of (TOP-REAL 2))
r is V11() real ext-real set
(r) is Element of K6( the carrier of (TOP-REAL 2))
{ b₁ where b₁ is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : b₁ `1 = r } is set
C /\ (r) is Element of K6( the carrier of (TOP-REAL 2))
x is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
x `1 is V11() real ext-real Element of REAL
fs is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
fs `1 is V11() real ext-real Element of REAL
P29 is non empty Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | P29 is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | P29) is non empty set
K7( the carrier of I[01], the carrier of ((TOP-REAL 2) | P29)) is set
K6(K7( the carrier of I[01], the carrier of ((TOP-REAL 2) | P29))) is set
f is non empty V22() V25( the carrier of I[01]) V26( the carrier of ((TOP-REAL 2) | P29)) Function-like total quasi_total Element of K6(K7( the carrier of I[01], the carrier of ((TOP-REAL 2) | P29)))
f . 0 is set
f . 1 is set
(TOP-REAL 2) | C is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
[#] ((TOP-REAL 2) | C) is non proper closed Element of K6( the carrier of ((TOP-REAL 2) | C))
the carrier of ((TOP-REAL 2) | C) is set
K6( the carrier of ((TOP-REAL 2) | C)) is set
K7( the carrier of I[01], the carrier of (TOP-REAL 2)) is set
K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2))) is set
f1 is non empty V22() V25( the carrier of I[01]) V26( the carrier of (TOP-REAL 2)) Function-like total quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
K7( the carrier of I[01],REAL) is set
K6(K7( the carrier of I[01],REAL)) is set
proj11 is non empty V22() V25( the carrier of (TOP-REAL 2)) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of (TOP-REAL 2),REAL))
proj11 * f1 is non empty V22() V25( the carrier of I[01]) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of I[01],REAL))
g1 is non empty V22() V25( the carrier of I[01]) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of I[01],REAL))
f2 is non empty V22() V25( the carrier of I[01]) V26( the carrier of (TOP-REAL 2)) Function-like total quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
proj12 is non empty V22() V25( the carrier of (TOP-REAL 2)) V26( the carrier of R^1) Function-like total quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of R^1))
dom f is V146() V147() V148() Element of K6( the carrier of I[01])
g is non empty V22() V25( the carrier of I[01]) V26( the carrier of R^1) Function-like total quasi_total Element of K6(K7( the carrier of I[01], the carrier of R^1))
g . 0 is set
proj1 . x is V11() real ext-real Element of REAL
g . 1 is set
proj1 . fs is V11() real ext-real Element of REAL
P19 is non empty Element of K6( the carrier of (TOP-REAL 2))
rng f is Element of K6( the carrier of ((TOP-REAL 2) | P29))
K6( the carrier of ((TOP-REAL 2) | P29)) is set
r1 is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
r1 `1 is V11() real ext-real Element of REAL
proj1 . (f . 0) is set
g . 0[01] is V11() real ext-real Element of the carrier of R^1
rng f is Element of K6( the carrier of ((TOP-REAL 2) | P29))
K6( the carrier of ((TOP-REAL 2) | P29)) is set
r1 is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
r1 `1 is V11() real ext-real Element of REAL
proj1 . (f . 0) is set
g . 1[01] is V11() real ext-real Element of the carrier of R^1
rng f is Element of K6( the carrier of ((TOP-REAL 2) | P29))
K6( the carrier of ((TOP-REAL 2) | P29)) is set
r1 is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
r1 `1 is V11() real ext-real Element of REAL
proj1 . (f . 1) is set
g . 0[01] is V11() real ext-real Element of the carrier of R^1
g . 1[01] is V11() real ext-real Element of the carrier of R^1
r1 is V11() real ext-real Element of REAL
g . r1 is set
f . r1 is set
rng f is Element of K6( the carrier of ((TOP-REAL 2) | P29))
K6( the carrier of ((TOP-REAL 2) | P29)) is set
p is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
p `1 is V11() real ext-real Element of REAL
proj1 . (f . r1) is set
g . 0[01] is V11() real ext-real Element of the carrier of R^1
g . 1[01] is V11() real ext-real Element of the carrier of R^1
g . 0[01] is V11() real ext-real Element of the carrier of R^1
g . 1[01] is V11() real ext-real Element of the carrier of R^1
C is non empty closed compact being_simple_closed_curve Element of K6( the carrier of (TOP-REAL 2))
W-min C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
W-bound C is V11() real ext-real Element of REAL
(TOP-REAL 2) | C is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj1 | C is non empty V22() V25( the carrier of ((TOP-REAL 2) | C)) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | C),REAL))
the carrier of ((TOP-REAL 2) | C) is non empty set
K7( the carrier of ((TOP-REAL 2) | C),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | C),REAL)) is set
lower_bound (proj1 | C) is V11() real ext-real Element of REAL
(proj1 | C) .: the carrier of ((TOP-REAL 2) | C) is non empty V146() V147() V148() Element of K6(REAL)
lower_bound ((proj1 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
W-most C is Element of K6( the carrier of (TOP-REAL 2))
SW-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
S-bound C is V11() real ext-real Element of REAL
proj2 is non empty V22() V25( the carrier of (TOP-REAL 2)) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of (TOP-REAL 2),REAL))
proj2 | C is non empty V22() V25( the carrier of ((TOP-REAL 2) | C)) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | C),REAL))
lower_bound (proj2 | C) is V11() real ext-real Element of REAL
(proj2 | C) .: the carrier of ((TOP-REAL 2) | C) is non empty V146() V147() V148() Element of K6(REAL)
lower_bound ((proj2 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
|[(W-bound C),(S-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
NW-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
N-bound C is V11() real ext-real Element of REAL
upper_bound (proj2 | C) is V11() real ext-real Element of REAL
upper_bound ((proj2 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
|[(W-bound C),(N-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner C),(NW-corner C)) is Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner C),(NW-corner C))) /\ C is Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (W-most C) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj2 | (W-most C) is V22() V25( the carrier of ((TOP-REAL 2) | (W-most C))) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL))
the carrier of ((TOP-REAL 2) | (W-most C)) is set
K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL)) is set
lower_bound (proj2 | (W-most C)) is V11() real ext-real Element of REAL
(proj2 | (W-most C)) .: the carrier of ((TOP-REAL 2) | (W-most C)) is V146() V147() V148() Element of K6(REAL)
lower_bound ((proj2 | (W-most C)) .: the carrier of ((TOP-REAL 2) | (W-most C))) is V11() real ext-real Element of REAL
|[(W-bound C),(lower_bound (proj2 | (W-most C)))]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
E-max C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
E-bound C is V11() real ext-real Element of REAL
upper_bound (proj1 | C) is V11() real ext-real Element of REAL
upper_bound ((proj1 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
E-most C is Element of K6( the carrier of (TOP-REAL 2))
SE-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
|[(E-bound C),(S-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
NE-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
|[(E-bound C),(N-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner C),(NE-corner C)) is Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SE-corner C),(NE-corner C))) /\ C is Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (E-most C) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj2 | (E-most C) is V22() V25( the carrier of ((TOP-REAL 2) | (E-most C))) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL))
the carrier of ((TOP-REAL 2) | (E-most C)) is set
K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL)) is set
upper_bound (proj2 | (E-most C)) is V11() real ext-real Element of REAL
(proj2 | (E-most C)) .: the carrier of ((TOP-REAL 2) | (E-most C)) is V146() V147() V148() Element of K6(REAL)
upper_bound ((proj2 | (E-most C)) .: the carrier of ((TOP-REAL 2) | (E-most C))) is V11() real ext-real Element of REAL
|[(E-bound C),(upper_bound (proj2 | (E-most C)))]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
r is non empty Element of K6( the carrier of (TOP-REAL 2))
{(W-min C),(E-max C)} is non empty set
(W-bound C) + (E-bound C) is V11() real ext-real Element of REAL
((W-bound C) + (E-bound C)) / 2 is V11() real ext-real Element of REAL
((((W-bound C) + (E-bound C)) / 2)) is Element of K6( the carrier of (TOP-REAL 2))
{ b<sub>1</sub> where b<sub>1</sub> is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : b<sub>1</sub> `1 = ((W-bound C) + (E-bound C)) / 2 } is set
First_Point (r,(W-min C),(E-max C),((((W-bound C) + (E-bound C)) / 2))) is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(First_Point (r,(W-min C),(E-max C),((((W-bound C) + (E-bound C)) / 2)))) `2 is V11() real ext-real Element of REAL
x is non empty Element of K6( the carrier of (TOP-REAL 2))
First_Point (x,(W-min C),(E-max C),((((W-bound C) + (E-bound C)) / 2))) is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(First_Point (x,(W-min C),(E-max C),((((W-bound C) + (E-bound C)) / 2)))) `2 is V11() real ext-real Element of REAL
fs is non empty Element of K6( the carrier of (TOP-REAL 2))
r /\ fs is Element of K6( the carrier of (TOP-REAL 2))
r \/ fs is non empty Element of K6( the carrier of (TOP-REAL 2))
Last_Point (fs,(E-max C),(W-min C),((((W-bound C) + (E-bound C)) / 2))) is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(Last_Point (fs,(E-max C),(W-min C),((((W-bound C) + (E-bound C)) / 2)))) `2 is V11() real ext-real Element of REAL
fs is non empty Element of K6( the carrier of (TOP-REAL 2))
r /\ fs is Element of K6( the carrier of (TOP-REAL 2))
r \/ fs is non empty Element of K6( the carrier of (TOP-REAL 2))
Last_Point (fs,(E-max C),(W-min C),((((W-bound C) + (E-bound C)) / 2))) is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(Last_Point (fs,(E-max C),(W-min C),((((W-bound C) + (E-bound C)) / 2)))) `2 is V11() real ext-real Element of REAL
P29 is non empty Element of K6( the carrier of (TOP-REAL 2))
x /\ P29 is Element of K6( the carrier of (TOP-REAL 2))
x \/ P29 is non empty Element of K6( the carrier of (TOP-REAL 2))
Last_Point (P29,(E-max C),(W-min C),((((W-bound C) + (E-bound C)) / 2))) is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(Last_Point (P29,(E-max C),(W-min C),((((W-bound C) + (E-bound C)) / 2)))) `2 is V11() real ext-real Element of REAL
P29 is non empty Element of K6( the carrier of (TOP-REAL 2))
x /\ P29 is Element of K6( the carrier of (TOP-REAL 2))
x \/ P29 is non empty Element of K6( the carrier of (TOP-REAL 2))
Last_Point (P29,(E-max C),(W-min C),((((W-bound C) + (E-bound C)) / 2))) is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(Last_Point (P29,(E-max C),(W-min C),((((W-bound C) + (E-bound C)) / 2)))) `2 is V11() real ext-real Element of REAL
(W-min C) `1 is V11() real ext-real Element of REAL
(E-max C) `1 is V11() real ext-real Element of REAL
fs /\ ((((W-bound C) + (E-bound C)) / 2)) is Element of K6( the carrier of (TOP-REAL 2))
First_Point (fs,(W-min C),(E-max C),((((W-bound C) + (E-bound C)) / 2))) is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(First_Point (fs,(W-min C),(E-max C),((((W-bound C) + (E-bound C)) / 2)))) `2 is V11() real ext-real Element of REAL
P29 /\ ((((W-bound C) + (E-bound C)) / 2)) is Element of K6( the carrier of (TOP-REAL 2))
C is Element of K6( the carrier of (TOP-REAL 2))
W-min C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
W-bound C is V11() real ext-real Element of REAL
(TOP-REAL 2) | C is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj1 | C is V22() V25( the carrier of ((TOP-REAL 2) | C)) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | C),REAL))
the carrier of ((TOP-REAL 2) | C) is set
K7( the carrier of ((TOP-REAL 2) | C),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | C),REAL)) is set
lower_bound (proj1 | C) is V11() real ext-real Element of REAL
(proj1 | C) .: the carrier of ((TOP-REAL 2) | C) is V146() V147() V148() Element of K6(REAL)
lower_bound ((proj1 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
W-most C is Element of K6( the carrier of (TOP-REAL 2))
SW-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
S-bound C is V11() real ext-real Element of REAL
proj2 | C is V22() V25( the carrier of ((TOP-REAL 2) | C)) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | C),REAL))
lower_bound (proj2 | C) is V11() real ext-real Element of REAL
(proj2 | C) .: the carrier of ((TOP-REAL 2) | C) is V146() V147() V148() Element of K6(REAL)
lower_bound ((proj2 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
|[(W-bound C),(S-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
NW-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
N-bound C is V11() real ext-real Element of REAL
upper_bound (proj2 | C) is V11() real ext-real Element of REAL
upper_bound ((proj2 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
|[(W-bound C),(N-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner C),(NW-corner C)) is Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner C),(NW-corner C))) /\ C is Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (W-most C) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj2 | (W-most C) is V22() V25( the carrier of ((TOP-REAL 2) | (W-most C))) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL))
the carrier of ((TOP-REAL 2) | (W-most C)) is set
K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL)) is set
lower_bound (proj2 | (W-most C)) is V11() real ext-real Element of REAL
(proj2 | (W-most C)) .: the carrier of ((TOP-REAL 2) | (W-most C)) is V146() V147() V148() Element of K6(REAL)
lower_bound ((proj2 | (W-most C)) .: the carrier of ((TOP-REAL 2) | (W-most C))) is V11() real ext-real Element of REAL
|[(W-bound C),(lower_bound (proj2 | (W-most C)))]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
E-max C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
