:: SPRECT_2 semantic presentation

REAL is non empty V26() V137() V138() V139() V143() set
NAT is V137() V138() V139() V140() V141() V142() V143() Element of bool REAL
bool REAL is set
omega is V137() V138() V139() V140() V141() V142() V143() set
bool omega is set
bool NAT is set
COMPLEX is non empty V26() V137() V143() set
1 is non empty natural V11() real V37() ext-real positive non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
INT is non empty V26() V137() V138() V139() V140() V141() V143() set
[:1,1:] is V17( RAT ) V17( INT ) V127() V128() V129() V130() set
RAT is non empty V26() V137() V138() V139() V140() V143() set
bool [:1,1:] is set
[:[:1,1:],1:] is V17( RAT ) V17( INT ) V127() V128() V129() V130() set
bool [:[:1,1:],1:] is set
[:[:1,1:],REAL:] is V127() V128() V129() set
bool [:[:1,1:],REAL:] is set
[:REAL,REAL:] is V127() V128() V129() set
[:[:REAL,REAL:],REAL:] is V127() V128() V129() set
bool [:[:REAL,REAL:],REAL:] is set
2 is non empty natural V11() real V37() ext-real positive non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
[:2,2:] is V17( RAT ) V17( INT ) V127() V128() V129() V130() set
[:[:2,2:],REAL:] is V127() V128() V129() set
bool [:[:2,2:],REAL:] is set
bool [:REAL,REAL:] is set
TOP-REAL 2 is non empty TopSpace-like V103() V149() V150() V151() V152() V153() V154() V155() strict RLTopStruct
the carrier of (TOP-REAL 2) is non empty set
K328( the carrier of (TOP-REAL 2)) is non empty functional FinSequence-membered M11( the carrier of (TOP-REAL 2))
bool the carrier of (TOP-REAL 2) is set
[: the carrier of (TOP-REAL 2),REAL:] is V127() V128() V129() set
bool [: the carrier of (TOP-REAL 2),REAL:] is set
[:COMPLEX,COMPLEX:] is V127() set
bool [:COMPLEX,COMPLEX:] is set
[:COMPLEX,REAL:] is V127() V128() V129() set
bool [:COMPLEX,REAL:] is set
{} is empty trivial Function-like functional FinSequence-membered V137() V138() V139() V140() V141() V142() V143() set
the empty trivial Function-like functional FinSequence-membered V137() V138() V139() V140() V141() V142() V143() set is empty trivial Function-like functional FinSequence-membered V137() V138() V139() V140() V141() V142() V143() set
3 is non empty natural V11() real V37() ext-real positive non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
proj1 is V13() V16( the carrier of (TOP-REAL 2)) V17( REAL ) Function-like V40( the carrier of (TOP-REAL 2), REAL ) V127() V128() V129() Element of bool [: the carrier of (TOP-REAL 2),REAL:]
proj2 is V13() V16( the carrier of (TOP-REAL 2)) V17( REAL ) Function-like V40( the carrier of (TOP-REAL 2), REAL ) V127() V128() V129() Element of bool [: the carrier of (TOP-REAL 2),REAL:]
0 is empty trivial natural V11() real Function-like functional FinSequence-membered V37() ext-real non positive non negative V90() V137() V138() V139() V140() V141() V142() V143() Element of NAT
Seg 1 is non empty V26() V33(1) V137() V138() V139() V140() V141() V142() Element of bool NAT
{1} is non empty trivial V137() V138() V139() V140() V141() V142() set
Seg 2 is non empty V26() V33(2) V137() V138() V139() V140() V141() V142() Element of bool NAT
{1,2} is non empty V137() V138() V139() V140() V141() V142() set
union {} is set
R^2-unit_square is Element of bool the carrier of (TOP-REAL 2)
|[0,0]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
|[0,1]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg (|[0,0]|,|[0,1]|) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * |[0,0]|) + (b₁ * |[0,1]|)) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
|[1,1]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg (|[0,1]|,|[1,1]|) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * |[0,1]|) + (b₁ * |[1,1]|)) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|)) is non empty Element of bool the carrier of (TOP-REAL 2)
|[1,0]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg (|[1,1]|,|[1,0]|) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * |[1,1]|) + (b₁ * |[1,0]|)) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
LSeg (|[1,0]|,|[0,0]|) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * |[1,0]|) + (b₁ * |[0,0]|)) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg (|[1,1]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[0,0]|)) is non empty Element of bool the carrier of (TOP-REAL 2)
((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ ((LSeg (|[1,1]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[0,0]|))) is non empty Element of bool the carrier of (TOP-REAL 2)
{ b₁ where b₁ is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2) : ( ( b₁ `1 = 0 & b<sub>1</sub> `2 <= 1 & 0 <= b₁ `2 ) or ( b<sub>1</sub> `1 <= 1 & 0 <= b₁ `1 & b<sub>1</sub> `2 = 1 ) or ( b₁ `1 <= 1 & 0 <= b<sub>1</sub> `1 & b₁ `2 = 0 ) or ( b<sub>1</sub> `1 = 1 & b₁ `2 <= 1 & 0 <= b<sub>1</sub> `2 ) ) } is set
4 is non empty natural V11() real V37() ext-real positive non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
K74({}) is set
rng {} is set
len {} is V31() set
f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
i1 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
i2 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
i2 + f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
(i2 + f) -' 1 is natural V11() real V37() ext-real non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
j is non empty set
M is V13() V16( NAT ) V17(j) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of j
dom M is V137() V138() V139() V140() V141() V142() Element of bool NAT
mid (M,f,i1) is V13() V16( NAT ) V17(j) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of j
dom (mid (M,f,i1)) is V137() V138() V139() V140() V141() V142() Element of bool NAT
len M is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
1 + 0 is non empty natural V11() real V37() ext-real positive non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
f - 1 is V11() real ext-real Element of REAL
i2 + 0 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
i2 + (f - 1) is V11() real ext-real Element of REAL
len (mid (M,f,i1)) is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
i1 -' f is natural V11() real V37() ext-real non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
(i1 -' f) + 1 is non empty natural V11() real V37() ext-real positive non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
i1 - f is V11() real ext-real set
(i1 - f) + 1 is V11() real ext-real Element of REAL
i1 + 1 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
(i1 + 1) - f is V11() real ext-real Element of REAL
(i2 + f) - 1 is V11() real ext-real Element of REAL
f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
i1 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
i2 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
f -' i2 is natural V11() real V37() ext-real non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
(f -' i2) + 1 is non empty natural V11() real V37() ext-real positive non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
j is non empty set
M is V13() V16( NAT ) V17(j) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of j
dom M is V137() V138() V139() V140() V141() V142() Element of bool NAT
mid (M,f,i1) is V13() V16( NAT ) V17(j) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of j
dom (mid (M,f,i1)) is V137() V138() V139() V140() V141() V142() Element of bool NAT
len M is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
1 + 0 is non empty natural V11() real V37() ext-real positive non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
1 - i1 is V11() real ext-real Element of REAL
f + (1 - i1) is V11() real ext-real Element of REAL
f + 0 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
len (mid (M,f,i1)) is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
1 - i2 is V11() real ext-real Element of REAL
f + (1 - i2) is V11() real ext-real Element of REAL
f - i2 is V11() real ext-real set
(f - i2) + 1 is V11() real ext-real Element of REAL
f -' i1 is natural V11() real V37() ext-real non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
(f -' i1) + 1 is non empty natural V11() real V37() ext-real positive non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
f - i1 is V11() real ext-real set
(f - i1) + 1 is V11() real ext-real Element of REAL
f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
i1 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
i2 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
i2 + f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
(i2 + f) -' 1 is natural V11() real V37() ext-real non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
j is non empty set
M is V13() V16( NAT ) V17(j) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of j
dom M is V137() V138() V139() V140() V141() V142() Element of bool NAT
mid (M,f,i1) is V13() V16( NAT ) V17(j) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of j
dom (mid (M,f,i1)) is V137() V138() V139() V140() V141() V142() Element of bool NAT
(mid (M,f,i1)) /. i2 is Element of j
M /. ((i2 + f) -' 1) is Element of j
len M is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
len (mid (M,f,i1)) is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
(mid (M,f,i1)) . i2 is set
M . ((i2 + f) -' 1) is set
f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
i1 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
i2 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
f -' i2 is natural V11() real V37() ext-real non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
(f -' i2) + 1 is non empty natural V11() real V37() ext-real positive non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
j is non empty set
M is V13() V16( NAT ) V17(j) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of j
dom M is V137() V138() V139() V140() V141() V142() Element of bool NAT
mid (M,f,i1) is V13() V16( NAT ) V17(j) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of j
dom (mid (M,f,i1)) is V137() V138() V139() V140() V141() V142() Element of bool NAT
(mid (M,f,i1)) /. i2 is Element of j
M /. ((f -' i2) + 1) is Element of j
len M is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
len (mid (M,f,i1)) is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
(mid (M,f,i1)) . i2 is set
M . ((f -' i2) + 1) is set
f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
i1 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
i2 is non empty set
j is V13() V16( NAT ) V17(i2) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of i2
dom j is V137() V138() V139() V140() V141() V142() Element of bool NAT
mid (j,f,i1) is V13() V16( NAT ) V17(i2) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of i2
len (mid (j,f,i1)) is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
len j is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
f -' i1 is natural V11() real V37() ext-real non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
(f -' i1) + 1 is non empty natural V11() real V37() ext-real positive non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
i1 -' f is natural V11() real V37() ext-real non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
(i1 -' f) + 1 is non empty natural V11() real V37() ext-real positive non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
i1 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
i2 is non empty set
j is V13() V16( NAT ) V17(i2) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of i2
dom j is V137() V138() V139() V140() V141() V142() Element of bool NAT
mid (j,f,i1) is V13() V16( NAT ) V17(i2) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of i2
len (mid (j,f,i1)) is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
len j is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
0 + 1 is non empty natural V11() real V37() ext-real positive non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
i1 -' f is natural V11() real V37() ext-real non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
(i1 -' f) + 1 is non empty natural V11() real V37() ext-real positive non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
i1 - f is V11() real ext-real set
0 + 1 is non empty natural V11() real V37() ext-real positive non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
f -' i1 is natural V11() real V37() ext-real non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
(f -' i1) + 1 is non empty natural V11() real V37() ext-real positive non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
f - i1 is V11() real ext-real set
f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
i1 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
i2 is non empty set
j is V13() V16( NAT ) V17(i2) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of i2
dom j is V137() V138() V139() V140() V141() V142() Element of bool NAT
mid (j,f,i1) is V13() V16( NAT ) V17(i2) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of i2
len (mid (j,f,i1)) is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
i1 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
i2 is non empty set
j is V13() V16( NAT ) V17(i2) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of i2
dom j is V137() V138() V139() V140() V141() V142() Element of bool NAT
mid (j,f,i1) is V13() V16( NAT ) V17(i2) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of i2
(mid (j,f,i1)) /. 1 is Element of i2
j /. f is Element of i2
len j is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
dom (mid (j,f,i1)) is V137() V138() V139() V140() V141() V142() Element of bool NAT
(mid (j,f,i1)) . 1 is set
j . f is set
f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
i1 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
i2 is non empty set
j is V13() V16( NAT ) V17(i2) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of i2
dom j is V137() V138() V139() V140() V141() V142() Element of bool NAT
mid (j,f,i1) is V13() V16( NAT ) V17(i2) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of i2
len (mid (j,f,i1)) is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
(mid (j,f,i1)) /. (len (mid (j,f,i1))) is Element of i2
j /. i1 is Element of i2
len j is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
dom (mid (j,f,i1)) is V137() V138() V139() V140() V141() V142() Element of bool NAT
(mid (j,f,i1)) . (len (mid (j,f,i1))) is set
j . i1 is set
f is compact Element of bool the carrier of (TOP-REAL 2)
N-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | f is V13() V16( the carrier of ((TOP-REAL 2) | f)) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | f), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is set
upper_bound (proj2 | f) is V11() real ext-real Element of REAL
(proj2 | f) .: the carrier of ((TOP-REAL 2) | f) is V137() V138() V139() Element of bool REAL
K429(((proj2 | f) .: the carrier of ((TOP-REAL 2) | f))) is V11() real ext-real Element of REAL
N-most f is Element of bool the carrier of (TOP-REAL 2)
NW-corner f is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
W-bound f is V11() real ext-real Element of REAL
proj1 | f is V13() V16( the carrier of ((TOP-REAL 2) | f)) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | f), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
lower_bound (proj1 | f) is V11() real ext-real Element of REAL
(proj1 | f) .: the carrier of ((TOP-REAL 2) | f) is V137() V138() V139() Element of bool REAL
K430(((proj1 | f) .: the carrier of ((TOP-REAL 2) | f))) is V11() real ext-real Element of REAL
|[(W-bound f),(N-bound f)]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
NE-corner f is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
E-bound f is V11() real ext-real Element of REAL
upper_bound (proj1 | f) is V11() real ext-real Element of REAL
K429(((proj1 | f) .: the carrier of ((TOP-REAL 2) | f))) is V11() real ext-real Element of REAL
|[(E-bound f),(N-bound f)]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((NW-corner f),(NE-corner f)) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NW-corner f)) + (b₁ * (NE-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((NW-corner f),(NE-corner f))) /\ f is Element of bool the carrier of (TOP-REAL 2)
i1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
i1 `2 is V11() real ext-real Element of REAL
(NW-corner f) `2 is V11() real ext-real Element of REAL
(NE-corner f) `2 is V11() real ext-real Element of REAL
(NW-corner f) `1 is V11() real ext-real Element of REAL
(NE-corner f) `1 is V11() real ext-real Element of REAL
i1 `1 is V11() real ext-real Element of REAL
f is compact Element of bool the carrier of (TOP-REAL 2)
S-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | f is V13() V16( the carrier of ((TOP-REAL 2) | f)) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | f), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is set
lower_bound (proj2 | f) is V11() real ext-real Element of REAL
(proj2 | f) .: the carrier of ((TOP-REAL 2) | f) is V137() V138() V139() Element of bool REAL
K430(((proj2 | f) .: the carrier of ((TOP-REAL 2) | f))) is V11() real ext-real Element of REAL
S-most f is Element of bool the carrier of (TOP-REAL 2)
SW-corner f is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
W-bound f is V11() real ext-real Element of REAL
proj1 | f is V13() V16( the carrier of ((TOP-REAL 2) | f)) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | f), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
lower_bound (proj1 | f) is V11() real ext-real Element of REAL
(proj1 | f) .: the carrier of ((TOP-REAL 2) | f) is V137() V138() V139() Element of bool REAL
K430(((proj1 | f) .: the carrier of ((TOP-REAL 2) | f))) is V11() real ext-real Element of REAL
|[(W-bound f),(S-bound f)]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
SE-corner f is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
E-bound f is V11() real ext-real Element of REAL
upper_bound (proj1 | f) is V11() real ext-real Element of REAL
K429(((proj1 | f) .: the carrier of ((TOP-REAL 2) | f))) is V11() real ext-real Element of REAL
|[(E-bound f),(S-bound f)]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner f),(SE-corner f)) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SW-corner f)) + (b₁ * (SE-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((SW-corner f),(SE-corner f))) /\ f is Element of bool the carrier of (TOP-REAL 2)
i1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
i1 `2 is V11() real ext-real Element of REAL
(SW-corner f) `2 is V11() real ext-real Element of REAL
(SE-corner f) `2 is V11() real ext-real Element of REAL
(SW-corner f) `1 is V11() real ext-real Element of REAL
(SE-corner f) `1 is V11() real ext-real Element of REAL
i1 `1 is V11() real ext-real Element of REAL
f is compact Element of bool the carrier of (TOP-REAL 2)
W-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | f is V13() V16( the carrier of ((TOP-REAL 2) | f)) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | f), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is set
lower_bound (proj1 | f) is V11() real ext-real Element of REAL
(proj1 | f) .: the carrier of ((TOP-REAL 2) | f) is V137() V138() V139() Element of bool REAL
K430(((proj1 | f) .: the carrier of ((TOP-REAL 2) | f))) is V11() real ext-real Element of REAL
W-most f is Element of bool the carrier of (TOP-REAL 2)
SW-corner f is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
S-bound f is V11() real ext-real Element of REAL
proj2 | f is V13() V16( the carrier of ((TOP-REAL 2) | f)) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | f), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
lower_bound (proj2 | f) is V11() real ext-real Element of REAL
(proj2 | f) .: the carrier of ((TOP-REAL 2) | f) is V137() V138() V139() Element of bool REAL
K430(((proj2 | f) .: the carrier of ((TOP-REAL 2) | f))) is V11() real ext-real Element of REAL
|[(W-bound f),(S-bound f)]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
NW-corner f is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
N-bound f is V11() real ext-real Element of REAL
upper_bound (proj2 | f) is V11() real ext-real Element of REAL
K429(((proj2 | f) .: the carrier of ((TOP-REAL 2) | f))) is V11() real ext-real Element of REAL
|[(W-bound f),(N-bound f)]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner f),(NW-corner f)) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SW-corner f)) + (b₁ * (NW-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((SW-corner f),(NW-corner f))) /\ f is Element of bool the carrier of (TOP-REAL 2)
i1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
i1 `1 is V11() real ext-real Element of REAL
(SW-corner f) `1 is V11() real ext-real Element of REAL
(NW-corner f) `1 is V11() real ext-real Element of REAL
(SW-corner f) `2 is V11() real ext-real Element of REAL
(NW-corner f) `2 is V11() real ext-real Element of REAL
i1 `2 is V11() real ext-real Element of REAL
f is compact Element of bool the carrier of (TOP-REAL 2)
E-bound f is V11() real ext-real Element of REAL
(TOP-REAL 2) | f is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | f is V13() V16( the carrier of ((TOP-REAL 2) | f)) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | f), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
the carrier of ((TOP-REAL 2) | f) is set
[: the carrier of ((TOP-REAL 2) | f),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | f),REAL:] is set
upper_bound (proj1 | f) is V11() real ext-real Element of REAL
(proj1 | f) .: the carrier of ((TOP-REAL 2) | f) is V137() V138() V139() Element of bool REAL
K429(((proj1 | f) .: the carrier of ((TOP-REAL 2) | f))) is V11() real ext-real Element of REAL
E-most f is Element of bool the carrier of (TOP-REAL 2)
SE-corner f is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
S-bound f is V11() real ext-real Element of REAL
proj2 | f is V13() V16( the carrier of ((TOP-REAL 2) | f)) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | f), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | f),REAL:]
lower_bound (proj2 | f) is V11() real ext-real Element of REAL
(proj2 | f) .: the carrier of ((TOP-REAL 2) | f) is V137() V138() V139() Element of bool REAL
K430(((proj2 | f) .: the carrier of ((TOP-REAL 2) | f))) is V11() real ext-real Element of REAL
|[(E-bound f),(S-bound f)]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
NE-corner f is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
N-bound f is V11() real ext-real Element of REAL
upper_bound (proj2 | f) is V11() real ext-real Element of REAL
K429(((proj2 | f) .: the carrier of ((TOP-REAL 2) | f))) is V11() real ext-real Element of REAL
|[(E-bound f),(N-bound f)]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner f),(NE-corner f)) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SE-corner f)) + (b₁ * (NE-corner f))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((SE-corner f),(NE-corner f))) /\ f is Element of bool the carrier of (TOP-REAL 2)
i1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
i1 `1 is V11() real ext-real Element of REAL
(SE-corner f) `1 is V11() real ext-real Element of REAL
(NE-corner f) `1 is V11() real ext-real Element of REAL
(SE-corner f) `2 is V11() real ext-real Element of REAL
(NE-corner f) `2 is V11() real ext-real Element of REAL
i1 `2 is V11() real ext-real Element of REAL
f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
i1 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
i2 is V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len i2 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
mid (i2,f,i1) is V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ (mid (i2,f,i1)) is compact Element of bool the carrier of (TOP-REAL 2)
len (mid (i2,f,i1)) is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
{ (LSeg ((mid (i2,f,i1)),b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (mid (i2,f,i1)) ) } is set
union { (LSeg ((mid (i2,f,i1)),b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (mid (i2,f,i1)) ) } is set
{ (LSeg (i2,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( f <= b₁ & not i1 <= b₁ ) } is set
union { (LSeg (i2,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( f <= b₁ & not i1 <= b₁ ) } is set
h is set
g is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
LSeg (i2,g) is Element of bool the carrier of (TOP-REAL 2)
i2 /. f is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
<*(i2 /. f)*> is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() V33(1) FinSequence-like FinSubsequence-like special FinSequence of the carrier of (TOP-REAL 2)
h is set
0 + 1 is non empty natural V11() real V37() ext-real positive non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
g is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
LSeg ((mid (i2,f,i1)),g) is Element of bool the carrier of (TOP-REAL 2)
g + 1 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
g + f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
(g + f) -' 1 is natural V11() real V37() ext-real non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
i1 -' f is natural V11() real V37() ext-real non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
(i1 -' f) + 1 is non empty natural V11() real V37() ext-real positive non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
i1 - f is V11() real ext-real set
((g + f) -' 1) + 1 is non empty natural V11() real V37() ext-real positive non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
LSeg (i2,((g + f) -' 1)) is Element of bool the carrier of (TOP-REAL 2)
h is set
g is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
LSeg (i2,g) is Element of bool the carrier of (TOP-REAL 2)
g -' f is natural V11() real V37() ext-real non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
(g -' f) + 1 is non empty natural V11() real V37() ext-real positive non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
g - f is V11() real ext-real set
((g -' f) + 1) + 1 is non empty natural V11() real V37() ext-real positive non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
((g -' f) + 1) + f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
(((g -' f) + 1) + f) -' 1 is natural V11() real V37() ext-real non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
(g -' f) + f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
((g -' f) + f) + 1 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
(((g -' f) + f) + 1) -' 1 is natural V11() real V37() ext-real non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
g + 1 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
(g + 1) -' 1 is natural V11() real V37() ext-real non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
LSeg ((mid (i2,f,i1)),((g -' f) + 1)) is Element of bool the carrier of (TOP-REAL 2)
f is V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
X_axis f is V13() V16( NAT ) V17( REAL ) Function-like V26() FinSequence-like FinSubsequence-like V127() V128() V129() FinSequence of REAL
dom (X_axis f) is V137() V138() V139() V140() V141() V142() Element of bool NAT
dom f is V137() V138() V139() V140() V141() V142() Element of bool NAT
len (X_axis f) is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
len f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
f is V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
Y_axis f is V13() V16( NAT ) V17( REAL ) Function-like V26() FinSequence-like FinSubsequence-like V127() V128() V129() FinSequence of REAL
dom (Y_axis f) is V137() V138() V139() V140() V141() V142() Element of bool NAT
dom f is V137() V138() V139() V140() V141() V142() Element of bool NAT
len (Y_axis f) is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
len f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
i1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
f is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
i2 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
LSeg (f,i2) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * f) + (b₁ * i2)) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
f `1 is V11() real ext-real Element of REAL
i1 `1 is V11() real ext-real Element of REAL
i2 `1 is V11() real ext-real Element of REAL
j is V11() real ext-real Element of REAL
1 - j is V11() real ext-real Element of REAL
(1 - j) * f is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
j * i2 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
((1 - j) * f) + (j * i2) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(i1 `1) + 0 is V11() real ext-real Element of REAL
((1 - j) * f) `1 is V11() real ext-real Element of REAL
(j * i2) `1 is V11() real ext-real Element of REAL
(((1 - j) * f) `1) + ((j * i2) `1) is V11() real ext-real Element of REAL
j * (i2 `1) is V11() real ext-real Element of REAL
(((1 - j) * f) `1) + (j * (i2 `1)) is V11() real ext-real Element of REAL
(1 - j) * (i1 `1) is V11() real ext-real Element of REAL
((1 - j) * (i1 `1)) + (j * (i2 `1)) is V11() real ext-real Element of REAL
j * (i1 `1) is V11() real ext-real Element of REAL
(j * (i2 `1)) - (j * (i1 `1)) is V11() real ext-real Element of REAL
(i1 `1) + ((j * (i2 `1)) - (j * (i1 `1))) is V11() real ext-real Element of REAL
(i2 `1) - (i1 `1) is V11() real ext-real Element of REAL
j * ((i2 `1) - (i1 `1)) is V11() real ext-real Element of REAL
1 * f is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
0. (TOP-REAL 2) is V33(2) FinSequence-like V51( TOP-REAL 2) V129() Element of the carrier of (TOP-REAL 2)
the ZeroF of (TOP-REAL 2) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(1 * f) + (0. (TOP-REAL 2)) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
((1 - j) * f) `1 is V11() real ext-real Element of REAL
(j * i2) `1 is V11() real ext-real Element of REAL
(((1 - j) * f) `1) + ((j * i2) `1) is V11() real ext-real Element of REAL
j * (i2 `1) is V11() real ext-real Element of REAL
(((1 - j) * f) `1) + (j * (i2 `1)) is V11() real ext-real Element of REAL
(1 - j) * (f `1) is V11() real ext-real Element of REAL
j * (i1 `1) is V11() real ext-real Element of REAL
((1 - j) * (f `1)) + (j * (i1 `1)) is V11() real ext-real Element of REAL
(f `1) - (i1 `1) is V11() real ext-real Element of REAL
(1 - j) * ((f `1) - (i1 `1)) is V11() real ext-real Element of REAL
0. (TOP-REAL 2) is V33(2) FinSequence-like V51( TOP-REAL 2) V129() Element of the carrier of (TOP-REAL 2)
the ZeroF of (TOP-REAL 2) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
1 * i2 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(0. (TOP-REAL 2)) + (1 * i2) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
i1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
f is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
i2 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
LSeg (f,i2) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * f) + (b₁ * i2)) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