E-bound C is V11() real ext-real Element of REAL
upper_bound (proj1 | C) is V11() real ext-real Element of REAL
upper_bound ((proj1 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
E-most C is Element of K6( the carrier of (TOP-REAL 2))
SE-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
|[(E-bound C),(S-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
NE-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
|[(E-bound C),(N-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner C),(NE-corner C)) is Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SE-corner C),(NE-corner C))) /\ C is Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (E-most C) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj2 | (E-most C) is V22() V25( the carrier of ((TOP-REAL 2) | (E-most C))) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL))
the carrier of ((TOP-REAL 2) | (E-most C)) is set
K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL)) is set
upper_bound (proj2 | (E-most C)) is V11() real ext-real Element of REAL
(proj2 | (E-most C)) .: the carrier of ((TOP-REAL 2) | (E-most C)) is V146() V147() V148() Element of K6(REAL)
upper_bound ((proj2 | (E-most C)) .: the carrier of ((TOP-REAL 2) | (E-most C))) is V11() real ext-real Element of REAL
|[(E-bound C),(upper_bound (proj2 | (E-most C)))]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
{(W-min C),(E-max C)} is non empty set
(W-bound C) + (E-bound C) is V11() real ext-real Element of REAL
((W-bound C) + (E-bound C)) / 2 is V11() real ext-real Element of REAL
((((W-bound C) + (E-bound C)) / 2)) is Element of K6( the carrier of (TOP-REAL 2))
{ b<sub>1</sub> where b<sub>1</sub> is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : b<sub>1</sub> `1 = ((W-bound C) + (E-bound C)) / 2 } is set
r is non empty Element of K6( the carrier of (TOP-REAL 2))
x is non empty Element of K6( the carrier of (TOP-REAL 2))
r /\ x is Element of K6( the carrier of (TOP-REAL 2))
r \/ x is non empty Element of K6( the carrier of (TOP-REAL 2))
First_Point (r,(W-min C),(E-max C),((((W-bound C) + (E-bound C)) / 2))) is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(First_Point (r,(W-min C),(E-max C),((((W-bound C) + (E-bound C)) / 2)))) `2 is V11() real ext-real Element of REAL
Last_Point (x,(E-max C),(W-min C),((((W-bound C) + (E-bound C)) / 2))) is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(Last_Point (x,(E-max C),(W-min C),((((W-bound C) + (E-bound C)) / 2)))) `2 is V11() real ext-real Element of REAL
r is non empty Element of K6( the carrier of (TOP-REAL 2))
fs is non empty Element of K6( the carrier of (TOP-REAL 2))
r /\ fs is Element of K6( the carrier of (TOP-REAL 2))
r \/ fs is non empty Element of K6( the carrier of (TOP-REAL 2))
First_Point (r,(W-min C),(E-max C),((((W-bound C) + (E-bound C)) / 2))) is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(First_Point (r,(W-min C),(E-max C),((((W-bound C) + (E-bound C)) / 2)))) `2 is V11() real ext-real Element of REAL
Last_Point (fs,(E-max C),(W-min C),((((W-bound C) + (E-bound C)) / 2))) is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(Last_Point (fs,(E-max C),(W-min C),((((W-bound C) + (E-bound C)) / 2)))) `2 is V11() real ext-real Element of REAL
x is non empty Element of K6( the carrier of (TOP-REAL 2))
P29 is non empty Element of K6( the carrier of (TOP-REAL 2))
x /\ P29 is Element of K6( the carrier of (TOP-REAL 2))
x \/ P29 is non empty Element of K6( the carrier of (TOP-REAL 2))
First_Point (x,(W-min C),(E-max C),((((W-bound C) + (E-bound C)) / 2))) is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(First_Point (x,(W-min C),(E-max C),((((W-bound C) + (E-bound C)) / 2)))) `2 is V11() real ext-real Element of REAL
Last_Point (P29,(E-max C),(W-min C),((((W-bound C) + (E-bound C)) / 2))) is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(Last_Point (P29,(E-max C),(W-min C),((((W-bound C) + (E-bound C)) / 2)))) `2 is V11() real ext-real Element of REAL
C is Element of K6( the carrier of (TOP-REAL 2))
W-min C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
W-bound C is V11() real ext-real Element of REAL
(TOP-REAL 2) | C is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj1 | C is V22() V25( the carrier of ((TOP-REAL 2) | C)) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | C),REAL))
the carrier of ((TOP-REAL 2) | C) is set
K7( the carrier of ((TOP-REAL 2) | C),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | C),REAL)) is set
lower_bound (proj1 | C) is V11() real ext-real Element of REAL
(proj1 | C) .: the carrier of ((TOP-REAL 2) | C) is V146() V147() V148() Element of K6(REAL)
lower_bound ((proj1 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
W-most C is Element of K6( the carrier of (TOP-REAL 2))
SW-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
S-bound C is V11() real ext-real Element of REAL
proj2 | C is V22() V25( the carrier of ((TOP-REAL 2) | C)) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | C),REAL))
lower_bound (proj2 | C) is V11() real ext-real Element of REAL
(proj2 | C) .: the carrier of ((TOP-REAL 2) | C) is V146() V147() V148() Element of K6(REAL)
lower_bound ((proj2 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
|[(W-bound C),(S-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
NW-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
N-bound C is V11() real ext-real Element of REAL
upper_bound (proj2 | C) is V11() real ext-real Element of REAL
upper_bound ((proj2 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
|[(W-bound C),(N-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner C),(NW-corner C)) is Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner C),(NW-corner C))) /\ C is Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (W-most C) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj2 | (W-most C) is V22() V25( the carrier of ((TOP-REAL 2) | (W-most C))) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL))
the carrier of ((TOP-REAL 2) | (W-most C)) is set
K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL)) is set
lower_bound (proj2 | (W-most C)) is V11() real ext-real Element of REAL
(proj2 | (W-most C)) .: the carrier of ((TOP-REAL 2) | (W-most C)) is V146() V147() V148() Element of K6(REAL)
lower_bound ((proj2 | (W-most C)) .: the carrier of ((TOP-REAL 2) | (W-most C))) is V11() real ext-real Element of REAL
|[(W-bound C),(lower_bound (proj2 | (W-most C)))]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
E-max C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
E-bound C is V11() real ext-real Element of REAL
upper_bound (proj1 | C) is V11() real ext-real Element of REAL
upper_bound ((proj1 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
E-most C is Element of K6( the carrier of (TOP-REAL 2))
SE-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
|[(E-bound C),(S-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
NE-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
|[(E-bound C),(N-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner C),(NE-corner C)) is Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SE-corner C),(NE-corner C))) /\ C is Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (E-most C) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj2 | (E-most C) is V22() V25( the carrier of ((TOP-REAL 2) | (E-most C))) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL))
the carrier of ((TOP-REAL 2) | (E-most C)) is set
K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL)) is set
upper_bound (proj2 | (E-most C)) is V11() real ext-real Element of REAL
(proj2 | (E-most C)) .: the carrier of ((TOP-REAL 2) | (E-most C)) is V146() V147() V148() Element of K6(REAL)
upper_bound ((proj2 | (E-most C)) .: the carrier of ((TOP-REAL 2) | (E-most C))) is V11() real ext-real Element of REAL
|[(E-bound C),(upper_bound (proj2 | (E-most C)))]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(C) is non empty Element of K6( the carrier of (TOP-REAL 2))
{(W-min C),(E-max C)} is non empty set
(W-bound C) + (E-bound C) is V11() real ext-real Element of REAL
((W-bound C) + (E-bound C)) / 2 is V11() real ext-real Element of REAL
((((W-bound C) + (E-bound C)) / 2)) is Element of K6( the carrier of (TOP-REAL 2))
{ b₁ where b₁ is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : b₁ `1 = ((W-bound C) + (E-bound C)) / 2 } is set
First_Point ((C),(W-min C),(E-max C),((((W-bound C) + (E-bound C)) / 2))) is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(First_Point ((C),(W-min C),(E-max C),((((W-bound C) + (E-bound C)) / 2)))) `2 is V11() real ext-real Element of REAL
r is non empty Element of K6( the carrier of (TOP-REAL 2))
(C) /\ r is Element of K6( the carrier of (TOP-REAL 2))
(C) \/ r is non empty Element of K6( the carrier of (TOP-REAL 2))
Last_Point (r,(E-max C),(W-min C),((((W-bound C) + (E-bound C)) / 2))) is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(Last_Point (r,(E-max C),(W-min C),((((W-bound C) + (E-bound C)) / 2)))) `2 is V11() real ext-real Element of REAL
x is non empty Element of K6( the carrier of (TOP-REAL 2))
(C) /\ x is Element of K6( the carrier of (TOP-REAL 2))
(C) \/ x is non empty Element of K6( the carrier of (TOP-REAL 2))
Last_Point (x,(E-max C),(W-min C),((((W-bound C) + (E-bound C)) / 2))) is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(Last_Point (x,(E-max C),(W-min C),((((W-bound C) + (E-bound C)) / 2)))) `2 is V11() real ext-real Element of REAL
C is Element of K6( the carrier of (TOP-REAL 2))
W-min C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
W-bound C is V11() real ext-real Element of REAL
(TOP-REAL 2) | C is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj1 | C is V22() V25( the carrier of ((TOP-REAL 2) | C)) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | C),REAL))
the carrier of ((TOP-REAL 2) | C) is set
K7( the carrier of ((TOP-REAL 2) | C),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | C),REAL)) is set
lower_bound (proj1 | C) is V11() real ext-real Element of REAL
(proj1 | C) .: the carrier of ((TOP-REAL 2) | C) is V146() V147() V148() Element of K6(REAL)
lower_bound ((proj1 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
W-most C is Element of K6( the carrier of (TOP-REAL 2))
SW-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
S-bound C is V11() real ext-real Element of REAL
proj2 | C is V22() V25( the carrier of ((TOP-REAL 2) | C)) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | C),REAL))
lower_bound (proj2 | C) is V11() real ext-real Element of REAL
(proj2 | C) .: the carrier of ((TOP-REAL 2) | C) is V146() V147() V148() Element of K6(REAL)
lower_bound ((proj2 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
|[(W-bound C),(S-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
NW-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
N-bound C is V11() real ext-real Element of REAL
upper_bound (proj2 | C) is V11() real ext-real Element of REAL
upper_bound ((proj2 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
|[(W-bound C),(N-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner C),(NW-corner C)) is Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner C),(NW-corner C))) /\ C is Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (W-most C) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj2 | (W-most C) is V22() V25( the carrier of ((TOP-REAL 2) | (W-most C))) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL))
the carrier of ((TOP-REAL 2) | (W-most C)) is set
K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL)) is set
lower_bound (proj2 | (W-most C)) is V11() real ext-real Element of REAL
(proj2 | (W-most C)) .: the carrier of ((TOP-REAL 2) | (W-most C)) is V146() V147() V148() Element of K6(REAL)
lower_bound ((proj2 | (W-most C)) .: the carrier of ((TOP-REAL 2) | (W-most C))) is V11() real ext-real Element of REAL
|[(W-bound C),(lower_bound (proj2 | (W-most C)))]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
E-max C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
E-bound C is V11() real ext-real Element of REAL
upper_bound (proj1 | C) is V11() real ext-real Element of REAL
upper_bound ((proj1 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
E-most C is Element of K6( the carrier of (TOP-REAL 2))
SE-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
|[(E-bound C),(S-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
NE-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
|[(E-bound C),(N-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner C),(NE-corner C)) is Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SE-corner C),(NE-corner C))) /\ C is Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (E-most C) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj2 | (E-most C) is V22() V25( the carrier of ((TOP-REAL 2) | (E-most C))) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL))
the carrier of ((TOP-REAL 2) | (E-most C)) is set
K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL)) is set
upper_bound (proj2 | (E-most C)) is V11() real ext-real Element of REAL
(proj2 | (E-most C)) .: the carrier of ((TOP-REAL 2) | (E-most C)) is V146() V147() V148() Element of K6(REAL)
upper_bound ((proj2 | (E-most C)) .: the carrier of ((TOP-REAL 2) | (E-most C))) is V11() real ext-real Element of REAL
|[(E-bound C),(upper_bound (proj2 | (E-most C)))]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(C) is non empty Element of K6( the carrier of (TOP-REAL 2))
(C) is non empty Element of K6( the carrier of (TOP-REAL 2))
(C) /\ (C) is Element of K6( the carrier of (TOP-REAL 2))
{(W-min C),(E-max C)} is non empty set
(C) \/ (C) is non empty Element of K6( the carrier of (TOP-REAL 2))
(W-bound C) + (E-bound C) is V11() real ext-real Element of REAL
((W-bound C) + (E-bound C)) / 2 is V11() real ext-real Element of REAL
((((W-bound C) + (E-bound C)) / 2)) is Element of K6( the carrier of (TOP-REAL 2))
{ b₁ where b₁ is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : b₁ `1 = ((W-bound C) + (E-bound C)) / 2 } is set
First_Point ((C),(W-min C),(E-max C),((((W-bound C) + (E-bound C)) / 2))) is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(First_Point ((C),(W-min C),(E-max C),((((W-bound C) + (E-bound C)) / 2)))) `2 is V11() real ext-real Element of REAL
Last_Point ((C),(E-max C),(W-min C),((((W-bound C) + (E-bound C)) / 2))) is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(Last_Point ((C),(E-max C),(W-min C),((((W-bound C) + (E-bound C)) / 2)))) `2 is V11() real ext-real Element of REAL
C is Element of K6( the carrier of (TOP-REAL 2))
(C) is non empty Element of K6( the carrier of (TOP-REAL 2))
(C) is non empty Element of K6( the carrier of (TOP-REAL 2))
C \ (C) is Element of K6( the carrier of (TOP-REAL 2))
W-min C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
W-bound C is V11() real ext-real Element of REAL
(TOP-REAL 2) | C is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj1 | C is V22() V25( the carrier of ((TOP-REAL 2) | C)) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | C),REAL))
the carrier of ((TOP-REAL 2) | C) is set
K7( the carrier of ((TOP-REAL 2) | C),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | C),REAL)) is set
lower_bound (proj1 | C) is V11() real ext-real Element of REAL
(proj1 | C) .: the carrier of ((TOP-REAL 2) | C) is V146() V147() V148() Element of K6(REAL)
lower_bound ((proj1 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
W-most C is Element of K6( the carrier of (TOP-REAL 2))
SW-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
S-bound C is V11() real ext-real Element of REAL
proj2 | C is V22() V25( the carrier of ((TOP-REAL 2) | C)) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | C),REAL))
lower_bound (proj2 | C) is V11() real ext-real Element of REAL
(proj2 | C) .: the carrier of ((TOP-REAL 2) | C) is V146() V147() V148() Element of K6(REAL)
lower_bound ((proj2 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
|[(W-bound C),(S-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
NW-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
N-bound C is V11() real ext-real Element of REAL
upper_bound (proj2 | C) is V11() real ext-real Element of REAL
upper_bound ((proj2 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
|[(W-bound C),(N-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner C),(NW-corner C)) is Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner C),(NW-corner C))) /\ C is Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (W-most C) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj2 | (W-most C) is V22() V25( the carrier of ((TOP-REAL 2) | (W-most C))) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL))
the carrier of ((TOP-REAL 2) | (W-most C)) is set
K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL)) is set
lower_bound (proj2 | (W-most C)) is V11() real ext-real Element of REAL
(proj2 | (W-most C)) .: the carrier of ((TOP-REAL 2) | (W-most C)) is V146() V147() V148() Element of K6(REAL)
lower_bound ((proj2 | (W-most C)) .: the carrier of ((TOP-REAL 2) | (W-most C))) is V11() real ext-real Element of REAL
|[(W-bound C),(lower_bound (proj2 | (W-most C)))]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
E-max C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
E-bound C is V11() real ext-real Element of REAL
upper_bound (proj1 | C) is V11() real ext-real Element of REAL
upper_bound ((proj1 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
E-most C is Element of K6( the carrier of (TOP-REAL 2))
SE-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
|[(E-bound C),(S-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
NE-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
|[(E-bound C),(N-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner C),(NE-corner C)) is Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SE-corner C),(NE-corner C))) /\ C is Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (E-most C) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj2 | (E-most C) is V22() V25( the carrier of ((TOP-REAL 2) | (E-most C))) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL))
the carrier of ((TOP-REAL 2) | (E-most C)) is set
K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL)) is set
upper_bound (proj2 | (E-most C)) is V11() real ext-real Element of REAL
(proj2 | (E-most C)) .: the carrier of ((TOP-REAL 2) | (E-most C)) is V146() V147() V148() Element of K6(REAL)
upper_bound ((proj2 | (E-most C)) .: the carrier of ((TOP-REAL 2) | (E-most C))) is V11() real ext-real Element of REAL
|[(E-bound C),(upper_bound (proj2 | (E-most C)))]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
{(W-min C),(E-max C)} is non empty set
(C \ (C)) \/ {(W-min C),(E-max C)} is non empty set
C \ (C) is Element of K6( the carrier of (TOP-REAL 2))
(C \ (C)) \/ {(W-min C),(E-max C)} is non empty set
(C) /\ (C) is Element of K6( the carrier of (TOP-REAL 2))
(C) \/ (C) is non empty Element of K6( the carrier of (TOP-REAL 2))
((C) \/ (C)) \ (C) is Element of K6( the carrier of (TOP-REAL 2))
(((C) \/ (C)) \ (C)) \/ ((C) /\ (C)) is Element of K6( the carrier of (TOP-REAL 2))
(C) \ (C) is Element of K6( the carrier of (TOP-REAL 2))
(C) /\ (C) is Element of K6( the carrier of (TOP-REAL 2))
((C) \ (C)) \/ ((C) /\ (C)) is Element of K6( the carrier of (TOP-REAL 2))
((C) \/ (C)) \ (C) is Element of K6( the carrier of (TOP-REAL 2))
(((C) \/ (C)) \ (C)) \/ ((C) /\ (C)) is Element of K6( the carrier of (TOP-REAL 2))
(C) \ (C) is Element of K6( the carrier of (TOP-REAL 2))
((C) \ (C)) \/ ((C) /\ (C)) is Element of K6( the carrier of (TOP-REAL 2))
C is Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | C is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | C) is set
K6( the carrier of ((TOP-REAL 2) | C)) is set
(C) is non empty Element of K6( the carrier of (TOP-REAL 2))
W-min C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
W-bound C is V11() real ext-real Element of REAL
proj1 | C is V22() V25( the carrier of ((TOP-REAL 2) | C)) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | C),REAL))
K7( the carrier of ((TOP-REAL 2) | C),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | C),REAL)) is set
lower_bound (proj1 | C) is V11() real ext-real Element of REAL
(proj1 | C) .: the carrier of ((TOP-REAL 2) | C) is V146() V147() V148() Element of K6(REAL)
lower_bound ((proj1 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
W-most C is Element of K6( the carrier of (TOP-REAL 2))
SW-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
S-bound C is V11() real ext-real Element of REAL
proj2 | C is V22() V25( the carrier of ((TOP-REAL 2) | C)) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | C),REAL))
lower_bound (proj2 | C) is V11() real ext-real Element of REAL
(proj2 | C) .: the carrier of ((TOP-REAL 2) | C) is V146() V147() V148() Element of K6(REAL)
lower_bound ((proj2 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
|[(W-bound C),(S-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
NW-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
N-bound C is V11() real ext-real Element of REAL
upper_bound (proj2 | C) is V11() real ext-real Element of REAL
upper_bound ((proj2 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
|[(W-bound C),(N-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner C),(NW-corner C)) is Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner C),(NW-corner C))) /\ C is Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (W-most C) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj2 | (W-most C) is V22() V25( the carrier of ((TOP-REAL 2) | (W-most C))) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL))
the carrier of ((TOP-REAL 2) | (W-most C)) is set
K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL)) is set
lower_bound (proj2 | (W-most C)) is V11() real ext-real Element of REAL
(proj2 | (W-most C)) .: the carrier of ((TOP-REAL 2) | (W-most C)) is V146() V147() V148() Element of K6(REAL)
lower_bound ((proj2 | (W-most C)) .: the carrier of ((TOP-REAL 2) | (W-most C))) is V11() real ext-real Element of REAL
|[(W-bound C),(lower_bound (proj2 | (W-most C)))]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
E-max C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
E-bound C is V11() real ext-real Element of REAL
upper_bound (proj1 | C) is V11() real ext-real Element of REAL
upper_bound ((proj1 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
E-most C is Element of K6( the carrier of (TOP-REAL 2))
SE-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
|[(E-bound C),(S-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
NE-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
|[(E-bound C),(N-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner C),(NE-corner C)) is Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SE-corner C),(NE-corner C))) /\ C is Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (E-most C) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj2 | (E-most C) is V22() V25( the carrier of ((TOP-REAL 2) | (E-most C))) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL))
the carrier of ((TOP-REAL 2) | (E-most C)) is set
K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL)) is set
upper_bound (proj2 | (E-most C)) is V11() real ext-real Element of REAL
(proj2 | (E-most C)) .: the carrier of ((TOP-REAL 2) | (E-most C)) is V146() V147() V148() Element of K6(REAL)
upper_bound ((proj2 | (E-most C)) .: the carrier of ((TOP-REAL 2) | (E-most C))) is V11() real ext-real Element of REAL
|[(E-bound C),(upper_bound (proj2 | (E-most C)))]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
{(W-min C),(E-max C)} is non empty set
(C) is non empty Element of K6( the carrier of (TOP-REAL 2))
r is Element of K6( the carrier of ((TOP-REAL 2) | C))
(C) /\ r is Element of K6( the carrier of ((TOP-REAL 2) | C))
(C) \/ r is non empty set
((C) \/ r) \ (C) is Element of K6(((C) \/ r))
K6(((C) \/ r)) is set
(((C) \/ r) \ (C)) \/ ((C) /\ r) is set
r \ (C) is Element of K6( the carrier of ((TOP-REAL 2) | C))
r /\ (C) is Element of K6( the carrier of (TOP-REAL 2))
(r \ (C)) \/ (r /\ (C)) is set
C is Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | C is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | C) is set
K6( the carrier of ((TOP-REAL 2) | C)) is set
(C) is non empty Element of K6( the carrier of (TOP-REAL 2))
W-min C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
W-bound C is V11() real ext-real Element of REAL
proj1 | C is V22() V25( the carrier of ((TOP-REAL 2) | C)) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | C),REAL))
K7( the carrier of ((TOP-REAL 2) | C),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | C),REAL)) is set
lower_bound (proj1 | C) is V11() real ext-real Element of REAL
(proj1 | C) .: the carrier of ((TOP-REAL 2) | C) is V146() V147() V148() Element of K6(REAL)
lower_bound ((proj1 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
W-most C is Element of K6( the carrier of (TOP-REAL 2))
SW-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
S-bound C is V11() real ext-real Element of REAL
proj2 | C is V22() V25( the carrier of ((TOP-REAL 2) | C)) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | C),REAL))
lower_bound (proj2 | C) is V11() real ext-real Element of REAL
(proj2 | C) .: the carrier of ((TOP-REAL 2) | C) is V146() V147() V148() Element of K6(REAL)
lower_bound ((proj2 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
|[(W-bound C),(S-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
NW-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
N-bound C is V11() real ext-real Element of REAL
upper_bound (proj2 | C) is V11() real ext-real Element of REAL
upper_bound ((proj2 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
|[(W-bound C),(N-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner C),(NW-corner C)) is Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner C),(NW-corner C))) /\ C is Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (W-most C) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj2 | (W-most C) is V22() V25( the carrier of ((TOP-REAL 2) | (W-most C))) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL))
the carrier of ((TOP-REAL 2) | (W-most C)) is set
K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL)) is set
lower_bound (proj2 | (W-most C)) is V11() real ext-real Element of REAL
(proj2 | (W-most C)) .: the carrier of ((TOP-REAL 2) | (W-most C)) is V146() V147() V148() Element of K6(REAL)
lower_bound ((proj2 | (W-most C)) .: the carrier of ((TOP-REAL 2) | (W-most C))) is V11() real ext-real Element of REAL
|[(W-bound C),(lower_bound (proj2 | (W-most C)))]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
E-max C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
E-bound C is V11() real ext-real Element of REAL
upper_bound (proj1 | C) is V11() real ext-real Element of REAL
upper_bound ((proj1 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
E-most C is Element of K6( the carrier of (TOP-REAL 2))
SE-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
|[(E-bound C),(S-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
NE-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
|[(E-bound C),(N-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner C),(NE-corner C)) is Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SE-corner C),(NE-corner C))) /\ C is Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (E-most C) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj2 | (E-most C) is V22() V25( the carrier of ((TOP-REAL 2) | (E-most C))) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL))
the carrier of ((TOP-REAL 2) | (E-most C)) is set
K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL)) is set
upper_bound (proj2 | (E-most C)) is V11() real ext-real Element of REAL
(proj2 | (E-most C)) .: the carrier of ((TOP-REAL 2) | (E-most C)) is V146() V147() V148() Element of K6(REAL)
upper_bound ((proj2 | (E-most C)) .: the carrier of ((TOP-REAL 2) | (E-most C))) is V11() real ext-real Element of REAL
|[(E-bound C),(upper_bound (proj2 | (E-most C)))]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
{(W-min C),(E-max C)} is non empty set
(C) is non empty Element of K6( the carrier of (TOP-REAL 2))
r is Element of K6( the carrier of ((TOP-REAL 2) | C))
r /\ (C) is Element of K6( the carrier of (TOP-REAL 2))
r \/ (C) is non empty set
(r \/ (C)) \ (C) is Element of K6((r \/ (C)))
K6((r \/ (C))) is set