f `2 is V11() real ext-real Element of REAL
i1 `2 is V11() real ext-real Element of REAL
i2 `2 is V11() real ext-real Element of REAL
j is V11() real ext-real Element of REAL
1 - j is V11() real ext-real Element of REAL
(1 - j) * f is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
j * i2 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
((1 - j) * f) + (j * i2) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(i1 `2) + 0 is V11() real ext-real Element of REAL
((1 - j) * f) `2 is V11() real ext-real Element of REAL
(j * i2) `2 is V11() real ext-real Element of REAL
(((1 - j) * f) `2) + ((j * i2) `2) is V11() real ext-real Element of REAL
j * (i2 `2) is V11() real ext-real Element of REAL
(((1 - j) * f) `2) + (j * (i2 `2)) is V11() real ext-real Element of REAL
(1 - j) * (i1 `2) is V11() real ext-real Element of REAL
((1 - j) * (i1 `2)) + (j * (i2 `2)) is V11() real ext-real Element of REAL
j * (i1 `2) is V11() real ext-real Element of REAL
(j * (i2 `2)) - (j * (i1 `2)) is V11() real ext-real Element of REAL
(i1 `2) + ((j * (i2 `2)) - (j * (i1 `2))) is V11() real ext-real Element of REAL
(i2 `2) - (i1 `2) is V11() real ext-real Element of REAL
j * ((i2 `2) - (i1 `2)) is V11() real ext-real Element of REAL
1 * f is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
0. (TOP-REAL 2) is V33(2) FinSequence-like V51( TOP-REAL 2) V129() Element of the carrier of (TOP-REAL 2)
the ZeroF of (TOP-REAL 2) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(1 * f) + (0. (TOP-REAL 2)) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
((1 - j) * f) `2 is V11() real ext-real Element of REAL
(j * i2) `2 is V11() real ext-real Element of REAL
(((1 - j) * f) `2) + ((j * i2) `2) is V11() real ext-real Element of REAL
j * (i2 `2) is V11() real ext-real Element of REAL
(((1 - j) * f) `2) + (j * (i2 `2)) is V11() real ext-real Element of REAL
(1 - j) * (f `2) is V11() real ext-real Element of REAL
j * (i1 `2) is V11() real ext-real Element of REAL
((1 - j) * (f `2)) + (j * (i1 `2)) is V11() real ext-real Element of REAL
(f `2) - (i1 `2) is V11() real ext-real Element of REAL
(1 - j) * ((f `2) - (i1 `2)) is V11() real ext-real Element of REAL
0. (TOP-REAL 2) is V33(2) FinSequence-like V51( TOP-REAL 2) V129() Element of the carrier of (TOP-REAL 2)
the ZeroF of (TOP-REAL 2) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
1 * i2 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(0. (TOP-REAL 2)) + (1 * i2) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
i1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
f is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
i2 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
LSeg (f,i2) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * f) + (b₁ * i2)) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
i1 `1 is V11() real ext-real Element of REAL
f `1 is V11() real ext-real Element of REAL
i2 `1 is V11() real ext-real Element of REAL
j is V11() real ext-real Element of REAL
1 - j is V11() real ext-real Element of REAL
(1 - j) * f is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
j * i2 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
((1 - j) * f) + (j * i2) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(i1 `1) + 0 is V11() real ext-real Element of REAL
((1 - j) * f) `1 is V11() real ext-real Element of REAL
(j * i2) `1 is V11() real ext-real Element of REAL
(((1 - j) * f) `1) + ((j * i2) `1) is V11() real ext-real Element of REAL
j * (i2 `1) is V11() real ext-real Element of REAL
(((1 - j) * f) `1) + (j * (i2 `1)) is V11() real ext-real Element of REAL
(1 - j) * (i1 `1) is V11() real ext-real Element of REAL
((1 - j) * (i1 `1)) + (j * (i2 `1)) is V11() real ext-real Element of REAL
j * (i1 `1) is V11() real ext-real Element of REAL
(j * (i2 `1)) - (j * (i1 `1)) is V11() real ext-real Element of REAL
(i1 `1) + ((j * (i2 `1)) - (j * (i1 `1))) is V11() real ext-real Element of REAL
(i2 `1) - (i1 `1) is V11() real ext-real Element of REAL
j * ((i2 `1) - (i1 `1)) is V11() real ext-real Element of REAL
1 * f is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
0. (TOP-REAL 2) is V33(2) FinSequence-like V51( TOP-REAL 2) V129() Element of the carrier of (TOP-REAL 2)
the ZeroF of (TOP-REAL 2) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(1 * f) + (0. (TOP-REAL 2)) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
((1 - j) * f) `1 is V11() real ext-real Element of REAL
(j * i2) `1 is V11() real ext-real Element of REAL
(((1 - j) * f) `1) + ((j * i2) `1) is V11() real ext-real Element of REAL
j * (i2 `1) is V11() real ext-real Element of REAL
(((1 - j) * f) `1) + (j * (i2 `1)) is V11() real ext-real Element of REAL
(1 - j) * (f `1) is V11() real ext-real Element of REAL
j * (i1 `1) is V11() real ext-real Element of REAL
((1 - j) * (f `1)) + (j * (i1 `1)) is V11() real ext-real Element of REAL
(f `1) - (i1 `1) is V11() real ext-real Element of REAL
(1 - j) * ((f `1) - (i1 `1)) is V11() real ext-real Element of REAL
0. (TOP-REAL 2) is V33(2) FinSequence-like V51( TOP-REAL 2) V129() Element of the carrier of (TOP-REAL 2)
the ZeroF of (TOP-REAL 2) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
1 * i2 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(0. (TOP-REAL 2)) + (1 * i2) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
i1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
f is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
i2 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
LSeg (f,i2) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * f) + (b₁ * i2)) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
i1 `2 is V11() real ext-real Element of REAL
f `2 is V11() real ext-real Element of REAL
i2 `2 is V11() real ext-real Element of REAL
j is V11() real ext-real Element of REAL
1 - j is V11() real ext-real Element of REAL
(1 - j) * f is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
j * i2 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
((1 - j) * f) + (j * i2) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(i1 `2) + 0 is V11() real ext-real Element of REAL
((1 - j) * f) `2 is V11() real ext-real Element of REAL
(j * i2) `2 is V11() real ext-real Element of REAL
(((1 - j) * f) `2) + ((j * i2) `2) is V11() real ext-real Element of REAL
j * (i2 `2) is V11() real ext-real Element of REAL
(((1 - j) * f) `2) + (j * (i2 `2)) is V11() real ext-real Element of REAL
(1 - j) * (i1 `2) is V11() real ext-real Element of REAL
((1 - j) * (i1 `2)) + (j * (i2 `2)) is V11() real ext-real Element of REAL
j * (i1 `2) is V11() real ext-real Element of REAL
(j * (i2 `2)) - (j * (i1 `2)) is V11() real ext-real Element of REAL
(i1 `2) + ((j * (i2 `2)) - (j * (i1 `2))) is V11() real ext-real Element of REAL
(i2 `2) - (i1 `2) is V11() real ext-real Element of REAL
j * ((i2 `2) - (i1 `2)) is V11() real ext-real Element of REAL
1 * f is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
0. (TOP-REAL 2) is V33(2) FinSequence-like V51( TOP-REAL 2) V129() Element of the carrier of (TOP-REAL 2)
the ZeroF of (TOP-REAL 2) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(1 * f) + (0. (TOP-REAL 2)) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
((1 - j) * f) `2 is V11() real ext-real Element of REAL
(j * i2) `2 is V11() real ext-real Element of REAL
(((1 - j) * f) `2) + ((j * i2) `2) is V11() real ext-real Element of REAL
j * (i2 `2) is V11() real ext-real Element of REAL
(((1 - j) * f) `2) + (j * (i2 `2)) is V11() real ext-real Element of REAL
(1 - j) * (f `2) is V11() real ext-real Element of REAL
j * (i1 `2) is V11() real ext-real Element of REAL
((1 - j) * (f `2)) + (j * (i1 `2)) is V11() real ext-real Element of REAL
(f `2) - (i1 `2) is V11() real ext-real Element of REAL
(1 - j) * ((f `2) - (i1 `2)) is V11() real ext-real Element of REAL
0. (TOP-REAL 2) is V33(2) FinSequence-like V51( TOP-REAL 2) V129() Element of the carrier of (TOP-REAL 2)
the ZeroF of (TOP-REAL 2) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
1 * i2 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(0. (TOP-REAL 2)) + (1 * i2) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
f is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
i1 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
dom f is non empty non trivial V137() V138() V139() V140() V141() V142() Element of bool NAT
L~ f is non empty compact Element of bool the carrier of (TOP-REAL 2)
len f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
{ (LSeg (f,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
union { (LSeg (f,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
W-bound (L~ f) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ f) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
the carrier of ((TOP-REAL 2) | (L~ f)) is non empty set
[: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is set
lower_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
(proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K430(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
f /. i1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(f /. i1) `1 is V11() real ext-real Element of REAL
E-bound (L~ f) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
K429(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
S-bound (L~ f) is V11() real ext-real Element of REAL
proj2 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
lower_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
(proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K430(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
(f /. i1) `2 is V11() real ext-real Element of REAL
N-bound (L~ f) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
K429(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
f is V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
i1 is V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
dom i1 is V137() V138() V139() V140() V141() V142() Element of bool NAT
L~ f is compact Element of bool the carrier of (TOP-REAL 2)
len f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
{ (LSeg (f,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
union { (LSeg (f,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
W-bound (L~ f) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ f) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
the carrier of ((TOP-REAL 2) | (L~ f)) is set
[: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is set
lower_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
(proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is V137() V138() V139() Element of bool REAL
K430(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
E-bound (L~ f) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
K429(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
S-bound (L~ f) is V11() real ext-real Element of REAL
proj2 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
lower_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
(proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is V137() V138() V139() Element of bool REAL
K430(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
N-bound (L~ f) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
K429(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
i2 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
j is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
mid (i1,i2,j) is V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
h is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
dom (mid (i1,i2,j)) is V137() V138() V139() V140() V141() V142() Element of bool NAT
(mid (i1,i2,j)) /. h is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
((mid (i1,i2,j)) /. h) `1 is V11() real ext-real Element of REAL
((mid (i1,i2,j)) /. h) `2 is V11() real ext-real Element of REAL
h + i2 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
(h + i2) -' 1 is natural V11() real V37() ext-real non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
i1 /. ((h + i2) -' 1) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
h is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
dom (mid (i1,i2,j)) is V137() V138() V139() V140() V141() V142() Element of bool NAT
(mid (i1,i2,j)) /. h is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
((mid (i1,i2,j)) /. h) `1 is V11() real ext-real Element of REAL
((mid (i1,i2,j)) /. h) `2 is V11() real ext-real Element of REAL
i2 -' h is natural V11() real V37() ext-real non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
(i2 -' h) + 1 is non empty natural V11() real V37() ext-real positive non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
i1 /. ((i2 -' h) + 1) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
i1 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
f is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
dom f is non empty non trivial V137() V138() V139() V140() V141() V142() Element of bool NAT
i2 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
mid (f,i1,i2) is V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
f is V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
i1 is V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
i2 is V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
i1 ^ i2 is V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
j is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
dom (i1 ^ i2) is V137() V138() V139() V140() V141() V142() Element of bool NAT
L~ f is compact Element of bool the carrier of (TOP-REAL 2)
len f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
{ (LSeg (f,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
union { (LSeg (f,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
W-bound (L~ f) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ f) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
the carrier of ((TOP-REAL 2) | (L~ f)) is set
[: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is set
lower_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
(proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is V137() V138() V139() Element of bool REAL
K430(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
(i1 ^ i2) /. j is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
((i1 ^ i2) /. j) `1 is V11() real ext-real Element of REAL
E-bound (L~ f) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
K429(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
S-bound (L~ f) is V11() real ext-real Element of REAL
proj2 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
lower_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
(proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is V137() V138() V139() Element of bool REAL
K430(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
((i1 ^ i2) /. j) `2 is V11() real ext-real Element of REAL
N-bound (L~ f) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
K429(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
dom i1 is V137() V138() V139() V140() V141() V142() Element of bool NAT
i1 /. j is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
dom i2 is V137() V138() V139() V140() V141() V142() Element of bool NAT
len i1 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
M is natural V11() real ext-real set
(len i1) + M is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
M is natural V11() real ext-real set
(len i1) + M is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
i2 /. M is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
dom i1 is V137() V138() V139() V140() V141() V142() Element of bool NAT
dom i2 is V137() V138() V139() V140() V141() V142() Element of bool NAT
len i1 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
f is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ f is non empty compact Element of bool the carrier of (TOP-REAL 2)
len f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
{ (LSeg (f,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
union { (LSeg (f,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
NE-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
E-bound (L~ f) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ f) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
the carrier of ((TOP-REAL 2) | (L~ f)) is non empty set
[: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is set
upper_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
(proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K429(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
N-bound (L~ f) is V11() real ext-real Element of REAL
proj2 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
upper_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
(proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K429(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
<*(NE-corner (L~ f))*> is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() V33(1) FinSequence-like FinSubsequence-like special FinSequence of the carrier of (TOP-REAL 2)
i2 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
dom <*(NE-corner (L~ f))*> is V137() V138() V139() V140() V141() V142() Element of bool NAT
W-bound (L~ f) is V11() real ext-real Element of REAL
lower_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
K430(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
<*(NE-corner (L~ f))*> /. i2 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(<*(NE-corner (L~ f))*> /. i2) `1 is V11() real ext-real Element of REAL
S-bound (L~ f) is V11() real ext-real Element of REAL
lower_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
K430(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
(<*(NE-corner (L~ f))*> /. i2) `2 is V11() real ext-real Element of REAL
f is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ f is non empty compact Element of bool the carrier of (TOP-REAL 2)
len f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
{ (LSeg (f,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
union { (LSeg (f,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
NW-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
W-bound (L~ f) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ f) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
the carrier of ((TOP-REAL 2) | (L~ f)) is non empty set
[: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is set
lower_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
(proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K430(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
N-bound (L~ f) is V11() real ext-real Element of REAL
proj2 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
upper_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
(proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K429(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
<*(NW-corner (L~ f))*> is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() V33(1) FinSequence-like FinSubsequence-like special FinSequence of the carrier of (TOP-REAL 2)
i2 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
dom <*(NW-corner (L~ f))*> is V137() V138() V139() V140() V141() V142() Element of bool NAT
<*(NW-corner (L~ f))*> /. i2 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(<*(NW-corner (L~ f))*> /. i2) `1 is V11() real ext-real Element of REAL
E-bound (L~ f) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
K429(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
S-bound (L~ f) is V11() real ext-real Element of REAL
lower_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
K430(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
(<*(NW-corner (L~ f))*> /. i2) `2 is V11() real ext-real Element of REAL
f is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ f is non empty compact Element of bool the carrier of (TOP-REAL 2)
len f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
{ (LSeg (f,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
union { (LSeg (f,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
SE-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
E-bound (L~ f) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ f) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
the carrier of ((TOP-REAL 2) | (L~ f)) is non empty set
[: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is set
upper_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
(proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K429(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
S-bound (L~ f) is V11() real ext-real Element of REAL
proj2 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
lower_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
(proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K430(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
<*(SE-corner (L~ f))*> is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() V33(1) FinSequence-like FinSubsequence-like special FinSequence of the carrier of (TOP-REAL 2)
i2 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
dom <*(SE-corner (L~ f))*> is V137() V138() V139() V140() V141() V142() Element of bool NAT
W-bound (L~ f) is V11() real ext-real Element of REAL
lower_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
K430(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
<*(SE-corner (L~ f))*> /. i2 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(<*(SE-corner (L~ f))*> /. i2) `1 is V11() real ext-real Element of REAL
(<*(SE-corner (L~ f))*> /. i2) `2 is V11() real ext-real Element of REAL
N-bound (L~ f) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
K429(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
f is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ f is non empty compact Element of bool the carrier of (TOP-REAL 2)
len f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
{ (LSeg (f,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
union { (LSeg (f,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
SW-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
W-bound (L~ f) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ f) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
the carrier of ((TOP-REAL 2) | (L~ f)) is non empty set
[: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is set
lower_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
(proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K430(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
S-bound (L~ f) is V11() real ext-real Element of REAL
proj2 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
lower_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
(proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K430(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
<*(SW-corner (L~ f))*> is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() V33(1) FinSequence-like FinSubsequence-like special FinSequence of the carrier of (TOP-REAL 2)
i2 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
dom <*(SW-corner (L~ f))*> is V137() V138() V139() V140() V141() V142() Element of bool NAT
<*(SW-corner (L~ f))*> /. i2 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(<*(SW-corner (L~ f))*> /. i2) `1 is V11() real ext-real Element of REAL
E-bound (L~ f) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
K429(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
(<*(SW-corner (L~ f))*> /. i2) `2 is V11() real ext-real Element of REAL
N-bound (L~ f) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
K429(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
f is V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
i1 is V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special FinSequence of the carrier of (TOP-REAL 2)
len i1 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
i2 is V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special FinSequence of the carrier of (TOP-REAL 2)
len i2 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
L~ i1 is compact Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (i1,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len i1 ) } is set
union { (LSeg (i1,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len i1 ) } is set
L~ i2 is compact Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (i2,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len i2 ) } is set
union { (LSeg (i2,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len i2 ) } is set
dom i1 is V137() V138() V139() V140() V141() V142() Element of bool NAT
L~ f is compact Element of bool the carrier of (TOP-REAL 2)
len f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
{ (LSeg (f,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
union { (LSeg (f,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
W-bound (L~ f) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ f) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
the carrier of ((TOP-REAL 2) | (L~ f)) is set
[: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is set
lower_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
(proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is V137() V138() V139() Element of bool REAL
K430(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
E-bound (L~ f) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
K429(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
S-bound (L~ f) is V11() real ext-real Element of REAL
proj2 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
lower_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
(proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is V137() V138() V139() Element of bool REAL
K430(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
N-bound (L~ f) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
K429(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
i1 /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(i1 /. 1) `1 is V11() real ext-real Element of REAL
i1 /. (len i1) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(i1 /. (len i1)) `1 is V11() real ext-real Element of REAL
dom i2 is V137() V138() V139() V140() V141() V142() Element of bool NAT
i2 /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(i2 /. 1) `2 is V11() real ext-real Element of REAL
i2 /. (len i2) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(i2 /. (len i2)) `2 is V11() real ext-real Element of REAL
M is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special FinSequence of the carrier of (TOP-REAL 2)
X_axis M is non empty V13() V16( NAT ) V17( REAL ) Function-like V26() FinSequence-like FinSubsequence-like V127() V128() V129() FinSequence of REAL
j is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special FinSequence of the carrier of (TOP-REAL 2)
X_axis j is non empty V13() V16( NAT ) V17( REAL ) Function-like V26() FinSequence-like FinSubsequence-like V127() V128() V129() FinSequence of REAL
(X_axis j) . 1 is V11() real ext-real Element of REAL
len j is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
(X_axis j) . (len j) is V11() real ext-real Element of REAL
h is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
dom (X_axis M) is V137() V138() V139() V140() V141() V142() Element of bool NAT
(X_axis M) . h is V11() real ext-real Element of REAL
dom M is V137() V138() V139() V140() V141() V142() Element of bool NAT
M /. h is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(M /. h) `1 is V11() real ext-real Element of REAL
dom (X_axis j) is V137() V138() V139() V140() V141() V142() Element of bool NAT
len (X_axis j) is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
Y_axis M is non empty V13() V16( NAT ) V17( REAL ) Function-like V26() FinSequence-like FinSubsequence-like V127() V128() V129() FinSequence of REAL
(Y_axis M) . 1 is V11() real ext-real Element of REAL
len M is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
(Y_axis M) . (len M) is V11() real ext-real Element of REAL
h is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
dom (Y_axis M) is V137() V138() V139() V140() V141() V142() Element of bool NAT
(Y_axis M) . h is V11() real ext-real Element of REAL
dom M is V137() V138() V139() V140() V141() V142() Element of bool NAT
M /. h is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(M /. h) `2 is V11() real ext-real Element of REAL
len (Y_axis M) is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
Y_axis j is non empty V13() V16( NAT ) V17( REAL ) Function-like V26() FinSequence-like FinSubsequence-like V127() V128() V129() FinSequence of REAL
h is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
dom (Y_axis j) is V137() V138() V139() V140() V141() V142() Element of bool NAT
(Y_axis j) . h is V11() real ext-real Element of REAL
dom j is V137() V138() V139() V140() V141() V142() Element of bool NAT
j /. h is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(j /. h) `2 is V11() real ext-real Element of REAL
dom (Y_axis M) is V137() V138() V139() V140() V141() V142() Element of bool NAT
len (Y_axis M) is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
h is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
dom (X_axis j) is V137() V138() V139() V140() V141() V142() Element of bool NAT
(X_axis j) . h is V11() real ext-real Element of REAL
dom j is V137() V138() V139() V140() V141() V142() Element of bool NAT
j /. h is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(j /. h) `1 is V11() real ext-real Element of REAL
len (X_axis j) is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
f is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard FinSequence of the carrier of (TOP-REAL 2)
f /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
L~ f is non empty compact Element of bool the carrier of (TOP-REAL 2)
len f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
{ (LSeg (f,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
union { (LSeg (f,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
N-min (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
N-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
NW-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
W-bound (L~ f) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ f) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
the carrier of ((TOP-REAL 2) | (L~ f)) is non empty set
[: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is set
lower_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
(proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K430(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
N-bound (L~ f) is V11() real ext-real Element of REAL
proj2 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
upper_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
(proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K429(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