((r \/ (C)) \ (C)) \/ (r /\ (C)) is set
r \ (C) is Element of K6( the carrier of ((TOP-REAL 2) | C))
(r /\ (C)) \/ (r \ (C)) is set
C is Element of K6( the carrier of (TOP-REAL 2))
r is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
x is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
fs is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
C is Element of K6( the carrier of (TOP-REAL 2))
r is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
x is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
fs is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
C is Element of K6( the carrier of (TOP-REAL 2))
r is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(C) is non empty Element of K6( the carrier of (TOP-REAL 2))
(C) is non empty Element of K6( the carrier of (TOP-REAL 2))
(C) \/ (C) is non empty Element of K6( the carrier of (TOP-REAL 2))
W-min C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
W-bound C is V11() real ext-real Element of REAL
(TOP-REAL 2) | C is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj1 | C is V22() V25( the carrier of ((TOP-REAL 2) | C)) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | C),REAL))
the carrier of ((TOP-REAL 2) | C) is set
K7( the carrier of ((TOP-REAL 2) | C),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | C),REAL)) is set
lower_bound (proj1 | C) is V11() real ext-real Element of REAL
(proj1 | C) .: the carrier of ((TOP-REAL 2) | C) is V146() V147() V148() Element of K6(REAL)
lower_bound ((proj1 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
W-most C is Element of K6( the carrier of (TOP-REAL 2))
SW-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
S-bound C is V11() real ext-real Element of REAL
proj2 | C is V22() V25( the carrier of ((TOP-REAL 2) | C)) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | C),REAL))
lower_bound (proj2 | C) is V11() real ext-real Element of REAL
(proj2 | C) .: the carrier of ((TOP-REAL 2) | C) is V146() V147() V148() Element of K6(REAL)
lower_bound ((proj2 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
|[(W-bound C),(S-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
NW-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
N-bound C is V11() real ext-real Element of REAL
upper_bound (proj2 | C) is V11() real ext-real Element of REAL
upper_bound ((proj2 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
|[(W-bound C),(N-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner C),(NW-corner C)) is Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner C),(NW-corner C))) /\ C is Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (W-most C) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj2 | (W-most C) is V22() V25( the carrier of ((TOP-REAL 2) | (W-most C))) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL))
the carrier of ((TOP-REAL 2) | (W-most C)) is set
K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL)) is set
lower_bound (proj2 | (W-most C)) is V11() real ext-real Element of REAL
(proj2 | (W-most C)) .: the carrier of ((TOP-REAL 2) | (W-most C)) is V146() V147() V148() Element of K6(REAL)
lower_bound ((proj2 | (W-most C)) .: the carrier of ((TOP-REAL 2) | (W-most C))) is V11() real ext-real Element of REAL
|[(W-bound C),(lower_bound (proj2 | (W-most C)))]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
E-max C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
E-bound C is V11() real ext-real Element of REAL
upper_bound (proj1 | C) is V11() real ext-real Element of REAL
upper_bound ((proj1 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
E-most C is Element of K6( the carrier of (TOP-REAL 2))
SE-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
|[(E-bound C),(S-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
NE-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
|[(E-bound C),(N-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner C),(NE-corner C)) is Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SE-corner C),(NE-corner C))) /\ C is Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (E-most C) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj2 | (E-most C) is V22() V25( the carrier of ((TOP-REAL 2) | (E-most C))) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL))
the carrier of ((TOP-REAL 2) | (E-most C)) is set
K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL)) is set
upper_bound (proj2 | (E-most C)) is V11() real ext-real Element of REAL
(proj2 | (E-most C)) .: the carrier of ((TOP-REAL 2) | (E-most C)) is V146() V147() V148() Element of K6(REAL)
upper_bound ((proj2 | (E-most C)) .: the carrier of ((TOP-REAL 2) | (E-most C))) is V11() real ext-real Element of REAL
|[(E-bound C),(upper_bound (proj2 | (E-most C)))]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
C is Element of K6( the carrier of (TOP-REAL 2))
r is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
x is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
E-max C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
E-bound C is V11() real ext-real Element of REAL
(TOP-REAL 2) | C is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj1 | C is V22() V25( the carrier of ((TOP-REAL 2) | C)) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | C),REAL))
the carrier of ((TOP-REAL 2) | C) is set
K7( the carrier of ((TOP-REAL 2) | C),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | C),REAL)) is set
upper_bound (proj1 | C) is V11() real ext-real Element of REAL
(proj1 | C) .: the carrier of ((TOP-REAL 2) | C) is V146() V147() V148() Element of K6(REAL)
upper_bound ((proj1 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
E-most C is Element of K6( the carrier of (TOP-REAL 2))
SE-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
S-bound C is V11() real ext-real Element of REAL
proj2 | C is V22() V25( the carrier of ((TOP-REAL 2) | C)) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | C),REAL))
lower_bound (proj2 | C) is V11() real ext-real Element of REAL
(proj2 | C) .: the carrier of ((TOP-REAL 2) | C) is V146() V147() V148() Element of K6(REAL)
lower_bound ((proj2 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
|[(E-bound C),(S-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
NE-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
N-bound C is V11() real ext-real Element of REAL
upper_bound (proj2 | C) is V11() real ext-real Element of REAL
upper_bound ((proj2 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
|[(E-bound C),(N-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner C),(NE-corner C)) is Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SE-corner C),(NE-corner C))) /\ C is Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (E-most C) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj2 | (E-most C) is V22() V25( the carrier of ((TOP-REAL 2) | (E-most C))) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL))
the carrier of ((TOP-REAL 2) | (E-most C)) is set
K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL)) is set
upper_bound (proj2 | (E-most C)) is V11() real ext-real Element of REAL
(proj2 | (E-most C)) .: the carrier of ((TOP-REAL 2) | (E-most C)) is V146() V147() V148() Element of K6(REAL)
upper_bound ((proj2 | (E-most C)) .: the carrier of ((TOP-REAL 2) | (E-most C))) is V11() real ext-real Element of REAL
|[(E-bound C),(upper_bound (proj2 | (E-most C)))]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
W-min C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
W-bound C is V11() real ext-real Element of REAL
lower_bound (proj1 | C) is V11() real ext-real Element of REAL
lower_bound ((proj1 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
W-most C is Element of K6( the carrier of (TOP-REAL 2))
SW-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
|[(W-bound C),(S-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
NW-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
|[(W-bound C),(N-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner C),(NW-corner C)) is Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner C),(NW-corner C))) /\ C is Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (W-most C) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj2 | (W-most C) is V22() V25( the carrier of ((TOP-REAL 2) | (W-most C))) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL))
the carrier of ((TOP-REAL 2) | (W-most C)) is set
K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL)) is set
lower_bound (proj2 | (W-most C)) is V11() real ext-real Element of REAL
(proj2 | (W-most C)) .: the carrier of ((TOP-REAL 2) | (W-most C)) is V146() V147() V148() Element of K6(REAL)
lower_bound ((proj2 | (W-most C)) .: the carrier of ((TOP-REAL 2) | (W-most C))) is V11() real ext-real Element of REAL
|[(W-bound C),(lower_bound (proj2 | (W-most C)))]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(C) is non empty Element of K6( the carrier of (TOP-REAL 2))
(C) is non empty Element of K6( the carrier of (TOP-REAL 2))
(C) /\ (C) is Element of K6( the carrier of (TOP-REAL 2))
{(W-min C),(E-max C)} is non empty set
C is Element of K6( the carrier of (TOP-REAL 2))
r is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
x is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
fs is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
E-max C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
E-bound C is V11() real ext-real Element of REAL
(TOP-REAL 2) | C is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj1 | C is V22() V25( the carrier of ((TOP-REAL 2) | C)) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | C),REAL))
the carrier of ((TOP-REAL 2) | C) is set
K7( the carrier of ((TOP-REAL 2) | C),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | C),REAL)) is set
upper_bound (proj1 | C) is V11() real ext-real Element of REAL
(proj1 | C) .: the carrier of ((TOP-REAL 2) | C) is V146() V147() V148() Element of K6(REAL)
upper_bound ((proj1 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
E-most C is Element of K6( the carrier of (TOP-REAL 2))
SE-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
S-bound C is V11() real ext-real Element of REAL
proj2 | C is V22() V25( the carrier of ((TOP-REAL 2) | C)) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | C),REAL))
lower_bound (proj2 | C) is V11() real ext-real Element of REAL
(proj2 | C) .: the carrier of ((TOP-REAL 2) | C) is V146() V147() V148() Element of K6(REAL)
lower_bound ((proj2 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
|[(E-bound C),(S-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
NE-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
N-bound C is V11() real ext-real Element of REAL
upper_bound (proj2 | C) is V11() real ext-real Element of REAL
upper_bound ((proj2 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
|[(E-bound C),(N-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner C),(NE-corner C)) is Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SE-corner C),(NE-corner C))) /\ C is Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (E-most C) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj2 | (E-most C) is V22() V25( the carrier of ((TOP-REAL 2) | (E-most C))) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL))
the carrier of ((TOP-REAL 2) | (E-most C)) is set
K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL)) is set
upper_bound (proj2 | (E-most C)) is V11() real ext-real Element of REAL
(proj2 | (E-most C)) .: the carrier of ((TOP-REAL 2) | (E-most C)) is V146() V147() V148() Element of K6(REAL)
upper_bound ((proj2 | (E-most C)) .: the carrier of ((TOP-REAL 2) | (E-most C))) is V11() real ext-real Element of REAL
|[(E-bound C),(upper_bound (proj2 | (E-most C)))]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
W-min C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
W-bound C is V11() real ext-real Element of REAL
lower_bound (proj1 | C) is V11() real ext-real Element of REAL
lower_bound ((proj1 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
W-most C is Element of K6( the carrier of (TOP-REAL 2))
SW-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
|[(W-bound C),(S-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
NW-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
|[(W-bound C),(N-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner C),(NW-corner C)) is Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner C),(NW-corner C))) /\ C is Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (W-most C) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj2 | (W-most C) is V22() V25( the carrier of ((TOP-REAL 2) | (W-most C))) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL))
the carrier of ((TOP-REAL 2) | (W-most C)) is set
K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL)) is set
lower_bound (proj2 | (W-most C)) is V11() real ext-real Element of REAL
(proj2 | (W-most C)) .: the carrier of ((TOP-REAL 2) | (W-most C)) is V146() V147() V148() Element of K6(REAL)
lower_bound ((proj2 | (W-most C)) .: the carrier of ((TOP-REAL 2) | (W-most C))) is V11() real ext-real Element of REAL
|[(W-bound C),(lower_bound (proj2 | (W-most C)))]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(C) is non empty Element of K6( the carrier of (TOP-REAL 2))
(C) is non empty Element of K6( the carrier of (TOP-REAL 2))
(C) /\ (C) is Element of K6( the carrier of (TOP-REAL 2))
{(W-min C),(E-max C)} is non empty set
C is Element of K6( the carrier of (TOP-REAL 2))
r is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
x is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
fs is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(C,r,x,fs) is Element of K6( the carrier of (TOP-REAL 2))
{ b<sub>1</sub> where b<sub>1</sub> is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : LE b<sub>1</sub>,fs,C,r,x } is set
P29 is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
C is Element of K6( the carrier of (TOP-REAL 2))
r is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
x is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
fs is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(C,r,x,fs) is Element of K6( the carrier of (TOP-REAL 2))
{ b<sub>1</sub> where b<sub>1</sub> is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : LE fs,b<sub>1</sub>,C,r,x } is set
P29 is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
C is non empty closed compact being_simple_closed_curve Element of K6( the carrier of (TOP-REAL 2))
(C) is non empty Element of K6( the carrier of (TOP-REAL 2))
E-max C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
E-bound C is V11() real ext-real Element of REAL
(TOP-REAL 2) | C is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj1 | C is non empty V22() V25( the carrier of ((TOP-REAL 2) | C)) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | C),REAL))
the carrier of ((TOP-REAL 2) | C) is non empty set
K7( the carrier of ((TOP-REAL 2) | C),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | C),REAL)) is set
upper_bound (proj1 | C) is V11() real ext-real Element of REAL
(proj1 | C) .: the carrier of ((TOP-REAL 2) | C) is non empty V146() V147() V148() Element of K6(REAL)
upper_bound ((proj1 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
E-most C is Element of K6( the carrier of (TOP-REAL 2))
SE-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
S-bound C is V11() real ext-real Element of REAL
proj2 | C is non empty V22() V25( the carrier of ((TOP-REAL 2) | C)) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | C),REAL))
lower_bound (proj2 | C) is V11() real ext-real Element of REAL
(proj2 | C) .: the carrier of ((TOP-REAL 2) | C) is non empty V146() V147() V148() Element of K6(REAL)
lower_bound ((proj2 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
|[(E-bound C),(S-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
NE-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
N-bound C is V11() real ext-real Element of REAL
upper_bound (proj2 | C) is V11() real ext-real Element of REAL
upper_bound ((proj2 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
|[(E-bound C),(N-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner C),(NE-corner C)) is Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SE-corner C),(NE-corner C))) /\ C is Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (E-most C) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj2 | (E-most C) is V22() V25( the carrier of ((TOP-REAL 2) | (E-most C))) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL))
the carrier of ((TOP-REAL 2) | (E-most C)) is set
K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL)) is set
upper_bound (proj2 | (E-most C)) is V11() real ext-real Element of REAL
(proj2 | (E-most C)) .: the carrier of ((TOP-REAL 2) | (E-most C)) is V146() V147() V148() Element of K6(REAL)
upper_bound ((proj2 | (E-most C)) .: the carrier of ((TOP-REAL 2) | (E-most C))) is V11() real ext-real Element of REAL
|[(E-bound C),(upper_bound (proj2 | (E-most C)))]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
W-min C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
W-bound C is V11() real ext-real Element of REAL
lower_bound (proj1 | C) is V11() real ext-real Element of REAL
lower_bound ((proj1 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
W-most C is Element of K6( the carrier of (TOP-REAL 2))
SW-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
|[(W-bound C),(S-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
NW-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
|[(W-bound C),(N-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner C),(NW-corner C)) is Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner C),(NW-corner C))) /\ C is Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (W-most C) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj2 | (W-most C) is V22() V25( the carrier of ((TOP-REAL 2) | (W-most C))) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL))
the carrier of ((TOP-REAL 2) | (W-most C)) is set
K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL)) is set
lower_bound (proj2 | (W-most C)) is V11() real ext-real Element of REAL
(proj2 | (W-most C)) .: the carrier of ((TOP-REAL 2) | (W-most C)) is V146() V147() V148() Element of K6(REAL)
lower_bound ((proj2 | (W-most C)) .: the carrier of ((TOP-REAL 2) | (W-most C))) is V11() real ext-real Element of REAL
|[(W-bound C),(lower_bound (proj2 | (W-most C)))]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(C) is non empty Element of K6( the carrier of (TOP-REAL 2))
W-min C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
W-bound C is V11() real ext-real Element of REAL
(TOP-REAL 2) | C is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj1 | C is non empty V22() V25( the carrier of ((TOP-REAL 2) | C)) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | C),REAL))
the carrier of ((TOP-REAL 2) | C) is non empty set
K7( the carrier of ((TOP-REAL 2) | C),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | C),REAL)) is set
lower_bound (proj1 | C) is V11() real ext-real Element of REAL
(proj1 | C) .: the carrier of ((TOP-REAL 2) | C) is non empty V146() V147() V148() Element of K6(REAL)
lower_bound ((proj1 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
W-most C is Element of K6( the carrier of (TOP-REAL 2))
SW-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
S-bound C is V11() real ext-real Element of REAL
proj2 | C is non empty V22() V25( the carrier of ((TOP-REAL 2) | C)) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | C),REAL))
lower_bound (proj2 | C) is V11() real ext-real Element of REAL
(proj2 | C) .: the carrier of ((TOP-REAL 2) | C) is non empty V146() V147() V148() Element of K6(REAL)
lower_bound ((proj2 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
|[(W-bound C),(S-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
NW-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
N-bound C is V11() real ext-real Element of REAL
upper_bound (proj2 | C) is V11() real ext-real Element of REAL
upper_bound ((proj2 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
|[(W-bound C),(N-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner C),(NW-corner C)) is Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner C),(NW-corner C))) /\ C is Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (W-most C) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj2 | (W-most C) is V22() V25( the carrier of ((TOP-REAL 2) | (W-most C))) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL))
the carrier of ((TOP-REAL 2) | (W-most C)) is set
K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL)) is set
lower_bound (proj2 | (W-most C)) is V11() real ext-real Element of REAL
(proj2 | (W-most C)) .: the carrier of ((TOP-REAL 2) | (W-most C)) is V146() V147() V148() Element of K6(REAL)
lower_bound ((proj2 | (W-most C)) .: the carrier of ((TOP-REAL 2) | (W-most C))) is V11() real ext-real Element of REAL
|[(W-bound C),(lower_bound (proj2 | (W-most C)))]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
E-max C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
E-bound C is V11() real ext-real Element of REAL
upper_bound (proj1 | C) is V11() real ext-real Element of REAL
upper_bound ((proj1 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
E-most C is Element of K6( the carrier of (TOP-REAL 2))
SE-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
|[(E-bound C),(S-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
NE-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
|[(E-bound C),(N-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner C),(NE-corner C)) is Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SE-corner C),(NE-corner C))) /\ C is Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (E-most C) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj2 | (E-most C) is V22() V25( the carrier of ((TOP-REAL 2) | (E-most C))) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL))
the carrier of ((TOP-REAL 2) | (E-most C)) is set
K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL)) is set
upper_bound (proj2 | (E-most C)) is V11() real ext-real Element of REAL
(proj2 | (E-most C)) .: the carrier of ((TOP-REAL 2) | (E-most C)) is V146() V147() V148() Element of K6(REAL)
upper_bound ((proj2 | (E-most C)) .: the carrier of ((TOP-REAL 2) | (E-most C))) is V11() real ext-real Element of REAL
|[(E-bound C),(upper_bound (proj2 | (E-most C)))]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
C is non empty closed compact being_simple_closed_curve Element of K6( the carrier of (TOP-REAL 2))
(C) is non empty closed compact Element of K6( the carrier of (TOP-REAL 2))
(C) is non empty closed compact Element of K6( the carrier of (TOP-REAL 2))
(C) \/ (C) is non empty Element of K6( the carrier of (TOP-REAL 2))
C is non empty closed compact being_simple_closed_curve Element of K6( the carrier of (TOP-REAL 2))
(C) is non empty closed compact Element of K6( the carrier of (TOP-REAL 2))
W-bound C is V11() real ext-real Element of REAL
(TOP-REAL 2) | C is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj1 | C is non empty V22() V25( the carrier of ((TOP-REAL 2) | C)) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | C),REAL))
the carrier of ((TOP-REAL 2) | C) is non empty set
K7( the carrier of ((TOP-REAL 2) | C),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | C),REAL)) is set
lower_bound (proj1 | C) is V11() real ext-real Element of REAL
(proj1 | C) .: the carrier of ((TOP-REAL 2) | C) is non empty V146() V147() V148() Element of K6(REAL)
lower_bound ((proj1 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
E-bound C is V11() real ext-real Element of REAL
upper_bound (proj1 | C) is V11() real ext-real Element of REAL
upper_bound ((proj1 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
(W-bound C) + (E-bound C) is V11() real ext-real Element of REAL
((W-bound C) + (E-bound C)) / 2 is V11() real ext-real Element of REAL
((((W-bound C) + (E-bound C)) / 2)) is Element of K6( the carrier of (TOP-REAL 2))
{ b<sub>1</sub> where b<sub>1</sub> is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : b<sub>1</sub> `1 = ((W-bound C) + (E-bound C)) / 2 } is set
W-min C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
W-most C is Element of K6( the carrier of (TOP-REAL 2))
SW-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
S-bound C is V11() real ext-real Element of REAL
proj2 | C is non empty V22() V25( the carrier of ((TOP-REAL 2) | C)) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | C),REAL))
lower_bound (proj2 | C) is V11() real ext-real Element of REAL
(proj2 | C) .: the carrier of ((TOP-REAL 2) | C) is non empty V146() V147() V148() Element of K6(REAL)
lower_bound ((proj2 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
|[(W-bound C),(S-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
NW-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
N-bound C is V11() real ext-real Element of REAL
upper_bound (proj2 | C) is V11() real ext-real Element of REAL
upper_bound ((proj2 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
|[(W-bound C),(N-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner C),(NW-corner C)) is Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner C),(NW-corner C))) /\ C is Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (W-most C) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj2 | (W-most C) is V22() V25( the carrier of ((TOP-REAL 2) | (W-most C))) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL))
the carrier of ((TOP-REAL 2) | (W-most C)) is set
K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL)) is set
lower_bound (proj2 | (W-most C)) is V11() real ext-real Element of REAL
(proj2 | (W-most C)) .: the carrier of ((TOP-REAL 2) | (W-most C)) is V146() V147() V148() Element of K6(REAL)
lower_bound ((proj2 | (W-most C)) .: the carrier of ((TOP-REAL 2) | (W-most C))) is V11() real ext-real Element of REAL
|[(W-bound C),(lower_bound (proj2 | (W-most C)))]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
E-max C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
E-most C is Element of K6( the carrier of (TOP-REAL 2))
SE-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
|[(E-bound C),(S-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
NE-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
|[(E-bound C),(N-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner C),(NE-corner C)) is Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SE-corner C),(NE-corner C))) /\ C is Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (E-most C) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj2 | (E-most C) is V22() V25( the carrier of ((TOP-REAL 2) | (E-most C))) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL))
the carrier of ((TOP-REAL 2) | (E-most C)) is set
K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL)) is set
upper_bound (proj2 | (E-most C)) is V11() real ext-real Element of REAL
(proj2 | (E-most C)) .: the carrier of ((TOP-REAL 2) | (E-most C)) is V146() V147() V148() Element of K6(REAL)
upper_bound ((proj2 | (E-most C)) .: the carrier of ((TOP-REAL 2) | (E-most C))) is V11() real ext-real Element of REAL
|[(E-bound C),(upper_bound (proj2 | (E-most C)))]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
First_Point ((C),(W-min C),(E-max C),((((W-bound C) + (E-bound C)) / 2))) is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(C) is non empty closed compact Element of K6( the carrier of (TOP-REAL 2))
First_Point ((C),(W-min C),(E-max C),((((W-bound C) + (E-bound C)) / 2))) is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
C is non empty closed compact being_simple_closed_curve Element of K6( the carrier of (TOP-REAL 2))
(C) is non empty closed compact Element of K6( the carrier of (TOP-REAL 2))
W-bound C is V11() real ext-real Element of REAL
(TOP-REAL 2) | C is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj1 | C is non empty V22() V25( the carrier of ((TOP-REAL 2) | C)) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | C),REAL))
the carrier of ((TOP-REAL 2) | C) is non empty set
K7( the carrier of ((TOP-REAL 2) | C),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | C),REAL)) is set
lower_bound (proj1 | C) is V11() real ext-real Element of REAL
(proj1 | C) .: the carrier of ((TOP-REAL 2) | C) is non empty V146() V147() V148() Element of K6(REAL)
lower_bound ((proj1 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