NE-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
E-bound (L~ f) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
K429(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((NW-corner (L~ f)),(NE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NW-corner (L~ f))) + (b₁ * (NE-corner (L~ f)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((NW-corner (L~ f)),(NE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (N-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (N-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (N-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (N-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:] is set
lower_bound (proj1 | (N-most (L~ f))) is V11() real ext-real Element of REAL
(proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))) is V137() V138() V139() Element of bool REAL
K430(((proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (N-most (L~ f)))),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
f /. 2 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
Rotate (f,(N-min (L~ f))) is V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
N-bound R^2-unit_square is V11() real ext-real Element of REAL
(TOP-REAL 2) | R^2-unit_square is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | R^2-unit_square is V13() V16( the carrier of ((TOP-REAL 2) | R^2-unit_square)) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | R^2-unit_square), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | R^2-unit_square),REAL:]
the carrier of ((TOP-REAL 2) | R^2-unit_square) is set
[: the carrier of ((TOP-REAL 2) | R^2-unit_square),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | R^2-unit_square),REAL:] is set
upper_bound (proj2 | R^2-unit_square) is V11() real ext-real Element of REAL
(proj2 | R^2-unit_square) .: the carrier of ((TOP-REAL 2) | R^2-unit_square) is V137() V138() V139() Element of bool REAL
K429(((proj2 | R^2-unit_square) .: the carrier of ((TOP-REAL 2) | R^2-unit_square))) is V11() real ext-real Element of REAL
[#] ((TOP-REAL 2) | R^2-unit_square) is non proper closed Element of bool the carrier of ((TOP-REAL 2) | R^2-unit_square)
bool the carrier of ((TOP-REAL 2) | R^2-unit_square) is set
i1 is V137() V138() V139() Element of bool REAL
i2 is V11() real ext-real set
LSeg (|[1,0]|,|[1,1]|) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * |[1,0]|) + (b₁ * |[1,1]|)) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
LSeg (|[0,0]|,|[1,0]|) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * |[0,0]|) + (b₁ * |[1,0]|)) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|)) is non empty Element of bool the carrier of (TOP-REAL 2)
(proj2 | R^2-unit_square) . |[1,1]| is V11() real ext-real Element of REAL
|[1,1]| `2 is V11() real ext-real Element of REAL
i2 is V11() real ext-real set
j is set
(proj2 | R^2-unit_square) . j is V11() real ext-real Element of REAL
M is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
h is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
h `1 is V11() real ext-real Element of REAL
h `2 is V11() real ext-real Element of REAL
W-bound R^2-unit_square is V11() real ext-real Element of REAL
proj1 | R^2-unit_square is V13() V16( the carrier of ((TOP-REAL 2) | R^2-unit_square)) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | R^2-unit_square), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | R^2-unit_square),REAL:]
lower_bound (proj1 | R^2-unit_square) is V11() real ext-real Element of REAL
(proj1 | R^2-unit_square) .: the carrier of ((TOP-REAL 2) | R^2-unit_square) is V137() V138() V139() Element of bool REAL
K430(((proj1 | R^2-unit_square) .: the carrier of ((TOP-REAL 2) | R^2-unit_square))) is V11() real ext-real Element of REAL
[#] ((TOP-REAL 2) | R^2-unit_square) is non proper closed Element of bool the carrier of ((TOP-REAL 2) | R^2-unit_square)
bool the carrier of ((TOP-REAL 2) | R^2-unit_square) is set
i1 is V137() V138() V139() Element of bool REAL
i2 is V11() real ext-real set
LSeg (|[0,0]|,|[1,0]|) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * |[0,0]|) + (b<sub>1</sub> * |[1,0]|)) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
LSeg (|[1,0]|,|[1,1]|) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * |[1,0]|) + (b<sub>1</sub> * |[1,1]|)) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|)) is non empty Element of bool the carrier of (TOP-REAL 2)
(proj1 | R^2-unit_square) . |[0,0]| is V11() real ext-real Element of REAL
|[0,0]| `1 is V11() real ext-real Element of REAL
i2 is V11() real ext-real set
j is set
(proj1 | R^2-unit_square) . j is V11() real ext-real Element of REAL
M is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
h is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
h `1 is V11() real ext-real Element of REAL
h `2 is V11() real ext-real Element of REAL
E-bound R^2-unit_square is V11() real ext-real Element of REAL
upper_bound (proj1 | R^2-unit_square) is V11() real ext-real Element of REAL
K429(((proj1 | R^2-unit_square) .: the carrier of ((TOP-REAL 2) | R^2-unit_square))) is V11() real ext-real Element of REAL
[#] ((TOP-REAL 2) | R^2-unit_square) is non proper closed Element of bool the carrier of ((TOP-REAL 2) | R^2-unit_square)
bool the carrier of ((TOP-REAL 2) | R^2-unit_square) is set
i1 is V137() V138() V139() Element of bool REAL
i2 is V11() real ext-real set
LSeg (|[1,0]|,|[1,1]|) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * |[1,0]|) + (b₁ * |[1,1]|)) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
LSeg (|[0,0]|,|[1,0]|) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * |[0,0]|) + (b₁ * |[1,0]|)) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|)) is non empty Element of bool the carrier of (TOP-REAL 2)
(proj1 | R^2-unit_square) . |[1,1]| is V11() real ext-real Element of REAL
|[1,1]| `1 is V11() real ext-real Element of REAL
i2 is V11() real ext-real set
j is set
(proj1 | R^2-unit_square) . j is V11() real ext-real Element of REAL
M is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
h is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
h `1 is V11() real ext-real Element of REAL
h `2 is V11() real ext-real Element of REAL
S-bound R^2-unit_square is V11() real ext-real Element of REAL
lower_bound (proj2 | R^2-unit_square) is V11() real ext-real Element of REAL
K430(((proj2 | R^2-unit_square) .: the carrier of ((TOP-REAL 2) | R^2-unit_square))) is V11() real ext-real Element of REAL
[#] ((TOP-REAL 2) | R^2-unit_square) is non proper closed Element of bool the carrier of ((TOP-REAL 2) | R^2-unit_square)
bool the carrier of ((TOP-REAL 2) | R^2-unit_square) is set
i1 is V137() V138() V139() Element of bool REAL
i2 is V11() real ext-real set
LSeg (|[1,0]|,|[1,1]|) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * |[1,0]|) + (b<sub>1</sub> * |[1,1]|)) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
LSeg (|[0,0]|,|[1,0]|) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * |[0,0]|) + (b<sub>1</sub> * |[1,0]|)) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg (|[0,0]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[1,1]|)) is non empty Element of bool the carrier of (TOP-REAL 2)
(proj2 | R^2-unit_square) . |[1,0]| is V11() real ext-real Element of REAL
|[1,0]| `2 is V11() real ext-real Element of REAL
i2 is V11() real ext-real set
j is set
(proj2 | R^2-unit_square) . j is V11() real ext-real Element of REAL
M is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
h is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
h `1 is V11() real ext-real Element of REAL
h `2 is V11() real ext-real Element of REAL
N-most R^2-unit_square is Element of bool the carrier of (TOP-REAL 2)
NW-corner R^2-unit_square is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
|[(W-bound R^2-unit_square),(N-bound R^2-unit_square)]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
NE-corner R^2-unit_square is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
|[(E-bound R^2-unit_square),(N-bound R^2-unit_square)]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((NW-corner R^2-unit_square),(NE-corner R^2-unit_square)) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NW-corner R^2-unit_square)) + (b₁ * (NE-corner R^2-unit_square))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((NW-corner R^2-unit_square),(NE-corner R^2-unit_square))) /\ R^2-unit_square is Element of bool the carrier of (TOP-REAL 2)
N-min R^2-unit_square is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (N-most R^2-unit_square) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most R^2-unit_square) is V13() V16( the carrier of ((TOP-REAL 2) | (N-most R^2-unit_square))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (N-most R^2-unit_square)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (N-most R^2-unit_square)),REAL:]
the carrier of ((TOP-REAL 2) | (N-most R^2-unit_square)) is set
[: the carrier of ((TOP-REAL 2) | (N-most R^2-unit_square)),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (N-most R^2-unit_square)),REAL:] is set
lower_bound (proj1 | (N-most R^2-unit_square)) is V11() real ext-real Element of REAL
(proj1 | (N-most R^2-unit_square)) .: the carrier of ((TOP-REAL 2) | (N-most R^2-unit_square)) is V137() V138() V139() Element of bool REAL
K430(((proj1 | (N-most R^2-unit_square)) .: the carrier of ((TOP-REAL 2) | (N-most R^2-unit_square)))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (N-most R^2-unit_square))),(N-bound R^2-unit_square)]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (LSeg (|[0,1]|,|[1,1]|)) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (LSeg (|[0,1]|,|[1,1]|)) is V13() V16( the carrier of ((TOP-REAL 2) | (LSeg (|[0,1]|,|[1,1]|)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (LSeg (|[0,1]|,|[1,1]|))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (LSeg (|[0,1]|,|[1,1]|))),REAL:]
the carrier of ((TOP-REAL 2) | (LSeg (|[0,1]|,|[1,1]|))) is non empty set
[: the carrier of ((TOP-REAL 2) | (LSeg (|[0,1]|,|[1,1]|))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (LSeg (|[0,1]|,|[1,1]|))),REAL:] is set
lower_bound (proj1 | (LSeg (|[0,1]|,|[1,1]|))) is V11() real ext-real Element of REAL
(proj1 | (LSeg (|[0,1]|,|[1,1]|))) .: the carrier of ((TOP-REAL 2) | (LSeg (|[0,1]|,|[1,1]|))) is non empty V137() V138() V139() Element of bool REAL
K430(((proj1 | (LSeg (|[0,1]|,|[1,1]|))) .: the carrier of ((TOP-REAL 2) | (LSeg (|[0,1]|,|[1,1]|))))) is V11() real ext-real Element of REAL
[#] ((TOP-REAL 2) | (LSeg (|[0,1]|,|[1,1]|))) is non empty non proper closed Element of bool the carrier of ((TOP-REAL 2) | (LSeg (|[0,1]|,|[1,1]|)))
bool the carrier of ((TOP-REAL 2) | (LSeg (|[0,1]|,|[1,1]|))) is set
i1 is V137() V138() V139() Element of bool REAL
i2 is V11() real ext-real set
j is set
(proj1 | (LSeg (|[0,1]|,|[1,1]|))) . j is V11() real ext-real Element of REAL
|[0,1]| `1 is V11() real ext-real Element of REAL
|[1,1]| `1 is V11() real ext-real Element of REAL
M is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
M `1 is V11() real ext-real Element of REAL
(proj1 | (LSeg (|[0,1]|,|[1,1]|))) . |[0,1]| is V11() real ext-real Element of REAL
|[0,1]| `1 is V11() real ext-real Element of REAL
i2 is V11() real ext-real set
f is non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2)
SpStSeq f is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard rectangular FinSequence of the carrier of (TOP-REAL 2)
(SpStSeq f) /. 2 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
L~ (SpStSeq f) is non empty compact Element of bool the carrier of (TOP-REAL 2)
len (SpStSeq f) is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
{ (LSeg ((SpStSeq f),b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (SpStSeq f) ) } is set
union { (LSeg ((SpStSeq f),b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (SpStSeq f) ) } is set
N-max (L~ (SpStSeq f)) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
N-most (L~ (SpStSeq f)) is Element of bool the carrier of (TOP-REAL 2)
NW-corner (L~ (SpStSeq f)) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
W-bound (L~ (SpStSeq f)) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (SpStSeq f)) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ (SpStSeq f)) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ (SpStSeq f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ (SpStSeq f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ (SpStSeq f))),REAL:]
the carrier of ((TOP-REAL 2) | (L~ (SpStSeq f))) is non empty set
[: the carrier of ((TOP-REAL 2) | (L~ (SpStSeq f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (L~ (SpStSeq f))),REAL:] is set
lower_bound (proj1 | (L~ (SpStSeq f))) is V11() real ext-real Element of REAL
(proj1 | (L~ (SpStSeq f))) .: the carrier of ((TOP-REAL 2) | (L~ (SpStSeq f))) is non empty V137() V138() V139() Element of bool REAL
K430(((proj1 | (L~ (SpStSeq f))) .: the carrier of ((TOP-REAL 2) | (L~ (SpStSeq f))))) is V11() real ext-real Element of REAL
N-bound (L~ (SpStSeq f)) is V11() real ext-real Element of REAL
proj2 | (L~ (SpStSeq f)) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ (SpStSeq f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ (SpStSeq f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ (SpStSeq f))),REAL:]
upper_bound (proj2 | (L~ (SpStSeq f))) is V11() real ext-real Element of REAL
(proj2 | (L~ (SpStSeq f))) .: the carrier of ((TOP-REAL 2) | (L~ (SpStSeq f))) is non empty V137() V138() V139() Element of bool REAL
K429(((proj2 | (L~ (SpStSeq f))) .: the carrier of ((TOP-REAL 2) | (L~ (SpStSeq f))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (SpStSeq f))),(N-bound (L~ (SpStSeq f)))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
NE-corner (L~ (SpStSeq f)) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
E-bound (L~ (SpStSeq f)) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ (SpStSeq f))) is V11() real ext-real Element of REAL
K429(((proj1 | (L~ (SpStSeq f))) .: the carrier of ((TOP-REAL 2) | (L~ (SpStSeq f))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (SpStSeq f))),(N-bound (L~ (SpStSeq f)))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((NW-corner (L~ (SpStSeq f))),(NE-corner (L~ (SpStSeq f)))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NW-corner (L~ (SpStSeq f)))) + (b₁ * (NE-corner (L~ (SpStSeq f))))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((NW-corner (L~ (SpStSeq f))),(NE-corner (L~ (SpStSeq f))))) /\ (L~ (SpStSeq f)) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (N-most (L~ (SpStSeq f))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most (L~ (SpStSeq f))) is V13() V16( the carrier of ((TOP-REAL 2) | (N-most (L~ (SpStSeq f))))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (N-most (L~ (SpStSeq f)))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ (SpStSeq f)))),REAL:]
the carrier of ((TOP-REAL 2) | (N-most (L~ (SpStSeq f)))) is set
[: the carrier of ((TOP-REAL 2) | (N-most (L~ (SpStSeq f)))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ (SpStSeq f)))),REAL:] is set
upper_bound (proj1 | (N-most (L~ (SpStSeq f)))) is V11() real ext-real Element of REAL
(proj1 | (N-most (L~ (SpStSeq f)))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ (SpStSeq f)))) is V137() V138() V139() Element of bool REAL
K429(((proj1 | (N-most (L~ (SpStSeq f)))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ (SpStSeq f)))))) is V11() real ext-real Element of REAL
|[(upper_bound (proj1 | (N-most (L~ (SpStSeq f))))),(N-bound (L~ (SpStSeq f)))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
(SpStSeq f) /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
N-min (L~ (SpStSeq f)) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
lower_bound (proj1 | (N-most (L~ (SpStSeq f)))) is V11() real ext-real Element of REAL
K430(((proj1 | (N-most (L~ (SpStSeq f)))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ (SpStSeq f)))))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (N-most (L~ (SpStSeq f))))),(N-bound (L~ (SpStSeq f)))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
the non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2) is non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2)
SpStSeq the non empty compact non horizontal non vertical Element of bool the carrier of (TOP-REAL 2) is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard rectangular () FinSequence of the carrier of (TOP-REAL 2)
f is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard FinSequence of the carrier of (TOP-REAL 2)
len f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
i1 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
i2 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
mid (f,i1,i2) is V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
mid (f,i2,i1) is V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
Rev (mid (f,i2,i1)) is V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
i1 + 1 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
f is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard FinSequence of the carrier of (TOP-REAL 2)
len f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
i1 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
i2 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
mid (f,i1,i2) is V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
mid (f,i2,i1) is V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
Rev (mid (f,i1,i2)) is V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
Rev (Rev (mid (f,i1,i2))) is V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
f is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ f is non empty compact Element of bool the carrier of (TOP-REAL 2)
len f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
{ (LSeg (f,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
union { (LSeg (f,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
N-min (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
N-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
NW-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
W-bound (L~ f) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ f) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
the carrier of ((TOP-REAL 2) | (L~ f)) is non empty set
[: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is set
lower_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
(proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K430(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
N-bound (L~ f) is V11() real ext-real Element of REAL
proj2 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
upper_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
(proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K429(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
NE-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
E-bound (L~ f) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
K429(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((NW-corner (L~ f)),(NE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NW-corner (L~ f))) + (b₁ * (NE-corner (L~ f)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((NW-corner (L~ f)),(NE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (N-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (N-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (N-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (N-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:] is set
lower_bound (proj1 | (N-most (L~ f))) is V11() real ext-real Element of REAL
(proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))) is V137() V138() V139() Element of bool REAL
K430(((proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (N-most (L~ f)))),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
rng f is Element of bool the carrier of (TOP-REAL 2)
i2 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
i2 + 1 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
f /. i2 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
f /. (i2 + 1) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
LSeg ((f /. i2),(f /. (i2 + 1))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (f /. i2)) + (b₁ * (f /. (i2 + 1)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
dom f is non empty non trivial V137() V138() V139() V140() V141() V142() Element of bool NAT
(f /. (i2 + 1)) `2 is V11() real ext-real Element of REAL
(N-min (L~ f)) `2 is V11() real ext-real Element of REAL
(f /. i2) `2 is V11() real ext-real Element of REAL
(N-min (L~ f)) `1 is V11() real ext-real Element of REAL
(f /. (i2 + 1)) `1 is V11() real ext-real Element of REAL
(f /. i2) `1 is V11() real ext-real Element of REAL
f is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ f is non empty compact Element of bool the carrier of (TOP-REAL 2)
len f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
{ (LSeg (f,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
union { (LSeg (f,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
N-max (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
N-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
NW-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
W-bound (L~ f) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ f) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
the carrier of ((TOP-REAL 2) | (L~ f)) is non empty set
[: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is set
lower_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
(proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K430(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
N-bound (L~ f) is V11() real ext-real Element of REAL
proj2 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
upper_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
(proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K429(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
NE-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
E-bound (L~ f) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
K429(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((NW-corner (L~ f)),(NE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NW-corner (L~ f))) + (b₁ * (NE-corner (L~ f)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((NW-corner (L~ f)),(NE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (N-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (N-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (N-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (N-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:] is set
upper_bound (proj1 | (N-most (L~ f))) is V11() real ext-real Element of REAL
(proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))) is V137() V138() V139() Element of bool REAL
K429(((proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))))) is V11() real ext-real Element of REAL
|[(upper_bound (proj1 | (N-most (L~ f)))),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
rng f is Element of bool the carrier of (TOP-REAL 2)
i2 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
i2 + 1 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
f /. i2 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
f /. (i2 + 1) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
LSeg ((f /. i2),(f /. (i2 + 1))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (f /. i2)) + (b₁ * (f /. (i2 + 1)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
dom f is non empty non trivial V137() V138() V139() V140() V141() V142() Element of bool NAT
(f /. (i2 + 1)) `2 is V11() real ext-real Element of REAL
(N-max (L~ f)) `2 is V11() real ext-real Element of REAL
(f /. i2) `2 is V11() real ext-real Element of REAL
(f /. (i2 + 1)) `1 is V11() real ext-real Element of REAL
(N-max (L~ f)) `1 is V11() real ext-real Element of REAL
(f /. i2) `1 is V11() real ext-real Element of REAL
f is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ f is non empty compact Element of bool the carrier of (TOP-REAL 2)
len f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
{ (LSeg (f,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
union { (LSeg (f,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
S-min (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
S-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
SW-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
W-bound (L~ f) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ f) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
the carrier of ((TOP-REAL 2) | (L~ f)) is non empty set
[: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is set
lower_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
(proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K430(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
S-bound (L~ f) is V11() real ext-real Element of REAL
proj2 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
lower_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
(proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K430(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
SE-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
E-bound (L~ f) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
K429(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner (L~ f)),(SE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SW-corner (L~ f))) + (b₁ * (SE-corner (L~ f)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((SW-corner (L~ f)),(SE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (S-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (S-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (S-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (S-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (S-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (S-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (S-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (S-most (L~ f))),REAL:] is set
lower_bound (proj1 | (S-most (L~ f))) is V11() real ext-real Element of REAL
(proj1 | (S-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (S-most (L~ f))) is V137() V138() V139() Element of bool REAL
K430(((proj1 | (S-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (S-most (L~ f))))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (S-most (L~ f)))),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
rng f is Element of bool the carrier of (TOP-REAL 2)
i2 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
i2 + 1 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
f /. i2 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
f /. (i2 + 1) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
LSeg ((f /. i2),(f /. (i2 + 1))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (f /. i2)) + (b₁ * (f /. (i2 + 1)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
dom f is non empty non trivial V137() V138() V139() V140() V141() V142() Element of bool NAT
(f /. (i2 + 1)) `2 is V11() real ext-real Element of REAL
(S-min (L~ f)) `2 is V11() real ext-real Element of REAL
(f /. i2) `2 is V11() real ext-real Element of REAL
(S-min (L~ f)) `1 is V11() real ext-real Element of REAL
(f /. (i2 + 1)) `1 is V11() real ext-real Element of REAL
(f /. i2) `1 is V11() real ext-real Element of REAL
f is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ f is non empty compact Element of bool the carrier of (TOP-REAL 2)
len f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
{ (LSeg (f,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
union { (LSeg (f,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
S-max (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
S-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
SW-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
W-bound (L~ f) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ f) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
the carrier of ((TOP-REAL 2) | (L~ f)) is non empty set
[: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is set
lower_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
(proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K430(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
S-bound (L~ f) is V11() real ext-real Element of REAL
proj2 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
lower_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
(proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K430(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
SE-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
E-bound (L~ f) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
K429(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner (L~ f)),(SE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SW-corner (L~ f))) + (b₁ * (SE-corner (L~ f)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((SW-corner (L~ f)),(SE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (S-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (S-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (S-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (S-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (S-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (S-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (S-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (S-most (L~ f))),REAL:] is set
upper_bound (proj1 | (S-most (L~ f))) is V11() real ext-real Element of REAL
(proj1 | (S-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (S-most (L~ f))) is V137() V138() V139() Element of bool REAL
K429(((proj1 | (S-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (S-most (L~ f))))) is V11() real ext-real Element of REAL
|[(upper_bound (proj1 | (S-most (L~ f)))),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
rng f is Element of bool the carrier of (TOP-REAL 2)
i2 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
i2 + 1 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
f /. i2 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
f /. (i2 + 1) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
LSeg ((f /. i2),(f /. (i2 + 1))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (f /. i2)) + (b₁ * (f /. (i2 + 1)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
dom f is non empty non trivial V137() V138() V139() V140() V141() V142() Element of bool NAT
(f /. (i2 + 1)) `2 is V11() real ext-real Element of REAL
(S-max (L~ f)) `2 is V11() real ext-real Element of REAL
(f /. i2) `2 is V11() real ext-real Element of REAL
(f /. (i2 + 1)) `1 is V11() real ext-real Element of REAL
(S-max (L~ f)) `1 is V11() real ext-real Element of REAL
(f /. i2) `1 is V11() real ext-real Element of REAL
f is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ f is non empty compact Element of bool the carrier of (TOP-REAL 2)