E-bound C is V11() real ext-real Element of REAL
upper_bound (proj1 | C) is V11() real ext-real Element of REAL
upper_bound ((proj1 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
(W-bound C) + (E-bound C) is V11() real ext-real Element of REAL
((W-bound C) + (E-bound C)) / 2 is V11() real ext-real Element of REAL
((((W-bound C) + (E-bound C)) / 2)) is Element of K6( the carrier of (TOP-REAL 2))
{ b₁ where b₁ is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : b₁ `1 = ((W-bound C) + (E-bound C)) / 2 } is set
W-min C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
W-most C is Element of K6( the carrier of (TOP-REAL 2))
SW-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
S-bound C is V11() real ext-real Element of REAL
proj2 | C is non empty V22() V25( the carrier of ((TOP-REAL 2) | C)) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | C),REAL))
lower_bound (proj2 | C) is V11() real ext-real Element of REAL
(proj2 | C) .: the carrier of ((TOP-REAL 2) | C) is non empty V146() V147() V148() Element of K6(REAL)
lower_bound ((proj2 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
|[(W-bound C),(S-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
NW-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
N-bound C is V11() real ext-real Element of REAL
upper_bound (proj2 | C) is V11() real ext-real Element of REAL
upper_bound ((proj2 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
|[(W-bound C),(N-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner C),(NW-corner C)) is Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner C),(NW-corner C))) /\ C is Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (W-most C) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj2 | (W-most C) is V22() V25( the carrier of ((TOP-REAL 2) | (W-most C))) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL))
the carrier of ((TOP-REAL 2) | (W-most C)) is set
K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL)) is set
lower_bound (proj2 | (W-most C)) is V11() real ext-real Element of REAL
(proj2 | (W-most C)) .: the carrier of ((TOP-REAL 2) | (W-most C)) is V146() V147() V148() Element of K6(REAL)
lower_bound ((proj2 | (W-most C)) .: the carrier of ((TOP-REAL 2) | (W-most C))) is V11() real ext-real Element of REAL
|[(W-bound C),(lower_bound (proj2 | (W-most C)))]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(W-min C) `1 is V11() real ext-real Element of REAL
E-max C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
E-most C is Element of K6( the carrier of (TOP-REAL 2))
SE-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
|[(E-bound C),(S-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
NE-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
|[(E-bound C),(N-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner C),(NE-corner C)) is Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SE-corner C),(NE-corner C))) /\ C is Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (E-most C) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj2 | (E-most C) is V22() V25( the carrier of ((TOP-REAL 2) | (E-most C))) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL))
the carrier of ((TOP-REAL 2) | (E-most C)) is set
K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL)) is set
upper_bound (proj2 | (E-most C)) is V11() real ext-real Element of REAL
(proj2 | (E-most C)) .: the carrier of ((TOP-REAL 2) | (E-most C)) is V146() V147() V148() Element of K6(REAL)
upper_bound ((proj2 | (E-most C)) .: the carrier of ((TOP-REAL 2) | (E-most C))) is V11() real ext-real Element of REAL
|[(E-bound C),(upper_bound (proj2 | (E-most C)))]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(E-max C) `1 is V11() real ext-real Element of REAL
C is non empty closed compact being_simple_closed_curve Element of K6( the carrier of (TOP-REAL 2))
(C) is non empty closed compact Element of K6( the carrier of (TOP-REAL 2))
W-bound C is V11() real ext-real Element of REAL
(TOP-REAL 2) | C is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj1 | C is non empty V22() V25( the carrier of ((TOP-REAL 2) | C)) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | C),REAL))
the carrier of ((TOP-REAL 2) | C) is non empty set
K7( the carrier of ((TOP-REAL 2) | C),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | C),REAL)) is set
lower_bound (proj1 | C) is V11() real ext-real Element of REAL
(proj1 | C) .: the carrier of ((TOP-REAL 2) | C) is non empty V146() V147() V148() Element of K6(REAL)
lower_bound ((proj1 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
E-bound C is V11() real ext-real Element of REAL
upper_bound (proj1 | C) is V11() real ext-real Element of REAL
upper_bound ((proj1 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
(W-bound C) + (E-bound C) is V11() real ext-real Element of REAL
((W-bound C) + (E-bound C)) / 2 is V11() real ext-real Element of REAL
((((W-bound C) + (E-bound C)) / 2)) is Element of K6( the carrier of (TOP-REAL 2))
{ b<sub>1</sub> where b<sub>1</sub> is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : b<sub>1</sub> `1 = ((W-bound C) + (E-bound C)) / 2 } is set
W-min C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
W-most C is Element of K6( the carrier of (TOP-REAL 2))
SW-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
S-bound C is V11() real ext-real Element of REAL
proj2 | C is non empty V22() V25( the carrier of ((TOP-REAL 2) | C)) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | C),REAL))
lower_bound (proj2 | C) is V11() real ext-real Element of REAL
(proj2 | C) .: the carrier of ((TOP-REAL 2) | C) is non empty V146() V147() V148() Element of K6(REAL)
lower_bound ((proj2 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
|[(W-bound C),(S-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
NW-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
N-bound C is V11() real ext-real Element of REAL
upper_bound (proj2 | C) is V11() real ext-real Element of REAL
upper_bound ((proj2 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
|[(W-bound C),(N-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner C),(NW-corner C)) is Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner C),(NW-corner C))) /\ C is Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (W-most C) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj2 | (W-most C) is V22() V25( the carrier of ((TOP-REAL 2) | (W-most C))) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL))
the carrier of ((TOP-REAL 2) | (W-most C)) is set
K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL)) is set
lower_bound (proj2 | (W-most C)) is V11() real ext-real Element of REAL
(proj2 | (W-most C)) .: the carrier of ((TOP-REAL 2) | (W-most C)) is V146() V147() V148() Element of K6(REAL)
lower_bound ((proj2 | (W-most C)) .: the carrier of ((TOP-REAL 2) | (W-most C))) is V11() real ext-real Element of REAL
|[(W-bound C),(lower_bound (proj2 | (W-most C)))]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(W-min C) `1 is V11() real ext-real Element of REAL
E-max C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
E-most C is Element of K6( the carrier of (TOP-REAL 2))
SE-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
|[(E-bound C),(S-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
NE-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
|[(E-bound C),(N-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner C),(NE-corner C)) is Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SE-corner C),(NE-corner C))) /\ C is Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (E-most C) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj2 | (E-most C) is V22() V25( the carrier of ((TOP-REAL 2) | (E-most C))) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL))
the carrier of ((TOP-REAL 2) | (E-most C)) is set
K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL)) is set
upper_bound (proj2 | (E-most C)) is V11() real ext-real Element of REAL
(proj2 | (E-most C)) .: the carrier of ((TOP-REAL 2) | (E-most C)) is V146() V147() V148() Element of K6(REAL)
upper_bound ((proj2 | (E-most C)) .: the carrier of ((TOP-REAL 2) | (E-most C))) is V11() real ext-real Element of REAL
|[(E-bound C),(upper_bound (proj2 | (E-most C)))]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(E-max C) `1 is V11() real ext-real Element of REAL
C is non empty closed compact being_simple_closed_curve Element of K6( the carrier of (TOP-REAL 2))
(C) is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(C) is non empty closed compact Element of K6( the carrier of (TOP-REAL 2))
W-bound C is V11() real ext-real Element of REAL
(TOP-REAL 2) | C is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj1 | C is non empty V22() V25( the carrier of ((TOP-REAL 2) | C)) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | C),REAL))
the carrier of ((TOP-REAL 2) | C) is non empty set
K7( the carrier of ((TOP-REAL 2) | C),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | C),REAL)) is set
lower_bound (proj1 | C) is V11() real ext-real Element of REAL
(proj1 | C) .: the carrier of ((TOP-REAL 2) | C) is non empty V146() V147() V148() Element of K6(REAL)
lower_bound ((proj1 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
E-bound C is V11() real ext-real Element of REAL
upper_bound (proj1 | C) is V11() real ext-real Element of REAL
upper_bound ((proj1 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
(W-bound C) + (E-bound C) is V11() real ext-real Element of REAL
((W-bound C) + (E-bound C)) / 2 is V11() real ext-real Element of REAL
((((W-bound C) + (E-bound C)) / 2)) is Element of K6( the carrier of (TOP-REAL 2))
{ b₁ where b₁ is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : b₁ `1 = ((W-bound C) + (E-bound C)) / 2 } is set
W-min C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
W-most C is Element of K6( the carrier of (TOP-REAL 2))
SW-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
S-bound C is V11() real ext-real Element of REAL
proj2 | C is non empty V22() V25( the carrier of ((TOP-REAL 2) | C)) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | C),REAL))
lower_bound (proj2 | C) is V11() real ext-real Element of REAL
(proj2 | C) .: the carrier of ((TOP-REAL 2) | C) is non empty V146() V147() V148() Element of K6(REAL)
lower_bound ((proj2 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
|[(W-bound C),(S-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
NW-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
N-bound C is V11() real ext-real Element of REAL
upper_bound (proj2 | C) is V11() real ext-real Element of REAL
upper_bound ((proj2 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
|[(W-bound C),(N-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner C),(NW-corner C)) is Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner C),(NW-corner C))) /\ C is Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (W-most C) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj2 | (W-most C) is V22() V25( the carrier of ((TOP-REAL 2) | (W-most C))) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL))
the carrier of ((TOP-REAL 2) | (W-most C)) is set
K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL)) is set
lower_bound (proj2 | (W-most C)) is V11() real ext-real Element of REAL
(proj2 | (W-most C)) .: the carrier of ((TOP-REAL 2) | (W-most C)) is V146() V147() V148() Element of K6(REAL)
lower_bound ((proj2 | (W-most C)) .: the carrier of ((TOP-REAL 2) | (W-most C))) is V11() real ext-real Element of REAL
|[(W-bound C),(lower_bound (proj2 | (W-most C)))]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
E-max C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
E-most C is Element of K6( the carrier of (TOP-REAL 2))
SE-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
|[(E-bound C),(S-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
NE-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
|[(E-bound C),(N-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner C),(NE-corner C)) is Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SE-corner C),(NE-corner C))) /\ C is Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (E-most C) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj2 | (E-most C) is V22() V25( the carrier of ((TOP-REAL 2) | (E-most C))) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL))
the carrier of ((TOP-REAL 2) | (E-most C)) is set
K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL)) is set
upper_bound (proj2 | (E-most C)) is V11() real ext-real Element of REAL
(proj2 | (E-most C)) .: the carrier of ((TOP-REAL 2) | (E-most C)) is V146() V147() V148() Element of K6(REAL)
upper_bound ((proj2 | (E-most C)) .: the carrier of ((TOP-REAL 2) | (E-most C))) is V11() real ext-real Element of REAL
|[(E-bound C),(upper_bound (proj2 | (E-most C)))]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
First_Point ((C),(W-min C),(E-max C),((((W-bound C) + (E-bound C)) / 2))) is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(C) `1 is V11() real ext-real Element of REAL
(C) /\ ((((W-bound C) + (E-bound C)) / 2)) is Element of K6( the carrier of (TOP-REAL 2))
C is non empty closed compact being_simple_closed_curve Element of K6( the carrier of (TOP-REAL 2))
(C) is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(C) is non empty closed compact Element of K6( the carrier of (TOP-REAL 2))
W-bound C is V11() real ext-real Element of REAL
(TOP-REAL 2) | C is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj1 | C is non empty V22() V25( the carrier of ((TOP-REAL 2) | C)) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | C),REAL))
the carrier of ((TOP-REAL 2) | C) is non empty set
K7( the carrier of ((TOP-REAL 2) | C),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | C),REAL)) is set
lower_bound (proj1 | C) is V11() real ext-real Element of REAL
(proj1 | C) .: the carrier of ((TOP-REAL 2) | C) is non empty V146() V147() V148() Element of K6(REAL)
lower_bound ((proj1 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
E-bound C is V11() real ext-real Element of REAL
upper_bound (proj1 | C) is V11() real ext-real Element of REAL
upper_bound ((proj1 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
(W-bound C) + (E-bound C) is V11() real ext-real Element of REAL
((W-bound C) + (E-bound C)) / 2 is V11() real ext-real Element of REAL
((((W-bound C) + (E-bound C)) / 2)) is Element of K6( the carrier of (TOP-REAL 2))
{ b₁ where b₁ is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : b₁ `1 = ((W-bound C) + (E-bound C)) / 2 } is set
W-min C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
W-most C is Element of K6( the carrier of (TOP-REAL 2))
SW-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
S-bound C is V11() real ext-real Element of REAL
proj2 | C is non empty V22() V25( the carrier of ((TOP-REAL 2) | C)) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | C),REAL))
lower_bound (proj2 | C) is V11() real ext-real Element of REAL
(proj2 | C) .: the carrier of ((TOP-REAL 2) | C) is non empty V146() V147() V148() Element of K6(REAL)
lower_bound ((proj2 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
|[(W-bound C),(S-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
NW-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
N-bound C is V11() real ext-real Element of REAL
upper_bound (proj2 | C) is V11() real ext-real Element of REAL
upper_bound ((proj2 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
|[(W-bound C),(N-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner C),(NW-corner C)) is Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner C),(NW-corner C))) /\ C is Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (W-most C) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj2 | (W-most C) is V22() V25( the carrier of ((TOP-REAL 2) | (W-most C))) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL))
the carrier of ((TOP-REAL 2) | (W-most C)) is set
K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL)) is set
lower_bound (proj2 | (W-most C)) is V11() real ext-real Element of REAL
(proj2 | (W-most C)) .: the carrier of ((TOP-REAL 2) | (W-most C)) is V146() V147() V148() Element of K6(REAL)
lower_bound ((proj2 | (W-most C)) .: the carrier of ((TOP-REAL 2) | (W-most C))) is V11() real ext-real Element of REAL
|[(W-bound C),(lower_bound (proj2 | (W-most C)))]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
E-max C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
E-most C is Element of K6( the carrier of (TOP-REAL 2))
SE-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
|[(E-bound C),(S-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
NE-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
|[(E-bound C),(N-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner C),(NE-corner C)) is Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SE-corner C),(NE-corner C))) /\ C is Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (E-most C) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj2 | (E-most C) is V22() V25( the carrier of ((TOP-REAL 2) | (E-most C))) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL))
the carrier of ((TOP-REAL 2) | (E-most C)) is set
K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL)) is set
upper_bound (proj2 | (E-most C)) is V11() real ext-real Element of REAL
(proj2 | (E-most C)) .: the carrier of ((TOP-REAL 2) | (E-most C)) is V146() V147() V148() Element of K6(REAL)
upper_bound ((proj2 | (E-most C)) .: the carrier of ((TOP-REAL 2) | (E-most C))) is V11() real ext-real Element of REAL
|[(E-bound C),(upper_bound (proj2 | (E-most C)))]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
First_Point ((C),(W-min C),(E-max C),((((W-bound C) + (E-bound C)) / 2))) is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(C) `1 is V11() real ext-real Element of REAL
(C) /\ ((((W-bound C) + (E-bound C)) / 2)) is Element of K6( the carrier of (TOP-REAL 2))
C is non empty closed compact being_simple_closed_curve Element of K6( the carrier of (TOP-REAL 2))
(C) is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(C) is non empty closed compact Element of K6( the carrier of (TOP-REAL 2))
W-bound C is V11() real ext-real Element of REAL
(TOP-REAL 2) | C is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj1 | C is non empty V22() V25( the carrier of ((TOP-REAL 2) | C)) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | C),REAL))
the carrier of ((TOP-REAL 2) | C) is non empty set
K7( the carrier of ((TOP-REAL 2) | C),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | C),REAL)) is set
lower_bound (proj1 | C) is V11() real ext-real Element of REAL
(proj1 | C) .: the carrier of ((TOP-REAL 2) | C) is non empty V146() V147() V148() Element of K6(REAL)
lower_bound ((proj1 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
E-bound C is V11() real ext-real Element of REAL
upper_bound (proj1 | C) is V11() real ext-real Element of REAL
upper_bound ((proj1 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
(W-bound C) + (E-bound C) is V11() real ext-real Element of REAL
((W-bound C) + (E-bound C)) / 2 is V11() real ext-real Element of REAL
((((W-bound C) + (E-bound C)) / 2)) is Element of K6( the carrier of (TOP-REAL 2))
{ b₁ where b₁ is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : b₁ `1 = ((W-bound C) + (E-bound C)) / 2 } is set
W-min C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
W-most C is Element of K6( the carrier of (TOP-REAL 2))
SW-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
S-bound C is V11() real ext-real Element of REAL
proj2 | C is non empty V22() V25( the carrier of ((TOP-REAL 2) | C)) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | C),REAL))
lower_bound (proj2 | C) is V11() real ext-real Element of REAL
(proj2 | C) .: the carrier of ((TOP-REAL 2) | C) is non empty V146() V147() V148() Element of K6(REAL)
lower_bound ((proj2 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
|[(W-bound C),(S-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
NW-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
N-bound C is V11() real ext-real Element of REAL
upper_bound (proj2 | C) is V11() real ext-real Element of REAL
upper_bound ((proj2 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
|[(W-bound C),(N-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner C),(NW-corner C)) is Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner C),(NW-corner C))) /\ C is Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (W-most C) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj2 | (W-most C) is V22() V25( the carrier of ((TOP-REAL 2) | (W-most C))) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL))
the carrier of ((TOP-REAL 2) | (W-most C)) is set
K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL)) is set
lower_bound (proj2 | (W-most C)) is V11() real ext-real Element of REAL
(proj2 | (W-most C)) .: the carrier of ((TOP-REAL 2) | (W-most C)) is V146() V147() V148() Element of K6(REAL)
lower_bound ((proj2 | (W-most C)) .: the carrier of ((TOP-REAL 2) | (W-most C))) is V11() real ext-real Element of REAL
|[(W-bound C),(lower_bound (proj2 | (W-most C)))]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
E-max C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
E-most C is Element of K6( the carrier of (TOP-REAL 2))
SE-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
|[(E-bound C),(S-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
NE-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
|[(E-bound C),(N-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner C),(NE-corner C)) is Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SE-corner C),(NE-corner C))) /\ C is Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (E-most C) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj2 | (E-most C) is V22() V25( the carrier of ((TOP-REAL 2) | (E-most C))) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL))
the carrier of ((TOP-REAL 2) | (E-most C)) is set
K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL)) is set
upper_bound (proj2 | (E-most C)) is V11() real ext-real Element of REAL
(proj2 | (E-most C)) .: the carrier of ((TOP-REAL 2) | (E-most C)) is V146() V147() V148() Element of K6(REAL)
upper_bound ((proj2 | (E-most C)) .: the carrier of ((TOP-REAL 2) | (E-most C))) is V11() real ext-real Element of REAL
|[(E-bound C),(upper_bound (proj2 | (E-most C)))]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
First_Point ((C),(W-min C),(E-max C),((((W-bound C) + (E-bound C)) / 2))) is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(C) /\ ((((W-bound C) + (E-bound C)) / 2)) is Element of K6( the carrier of (TOP-REAL 2))
((((W-bound C) + (E-bound C)) / 2)) /\ (C) is Element of K6( the carrier of (TOP-REAL 2))
C is non empty closed compact being_simple_closed_curve Element of K6( the carrier of (TOP-REAL 2))
(C) is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(C) is non empty closed compact Element of K6( the carrier of (TOP-REAL 2))
W-bound C is V11() real ext-real Element of REAL
(TOP-REAL 2) | C is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj1 | C is non empty V22() V25( the carrier of ((TOP-REAL 2) | C)) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | C),REAL))
the carrier of ((TOP-REAL 2) | C) is non empty set
K7( the carrier of ((TOP-REAL 2) | C),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | C),REAL)) is set
lower_bound (proj1 | C) is V11() real ext-real Element of REAL
(proj1 | C) .: the carrier of ((TOP-REAL 2) | C) is non empty V146() V147() V148() Element of K6(REAL)
lower_bound ((proj1 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
E-bound C is V11() real ext-real Element of REAL
upper_bound (proj1 | C) is V11() real ext-real Element of REAL
upper_bound ((proj1 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
(W-bound C) + (E-bound C) is V11() real ext-real Element of REAL
((W-bound C) + (E-bound C)) / 2 is V11() real ext-real Element of REAL
((((W-bound C) + (E-bound C)) / 2)) is Element of K6( the carrier of (TOP-REAL 2))
{ b<sub>1</sub> where b<sub>1</sub> is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : b<sub>1</sub> `1 = ((W-bound C) + (E-bound C)) / 2 } is set
W-min C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
W-most C is Element of K6( the carrier of (TOP-REAL 2))
SW-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
S-bound C is V11() real ext-real Element of REAL
proj2 | C is non empty V22() V25( the carrier of ((TOP-REAL 2) | C)) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | C),REAL))
lower_bound (proj2 | C) is V11() real ext-real Element of REAL
(proj2 | C) .: the carrier of ((TOP-REAL 2) | C) is non empty V146() V147() V148() Element of K6(REAL)
lower_bound ((proj2 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
|[(W-bound C),(S-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
NW-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
N-bound C is V11() real ext-real Element of REAL
upper_bound (proj2 | C) is V11() real ext-real Element of REAL
upper_bound ((proj2 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
|[(W-bound C),(N-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner C),(NW-corner C)) is Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner C),(NW-corner C))) /\ C is Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (W-most C) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj2 | (W-most C) is V22() V25( the carrier of ((TOP-REAL 2) | (W-most C))) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL))
the carrier of ((TOP-REAL 2) | (W-most C)) is set
K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL)) is set
lower_bound (proj2 | (W-most C)) is V11() real ext-real Element of REAL
(proj2 | (W-most C)) .: the carrier of ((TOP-REAL 2) | (W-most C)) is V146() V147() V148() Element of K6(REAL)
lower_bound ((proj2 | (W-most C)) .: the carrier of ((TOP-REAL 2) | (W-most C))) is V11() real ext-real Element of REAL
|[(W-bound C),(lower_bound (proj2 | (W-most C)))]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
E-max C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
E-most C is Element of K6( the carrier of (TOP-REAL 2))
SE-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
|[(E-bound C),(S-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
NE-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
|[(E-bound C),(N-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner C),(NE-corner C)) is Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SE-corner C),(NE-corner C))) /\ C is Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (E-most C) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj2 | (E-most C) is V22() V25( the carrier of ((TOP-REAL 2) | (E-most C))) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL))
the carrier of ((TOP-REAL 2) | (E-most C)) is set
K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL)) is set
upper_bound (proj2 | (E-most C)) is V11() real ext-real Element of REAL
(proj2 | (E-most C)) .: the carrier of ((TOP-REAL 2) | (E-most C)) is V146() V147() V148() Element of K6(REAL)
upper_bound ((proj2 | (E-most C)) .: the carrier of ((TOP-REAL 2) | (E-most C))) is V11() real ext-real Element of REAL
|[(E-bound C),(upper_bound (proj2 | (E-most C)))]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
First_Point ((C),(W-min C),(E-max C),((((W-bound C) + (E-bound C)) / 2))) is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(C) /\ ((((W-bound C) + (E-bound C)) / 2)) is Element of K6( the carrier of (TOP-REAL 2))
Last_Point ((C),(E-max C),(W-min C),((((W-bound C) + (E-bound C)) / 2))) is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
((((W-bound C) + (E-bound C)) / 2)) /\ (C) is Element of K6( the carrier of (TOP-REAL 2))
C is non empty closed compact being_simple_closed_curve Element of K6( the carrier of (TOP-REAL 2))
(C) is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(C) is non empty closed compact Element of K6( the carrier of (TOP-REAL 2))
W-bound C is V11() real ext-real Element of REAL
(TOP-REAL 2) | C is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj1 | C is non empty V22() V25( the carrier of ((TOP-REAL 2) | C)) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | C),REAL))
the carrier of ((TOP-REAL 2) | C) is non empty set
K7( the carrier of ((TOP-REAL 2) | C),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | C),REAL)) is set
lower_bound (proj1 | C) is V11() real ext-real Element of REAL