len f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
{ (LSeg (f,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
union { (LSeg (f,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
W-min (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
W-bound (L~ f) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ f) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
the carrier of ((TOP-REAL 2) | (L~ f)) is non empty set
[: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is set
lower_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
(proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K430(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
W-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
SW-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
S-bound (L~ f) is V11() real ext-real Element of REAL
proj2 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
lower_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
(proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K430(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
NW-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
N-bound (L~ f) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
K429(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner (L~ f)),(NW-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SW-corner (L~ f))) + (b₁ * (NW-corner (L~ f)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((SW-corner (L~ f)),(NW-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (W-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (W-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (W-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (W-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (W-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (W-most (L~ f))),REAL:] is set
lower_bound (proj2 | (W-most (L~ f))) is V11() real ext-real Element of REAL
(proj2 | (W-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ f))) is V137() V138() V139() Element of bool REAL
K430(((proj2 | (W-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ f))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(lower_bound (proj2 | (W-most (L~ f))))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
rng f is Element of bool the carrier of (TOP-REAL 2)
i2 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
i2 + 1 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
f /. i2 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
f /. (i2 + 1) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
LSeg ((f /. i2),(f /. (i2 + 1))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (f /. i2)) + (b₁ * (f /. (i2 + 1)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
dom f is non empty non trivial V137() V138() V139() V140() V141() V142() Element of bool NAT
(f /. (i2 + 1)) `1 is V11() real ext-real Element of REAL
(W-min (L~ f)) `1 is V11() real ext-real Element of REAL
(f /. i2) `1 is V11() real ext-real Element of REAL
(W-min (L~ f)) `2 is V11() real ext-real Element of REAL
(f /. (i2 + 1)) `2 is V11() real ext-real Element of REAL
(f /. i2) `2 is V11() real ext-real Element of REAL
f is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ f is non empty compact Element of bool the carrier of (TOP-REAL 2)
len f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
{ (LSeg (f,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
union { (LSeg (f,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
W-max (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
W-bound (L~ f) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ f) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
the carrier of ((TOP-REAL 2) | (L~ f)) is non empty set
[: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is set
lower_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
(proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K430(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
W-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
SW-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
S-bound (L~ f) is V11() real ext-real Element of REAL
proj2 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
lower_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
(proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K430(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
NW-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
N-bound (L~ f) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
K429(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner (L~ f)),(NW-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SW-corner (L~ f))) + (b₁ * (NW-corner (L~ f)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((SW-corner (L~ f)),(NW-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (W-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (W-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (W-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (W-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (W-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (W-most (L~ f))),REAL:] is set
upper_bound (proj2 | (W-most (L~ f))) is V11() real ext-real Element of REAL
(proj2 | (W-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ f))) is V137() V138() V139() Element of bool REAL
K429(((proj2 | (W-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ f))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(upper_bound (proj2 | (W-most (L~ f))))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
rng f is Element of bool the carrier of (TOP-REAL 2)
i2 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
i2 + 1 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
f /. i2 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
f /. (i2 + 1) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
LSeg ((f /. i2),(f /. (i2 + 1))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (f /. i2)) + (b₁ * (f /. (i2 + 1)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
dom f is non empty non trivial V137() V138() V139() V140() V141() V142() Element of bool NAT
(f /. (i2 + 1)) `1 is V11() real ext-real Element of REAL
(W-max (L~ f)) `1 is V11() real ext-real Element of REAL
(f /. i2) `1 is V11() real ext-real Element of REAL
(f /. (i2 + 1)) `2 is V11() real ext-real Element of REAL
(W-max (L~ f)) `2 is V11() real ext-real Element of REAL
(f /. i2) `2 is V11() real ext-real Element of REAL
f is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ f is non empty compact Element of bool the carrier of (TOP-REAL 2)
len f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
{ (LSeg (f,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
union { (LSeg (f,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
E-min (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
E-bound (L~ f) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ f) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
the carrier of ((TOP-REAL 2) | (L~ f)) is non empty set
[: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is set
upper_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
(proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K429(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
E-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
SE-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
S-bound (L~ f) is V11() real ext-real Element of REAL
proj2 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
lower_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
(proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K430(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
NE-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
N-bound (L~ f) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
K429(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner (L~ f)),(NE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SE-corner (L~ f))) + (b₁ * (NE-corner (L~ f)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((SE-corner (L~ f)),(NE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (E-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (E-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (E-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (E-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (E-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (E-most (L~ f))),REAL:] is set
lower_bound (proj2 | (E-most (L~ f))) is V11() real ext-real Element of REAL
(proj2 | (E-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ f))) is V137() V138() V139() Element of bool REAL
K430(((proj2 | (E-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ f))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(lower_bound (proj2 | (E-most (L~ f))))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
rng f is Element of bool the carrier of (TOP-REAL 2)
i2 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
i2 + 1 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
f /. i2 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
f /. (i2 + 1) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
LSeg ((f /. i2),(f /. (i2 + 1))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (f /. i2)) + (b₁ * (f /. (i2 + 1)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
dom f is non empty non trivial V137() V138() V139() V140() V141() V142() Element of bool NAT
(f /. (i2 + 1)) `1 is V11() real ext-real Element of REAL
(E-min (L~ f)) `1 is V11() real ext-real Element of REAL
(f /. i2) `1 is V11() real ext-real Element of REAL
(E-min (L~ f)) `2 is V11() real ext-real Element of REAL
(f /. (i2 + 1)) `2 is V11() real ext-real Element of REAL
(f /. i2) `2 is V11() real ext-real Element of REAL
f is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ f is non empty compact Element of bool the carrier of (TOP-REAL 2)
len f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
{ (LSeg (f,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
union { (LSeg (f,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
E-max (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
E-bound (L~ f) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ f) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
the carrier of ((TOP-REAL 2) | (L~ f)) is non empty set
[: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is set
upper_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
(proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K429(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
E-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
SE-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
S-bound (L~ f) is V11() real ext-real Element of REAL
proj2 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
lower_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
(proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K430(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
NE-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
N-bound (L~ f) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
K429(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner (L~ f)),(NE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SE-corner (L~ f))) + (b₁ * (NE-corner (L~ f)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((SE-corner (L~ f)),(NE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (E-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (E-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (E-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (E-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (E-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (E-most (L~ f))),REAL:] is set
upper_bound (proj2 | (E-most (L~ f))) is V11() real ext-real Element of REAL
(proj2 | (E-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ f))) is V137() V138() V139() Element of bool REAL
K429(((proj2 | (E-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ f))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(upper_bound (proj2 | (E-most (L~ f))))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
rng f is Element of bool the carrier of (TOP-REAL 2)
i2 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
i2 + 1 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
f /. i2 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
f /. (i2 + 1) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
LSeg ((f /. i2),(f /. (i2 + 1))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (f /. i2)) + (b₁ * (f /. (i2 + 1)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
dom f is non empty non trivial V137() V138() V139() V140() V141() V142() Element of bool NAT
(f /. (i2 + 1)) `1 is V11() real ext-real Element of REAL
(E-max (L~ f)) `1 is V11() real ext-real Element of REAL
(f /. i2) `1 is V11() real ext-real Element of REAL
(f /. (i2 + 1)) `2 is V11() real ext-real Element of REAL
(E-max (L~ f)) `2 is V11() real ext-real Element of REAL
(f /. i2) `2 is V11() real ext-real Element of REAL
f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
i1 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
i2 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
j is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
M is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard FinSequence of the carrier of (TOP-REAL 2)
len M is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
mid (M,f,i1) is V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ (mid (M,f,i1)) is compact Element of bool the carrier of (TOP-REAL 2)
len (mid (M,f,i1)) is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
{ (LSeg ((mid (M,f,i1)),b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (mid (M,f,i1)) ) } is set
union { (LSeg ((mid (M,f,i1)),b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (mid (M,f,i1)) ) } is set
mid (M,i2,j) is V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ (mid (M,i2,j)) is compact Element of bool the carrier of (TOP-REAL 2)
len (mid (M,i2,j)) is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
{ (LSeg ((mid (M,i2,j)),b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (mid (M,i2,j)) ) } is set
union { (LSeg ((mid (M,i2,j)),b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (mid (M,i2,j)) ) } is set
{ (LSeg (M,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( f <= b₁ & not i1 <= b₁ ) } is set
{ (LSeg (M,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( i2 <= b₁ & not j <= b₁ ) } is set
union { (LSeg (M,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( i2 <= b₁ & not j <= b₁ ) } is set
g is set
y is set
k is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
LSeg (M,k) is Element of bool the carrier of (TOP-REAL 2)
l is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
LSeg (M,l) is Element of bool the carrier of (TOP-REAL 2)
l + 1 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
k + 1 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
union { (LSeg (M,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( f <= b₁ & not i1 <= b₁ ) } is set
f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
i1 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
i2 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
j is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
M is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard FinSequence of the carrier of (TOP-REAL 2)
len M is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
mid (M,f,i1) is V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ (mid (M,f,i1)) is compact Element of bool the carrier of (TOP-REAL 2)
len (mid (M,f,i1)) is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
{ (LSeg ((mid (M,f,i1)),b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (mid (M,f,i1)) ) } is set
union { (LSeg ((mid (M,f,i1)),b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (mid (M,f,i1)) ) } is set
mid (M,j,i2) is V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ (mid (M,j,i2)) is compact Element of bool the carrier of (TOP-REAL 2)
len (mid (M,j,i2)) is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
{ (LSeg ((mid (M,j,i2)),b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (mid (M,j,i2)) ) } is set
union { (LSeg ((mid (M,j,i2)),b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (mid (M,j,i2)) ) } is set
mid (M,i2,j) is V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
Rev (mid (M,i2,j)) is V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ (mid (M,i2,j)) is compact Element of bool the carrier of (TOP-REAL 2)
len (mid (M,i2,j)) is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
{ (LSeg ((mid (M,i2,j)),b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (mid (M,i2,j)) ) } is set
union { (LSeg ((mid (M,i2,j)),b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (mid (M,i2,j)) ) } is set
f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
i1 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
i2 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
j is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
M is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard FinSequence of the carrier of (TOP-REAL 2)
len M is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
mid (M,i1,f) is V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ (mid (M,i1,f)) is compact Element of bool the carrier of (TOP-REAL 2)
len (mid (M,i1,f)) is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
{ (LSeg ((mid (M,i1,f)),b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (mid (M,i1,f)) ) } is set
union { (LSeg ((mid (M,i1,f)),b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (mid (M,i1,f)) ) } is set
mid (M,j,i2) is V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ (mid (M,j,i2)) is compact Element of bool the carrier of (TOP-REAL 2)
len (mid (M,j,i2)) is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
{ (LSeg ((mid (M,j,i2)),b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (mid (M,j,i2)) ) } is set
union { (LSeg ((mid (M,j,i2)),b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (mid (M,j,i2)) ) } is set
mid (M,f,i1) is V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
Rev (mid (M,i1,f)) is V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ (mid (M,f,i1)) is compact Element of bool the carrier of (TOP-REAL 2)
len (mid (M,f,i1)) is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
{ (LSeg ((mid (M,f,i1)),b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (mid (M,f,i1)) ) } is set
union { (LSeg ((mid (M,f,i1)),b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (mid (M,f,i1)) ) } is set
f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
i1 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
i2 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
j is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
M is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard FinSequence of the carrier of (TOP-REAL 2)
len M is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
mid (M,i1,f) is V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ (mid (M,i1,f)) is compact Element of bool the carrier of (TOP-REAL 2)
len (mid (M,i1,f)) is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
{ (LSeg ((mid (M,i1,f)),b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (mid (M,i1,f)) ) } is set
union { (LSeg ((mid (M,i1,f)),b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (mid (M,i1,f)) ) } is set
mid (M,i2,j) is V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ (mid (M,i2,j)) is compact Element of bool the carrier of (TOP-REAL 2)
len (mid (M,i2,j)) is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
{ (LSeg ((mid (M,i2,j)),b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (mid (M,i2,j)) ) } is set
union { (LSeg ((mid (M,i2,j)),b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (mid (M,i2,j)) ) } is set
mid (M,f,i1) is V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
Rev (mid (M,i1,f)) is V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ (mid (M,f,i1)) is compact Element of bool the carrier of (TOP-REAL 2)
len (mid (M,f,i1)) is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
{ (LSeg ((mid (M,f,i1)),b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (mid (M,f,i1)) ) } is set
union { (LSeg ((mid (M,f,i1)),b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (mid (M,f,i1)) ) } is set
f is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard FinSequence of the carrier of (TOP-REAL 2)
L~ f is non empty compact Element of bool the carrier of (TOP-REAL 2)
len f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
{ (LSeg (f,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
union { (LSeg (f,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
N-max (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
N-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
NW-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
W-bound (L~ f) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ f) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
the carrier of ((TOP-REAL 2) | (L~ f)) is non empty set
[: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is set
lower_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
(proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K430(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
N-bound (L~ f) is V11() real ext-real Element of REAL
proj2 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
upper_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
(proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K429(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
NE-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
E-bound (L~ f) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
K429(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((NW-corner (L~ f)),(NE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NW-corner (L~ f))) + (b₁ * (NE-corner (L~ f)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((NW-corner (L~ f)),(NE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (N-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (N-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (N-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (N-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:] is set
upper_bound (proj1 | (N-most (L~ f))) is V11() real ext-real Element of REAL
(proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))) is V137() V138() V139() Element of bool REAL
K429(((proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))))) is V11() real ext-real Element of REAL
|[(upper_bound (proj1 | (N-most (L~ f)))),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
(N-max (L~ f)) `1 is V11() real ext-real Element of REAL
N-min (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
lower_bound (proj1 | (N-most (L~ f))) is V11() real ext-real Element of REAL
K430(((proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (N-most (L~ f)))),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
(N-min (L~ f)) `1 is V11() real ext-real Element of REAL
(N-min (L~ f)) .. f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
3 + 1 is non empty natural V11() real V37() ext-real positive non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
1 + 1 is non empty natural V11() real V37() ext-real positive non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
rng f is non empty non trivial Element of bool the carrier of (TOP-REAL 2)
dom f is non empty non trivial V137() V138() V139() V140() V141() V142() Element of bool NAT
f . ((N-min (L~ f)) .. f) is set
f /. ((N-min (L~ f)) .. f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(N-min (L~ f)) `2 is V11() real ext-real Element of REAL
f /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
LSeg (f,1) is Element of bool the carrier of (TOP-REAL 2)
f /. (1 + 1) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(len f) -' 1 is natural V11() real V37() ext-real non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
((len f) -' 1) + 1 is non empty natural V11() real V37() ext-real positive non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
f /. ((len f) -' 1) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
LSeg (f,((len f) -' 1)) is Element of bool the carrier of (TOP-REAL 2)
f /. (len f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(f /. (1 + 1)) `1 is V11() real ext-real Element of REAL
(f /. ((len f) -' 1)) `1 is V11() real ext-real Element of REAL
(f /. (1 + 1)) `2 is V11() real ext-real Element of REAL
(f /. ((len f) -' 1)) `2 is V11() real ext-real Element of REAL
LSeg ((f /. 1),(f /. (1 + 1))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (f /. 1)) + (b<sub>1</sub> * (f /. (1 + 1)))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
LSeg ((f /. 1),(f /. ((len f) -' 1))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (f /. 1)) + (b<sub>1</sub> * (f /. ((len f) -' 1)))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg (f,((len f) -' 1))) /\ (LSeg (f,1)) is Element of bool the carrier of (TOP-REAL 2)
{(f /. 1)} is non empty trivial set
f . 1 is set
(f /. ((len f) -' 1)) `2 is V11() real ext-real Element of REAL
(f /. ((len f) -' 1)) `1 is V11() real ext-real Element of REAL
(f /. (1 + 1)) `2 is V11() real ext-real Element of REAL
(f /. (1 + 1)) `1 is V11() real ext-real Element of REAL
((N-min (L~ f)) .. f) -' 1 is natural V11() real V37() ext-real non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
(((N-min (L~ f)) .. f) -' 1) + 1 is non empty natural V11() real V37() ext-real positive non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
f /. (((N-min (L~ f)) .. f) -' 1) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
LSeg (f,(((N-min (L~ f)) .. f) -' 1)) is Element of bool the carrier of (TOP-REAL 2)
((N-min (L~ f)) .. f) + 1 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
f /. (((N-min (L~ f)) .. f) + 1) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
LSeg (f,((N-min (L~ f)) .. f)) is Element of bool the carrier of (TOP-REAL 2)
(f /. (((N-min (L~ f)) .. f) + 1)) `1 is V11() real ext-real Element of REAL
(f /. (((N-min (L~ f)) .. f) -' 1)) `1 is V11() real ext-real Element of REAL
(f /. (((N-min (L~ f)) .. f) + 1)) `2 is V11() real ext-real Element of REAL
(f /. (((N-min (L~ f)) .. f) -' 1)) `2 is V11() real ext-real Element of REAL
LSeg ((f /. ((N-min (L~ f)) .. f)),(f /. (((N-min (L~ f)) .. f) + 1))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (f /. ((N-min (L~ f)) .. f))) + (b<sub>1</sub> * (f /. (((N-min (L~ f)) .. f) + 1)))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
LSeg ((f /. ((N-min (L~ f)) .. f)),(f /. (((N-min (L~ f)) .. f) -' 1))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (f /. ((N-min (L~ f)) .. f))) + (b<sub>1</sub> * (f /. (((N-min (L~ f)) .. f) -' 1)))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg (f,(((N-min (L~ f)) .. f) -' 1))) /\ (LSeg (f,((N-min (L~ f)) .. f))) is Element of bool the carrier of (TOP-REAL 2)
((((N-min (L~ f)) .. f) -' 1) + 1) + 1 is non empty natural V11() real V37() ext-real positive non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
(((N-min (L~ f)) .. f) -' 1) + (1 + 1) is non empty natural V11() real V37() ext-real positive non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
{(f /. ((N-min (L~ f)) .. f))} is non empty trivial set
(f /. (((N-min (L~ f)) .. f) -' 1)) `2 is V11() real ext-real Element of REAL
(f /. (((N-min (L~ f)) .. f) -' 1)) `1 is V11() real ext-real Element of REAL
(f /. (((N-min (L~ f)) .. f) + 1)) `2 is V11() real ext-real Element of REAL
(f /. (((N-min (L~ f)) .. f) + 1)) `1 is V11() real ext-real Element of REAL
f is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard FinSequence of the carrier of (TOP-REAL 2)
L~ f is non empty compact Element of bool the carrier of (TOP-REAL 2)
len f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
{ (LSeg (f,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len f ) } is set
union { (LSeg (f,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len f ) } is set
N-min (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
N-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
NW-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
W-bound (L~ f) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ f) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
the carrier of ((TOP-REAL 2) | (L~ f)) is non empty set
[: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is set
lower_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
(proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K430(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
N-bound (L~ f) is V11() real ext-real Element of REAL
proj2 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
upper_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
(proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K429(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
NE-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
E-bound (L~ f) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
K429(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((NW-corner (L~ f)),(NE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (NW-corner (L~ f))) + (b<sub>1</sub> * (NE-corner (L~ f)))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg ((NW-corner (L~ f)),(NE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (N-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (N-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (N-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (N-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:] is set
lower_bound (proj1 | (N-most (L~ f))) is V11() real ext-real Element of REAL
(proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))) is V137() V138() V139() Element of bool REAL
K430(((proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (N-most (L~ f)))),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
N-max (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
upper_bound (proj1 | (N-most (L~ f))) is V11() real ext-real Element of REAL
K429(((proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))))) is V11() real ext-real Element of REAL
|[(upper_bound (proj1 | (N-most (L~ f)))),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
(N-max (L~ f)) `1 is V11() real ext-real Element of REAL
(N-min (L~ f)) `1 is V11() real ext-real Element of REAL
f is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard FinSequence of the carrier of (TOP-REAL 2)
L~ f is non empty compact Element of bool the carrier of (TOP-REAL 2)
len f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
{ (LSeg (f,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len f ) } is set
union { (LSeg (f,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len f ) } is set
E-max (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
E-bound (L~ f) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ f) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
the carrier of ((TOP-REAL 2) | (L~ f)) is non empty set
[: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is set
upper_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
(proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K429(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
E-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
SE-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
S-bound (L~ f) is V11() real ext-real Element of REAL
proj2 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
lower_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
(proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K430(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
NE-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
N-bound (L~ f) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
K429(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner (L~ f)),(NE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (SE-corner (L~ f))) + (b<sub>1</sub> * (NE-corner (L~ f)))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg ((SE-corner (L~ f)),(NE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (E-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (E-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (E-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (E-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (E-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (E-most (L~ f))),REAL:] is set
upper_bound (proj2 | (E-most (L~ f))) is V11() real ext-real Element of REAL
(proj2 | (E-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ f))) is V137() V138() V139() Element of bool REAL
K429(((proj2 | (E-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ f))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(upper_bound (proj2 | (E-most (L~ f))))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
(E-max (L~ f)) `2 is V11() real ext-real Element of REAL
E-min (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
lower_bound (proj2 | (E-most (L~ f))) is V11() real ext-real Element of REAL
K430(((proj2 | (E-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ f))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(lower_bound (proj2 | (E-most (L~ f))))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
(E-min (L~ f)) `2 is V11() real ext-real Element of REAL
(E-min (L~ f)) .. f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
3 + 1 is non empty natural V11() real V37() ext-real positive non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
1 + 1 is non empty natural V11() real V37() ext-real positive non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
rng f is non empty non trivial Element of bool the carrier of (TOP-REAL 2)
dom f is non empty non trivial V137() V138() V139() V140() V141() V142() Element of bool NAT
f . ((E-min (L~ f)) .. f) is set
f /. ((E-min (L~ f)) .. f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(E-min (L~ f)) `1 is V11() real ext-real Element of REAL
f /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
LSeg (f,1) is Element of bool the carrier of (TOP-REAL 2)
f /. (1 + 1) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(len f) -' 1 is natural V11() real V37() ext-real non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
((len f) -' 1) + 1 is non empty natural V11() real V37() ext-real positive non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
f /. ((len f) -' 1) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
LSeg (f,((len f) -' 1)) is Element of bool the carrier of (TOP-REAL 2)
f /. (len f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(f /. (1 + 1)) `2 is V11() real ext-real Element of REAL
(f /. ((len f) -' 1)) `2 is V11() real ext-real Element of REAL
(f /. (1 + 1)) `1 is V11() real ext-real Element of REAL
(f /. ((len f) -' 1)) `1 is V11() real ext-real Element of REAL
LSeg ((f /. 1),(f /. (1 + 1))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (f /. 1)) + (b₁ * (f /. (1 + 1)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
LSeg ((f /. 1),(f /. ((len f) -' 1))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (f /. 1)) + (b₁ * (f /. ((len f) -' 1)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg (f,((len f) -' 1))) /\ (LSeg (f,1)) is Element of bool the carrier of (TOP-REAL 2)
{(f /. 1)} is non empty trivial set
f . 1 is set
(f /. ((len f) -' 1)) `1 is V11() real ext-real Element of REAL
(f /. ((len f) -' 1)) `2 is V11() real ext-real Element of REAL
(f /. (1 + 1)) `1 is V11() real ext-real Element of REAL
(f /. (1 + 1)) `2 is V11() real ext-real Element of REAL
((E-min (L~ f)) .. f) -' 1 is natural V11() real V37() ext-real non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
(((E-min (L~ f)) .. f) -' 1) + 1 is non empty natural V11() real V37() ext-real positive non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
f /. (((E-min (L~ f)) .. f) -' 1) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
LSeg (f,(((E-min (L~ f)) .. f) -' 1)) is Element of bool the carrier of (TOP-REAL 2)
((E-min (L~ f)) .. f) + 1 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
f /. (((E-min (L~ f)) .. f) + 1) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
LSeg (f,((E-min (L~ f)) .. f)) is Element of bool the carrier of (TOP-REAL 2)
(f /. (((E-min (L~ f)) .. f) + 1)) `2 is V11() real ext-real Element of REAL
(f /. (((E-min (L~ f)) .. f) -' 1)) `2 is V11() real ext-real Element of REAL
(f /. (((E-min (L~ f)) .. f) + 1)) `1 is V11() real ext-real Element of REAL
(f /. (((E-min (L~ f)) .. f) -' 1)) `1 is V11() real ext-real Element of REAL
LSeg ((f /. ((E-min (L~ f)) .. f)),(f /. (((E-min (L~ f)) .. f) + 1))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (f /. ((E-min (L~ f)) .. f))) + (b₁ * (f /. (((E-min (L~ f)) .. f) + 1)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
LSeg ((f /. ((E-min (L~ f)) .. f)),(f /. (((E-min (L~ f)) .. f) -' 1))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (f /. ((E-min (L~ f)) .. f))) + (b₁ * (f /. (((E-min (L~ f)) .. f) -' 1)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg (f,(((E-min (L~ f)) .. f) -' 1))) /\ (LSeg (f,((E-min (L~ f)) .. f))) is Element of bool the carrier of (TOP-REAL 2)
((((E-min (L~ f)) .. f) -' 1) + 1) + 1 is non empty natural V11() real V37() ext-real positive non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
(((E-min (L~ f)) .. f) -' 1) + (1 + 1) is non empty natural V11() real V37() ext-real positive non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
{(f /. ((E-min (L~ f)) .. f))} is non empty trivial set
(f /. (((E-min (L~ f)) .. f) -' 1)) `1 is V11() real ext-real Element of REAL
(f /. (((E-min (L~ f)) .. f) -' 1)) `2 is V11() real ext-real Element of REAL
(f /. (((E-min (L~ f)) .. f) + 1)) `1 is V11() real ext-real Element of REAL
(f /. (((E-min (L~ f)) .. f) + 1)) `2 is V11() real ext-real Element of REAL
f is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard FinSequence of the carrier of (TOP-REAL 2)
L~ f is non empty compact Element of bool the carrier of (TOP-REAL 2)
len f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
{ (LSeg (f,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
union { (LSeg (f,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
E-min (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
E-bound (L~ f) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ f) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
the carrier of ((TOP-REAL 2) | (L~ f)) is non empty set
[: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is set
upper_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
(proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K429(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
E-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
SE-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
S-bound (L~ f) is V11() real ext-real Element of REAL
proj2 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
lower_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
(proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K430(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
NE-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
N-bound (L~ f) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
K429(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner (L~ f)),(NE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SE-corner (L~ f))) + (b₁ * (NE-corner (L~ f)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((SE-corner (L~ f)),(NE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (E-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (E-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (E-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (E-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (E-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (E-most (L~ f))),REAL:] is set
lower_bound (proj2 | (E-most (L~ f))) is V11() real ext-real Element of REAL
(proj2 | (E-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ f))) is V137() V138() V139() Element of bool REAL
K430(((proj2 | (E-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ f))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(lower_bound (proj2 | (E-most (L~ f))))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
E-max (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
upper_bound (proj2 | (E-most (L~ f))) is V11() real ext-real Element of REAL
K429(((proj2 | (E-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ f))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(upper_bound (proj2 | (E-most (L~ f))))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
(E-max (L~ f)) `2 is V11() real ext-real Element of REAL
(E-min (L~ f)) `2 is V11() real ext-real Element of REAL
f is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard FinSequence of the carrier of (TOP-REAL 2)
L~ f is non empty compact Element of bool the carrier of (TOP-REAL 2)
len f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
{ (LSeg (f,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
union { (LSeg (f,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
S-max (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
S-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
SW-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
W-bound (L~ f) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ f) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
the carrier of ((TOP-REAL 2) | (L~ f)) is non empty set
[: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is set
lower_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
(proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K430(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
S-bound (L~ f) is V11() real ext-real Element of REAL
proj2 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
lower_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
(proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K430(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
SE-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
E-bound (L~ f) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
K429(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner (L~ f)),(SE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SW-corner (L~ f))) + (b₁ * (SE-corner (L~ f)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((SW-corner (L~ f)),(SE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (S-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (S-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (S-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (S-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (S-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (S-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (S-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (S-most (L~ f))),REAL:] is set
upper_bound (proj1 | (S-most (L~ f))) is V11() real ext-real Element of REAL
(proj1 | (S-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (S-most (L~ f))) is V137() V138() V139() Element of bool REAL
K429(((proj1 | (S-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (S-most (L~ f))))) is V11() real ext-real Element of REAL
|[(upper_bound (proj1 | (S-most (L~ f)))),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
(S-max (L~ f)) `1 is V11() real ext-real Element of REAL
S-min (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
lower_bound (proj1 | (S-most (L~ f))) is V11() real ext-real Element of REAL
K430(((proj1 | (S-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (S-most (L~ f))))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (S-most (L~ f)))),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
(S-min (L~ f)) `1 is V11() real ext-real Element of REAL
(S-min (L~ f)) .. f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
3 + 1 is non empty natural V11() real V37() ext-real positive non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
1 + 1 is non empty natural V11() real V37() ext-real positive non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
rng f is non empty non trivial Element of bool the carrier of (TOP-REAL 2)
dom f is non empty non trivial V137() V138() V139() V140() V141() V142() Element of bool NAT
f . ((S-min (L~ f)) .. f) is set
f /. ((S-min (L~ f)) .. f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(S-min (L~ f)) `2 is V11() real ext-real Element of REAL
f /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
LSeg (f,1) is Element of bool the carrier of (TOP-REAL 2)
f /. (1 + 1) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(len f) -' 1 is natural V11() real V37() ext-real non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
((len f) -' 1) + 1 is non empty natural V11() real V37() ext-real positive non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
f /. ((len f) -' 1) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
LSeg (f,((len f) -' 1)) is Element of bool the carrier of (TOP-REAL 2)
f /. (len f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(f /. (1 + 1)) `1 is V11() real ext-real Element of REAL
(f /. ((len f) -' 1)) `1 is V11() real ext-real Element of REAL
(f /. (1 + 1)) `2 is V11() real ext-real Element of REAL
(f /. ((len f) -' 1)) `2 is V11() real ext-real Element of REAL
LSeg ((f /. 1),(f /. (1 + 1))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (f /. 1)) + (b<sub>1</sub> * (f /. (1 + 1)))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
LSeg ((f /. 1),(f /. ((len f) -' 1))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (f /. 1)) + (b<sub>1</sub> * (f /. ((len f) -' 1)))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg (f,((len f) -' 1))) /\ (LSeg (f,1)) is Element of bool the carrier of (TOP-REAL 2)
{(f /. 1)} is non empty trivial set
f . 1 is set
(f /. ((len f) -' 1)) `2 is V11() real ext-real Element of REAL
(f /. ((len f) -' 1)) `1 is V11() real ext-real Element of REAL
(f /. (1 + 1)) `2 is V11() real ext-real Element of REAL
(f /. (1 + 1)) `1 is V11() real ext-real Element of REAL
((S-min (L~ f)) .. f) -' 1 is natural V11() real V37() ext-real non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
(((S-min (L~ f)) .. f) -' 1) + 1 is non empty natural V11() real V37() ext-real positive non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
f /. (((S-min (L~ f)) .. f) -' 1) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
LSeg (f,(((S-min (L~ f)) .. f) -' 1)) is Element of bool the carrier of (TOP-REAL 2)
((S-min (L~ f)) .. f) + 1 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
f /. (((S-min (L~ f)) .. f) + 1) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
LSeg (f,((S-min (L~ f)) .. f)) is Element of bool the carrier of (TOP-REAL 2)
(f /. (((S-min (L~ f)) .. f) + 1)) `1 is V11() real ext-real Element of REAL
(f /. (((S-min (L~ f)) .. f) -' 1)) `1 is V11() real ext-real Element of REAL
(f /. (((S-min (L~ f)) .. f) + 1)) `2 is V11() real ext-real Element of REAL
(f /. (((S-min (L~ f)) .. f) -' 1)) `2 is V11() real ext-real Element of REAL
LSeg ((f /. ((S-min (L~ f)) .. f)),(f /. (((S-min (L~ f)) .. f) + 1))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (f /. ((S-min (L~ f)) .. f))) + (b<sub>1</sub> * (f /. (((S-min (L~ f)) .. f) + 1)))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
LSeg ((f /. ((S-min (L~ f)) .. f)),(f /. (((S-min (L~ f)) .. f) -' 1))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (f /. ((S-min (L~ f)) .. f))) + (b<sub>1</sub> * (f /. (((S-min (L~ f)) .. f) -' 1)))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg (f,(((S-min (L~ f)) .. f) -' 1))) /\ (LSeg (f,((S-min (L~ f)) .. f))) is Element of bool the carrier of (TOP-REAL 2)
((((S-min (L~ f)) .. f) -' 1) + 1) + 1 is non empty natural V11() real V37() ext-real positive non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
(((S-min (L~ f)) .. f) -' 1) + (1 + 1) is non empty natural V11() real V37() ext-real positive non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
{(f /. ((S-min (L~ f)) .. f))} is non empty trivial set
(f /. (((S-min (L~ f)) .. f) -' 1)) `2 is V11() real ext-real Element of REAL
(f /. (((S-min (L~ f)) .. f) -' 1)) `1 is V11() real ext-real Element of REAL
(f /. (((S-min (L~ f)) .. f) + 1)) `2 is V11() real ext-real Element of REAL
(f /. (((S-min (L~ f)) .. f) + 1)) `1 is V11() real ext-real Element of REAL
f is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard FinSequence of the carrier of (TOP-REAL 2)
L~ f is non empty compact Element of bool the carrier of (TOP-REAL 2)
len f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
{ (LSeg (f,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len f ) } is set
union { (LSeg (f,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len f ) } is set
S-min (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
S-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
SW-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
W-bound (L~ f) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ f) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
the carrier of ((TOP-REAL 2) | (L~ f)) is non empty set
[: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is set
lower_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
(proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K430(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
S-bound (L~ f) is V11() real ext-real Element of REAL
proj2 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
lower_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
(proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K430(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
SE-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
E-bound (L~ f) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
K429(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner (L~ f)),(SE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (SW-corner (L~ f))) + (b<sub>1</sub> * (SE-corner (L~ f)))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg ((SW-corner (L~ f)),(SE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (S-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (S-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (S-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (S-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (S-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (S-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (S-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (S-most (L~ f))),REAL:] is set
lower_bound (proj1 | (S-most (L~ f))) is V11() real ext-real Element of REAL
(proj1 | (S-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (S-most (L~ f))) is V137() V138() V139() Element of bool REAL
K430(((proj1 | (S-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (S-most (L~ f))))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (S-most (L~ f)))),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
S-max (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
upper_bound (proj1 | (S-most (L~ f))) is V11() real ext-real Element of REAL
K429(((proj1 | (S-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (S-most (L~ f))))) is V11() real ext-real Element of REAL
|[(upper_bound (proj1 | (S-most (L~ f)))),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
(S-max (L~ f)) `1 is V11() real ext-real Element of REAL
(S-min (L~ f)) `1 is V11() real ext-real Element of REAL
f is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard FinSequence of the carrier of (TOP-REAL 2)
L~ f is non empty compact Element of bool the carrier of (TOP-REAL 2)
len f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
{ (LSeg (f,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len f ) } is set
union { (LSeg (f,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len f ) } is set
W-max (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
W-bound (L~ f) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ f) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
the carrier of ((TOP-REAL 2) | (L~ f)) is non empty set
[: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is set
lower_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
(proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K430(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
W-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
SW-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
S-bound (L~ f) is V11() real ext-real Element of REAL
proj2 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
lower_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
(proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K430(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
NW-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
N-bound (L~ f) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
K429(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner (L~ f)),(NW-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (SW-corner (L~ f))) + (b<sub>1</sub> * (NW-corner (L~ f)))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg ((SW-corner (L~ f)),(NW-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (W-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (W-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (W-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (W-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (W-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (W-most (L~ f))),REAL:] is set
upper_bound (proj2 | (W-most (L~ f))) is V11() real ext-real Element of REAL
(proj2 | (W-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ f))) is V137() V138() V139() Element of bool REAL
K429(((proj2 | (W-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ f))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(upper_bound (proj2 | (W-most (L~ f))))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
(W-max (L~ f)) `2 is V11() real ext-real Element of REAL
W-min (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
lower_bound (proj2 | (W-most (L~ f))) is V11() real ext-real Element of REAL
K430(((proj2 | (W-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ f))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(lower_bound (proj2 | (W-most (L~ f))))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
(W-min (L~ f)) `2 is V11() real ext-real Element of REAL
(W-min (L~ f)) .. f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
3 + 1 is non empty natural V11() real V37() ext-real positive non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
1 + 1 is non empty natural V11() real V37() ext-real positive non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
rng f is non empty non trivial Element of bool the carrier of (TOP-REAL 2)
dom f is non empty non trivial V137() V138() V139() V140() V141() V142() Element of bool NAT
f . ((W-min (L~ f)) .. f) is set
f /. ((W-min (L~ f)) .. f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(W-min (L~ f)) `1 is V11() real ext-real Element of REAL
f /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
LSeg (f,1) is Element of bool the carrier of (TOP-REAL 2)
f /. (1 + 1) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(len f) -' 1 is natural V11() real V37() ext-real non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
((len f) -' 1) + 1 is non empty natural V11() real V37() ext-real positive non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
f /. ((len f) -' 1) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
LSeg (f,((len f) -' 1)) is Element of bool the carrier of (TOP-REAL 2)
f /. (len f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(f /. (1 + 1)) `2 is V11() real ext-real Element of REAL
(f /. ((len f) -' 1)) `2 is V11() real ext-real Element of REAL
(f /. (1 + 1)) `1 is V11() real ext-real Element of REAL
(f /. ((len f) -' 1)) `1 is V11() real ext-real Element of REAL
LSeg ((f /. 1),(f /. (1 + 1))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (f /. 1)) + (b₁ * (f /. (1 + 1)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
LSeg ((f /. 1),(f /. ((len f) -' 1))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (f /. 1)) + (b₁ * (f /. ((len f) -' 1)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg (f,((len f) -' 1))) /\ (LSeg (f,1)) is Element of bool the carrier of (TOP-REAL 2)
{(f /. 1)} is non empty trivial set
f . 1 is set
(f /. ((len f) -' 1)) `1 is V11() real ext-real Element of REAL
(f /. ((len f) -' 1)) `2 is V11() real ext-real Element of REAL
(f /. (1 + 1)) `1 is V11() real ext-real Element of REAL
(f /. (1 + 1)) `2 is V11() real ext-real Element of REAL
((W-min (L~ f)) .. f) -' 1 is natural V11() real V37() ext-real non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
(((W-min (L~ f)) .. f) -' 1) + 1 is non empty natural V11() real V37() ext-real positive non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
f /. (((W-min (L~ f)) .. f) -' 1) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
LSeg (f,(((W-min (L~ f)) .. f) -' 1)) is Element of bool the carrier of (TOP-REAL 2)
((W-min (L~ f)) .. f) + 1 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
f /. (((W-min (L~ f)) .. f) + 1) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
LSeg (f,((W-min (L~ f)) .. f)) is Element of bool the carrier of (TOP-REAL 2)
(f /. (((W-min (L~ f)) .. f) + 1)) `2 is V11() real ext-real Element of REAL
(f /. (((W-min (L~ f)) .. f) -' 1)) `2 is V11() real ext-real Element of REAL
(f /. (((W-min (L~ f)) .. f) + 1)) `1 is V11() real ext-real Element of REAL
(f /. (((W-min (L~ f)) .. f) -' 1)) `1 is V11() real ext-real Element of REAL
LSeg ((f /. ((W-min (L~ f)) .. f)),(f /. (((W-min (L~ f)) .. f) + 1))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (f /. ((W-min (L~ f)) .. f))) + (b₁ * (f /. (((W-min (L~ f)) .. f) + 1)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
LSeg ((f /. ((W-min (L~ f)) .. f)),(f /. (((W-min (L~ f)) .. f) -' 1))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (f /. ((W-min (L~ f)) .. f))) + (b₁ * (f /. (((W-min (L~ f)) .. f) -' 1)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg (f,(((W-min (L~ f)) .. f) -' 1))) /\ (LSeg (f,((W-min (L~ f)) .. f))) is Element of bool the carrier of (TOP-REAL 2)
((((W-min (L~ f)) .. f) -' 1) + 1) + 1 is non empty natural V11() real V37() ext-real positive non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
(((W-min (L~ f)) .. f) -' 1) + (1 + 1) is non empty natural V11() real V37() ext-real positive non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
{(f /. ((W-min (L~ f)) .. f))} is non empty trivial set
(f /. (((W-min (L~ f)) .. f) -' 1)) `1 is V11() real ext-real Element of REAL
(f /. (((W-min (L~ f)) .. f) -' 1)) `2 is V11() real ext-real Element of REAL
(f /. (((W-min (L~ f)) .. f) + 1)) `1 is V11() real ext-real Element of REAL
(f /. (((W-min (L~ f)) .. f) + 1)) `2 is V11() real ext-real Element of REAL
f is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard FinSequence of the carrier of (TOP-REAL 2)
L~ f is non empty compact Element of bool the carrier of (TOP-REAL 2)
len f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
{ (LSeg (f,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
union { (LSeg (f,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
W-min (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
W-bound (L~ f) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ f) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
the carrier of ((TOP-REAL 2) | (L~ f)) is non empty set
[: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is set
lower_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
(proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K430(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
W-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
SW-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
S-bound (L~ f) is V11() real ext-real Element of REAL
proj2 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
lower_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
(proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K430(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
NW-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
N-bound (L~ f) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
K429(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner (L~ f)),(NW-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SW-corner (L~ f))) + (b₁ * (NW-corner (L~ f)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((SW-corner (L~ f)),(NW-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (W-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (W-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (W-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (W-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (W-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (W-most (L~ f))),REAL:] is set
lower_bound (proj2 | (W-most (L~ f))) is V11() real ext-real Element of REAL
(proj2 | (W-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ f))) is V137() V138() V139() Element of bool REAL
K430(((proj2 | (W-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ f))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(lower_bound (proj2 | (W-most (L~ f))))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
W-max (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
upper_bound (proj2 | (W-most (L~ f))) is V11() real ext-real Element of REAL