(proj1 | C) .: the carrier of ((TOP-REAL 2) | C) is non empty V146() V147() V148() Element of K6(REAL)
lower_bound ((proj1 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
E-bound C is V11() real ext-real Element of REAL
upper_bound (proj1 | C) is V11() real ext-real Element of REAL
upper_bound ((proj1 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
(W-bound C) + (E-bound C) is V11() real ext-real Element of REAL
((W-bound C) + (E-bound C)) / 2 is V11() real ext-real Element of REAL
((((W-bound C) + (E-bound C)) / 2)) is Element of K6( the carrier of (TOP-REAL 2))
{ b₁ where b₁ is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : b₁ `1 = ((W-bound C) + (E-bound C)) / 2 } is set
W-min C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
W-most C is Element of K6( the carrier of (TOP-REAL 2))
SW-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
S-bound C is V11() real ext-real Element of REAL
proj2 | C is non empty V22() V25( the carrier of ((TOP-REAL 2) | C)) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | C),REAL))
lower_bound (proj2 | C) is V11() real ext-real Element of REAL
(proj2 | C) .: the carrier of ((TOP-REAL 2) | C) is non empty V146() V147() V148() Element of K6(REAL)
lower_bound ((proj2 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
|[(W-bound C),(S-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
NW-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
N-bound C is V11() real ext-real Element of REAL
upper_bound (proj2 | C) is V11() real ext-real Element of REAL
upper_bound ((proj2 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
|[(W-bound C),(N-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner C),(NW-corner C)) is Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner C),(NW-corner C))) /\ C is Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (W-most C) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj2 | (W-most C) is V22() V25( the carrier of ((TOP-REAL 2) | (W-most C))) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL))
the carrier of ((TOP-REAL 2) | (W-most C)) is set
K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL)) is set
lower_bound (proj2 | (W-most C)) is V11() real ext-real Element of REAL
(proj2 | (W-most C)) .: the carrier of ((TOP-REAL 2) | (W-most C)) is V146() V147() V148() Element of K6(REAL)
lower_bound ((proj2 | (W-most C)) .: the carrier of ((TOP-REAL 2) | (W-most C))) is V11() real ext-real Element of REAL
|[(W-bound C),(lower_bound (proj2 | (W-most C)))]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
E-max C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
E-most C is Element of K6( the carrier of (TOP-REAL 2))
SE-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
|[(E-bound C),(S-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
NE-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
|[(E-bound C),(N-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner C),(NE-corner C)) is Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SE-corner C),(NE-corner C))) /\ C is Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (E-most C) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj2 | (E-most C) is V22() V25( the carrier of ((TOP-REAL 2) | (E-most C))) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL))
the carrier of ((TOP-REAL 2) | (E-most C)) is set
K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL)) is set
upper_bound (proj2 | (E-most C)) is V11() real ext-real Element of REAL
(proj2 | (E-most C)) .: the carrier of ((TOP-REAL 2) | (E-most C)) is V146() V147() V148() Element of K6(REAL)
upper_bound ((proj2 | (E-most C)) .: the carrier of ((TOP-REAL 2) | (E-most C))) is V11() real ext-real Element of REAL
|[(E-bound C),(upper_bound (proj2 | (E-most C)))]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
First_Point ((C),(W-min C),(E-max C),((((W-bound C) + (E-bound C)) / 2))) is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
C is non empty closed compact being_simple_closed_curve Element of K6( the carrier of (TOP-REAL 2))
W-bound C is V11() real ext-real Element of REAL
(TOP-REAL 2) | C is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj1 | C is non empty V22() V25( the carrier of ((TOP-REAL 2) | C)) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | C),REAL))
the carrier of ((TOP-REAL 2) | C) is non empty set
K7( the carrier of ((TOP-REAL 2) | C),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | C),REAL)) is set
lower_bound (proj1 | C) is V11() real ext-real Element of REAL
(proj1 | C) .: the carrier of ((TOP-REAL 2) | C) is non empty V146() V147() V148() Element of K6(REAL)
lower_bound ((proj1 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
E-bound C is V11() real ext-real Element of REAL
upper_bound (proj1 | C) is V11() real ext-real Element of REAL
upper_bound ((proj1 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
S-bound C is V11() real ext-real Element of REAL
proj2 | C is non empty V22() V25( the carrier of ((TOP-REAL 2) | C)) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | C),REAL))
lower_bound (proj2 | C) is V11() real ext-real Element of REAL
(proj2 | C) .: the carrier of ((TOP-REAL 2) | C) is non empty V146() V147() V148() Element of K6(REAL)
lower_bound ((proj2 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
N-bound C is V11() real ext-real Element of REAL
upper_bound (proj2 | C) is V11() real ext-real Element of REAL
upper_bound ((proj2 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
(C) is non empty closed compact Element of K6( the carrier of (TOP-REAL 2))
r is V11() real ext-real set
|[r,(S-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
|[r,(N-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
LSeg (|[r,(S-bound C)]|,|[r,(N-bound C)]|) is Element of K6( the carrier of (TOP-REAL 2))
W-min C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
W-most C is Element of K6( the carrier of (TOP-REAL 2))
SW-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
|[(W-bound C),(S-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
NW-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
|[(W-bound C),(N-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner C),(NW-corner C)) is Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner C),(NW-corner C))) /\ C is Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (W-most C) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj2 | (W-most C) is V22() V25( the carrier of ((TOP-REAL 2) | (W-most C))) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL))
the carrier of ((TOP-REAL 2) | (W-most C)) is set
K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL)) is set
lower_bound (proj2 | (W-most C)) is V11() real ext-real Element of REAL
(proj2 | (W-most C)) .: the carrier of ((TOP-REAL 2) | (W-most C)) is V146() V147() V148() Element of K6(REAL)
lower_bound ((proj2 | (W-most C)) .: the carrier of ((TOP-REAL 2) | (W-most C))) is V11() real ext-real Element of REAL
|[(W-bound C),(lower_bound (proj2 | (W-most C)))]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(W-min C) `1 is V11() real ext-real Element of REAL
E-max C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
E-most C is Element of K6( the carrier of (TOP-REAL 2))
SE-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
|[(E-bound C),(S-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
NE-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
|[(E-bound C),(N-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner C),(NE-corner C)) is Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SE-corner C),(NE-corner C))) /\ C is Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (E-most C) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj2 | (E-most C) is V22() V25( the carrier of ((TOP-REAL 2) | (E-most C))) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL))
the carrier of ((TOP-REAL 2) | (E-most C)) is set
K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL)) is set
upper_bound (proj2 | (E-most C)) is V11() real ext-real Element of REAL
(proj2 | (E-most C)) .: the carrier of ((TOP-REAL 2) | (E-most C)) is V146() V147() V148() Element of K6(REAL)
upper_bound ((proj2 | (E-most C)) .: the carrier of ((TOP-REAL 2) | (E-most C))) is V11() real ext-real Element of REAL
|[(E-bound C),(upper_bound (proj2 | (E-most C)))]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(E-max C) `1 is V11() real ext-real Element of REAL
(r) is Element of K6( the carrier of (TOP-REAL 2))
{ b<sub>1</sub> where b<sub>1</sub> is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : b<sub>1</sub> `1 = r } is set
(C) /\ (r) is Element of K6( the carrier of (TOP-REAL 2))
x is set
fs is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
fs `2 is V11() real ext-real Element of REAL
|[r,(S-bound C)]| `1 is V11() real ext-real Element of REAL
fs `1 is V11() real ext-real Element of REAL
|[r,(N-bound C)]| `1 is V11() real ext-real Element of REAL
|[r,(S-bound C)]| `2 is V11() real ext-real Element of REAL
|[r,(N-bound C)]| `2 is V11() real ext-real Element of REAL
C is non empty closed compact being_simple_closed_curve Element of K6( the carrier of (TOP-REAL 2))
W-bound C is V11() real ext-real Element of REAL
(TOP-REAL 2) | C is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj1 | C is non empty V22() V25( the carrier of ((TOP-REAL 2) | C)) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | C),REAL))
the carrier of ((TOP-REAL 2) | C) is non empty set
K7( the carrier of ((TOP-REAL 2) | C),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | C),REAL)) is set
lower_bound (proj1 | C) is V11() real ext-real Element of REAL
(proj1 | C) .: the carrier of ((TOP-REAL 2) | C) is non empty V146() V147() V148() Element of K6(REAL)
lower_bound ((proj1 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
E-bound C is V11() real ext-real Element of REAL
upper_bound (proj1 | C) is V11() real ext-real Element of REAL
upper_bound ((proj1 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
S-bound C is V11() real ext-real Element of REAL
proj2 | C is non empty V22() V25( the carrier of ((TOP-REAL 2) | C)) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | C),REAL))
lower_bound (proj2 | C) is V11() real ext-real Element of REAL
(proj2 | C) .: the carrier of ((TOP-REAL 2) | C) is non empty V146() V147() V148() Element of K6(REAL)
lower_bound ((proj2 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
N-bound C is V11() real ext-real Element of REAL
upper_bound (proj2 | C) is V11() real ext-real Element of REAL
upper_bound ((proj2 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
(C) is non empty closed compact Element of K6( the carrier of (TOP-REAL 2))
r is V11() real ext-real set
|[r,(S-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
|[r,(N-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
LSeg (|[r,(S-bound C)]|,|[r,(N-bound C)]|) is Element of K6( the carrier of (TOP-REAL 2))
W-min C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
W-most C is Element of K6( the carrier of (TOP-REAL 2))
SW-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
|[(W-bound C),(S-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
NW-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
|[(W-bound C),(N-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner C),(NW-corner C)) is Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner C),(NW-corner C))) /\ C is Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (W-most C) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj2 | (W-most C) is V22() V25( the carrier of ((TOP-REAL 2) | (W-most C))) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL))
the carrier of ((TOP-REAL 2) | (W-most C)) is set
K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL)) is set
lower_bound (proj2 | (W-most C)) is V11() real ext-real Element of REAL
(proj2 | (W-most C)) .: the carrier of ((TOP-REAL 2) | (W-most C)) is V146() V147() V148() Element of K6(REAL)
lower_bound ((proj2 | (W-most C)) .: the carrier of ((TOP-REAL 2) | (W-most C))) is V11() real ext-real Element of REAL
|[(W-bound C),(lower_bound (proj2 | (W-most C)))]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(W-min C) `1 is V11() real ext-real Element of REAL
E-max C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
E-most C is Element of K6( the carrier of (TOP-REAL 2))
SE-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
|[(E-bound C),(S-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
NE-corner C is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
|[(E-bound C),(N-bound C)]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner C),(NE-corner C)) is Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SE-corner C),(NE-corner C))) /\ C is Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (E-most C) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj2 | (E-most C) is V22() V25( the carrier of ((TOP-REAL 2) | (E-most C))) V26( REAL ) Function-like total quasi_total Element of K6(K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL))
the carrier of ((TOP-REAL 2) | (E-most C)) is set
K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL)) is set
upper_bound (proj2 | (E-most C)) is V11() real ext-real Element of REAL
(proj2 | (E-most C)) .: the carrier of ((TOP-REAL 2) | (E-most C)) is V146() V147() V148() Element of K6(REAL)
upper_bound ((proj2 | (E-most C)) .: the carrier of ((TOP-REAL 2) | (E-most C))) is V11() real ext-real Element of REAL
|[(E-bound C),(upper_bound (proj2 | (E-most C)))]| is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
(E-max C) `1 is V11() real ext-real Element of REAL
(r) is Element of K6( the carrier of (TOP-REAL 2))
{ b₁ where b₁ is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2) : b₁ `1 = r } is set
(C) /\ (r) is Element of K6( the carrier of (TOP-REAL 2))
x is set
fs is V22() V26( REAL ) Function-like V43(2) FinSequence-like V138() Element of the carrier of (TOP-REAL 2)
fs `2 is V11() real ext-real Element of REAL
|[r,(S-bound C)]| `1 is V11() real ext-real Element of REAL
fs `1 is V11() real ext-real Element of REAL
|[r,(N-bound C)]| `1 is V11() real ext-real Element of REAL
|[r,(S-bound C)]| `2 is V11() real ext-real Element of REAL
|[r,(N-bound C)]| `2 is V11() real ext-real Element of REAL