K429(((proj2 | (W-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ f))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(upper_bound (proj2 | (W-most (L~ f))))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
(W-max (L~ f)) `2 is V11() real ext-real Element of REAL
(W-min (L~ f)) `2 is V11() real ext-real Element of REAL
f is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard FinSequence of the carrier of (TOP-REAL 2)
L~ f is non empty compact Element of bool the carrier of (TOP-REAL 2)
len f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
{ (LSeg (f,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
union { (LSeg (f,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
NW-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
W-bound (L~ f) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ f) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
the carrier of ((TOP-REAL 2) | (L~ f)) is non empty set
[: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is set
lower_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
(proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K430(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
N-bound (L~ f) is V11() real ext-real Element of REAL
proj2 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
upper_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
(proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K429(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
N-min (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
N-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
NE-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
E-bound (L~ f) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
K429(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((NW-corner (L~ f)),(NE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NW-corner (L~ f))) + (b₁ * (NE-corner (L~ f)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((NW-corner (L~ f)),(NE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (N-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (N-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (N-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (N-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:] is set
lower_bound (proj1 | (N-most (L~ f))) is V11() real ext-real Element of REAL
(proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))) is V137() V138() V139() Element of bool REAL
K430(((proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (N-most (L~ f)))),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((NW-corner (L~ f)),(N-min (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NW-corner (L~ f))) + (b₁ * (N-min (L~ f)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
N-max (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
upper_bound (proj1 | (N-most (L~ f))) is V11() real ext-real Element of REAL
K429(((proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))))) is V11() real ext-real Element of REAL
|[(upper_bound (proj1 | (N-most (L~ f)))),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((N-max (L~ f)),(NE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (N-max (L~ f))) + (b₁ * (NE-corner (L~ f)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(N-min (L~ f)) `2 is V11() real ext-real Element of REAL
(N-max (L~ f)) `2 is V11() real ext-real Element of REAL
i1 is set
(N-max (L~ f)) `1 is V11() real ext-real Element of REAL
(NE-corner (L~ f)) `1 is V11() real ext-real Element of REAL
i2 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
i2 `1 is V11() real ext-real Element of REAL
(NW-corner (L~ f)) `1 is V11() real ext-real Element of REAL
(N-min (L~ f)) `1 is V11() real ext-real Element of REAL
f is V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
f /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(f /. 1) `1 is V11() real ext-real Element of REAL
(f /. 1) `2 is V11() real ext-real Element of REAL
L~ f is compact Element of bool the carrier of (TOP-REAL 2)
len f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
{ (LSeg (f,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len f ) } is set
union { (LSeg (f,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len f ) } is set
{(f /. 1)} is non empty trivial set
i1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
i1 `1 is V11() real ext-real Element of REAL
i1 `2 is V11() real ext-real Element of REAL
LSeg (i1,(f /. 1)) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * i1) + (b<sub>1</sub> * (f /. 1))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg (i1,(f /. 1))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
<*i1*> is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() V33(1) FinSequence-like FinSubsequence-like special FinSequence of the carrier of (TOP-REAL 2)
<*i1*> ^ f is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
1 + 1 is non empty natural V11() real V37() ext-real positive non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
i2 is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
len i2 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
i2 /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
LSeg (i2,1) is Element of bool the carrier of (TOP-REAL 2)
<*i1*> ^ i2 is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len (<*i1*> ^ i2) is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
len <*i1*> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
(len <*i1*>) + (len i2) is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
rng i2 is Element of bool the carrier of (TOP-REAL 2)
L~ i2 is non empty compact Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (i2,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len i2 ) } is set
union { (LSeg (i2,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len i2 ) } is set
LSeg (i1,(i2 /. 1)) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * i1) + (b<sub>1</sub> * (i2 /. 1))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
{(i2 /. 1)} is non empty trivial set
{i1} is non empty trivial set
rng <*i1*> is Element of bool the carrier of (TOP-REAL 2)
L~ <*i1*> is compact Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (<*i1*>,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len <*i1*> ) } is set
union { (LSeg (<*i1*>,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len <*i1*> ) } is set
(L~ <*i1*>) /\ (L~ i2) is Element of bool the carrier of (TOP-REAL 2)
dom i2 is non empty non trivial V137() V138() V139() V140() V141() V142() Element of bool NAT
M is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
M + 1 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
LSeg (i2,M) is Element of bool the carrier of (TOP-REAL 2)
(LSeg (i2,1)) /\ (LSeg (i2,M)) is Element of bool the carrier of (TOP-REAL 2)
LSeg (i2,(1 + 1)) is Element of bool the carrier of (TOP-REAL 2)
(LSeg (i2,1)) /\ (LSeg (i2,(1 + 1))) is Element of bool the carrier of (TOP-REAL 2)
i2 /. 2 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
{(i2 /. 2)} is non empty trivial set
i2 /. 2 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
i2 /. 2 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
i2 . 1 is set
i2 . 2 is set
(LSeg (i2,M)) /\ (LSeg (i1,(i2 /. 1))) is Element of bool the carrier of (TOP-REAL 2)
<*i1*> /. (len <*i1*>) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
M is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
M + 2 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
LSeg (<*i1*>,M) is Element of bool the carrier of (TOP-REAL 2)
(LSeg (i1,(i2 /. 1))) /\ (LSeg (i2,1)) is Element of bool the carrier of (TOP-REAL 2)
f is V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
f /. (len f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(f /. (len f)) `1 is V11() real ext-real Element of REAL
(f /. (len f)) `2 is V11() real ext-real Element of REAL
L~ f is compact Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (f,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len f ) } is set
union { (LSeg (f,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len f ) } is set
{(f /. (len f))} is non empty trivial set
i1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
i1 `1 is V11() real ext-real Element of REAL
i1 `2 is V11() real ext-real Element of REAL
LSeg (i1,(f /. (len f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * i1) + (b<sub>1</sub> * (f /. (len f)))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg (i1,(f /. (len f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
<*i1*> is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() V33(1) FinSequence-like FinSubsequence-like special FinSequence of the carrier of (TOP-REAL 2)
f ^ <*i1*> is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
<*(f /. (len f)),i1*> is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() V33(2) FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len <*(f /. (len f)),i1*> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
1 + 1 is non empty natural V11() real V37() ext-real positive non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
mid (<*(f /. (len f)),i1*>,2,(len <*(f /. (len f)),i1*>)) is V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
<*(f /. (len f)),i1*> /. 2 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
<*(<*(f /. (len f)),i1*> /. 2)*> is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() V33(1) FinSequence-like FinSubsequence-like special FinSequence of the carrier of (TOP-REAL 2)
j is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
len j is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
dom j is non empty non trivial V137() V138() V139() V140() V141() V142() Element of bool NAT
<*(f /. (len f)),i1*> . 1 is set
f . (len f) is set
L~ <*(f /. (len f)),i1*> is compact Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (<*(f /. (len f)),i1*>,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len <*(f /. (len f)),i1*> ) } is set
union { (LSeg (<*(f /. (len f)),i1*>,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len <*(f /. (len f)),i1*> ) } is set
(L~ f) /\ (L~ <*(f /. (len f)),i1*>) is Element of bool the carrier of (TOP-REAL 2)
{(f . (len f))} is non empty trivial set
f is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard FinSequence of the carrier of (TOP-REAL 2)
dom f is non empty non trivial V137() V138() V139() V140() V141() V142() Element of bool NAT
L~ f is non empty compact Element of bool the carrier of (TOP-REAL 2)
len f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
{ (LSeg (f,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len f ) } is set
union { (LSeg (f,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len f ) } is set
N-max (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
N-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
NW-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
W-bound (L~ f) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ f) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
the carrier of ((TOP-REAL 2) | (L~ f)) is non empty set
[: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is set
lower_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
(proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K430(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
N-bound (L~ f) is V11() real ext-real Element of REAL
proj2 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
upper_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
(proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K429(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
NE-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
E-bound (L~ f) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
K429(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((NW-corner (L~ f)),(NE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (NW-corner (L~ f))) + (b<sub>1</sub> * (NE-corner (L~ f)))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg ((NW-corner (L~ f)),(NE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (N-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (N-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (N-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (N-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:] is set
upper_bound (proj1 | (N-most (L~ f))) is V11() real ext-real Element of REAL
(proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))) is V137() V138() V139() Element of bool REAL
K429(((proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))))) is V11() real ext-real Element of REAL
|[(upper_bound (proj1 | (N-most (L~ f)))),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
<*(NE-corner (L~ f))*> is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() V33(1) FinSequence-like FinSubsequence-like special FinSequence of the carrier of (TOP-REAL 2)
i2 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
j is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
mid (f,i2,j) is V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
f /. j is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(mid (f,i2,j)) ^ <*(NE-corner (L~ f))*> is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len (mid (f,i2,j)) is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
(mid (f,i2,j)) /. (len (mid (f,i2,j))) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(NE-corner (L~ f)) `2 is V11() real ext-real Element of REAL
((mid (f,i2,j)) /. (len (mid (f,i2,j)))) `2 is V11() real ext-real Element of REAL
LSeg ((NE-corner (L~ f)),(N-max (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (NE-corner (L~ f))) + (b<sub>1</sub> * (N-max (L~ f)))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg ((NE-corner (L~ f)),(N-max (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
{(N-max (L~ f))} is non empty trivial set
L~ (mid (f,i2,j)) is compact Element of bool the carrier of (TOP-REAL 2)
{ (LSeg ((mid (f,i2,j)),b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len (mid (f,i2,j)) ) } is set
union { (LSeg ((mid (f,i2,j)),b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len (mid (f,i2,j)) ) } is set
LSeg ((NE-corner (L~ f)),((mid (f,i2,j)) /. (len (mid (f,i2,j))))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (NE-corner (L~ f))) + (b<sub>1</sub> * ((mid (f,i2,j)) /. (len (mid (f,i2,j)))))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg ((NE-corner (L~ f)),((mid (f,i2,j)) /. (len (mid (f,i2,j)))))) /\ (L~ (mid (f,i2,j))) is Element of bool the carrier of (TOP-REAL 2)
{((mid (f,i2,j)) /. (len (mid (f,i2,j))))} is non empty trivial set
f is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard FinSequence of the carrier of (TOP-REAL 2)
dom f is non empty non trivial V137() V138() V139() V140() V141() V142() Element of bool NAT
L~ f is non empty compact Element of bool the carrier of (TOP-REAL 2)
len f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
{ (LSeg (f,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len f ) } is set
union { (LSeg (f,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len f ) } is set
E-max (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
E-bound (L~ f) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ f) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
the carrier of ((TOP-REAL 2) | (L~ f)) is non empty set
[: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is set
upper_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
(proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K429(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
E-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
SE-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
S-bound (L~ f) is V11() real ext-real Element of REAL
proj2 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
lower_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
(proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K430(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
NE-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
N-bound (L~ f) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
K429(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner (L~ f)),(NE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (SE-corner (L~ f))) + (b<sub>1</sub> * (NE-corner (L~ f)))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg ((SE-corner (L~ f)),(NE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (E-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (E-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (E-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (E-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (E-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (E-most (L~ f))),REAL:] is set
upper_bound (proj2 | (E-most (L~ f))) is V11() real ext-real Element of REAL
(proj2 | (E-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ f))) is V137() V138() V139() Element of bool REAL
K429(((proj2 | (E-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ f))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(upper_bound (proj2 | (E-most (L~ f))))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
<*(NE-corner (L~ f))*> is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() V33(1) FinSequence-like FinSubsequence-like special FinSequence of the carrier of (TOP-REAL 2)
i2 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
j is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
mid (f,i2,j) is V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
f /. j is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(mid (f,i2,j)) ^ <*(NE-corner (L~ f))*> is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len (mid (f,i2,j)) is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
(mid (f,i2,j)) /. (len (mid (f,i2,j))) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(NE-corner (L~ f)) `1 is V11() real ext-real Element of REAL
((mid (f,i2,j)) /. (len (mid (f,i2,j)))) `1 is V11() real ext-real Element of REAL
LSeg ((NE-corner (L~ f)),(E-max (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (NE-corner (L~ f))) + (b<sub>1</sub> * (E-max (L~ f)))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg ((NE-corner (L~ f)),(E-max (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
{(E-max (L~ f))} is non empty trivial set
L~ (mid (f,i2,j)) is compact Element of bool the carrier of (TOP-REAL 2)
{ (LSeg ((mid (f,i2,j)),b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len (mid (f,i2,j)) ) } is set
union { (LSeg ((mid (f,i2,j)),b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len (mid (f,i2,j)) ) } is set
LSeg ((NE-corner (L~ f)),((mid (f,i2,j)) /. (len (mid (f,i2,j))))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (NE-corner (L~ f))) + (b<sub>1</sub> * ((mid (f,i2,j)) /. (len (mid (f,i2,j)))))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg ((NE-corner (L~ f)),((mid (f,i2,j)) /. (len (mid (f,i2,j)))))) /\ (L~ (mid (f,i2,j))) is Element of bool the carrier of (TOP-REAL 2)
{((mid (f,i2,j)) /. (len (mid (f,i2,j))))} is non empty trivial set
f is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard FinSequence of the carrier of (TOP-REAL 2)
dom f is non empty non trivial V137() V138() V139() V140() V141() V142() Element of bool NAT
L~ f is non empty compact Element of bool the carrier of (TOP-REAL 2)
len f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
{ (LSeg (f,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len f ) } is set
union { (LSeg (f,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len f ) } is set
S-max (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
S-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
SW-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
W-bound (L~ f) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ f) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
the carrier of ((TOP-REAL 2) | (L~ f)) is non empty set
[: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is set
lower_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
(proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K430(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
S-bound (L~ f) is V11() real ext-real Element of REAL
proj2 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
lower_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
(proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K430(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
SE-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
E-bound (L~ f) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
K429(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner (L~ f)),(SE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (SW-corner (L~ f))) + (b<sub>1</sub> * (SE-corner (L~ f)))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg ((SW-corner (L~ f)),(SE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (S-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (S-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (S-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (S-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (S-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (S-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (S-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (S-most (L~ f))),REAL:] is set
upper_bound (proj1 | (S-most (L~ f))) is V11() real ext-real Element of REAL
(proj1 | (S-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (S-most (L~ f))) is V137() V138() V139() Element of bool REAL
K429(((proj1 | (S-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (S-most (L~ f))))) is V11() real ext-real Element of REAL
|[(upper_bound (proj1 | (S-most (L~ f)))),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
<*(SE-corner (L~ f))*> is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() V33(1) FinSequence-like FinSubsequence-like special FinSequence of the carrier of (TOP-REAL 2)
i2 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
j is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
mid (f,i2,j) is V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
f /. j is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(mid (f,i2,j)) ^ <*(SE-corner (L~ f))*> is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len (mid (f,i2,j)) is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
(mid (f,i2,j)) /. (len (mid (f,i2,j))) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(SE-corner (L~ f)) `2 is V11() real ext-real Element of REAL
((mid (f,i2,j)) /. (len (mid (f,i2,j)))) `2 is V11() real ext-real Element of REAL
LSeg ((SE-corner (L~ f)),(S-max (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (SE-corner (L~ f))) + (b<sub>1</sub> * (S-max (L~ f)))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg ((SE-corner (L~ f)),(S-max (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
{(S-max (L~ f))} is non empty trivial set
L~ (mid (f,i2,j)) is compact Element of bool the carrier of (TOP-REAL 2)
{ (LSeg ((mid (f,i2,j)),b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len (mid (f,i2,j)) ) } is set
union { (LSeg ((mid (f,i2,j)),b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len (mid (f,i2,j)) ) } is set
LSeg ((SE-corner (L~ f)),((mid (f,i2,j)) /. (len (mid (f,i2,j))))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (SE-corner (L~ f))) + (b<sub>1</sub> * ((mid (f,i2,j)) /. (len (mid (f,i2,j)))))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg ((SE-corner (L~ f)),((mid (f,i2,j)) /. (len (mid (f,i2,j)))))) /\ (L~ (mid (f,i2,j))) is Element of bool the carrier of (TOP-REAL 2)
{((mid (f,i2,j)) /. (len (mid (f,i2,j))))} is non empty trivial set
f is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard FinSequence of the carrier of (TOP-REAL 2)
dom f is non empty non trivial V137() V138() V139() V140() V141() V142() Element of bool NAT
L~ f is non empty compact Element of bool the carrier of (TOP-REAL 2)
len f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
{ (LSeg (f,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len f ) } is set
union { (LSeg (f,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len f ) } is set
E-max (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
E-bound (L~ f) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ f) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
the carrier of ((TOP-REAL 2) | (L~ f)) is non empty set
[: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is set
upper_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
(proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K429(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
E-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
SE-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
S-bound (L~ f) is V11() real ext-real Element of REAL
proj2 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
lower_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
(proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K430(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
NE-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
N-bound (L~ f) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
K429(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner (L~ f)),(NE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (SE-corner (L~ f))) + (b<sub>1</sub> * (NE-corner (L~ f)))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg ((SE-corner (L~ f)),(NE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (E-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (E-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (E-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (E-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (E-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (E-most (L~ f))),REAL:] is set
upper_bound (proj2 | (E-most (L~ f))) is V11() real ext-real Element of REAL
(proj2 | (E-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ f))) is V137() V138() V139() Element of bool REAL
K429(((proj2 | (E-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ f))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(upper_bound (proj2 | (E-most (L~ f))))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
<*(NE-corner (L~ f))*> is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() V33(1) FinSequence-like FinSubsequence-like special FinSequence of the carrier of (TOP-REAL 2)
i2 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
j is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
mid (f,i2,j) is V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
f /. j is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(mid (f,i2,j)) ^ <*(NE-corner (L~ f))*> is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len (mid (f,i2,j)) is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
(mid (f,i2,j)) /. (len (mid (f,i2,j))) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(NE-corner (L~ f)) `1 is V11() real ext-real Element of REAL
((mid (f,i2,j)) /. (len (mid (f,i2,j)))) `1 is V11() real ext-real Element of REAL
LSeg ((NE-corner (L~ f)),(E-max (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (NE-corner (L~ f))) + (b<sub>1</sub> * (E-max (L~ f)))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg ((NE-corner (L~ f)),(E-max (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
{(E-max (L~ f))} is non empty trivial set
L~ (mid (f,i2,j)) is compact Element of bool the carrier of (TOP-REAL 2)
{ (LSeg ((mid (f,i2,j)),b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len (mid (f,i2,j)) ) } is set
union { (LSeg ((mid (f,i2,j)),b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len (mid (f,i2,j)) ) } is set
LSeg ((NE-corner (L~ f)),((mid (f,i2,j)) /. (len (mid (f,i2,j))))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (NE-corner (L~ f))) + (b<sub>1</sub> * ((mid (f,i2,j)) /. (len (mid (f,i2,j)))))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg ((NE-corner (L~ f)),((mid (f,i2,j)) /. (len (mid (f,i2,j)))))) /\ (L~ (mid (f,i2,j))) is Element of bool the carrier of (TOP-REAL 2)
{((mid (f,i2,j)) /. (len (mid (f,i2,j))))} is non empty trivial set
f is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard FinSequence of the carrier of (TOP-REAL 2)
dom f is non empty non trivial V137() V138() V139() V140() V141() V142() Element of bool NAT
L~ f is non empty compact Element of bool the carrier of (TOP-REAL 2)
len f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
{ (LSeg (f,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len f ) } is set
union { (LSeg (f,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len f ) } is set
N-min (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
N-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
NW-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
W-bound (L~ f) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ f) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
the carrier of ((TOP-REAL 2) | (L~ f)) is non empty set
[: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is set
lower_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
(proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K430(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
N-bound (L~ f) is V11() real ext-real Element of REAL
proj2 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
upper_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
(proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K429(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
NE-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
E-bound (L~ f) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
K429(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((NW-corner (L~ f)),(NE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (NW-corner (L~ f))) + (b<sub>1</sub> * (NE-corner (L~ f)))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg ((NW-corner (L~ f)),(NE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (N-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (N-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (N-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (N-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:] is set
lower_bound (proj1 | (N-most (L~ f))) is V11() real ext-real Element of REAL
(proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))) is V137() V138() V139() Element of bool REAL
K430(((proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (N-most (L~ f)))),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
<*(NW-corner (L~ f))*> is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() V33(1) FinSequence-like FinSubsequence-like special FinSequence of the carrier of (TOP-REAL 2)
i2 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
f /. i2 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
j is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
mid (f,i2,j) is V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
<*(NW-corner (L~ f))*> ^ (mid (f,i2,j)) is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
(mid (f,i2,j)) /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(NW-corner (L~ f)) `2 is V11() real ext-real Element of REAL
((mid (f,i2,j)) /. 1) `2 is V11() real ext-real Element of REAL
len (mid (f,i2,j)) is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
LSeg ((NW-corner (L~ f)),(N-min (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (NW-corner (L~ f))) + (b<sub>1</sub> * (N-min (L~ f)))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg ((NW-corner (L~ f)),(N-min (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
{(N-min (L~ f))} is non empty trivial set
L~ (mid (f,i2,j)) is compact Element of bool the carrier of (TOP-REAL 2)
{ (LSeg ((mid (f,i2,j)),b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len (mid (f,i2,j)) ) } is set
union { (LSeg ((mid (f,i2,j)),b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len (mid (f,i2,j)) ) } is set
LSeg ((NW-corner (L~ f)),((mid (f,i2,j)) /. 1)) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (NW-corner (L~ f))) + (b<sub>1</sub> * ((mid (f,i2,j)) /. 1))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg ((NW-corner (L~ f)),((mid (f,i2,j)) /. 1))) /\ (L~ (mid (f,i2,j))) is Element of bool the carrier of (TOP-REAL 2)
{((mid (f,i2,j)) /. 1)} is non empty trivial set
f is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard FinSequence of the carrier of (TOP-REAL 2)
dom f is non empty non trivial V137() V138() V139() V140() V141() V142() Element of bool NAT
L~ f is non empty compact Element of bool the carrier of (TOP-REAL 2)
len f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
{ (LSeg (f,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len f ) } is set
union { (LSeg (f,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len f ) } is set
W-min (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
W-bound (L~ f) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ f) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
the carrier of ((TOP-REAL 2) | (L~ f)) is non empty set
[: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is set
lower_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
(proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K430(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
W-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
SW-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
S-bound (L~ f) is V11() real ext-real Element of REAL
proj2 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
lower_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
(proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K430(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
NW-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
N-bound (L~ f) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
K429(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner (L~ f)),(NW-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (SW-corner (L~ f))) + (b<sub>1</sub> * (NW-corner (L~ f)))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg ((SW-corner (L~ f)),(NW-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (W-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (W-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (W-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (W-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (W-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (W-most (L~ f))),REAL:] is set
lower_bound (proj2 | (W-most (L~ f))) is V11() real ext-real Element of REAL
(proj2 | (W-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ f))) is V137() V138() V139() Element of bool REAL
K430(((proj2 | (W-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ f))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(lower_bound (proj2 | (W-most (L~ f))))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
<*(SW-corner (L~ f))*> is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() V33(1) FinSequence-like FinSubsequence-like special FinSequence of the carrier of (TOP-REAL 2)
i2 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
f /. i2 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
j is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
mid (f,i2,j) is V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
<*(SW-corner (L~ f))*> ^ (mid (f,i2,j)) is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
(mid (f,i2,j)) /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(SW-corner (L~ f)) `1 is V11() real ext-real Element of REAL
((mid (f,i2,j)) /. 1) `1 is V11() real ext-real Element of REAL
len (mid (f,i2,j)) is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
LSeg ((SW-corner (L~ f)),(W-min (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (SW-corner (L~ f))) + (b<sub>1</sub> * (W-min (L~ f)))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg ((SW-corner (L~ f)),(W-min (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
{(W-min (L~ f))} is non empty trivial set
L~ (mid (f,i2,j)) is compact Element of bool the carrier of (TOP-REAL 2)
{ (LSeg ((mid (f,i2,j)),b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len (mid (f,i2,j)) ) } is set
union { (LSeg ((mid (f,i2,j)),b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len (mid (f,i2,j)) ) } is set
LSeg ((SW-corner (L~ f)),((mid (f,i2,j)) /. 1)) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (SW-corner (L~ f))) + (b<sub>1</sub> * ((mid (f,i2,j)) /. 1))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg ((SW-corner (L~ f)),((mid (f,i2,j)) /. 1))) /\ (L~ (mid (f,i2,j))) is Element of bool the carrier of (TOP-REAL 2)
{((mid (f,i2,j)) /. 1)} is non empty trivial set
f is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard FinSequence of the carrier of (TOP-REAL 2)
dom f is non empty non trivial V137() V138() V139() V140() V141() V142() Element of bool NAT
L~ f is non empty compact Element of bool the carrier of (TOP-REAL 2)
len f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
{ (LSeg (f,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len f ) } is set
union { (LSeg (f,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len f ) } is set
N-min (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
N-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
NW-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
W-bound (L~ f) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ f) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
the carrier of ((TOP-REAL 2) | (L~ f)) is non empty set
[: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is set
lower_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
(proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K430(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
N-bound (L~ f) is V11() real ext-real Element of REAL
proj2 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
upper_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
(proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K429(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
NE-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
E-bound (L~ f) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
K429(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((NW-corner (L~ f)),(NE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (NW-corner (L~ f))) + (b<sub>1</sub> * (NE-corner (L~ f)))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg ((NW-corner (L~ f)),(NE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (N-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (N-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (N-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (N-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:] is set
lower_bound (proj1 | (N-most (L~ f))) is V11() real ext-real Element of REAL
(proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))) is V137() V138() V139() Element of bool REAL
K430(((proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (N-most (L~ f)))),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
N-max (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
upper_bound (proj1 | (N-most (L~ f))) is V11() real ext-real Element of REAL
K429(((proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))))) is V11() real ext-real Element of REAL
|[(upper_bound (proj1 | (N-most (L~ f)))),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
<*(NW-corner (L~ f))*> is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() V33(1) FinSequence-like FinSubsequence-like special FinSequence of the carrier of (TOP-REAL 2)
<*(NE-corner (L~ f))*> is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() V33(1) FinSequence-like FinSubsequence-like special FinSequence of the carrier of (TOP-REAL 2)
j is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
f /. j is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
M is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
mid (f,j,M) is V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
f /. M is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
<*(NW-corner (L~ f))*> ^ (mid (f,j,M)) is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
(<*(NW-corner (L~ f))*> ^ (mid (f,j,M))) ^ <*(NE-corner (L~ f))*> is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len (<*(NW-corner (L~ f))*> ^ (mid (f,j,M))) is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
len <*(NW-corner (L~ f))*> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
len (mid (f,j,M)) is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
(len <*(NW-corner (L~ f))*>) + (len (mid (f,j,M))) is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
dom (mid (f,j,M)) is V137() V138() V139() V140() V141() V142() Element of bool NAT
(<*(NW-corner (L~ f))*> ^ (mid (f,j,M))) /. (len (<*(NW-corner (L~ f))*> ^ (mid (f,j,M)))) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(mid (f,j,M)) /. (len (mid (f,j,M))) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(NE-corner (L~ f)) `2 is V11() real ext-real Element of REAL
((<*(NW-corner (L~ f))*> ^ (mid (f,j,M))) /. (len (<*(NW-corner (L~ f))*> ^ (mid (f,j,M))))) `2 is V11() real ext-real Element of REAL
(mid (f,j,M)) /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
L~ (<*(NW-corner (L~ f))*> ^ (mid (f,j,M))) is compact Element of bool the carrier of (TOP-REAL 2)
{ (LSeg ((<*(NW-corner (L~ f))*> ^ (mid (f,j,M))),b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len (<*(NW-corner (L~ f))*> ^ (mid (f,j,M))) ) } is set
union { (LSeg ((<*(NW-corner (L~ f))*> ^ (mid (f,j,M))),b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len (<*(NW-corner (L~ f))*> ^ (mid (f,j,M))) ) } is set
LSeg ((NW-corner (L~ f)),(N-min (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (NW-corner (L~ f))) + (b<sub>1</sub> * (N-min (L~ f)))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
L~ (mid (f,j,M)) is compact Element of bool the carrier of (TOP-REAL 2)
{ (LSeg ((mid (f,j,M)),b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len (mid (f,j,M)) ) } is set
union { (LSeg ((mid (f,j,M)),b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len (mid (f,j,M)) ) } is set
(LSeg ((NW-corner (L~ f)),(N-min (L~ f)))) \/ (L~ (mid (f,j,M))) is non empty Element of bool the carrier of (TOP-REAL 2)
LSeg ((NE-corner (L~ f)),(N-max (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (NE-corner (L~ f))) + (b<sub>1</sub> * (N-max (L~ f)))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg ((NE-corner (L~ f)),(N-max (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
{(N-max (L~ f))} is non empty trivial set
LSeg (((<*(NW-corner (L~ f))*> ^ (mid (f,j,M))) /. (len (<*(NW-corner (L~ f))*> ^ (mid (f,j,M))))),(NE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * ((<*(NW-corner (L~ f))*> ^ (mid (f,j,M))) /. (len (<*(NW-corner (L~ f))*> ^ (mid (f,j,M)))))) + (b<sub>1</sub> * (NE-corner (L~ f)))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
LSeg ((NE-corner (L~ f)),((<*(NW-corner (L~ f))*> ^ (mid (f,j,M))) /. (len (<*(NW-corner (L~ f))*> ^ (mid (f,j,M)))))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (NE-corner (L~ f))) + (b<sub>1</sub> * ((<*(NW-corner (L~ f))*> ^ (mid (f,j,M))) /. (len (<*(NW-corner (L~ f))*> ^ (mid (f,j,M))))))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg ((NE-corner (L~ f)),((<*(NW-corner (L~ f))*> ^ (mid (f,j,M))) /. (len (<*(NW-corner (L~ f))*> ^ (mid (f,j,M))))))) /\ (LSeg ((NW-corner (L~ f)),(N-min (L~ f)))) is Element of bool the carrier of (TOP-REAL 2)
(LSeg ((NE-corner (L~ f)),((<*(NW-corner (L~ f))*> ^ (mid (f,j,M))) /. (len (<*(NW-corner (L~ f))*> ^ (mid (f,j,M))))))) /\ (L~ (<*(NW-corner (L~ f))*> ^ (mid (f,j,M)))) is Element of bool the carrier of (TOP-REAL 2)
(LSeg ((NE-corner (L~ f)),((<*(NW-corner (L~ f))*> ^ (mid (f,j,M))) /. (len (<*(NW-corner (L~ f))*> ^ (mid (f,j,M))))))) /\ (L~ (mid (f,j,M))) is Element of bool the carrier of (TOP-REAL 2)
((LSeg ((NE-corner (L~ f)),((<*(NW-corner (L~ f))*> ^ (mid (f,j,M))) /. (len (<*(NW-corner (L~ f))*> ^ (mid (f,j,M))))))) /\ (L~ (mid (f,j,M)))) \/ {} is set
{((<*(NW-corner (L~ f))*> ^ (mid (f,j,M))) /. (len (<*(NW-corner (L~ f))*> ^ (mid (f,j,M)))))} is non empty trivial set
f is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard FinSequence of the carrier of (TOP-REAL 2)
L~ f is non empty compact Element of bool the carrier of (TOP-REAL 2)
len f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
{ (LSeg (f,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len f ) } is set
union { (LSeg (f,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len f ) } is set
f is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard FinSequence of the carrier of (TOP-REAL 2)
L~ f is non empty compact being_simple_closed_curve Element of bool the carrier of (TOP-REAL 2)
len f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
{ (LSeg (f,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len f ) } is set
union { (LSeg (f,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len f ) } is set
S-max (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
S-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
SW-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
W-bound (L~ f) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ f) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
the carrier of ((TOP-REAL 2) | (L~ f)) is non empty set
[: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is set
lower_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
(proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K430(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
S-bound (L~ f) is V11() real ext-real Element of REAL
proj2 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
lower_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
(proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K430(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
SE-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
E-bound (L~ f) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
K429(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner (L~ f)),(SE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (SW-corner (L~ f))) + (b<sub>1</sub> * (SE-corner (L~ f)))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg ((SW-corner (L~ f)),(SE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (S-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (S-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (S-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (S-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (S-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (S-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (S-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (S-most (L~ f))),REAL:] is set
upper_bound (proj1 | (S-most (L~ f))) is V11() real ext-real Element of REAL
(proj1 | (S-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (S-most (L~ f))) is V137() V138() V139() Element of bool REAL
K429(((proj1 | (S-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (S-most (L~ f))))) is V11() real ext-real Element of REAL
|[(upper_bound (proj1 | (S-most (L~ f)))),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((S-max (L~ f)),(SE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (S-max (L~ f))) + (b<sub>1</sub> * (SE-corner (L~ f)))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
NW-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
N-bound (L~ f) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
K429(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
N-min (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
N-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
NE-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
|[(E-bound (L~ f)),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((NW-corner (L~ f)),(NE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (NW-corner (L~ f))) + (b<sub>1</sub> * (NE-corner (L~ f)))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg ((NW-corner (L~ f)),(NE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (N-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (N-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (N-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (N-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:] is set
lower_bound (proj1 | (N-most (L~ f))) is V11() real ext-real Element of REAL
(proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))) is V137() V138() V139() Element of bool REAL
K430(((proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (N-most (L~ f)))),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((NW-corner (L~ f)),(N-min (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (NW-corner (L~ f))) + (b<sub>1</sub> * (N-min (L~ f)))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(NW-corner (L~ f)) `2 is V11() real ext-real Element of REAL
(N-min (L~ f)) `2 is V11() real ext-real Element of REAL
(LSeg ((S-max (L~ f)),(SE-corner (L~ f)))) /\ (LSeg ((NW-corner (L~ f)),(N-min (L~ f)))) is Element of bool the carrier of (TOP-REAL 2)
i1 is set
i2 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
i2 `2 is V11() real ext-real Element of REAL
(SE-corner (L~ f)) `2 is V11() real ext-real Element of REAL
(S-max (L~ f)) `2 is V11() real ext-real Element of REAL
f is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard FinSequence of the carrier of (TOP-REAL 2)
dom f is non empty non trivial V137() V138() V139() V140() V141() V142() Element of bool NAT
L~ f is non empty compact being_simple_closed_curve Element of bool the carrier of (TOP-REAL 2)
len f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
{ (LSeg (f,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
union { (LSeg (f,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
N-min (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
N-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
NW-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
W-bound (L~ f) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ f) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
the carrier of ((TOP-REAL 2) | (L~ f)) is non empty set
[: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is set
lower_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
(proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K430(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
N-bound (L~ f) is V11() real ext-real Element of REAL
proj2 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
upper_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
(proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K429(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
NE-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
E-bound (L~ f) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
K429(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((NW-corner (L~ f)),(NE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NW-corner (L~ f))) + (b₁ * (NE-corner (L~ f)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((NW-corner (L~ f)),(NE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (N-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (N-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (N-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (N-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:] is set
lower_bound (proj1 | (N-most (L~ f))) is V11() real ext-real Element of REAL
(proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))) is V137() V138() V139() Element of bool REAL
K430(((proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (N-most (L~ f)))),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
S-max (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
S-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
SW-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
S-bound (L~ f) is V11() real ext-real Element of REAL
lower_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
K430(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
SE-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
|[(E-bound (L~ f)),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner (L~ f)),(SE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SW-corner (L~ f))) + (b₁ * (SE-corner (L~ f)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((SW-corner (L~ f)),(SE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (S-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (S-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (S-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (S-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (S-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (S-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (S-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (S-most (L~ f))),REAL:] is set
upper_bound (proj1 | (S-most (L~ f))) is V11() real ext-real Element of REAL
(proj1 | (S-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (S-most (L~ f))) is V137() V138() V139() Element of bool REAL
K429(((proj1 | (S-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (S-most (L~ f))))) is V11() real ext-real Element of REAL
|[(upper_bound (proj1 | (S-most (L~ f)))),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
<*(NW-corner (L~ f))*> is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() V33(1) FinSequence-like FinSubsequence-like special FinSequence of the carrier of (TOP-REAL 2)
<*(SE-corner (L~ f))*> is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() V33(1) FinSequence-like FinSubsequence-like special FinSequence of the carrier of (TOP-REAL 2)
j is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
f /. j is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
M is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
mid (f,j,M) is V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
f /. M is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
<*(NW-corner (L~ f))*> ^ (mid (f,j,M)) is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
(<*(NW-corner (L~ f))*> ^ (mid (f,j,M))) ^ <*(SE-corner (L~ f))*> is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len (<*(NW-corner (L~ f))*> ^ (mid (f,j,M))) is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
len <*(NW-corner (L~ f))*> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
len (mid (f,j,M)) is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
(len <*(NW-corner (L~ f))*>) + (len (mid (f,j,M))) is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
dom (mid (f,j,M)) is V137() V138() V139() V140() V141() V142() Element of bool NAT
(<*(NW-corner (L~ f))*> ^ (mid (f,j,M))) /. (len (<*(NW-corner (L~ f))*> ^ (mid (f,j,M)))) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(mid (f,j,M)) /. (len (mid (f,j,M))) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(SE-corner (L~ f)) `2 is V11() real ext-real Element of REAL
((<*(NW-corner (L~ f))*> ^ (mid (f,j,M))) /. (len (<*(NW-corner (L~ f))*> ^ (mid (f,j,M))))) `2 is V11() real ext-real Element of REAL
(mid (f,j,M)) /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
L~ (<*(NW-corner (L~ f))*> ^ (mid (f,j,M))) is compact Element of bool the carrier of (TOP-REAL 2)
{ (LSeg ((<*(NW-corner (L~ f))*> ^ (mid (f,j,M))),b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (<*(NW-corner (L~ f))*> ^ (mid (f,j,M))) ) } is set
union { (LSeg ((<*(NW-corner (L~ f))*> ^ (mid (f,j,M))),b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (<*(NW-corner (L~ f))*> ^ (mid (f,j,M))) ) } is set
LSeg ((NW-corner (L~ f)),(N-min (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NW-corner (L~ f))) + (b₁ * (N-min (L~ f)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
L~ (mid (f,j,M)) is compact Element of bool the carrier of (TOP-REAL 2)
{ (LSeg ((mid (f,j,M)),b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (mid (f,j,M)) ) } is set
union { (LSeg ((mid (f,j,M)),b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (mid (f,j,M)) ) } is set
(LSeg ((NW-corner (L~ f)),(N-min (L~ f)))) \/ (L~ (mid (f,j,M))) is non empty Element of bool the carrier of (TOP-REAL 2)
LSeg ((SE-corner (L~ f)),(S-max (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SE-corner (L~ f))) + (b₁ * (S-max (L~ f)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((SE-corner (L~ f)),(S-max (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
{(S-max (L~ f))} is non empty trivial set
LSeg (((<*(NW-corner (L~ f))*> ^ (mid (f,j,M))) /. (len (<*(NW-corner (L~ f))*> ^ (mid (f,j,M))))),(SE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * ((<*(NW-corner (L~ f))*> ^ (mid (f,j,M))) /. (len (<*(NW-corner (L~ f))*> ^ (mid (f,j,M)))))) + (b₁ * (SE-corner (L~ f)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
LSeg ((SE-corner (L~ f)),((<*(NW-corner (L~ f))*> ^ (mid (f,j,M))) /. (len (<*(NW-corner (L~ f))*> ^ (mid (f,j,M)))))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SE-corner (L~ f))) + (b₁ * ((<*(NW-corner (L~ f))*> ^ (mid (f,j,M))) /. (len (<*(NW-corner (L~ f))*> ^ (mid (f,j,M))))))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((SE-corner (L~ f)),((<*(NW-corner (L~ f))*> ^ (mid (f,j,M))) /. (len (<*(NW-corner (L~ f))*> ^ (mid (f,j,M))))))) /\ (LSeg ((NW-corner (L~ f)),(N-min (L~ f)))) is Element of bool the carrier of (TOP-REAL 2)
(LSeg ((SE-corner (L~ f)),((<*(NW-corner (L~ f))*> ^ (mid (f,j,M))) /. (len (<*(NW-corner (L~ f))*> ^ (mid (f,j,M))))))) /\ (L~ (<*(NW-corner (L~ f))*> ^ (mid (f,j,M)))) is Element of bool the carrier of (TOP-REAL 2)
(LSeg ((SE-corner (L~ f)),((<*(NW-corner (L~ f))*> ^ (mid (f,j,M))) /. (len (<*(NW-corner (L~ f))*> ^ (mid (f,j,M))))))) /\ (L~ (mid (f,j,M))) is Element of bool the carrier of (TOP-REAL 2)
((LSeg ((SE-corner (L~ f)),((<*(NW-corner (L~ f))*> ^ (mid (f,j,M))) /. (len (<*(NW-corner (L~ f))*> ^ (mid (f,j,M))))))) /\ (L~ (mid (f,j,M)))) \/ {} is set
{((<*(NW-corner (L~ f))*> ^ (mid (f,j,M))) /. (len (<*(NW-corner (L~ f))*> ^ (mid (f,j,M)))))} is non empty trivial set
f is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard FinSequence of the carrier of (TOP-REAL 2)
f /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
L~ f is non empty compact being_simple_closed_curve Element of bool the carrier of (TOP-REAL 2)
len f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
{ (LSeg (f,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
union { (LSeg (f,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
N-min (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
N-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
NW-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
W-bound (L~ f) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ f) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
the carrier of ((TOP-REAL 2) | (L~ f)) is non empty set
[: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is set
lower_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
(proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K430(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
N-bound (L~ f) is V11() real ext-real Element of REAL
proj2 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
upper_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
(proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K429(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
NE-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
E-bound (L~ f) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
K429(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((NW-corner (L~ f)),(NE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NW-corner (L~ f))) + (b₁ * (NE-corner (L~ f)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((NW-corner (L~ f)),(NE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (N-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (N-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (N-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (N-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:] is set
lower_bound (proj1 | (N-most (L~ f))) is V11() real ext-real Element of REAL
(proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))) is V137() V138() V139() Element of bool REAL
K430(((proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (N-most (L~ f)))),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
N-max (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
upper_bound (proj1 | (N-most (L~ f))) is V11() real ext-real Element of REAL
K429(((proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))))) is V11() real ext-real Element of REAL
|[(upper_bound (proj1 | (N-most (L~ f)))),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
(N-max (L~ f)) .. f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
(N-min (L~ f)) .. f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
rng f is non empty non trivial Element of bool the carrier of (TOP-REAL 2)
dom f is non empty non trivial V137() V138() V139() V140() V141() V142() Element of bool NAT
f is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard FinSequence of the carrier of (TOP-REAL 2)
f /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
L~ f is non empty compact being_simple_closed_curve Element of bool the carrier of (TOP-REAL 2)
len f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
{ (LSeg (f,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
union { (LSeg (f,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
N-min (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
N-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
NW-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
W-bound (L~ f) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ f) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
the carrier of ((TOP-REAL 2) | (L~ f)) is non empty set
[: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is set
lower_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
(proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K430(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
N-bound (L~ f) is V11() real ext-real Element of REAL
proj2 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
upper_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
(proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K429(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
NE-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
E-bound (L~ f) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
K429(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((NW-corner (L~ f)),(NE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NW-corner (L~ f))) + (b₁ * (NE-corner (L~ f)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((NW-corner (L~ f)),(NE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (N-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (N-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (N-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (N-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:] is set
lower_bound (proj1 | (N-most (L~ f))) is V11() real ext-real Element of REAL
(proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))) is V137() V138() V139() Element of bool REAL
K430(((proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (N-most (L~ f)))),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
N-max (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
upper_bound (proj1 | (N-most (L~ f))) is V11() real ext-real Element of REAL
K429(((proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))))) is V11() real ext-real Element of REAL
|[(upper_bound (proj1 | (N-most (L~ f)))),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
(N-max (L~ f)) .. f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
(N-min (L~ f)) .. f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
f is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard FinSequence of the carrier of (TOP-REAL 2)
f /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
L~ f is non empty compact being_simple_closed_curve Element of bool the carrier of (TOP-REAL 2)
len f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
{ (LSeg (f,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
union { (LSeg (f,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
N-min (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
N-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
NW-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
W-bound (L~ f) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ f) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
the carrier of ((TOP-REAL 2) | (L~ f)) is non empty set
[: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is set
lower_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
(proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K430(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
N-bound (L~ f) is V11() real ext-real Element of REAL
proj2 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
upper_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
(proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K429(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
NE-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
E-bound (L~ f) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
K429(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((NW-corner (L~ f)),(NE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NW-corner (L~ f))) + (b₁ * (NE-corner (L~ f)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((NW-corner (L~ f)),(NE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (N-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (N-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (N-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (N-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:] is set
lower_bound (proj1 | (N-most (L~ f))) is V11() real ext-real Element of REAL
(proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))) is V137() V138() V139() Element of bool REAL
K430(((proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (N-most (L~ f)))),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
E-max (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
E-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
SE-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
S-bound (L~ f) is V11() real ext-real Element of REAL
lower_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
K430(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner (L~ f)),(NE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SE-corner (L~ f))) + (b₁ * (NE-corner (L~ f)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((SE-corner (L~ f)),(NE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (E-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (E-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (E-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (E-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (E-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (E-most (L~ f))),REAL:] is set
upper_bound (proj2 | (E-most (L~ f))) is V11() real ext-real Element of REAL
(proj2 | (E-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ f))) is V137() V138() V139() Element of bool REAL
K429(((proj2 | (E-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ f))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(upper_bound (proj2 | (E-most (L~ f))))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
(E-max (L~ f)) .. f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
(N-min (L~ f)) .. f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
rng f is non empty non trivial Element of bool the carrier of (TOP-REAL 2)
N-max (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
upper_bound (proj1 | (N-most (L~ f))) is V11() real ext-real Element of REAL
K429(((proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))))) is V11() real ext-real Element of REAL
|[(upper_bound (proj1 | (N-most (L~ f)))),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
(N-max (L~ f)) `1 is V11() real ext-real Element of REAL
(NE-corner (L~ f)) `1 is V11() real ext-real Element of REAL
(N-min (L~ f)) `1 is V11() real ext-real Element of REAL
(E-max (L~ f)) `1 is V11() real ext-real Element of REAL
f is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard () FinSequence of the carrier of (TOP-REAL 2)
f /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
L~ f is non empty compact being_simple_closed_curve Element of bool the carrier of (TOP-REAL 2)
len f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
{ (LSeg (f,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
union { (LSeg (f,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
N-min (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
N-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
NW-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
W-bound (L~ f) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ f) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
the carrier of ((TOP-REAL 2) | (L~ f)) is non empty set
[: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is set
lower_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
(proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K430(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
N-bound (L~ f) is V11() real ext-real Element of REAL
proj2 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
upper_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
(proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K429(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
NE-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
E-bound (L~ f) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
K429(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((NW-corner (L~ f)),(NE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NW-corner (L~ f))) + (b₁ * (NE-corner (L~ f)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((NW-corner (L~ f)),(NE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (N-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (N-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (N-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (N-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:] is set
lower_bound (proj1 | (N-most (L~ f))) is V11() real ext-real Element of REAL
(proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))) is V137() V138() V139() Element of bool REAL
K430(((proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (N-most (L~ f)))),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
S-max (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
S-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
SW-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
S-bound (L~ f) is V11() real ext-real Element of REAL
lower_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
K430(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
SE-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
|[(E-bound (L~ f)),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner (L~ f)),(SE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SW-corner (L~ f))) + (b₁ * (SE-corner (L~ f)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((SW-corner (L~ f)),(SE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (S-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (S-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (S-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (S-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (S-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (S-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (S-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (S-most (L~ f))),REAL:] is set
upper_bound (proj1 | (S-most (L~ f))) is V11() real ext-real Element of REAL
(proj1 | (S-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (S-most (L~ f))) is V137() V138() V139() Element of bool REAL
K429(((proj1 | (S-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (S-most (L~ f))))) is V11() real ext-real Element of REAL
|[(upper_bound (proj1 | (S-most (L~ f)))),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
(S-max (L~ f)) .. f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
N-max (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
upper_bound (proj1 | (N-most (L~ f))) is V11() real ext-real Element of REAL
K429(((proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))))) is V11() real ext-real Element of REAL
|[(upper_bound (proj1 | (N-most (L~ f)))),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
(N-max (L~ f)) .. f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
rng f is non empty non trivial Element of bool the carrier of (TOP-REAL 2)
dom f is non empty non trivial V137() V138() V139() V140() V141() V142() Element of bool NAT
f /. ((S-max (L~ f)) .. f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
f . ((S-max (L~ f)) .. f) is set
(f /. ((S-max (L~ f)) .. f)) `2 is V11() real ext-real Element of REAL
(f /. 1) `2 is V11() real ext-real Element of REAL
f /. 2 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(f /. 2) `2 is V11() real ext-real Element of REAL
(N-min (L~ f)) `2 is V11() real ext-real Element of REAL
mid (f,((S-max (L~ f)) .. f),2) is V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
j is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
len j is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
j /. (len j) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(j /. (len j)) `2 is V11() real ext-real Element of REAL
j /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(j /. 1) `2 is V11() real ext-real Element of REAL
f /. ((N-max (L~ f)) .. f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
f . ((N-max (L~ f)) .. f) is set
f /. (len f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
((N-max (L~ f)) .. f) + 1 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
(len f) - ((N-max (L~ f)) .. f) is V11() real ext-real Element of REAL
(len f) -' ((N-max (L~ f)) .. f) is natural V11() real V37() ext-real non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
1 + 1 is non empty natural V11() real V37() ext-real positive non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
((len f) -' ((N-max (L~ f)) .. f)) + 1 is non empty natural V11() real V37() ext-real positive non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
(N-max (L~ f)) `2 is V11() real ext-real Element of REAL
(S-max (L~ f)) `2 is V11() real ext-real Element of REAL
mid (f,(len f),((N-max (L~ f)) .. f)) is V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
M is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
dom M is non empty non trivial V137() V138() V139() V140() V141() V142() Element of bool NAT
len M is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
M /. (len M) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
L~ M is non empty compact Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (M,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len M ) } is set
union { (LSeg (M,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len M ) } is set
L~ j is non empty compact Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (j,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len j ) } is set
union { (LSeg (j,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len j ) } is set
M /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(M /. (len M)) `1 is V11() real ext-real Element of REAL
(M /. 1) `1 is V11() real ext-real Element of REAL
<*(NE-corner (L~ f))*> is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() V33(1) FinSequence-like FinSubsequence-like special FinSequence of the carrier of (TOP-REAL 2)
M ^ <*(NE-corner (L~ f))*> is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
h is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
len h is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
L~ h is non empty compact Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (h,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len h ) } is set
union { (LSeg (h,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len h ) } is set
LSeg ((M /. (len M)),(NE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (M /. (len M))) + (b₁ * (NE-corner (L~ f)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(L~ M) \/ (LSeg ((M /. (len M)),(NE-corner (L~ f)))) is non empty Element of bool the carrier of (TOP-REAL 2)
len <*(NE-corner (L~ f))*> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
(len M) + (len <*(NE-corner (L~ f))*>) is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
(len M) + 1 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
h /. (len h) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(h /. (len h)) `1 is V11() real ext-real Element of REAL
(LSeg ((M /. (len M)),(NE-corner (L~ f)))) /\ (L~ j) is Element of bool the carrier of (TOP-REAL 2)
(LSeg ((M /. (len M)),(NE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
{(M /. (len M))} is non empty trivial set
h /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(h /. 1) `1 is V11() real ext-real Element of REAL
<*(NW-corner (L~ f))*> is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() V33(1) FinSequence-like FinSubsequence-like special FinSequence of the carrier of (TOP-REAL 2)
<*(NW-corner (L~ f))*> ^ M is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
h is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
len h is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
len <*(NW-corner (L~ f))*> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
(len M) + (len <*(NW-corner (L~ f))*>) is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
h /. (len h) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(h /. (len h)) `1 is V11() real ext-real Element of REAL
L~ h is non empty compact Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (h,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len h ) } is set
union { (LSeg (h,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len h ) } is set
LSeg ((NW-corner (L~ f)),(M /. 1)) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (NW-corner (L~ f))) + (b<sub>1</sub> * (M /. 1))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(L~ M) \/ (LSeg ((NW-corner (L~ f)),(M /. 1))) is non empty Element of bool the carrier of (TOP-REAL 2)
h /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(h /. 1) `1 is V11() real ext-real Element of REAL
LSeg ((M /. 1),(NW-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (M /. 1)) + (b₁ * (NW-corner (L~ f)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((M /. 1),(NW-corner (L~ f)))) /\ (L~ j) is Element of bool the carrier of (TOP-REAL 2)
(LSeg ((M /. 1),(NW-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
{(M /. 1)} is non empty trivial set
<*(NW-corner (L~ f))*> is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() V33(1) FinSequence-like FinSubsequence-like special FinSequence of the carrier of (TOP-REAL 2)
<*(NW-corner (L~ f))*> ^ M is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
<*(NE-corner (L~ f))*> is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() V33(1) FinSequence-like FinSubsequence-like special FinSequence of the carrier of (TOP-REAL 2)
(<*(NW-corner (L~ f))*> ^ M) ^ <*(NE-corner (L~ f))*> is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
dom (<*(NW-corner (L~ f))*> ^ M) is V137() V138() V139() V140() V141() V142() Element of bool NAT
g is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
g /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(<*(NW-corner (L~ f))*> ^ M) /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(g /. 1) `1 is V11() real ext-real Element of REAL
len g is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
len (<*(NW-corner (L~ f))*> ^ M) is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
len <*(NE-corner (L~ f))*> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
(len (<*(NW-corner (L~ f))*> ^ M)) + (len <*(NE-corner (L~ f))*>) is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
(len (<*(NW-corner (L~ f))*> ^ M)) + 1 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
g /. (len g) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(g /. (len g)) `1 is V11() real ext-real Element of REAL
len <*(NW-corner (L~ f))*> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
(len M) + (len <*(NW-corner (L~ f))*>) is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
(<*(NW-corner (L~ f))*> ^ M) /. (len (<*(NW-corner (L~ f))*> ^ M)) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
L~ (<*(NW-corner (L~ f))*> ^ M) is compact Element of bool the carrier of (TOP-REAL 2)
{ (LSeg ((<*(NW-corner (L~ f))*> ^ M),b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (<*(NW-corner (L~ f))*> ^ M) ) } is set
union { (LSeg ((<*(NW-corner (L~ f))*> ^ M),b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (<*(NW-corner (L~ f))*> ^ M) ) } is set
LSeg ((M /. 1),(NW-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (M /. 1)) + (b₁ * (NW-corner (L~ f)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((M /. 1),(NW-corner (L~ f)))) /\ (L~ j) is Element of bool the carrier of (TOP-REAL 2)
(LSeg ((M /. 1),(NW-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
{(M /. 1)} is non empty trivial set
LSeg ((NW-corner (L~ f)),(M /. 1)) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NW-corner (L~ f))) + (b₁ * (M /. 1))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(L~ M) \/ (LSeg ((NW-corner (L~ f)),(M /. 1))) is non empty Element of bool the carrier of (TOP-REAL 2)
LSeg (((<*(NW-corner (L~ f))*> ^ M) /. (len (<*(NW-corner (L~ f))*> ^ M))),(NE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * ((<*(NW-corner (L~ f))*> ^ M) /. (len (<*(NW-corner (L~ f))*> ^ M)))) + (b₁ * (NE-corner (L~ f)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg (((<*(NW-corner (L~ f))*> ^ M) /. (len (<*(NW-corner (L~ f))*> ^ M))),(NE-corner (L~ f)))) /\ (L~ j) is Element of bool the carrier of (TOP-REAL 2)
(LSeg (((<*(NW-corner (L~ f))*> ^ M) /. (len (<*(NW-corner (L~ f))*> ^ M))),(NE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
{((<*(NW-corner (L~ f))*> ^ M) /. (len (<*(NW-corner (L~ f))*> ^ M)))} is non empty trivial set
L~ g is non empty compact Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (g,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len g ) } is set
union { (LSeg (g,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len g ) } is set
(L~ (<*(NW-corner (L~ f))*> ^ M)) \/ (LSeg (((<*(NW-corner (L~ f))*> ^ M) /. (len (<*(NW-corner (L~ f))*> ^ M))),(NE-corner (L~ f)))) is non empty Element of bool the carrier of (TOP-REAL 2)
f is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard () FinSequence of the carrier of (TOP-REAL 2)
f /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
L~ f is non empty compact being_simple_closed_curve Element of bool the carrier of (TOP-REAL 2)
len f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
{ (LSeg (f,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
union { (LSeg (f,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
N-min (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
N-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
NW-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
W-bound (L~ f) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ f) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
the carrier of ((TOP-REAL 2) | (L~ f)) is non empty set
[: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is set
lower_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
(proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K430(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
N-bound (L~ f) is V11() real ext-real Element of REAL
proj2 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
upper_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
(proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K429(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
NE-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
E-bound (L~ f) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
K429(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((NW-corner (L~ f)),(NE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NW-corner (L~ f))) + (b₁ * (NE-corner (L~ f)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((NW-corner (L~ f)),(NE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (N-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (N-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (N-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (N-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:] is set
lower_bound (proj1 | (N-most (L~ f))) is V11() real ext-real Element of REAL
(proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))) is V137() V138() V139() Element of bool REAL
K430(((proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (N-most (L~ f)))),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
S-min (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
S-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
SW-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
S-bound (L~ f) is V11() real ext-real Element of REAL
lower_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
K430(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
SE-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
|[(E-bound (L~ f)),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner (L~ f)),(SE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SW-corner (L~ f))) + (b₁ * (SE-corner (L~ f)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((SW-corner (L~ f)),(SE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (S-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (S-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (S-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (S-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (S-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (S-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (S-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (S-most (L~ f))),REAL:] is set
lower_bound (proj1 | (S-most (L~ f))) is V11() real ext-real Element of REAL
(proj1 | (S-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (S-most (L~ f))) is V137() V138() V139() Element of bool REAL
K430(((proj1 | (S-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (S-most (L~ f))))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (S-most (L~ f)))),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
(S-min (L~ f)) .. f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
N-max (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
upper_bound (proj1 | (N-most (L~ f))) is V11() real ext-real Element of REAL
K429(((proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))))) is V11() real ext-real Element of REAL
|[(upper_bound (proj1 | (N-most (L~ f)))),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
(N-max (L~ f)) .. f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
f /. 2 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(f /. 2) `2 is V11() real ext-real Element of REAL
(N-min (L~ f)) `2 is V11() real ext-real Element of REAL
rng f is non empty non trivial Element of bool the carrier of (TOP-REAL 2)
dom f is non empty non trivial V137() V138() V139() V140() V141() V142() Element of bool NAT
f /. ((S-min (L~ f)) .. f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
f . ((S-min (L~ f)) .. f) is set
(f /. ((S-min (L~ f)) .. f)) `2 is V11() real ext-real Element of REAL
(f /. 1) `2 is V11() real ext-real Element of REAL
mid (f,((S-min (L~ f)) .. f),2) is V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
j is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
j /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(j /. 1) `2 is V11() real ext-real Element of REAL
len j is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
j /. (len j) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
f /. ((N-max (L~ f)) .. f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
f . ((N-max (L~ f)) .. f) is set
f /. (len f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
((N-max (L~ f)) .. f) + 1 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
(len f) - ((N-max (L~ f)) .. f) is V11() real ext-real Element of REAL
(len f) -' ((N-max (L~ f)) .. f) is natural V11() real V37() ext-real non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
1 + 1 is non empty natural V11() real V37() ext-real positive non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
((len f) -' ((N-max (L~ f)) .. f)) + 1 is non empty natural V11() real V37() ext-real positive non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
(N-max (L~ f)) `2 is V11() real ext-real Element of REAL
(S-min (L~ f)) `2 is V11() real ext-real Element of REAL
mid (f,(len f),((N-max (L~ f)) .. f)) is V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
M is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
dom M is non empty non trivial V137() V138() V139() V140() V141() V142() Element of bool NAT
len M is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
M /. (len M) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
L~ M is non empty compact Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (M,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len M ) } is set
union { (LSeg (M,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len M ) } is set
L~ j is non empty compact Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (j,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len j ) } is set
union { (LSeg (j,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len j ) } is set
M /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(M /. (len M)) `1 is V11() real ext-real Element of REAL
(M /. 1) `1 is V11() real ext-real Element of REAL
<*(NE-corner (L~ f))*> is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() V33(1) FinSequence-like FinSubsequence-like special FinSequence of the carrier of (TOP-REAL 2)
M ^ <*(NE-corner (L~ f))*> is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
h is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
len h is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
L~ h is non empty compact Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (h,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len h ) } is set
union { (LSeg (h,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len h ) } is set
LSeg ((M /. (len M)),(NE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (M /. (len M))) + (b<sub>1</sub> * (NE-corner (L~ f)))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(L~ M) \/ (LSeg ((M /. (len M)),(NE-corner (L~ f)))) is non empty Element of bool the carrier of (TOP-REAL 2)
len <*(NE-corner (L~ f))*> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
(len M) + (len <*(NE-corner (L~ f))*>) is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
(len M) + 1 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
h /. (len h) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(h /. (len h)) `1 is V11() real ext-real Element of REAL
(LSeg ((M /. (len M)),(NE-corner (L~ f)))) /\ (L~ j) is Element of bool the carrier of (TOP-REAL 2)
(LSeg ((M /. (len M)),(NE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
{(M /. (len M))} is non empty trivial set
h /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(h /. 1) `1 is V11() real ext-real Element of REAL
<*(NW-corner (L~ f))*> is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() V33(1) FinSequence-like FinSubsequence-like special FinSequence of the carrier of (TOP-REAL 2)
<*(NW-corner (L~ f))*> ^ M is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
h is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
len h is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
len <*(NW-corner (L~ f))*> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
(len M) + (len <*(NW-corner (L~ f))*>) is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
h /. (len h) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(h /. (len h)) `1 is V11() real ext-real Element of REAL
L~ h is non empty compact Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (h,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len h ) } is set
union { (LSeg (h,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len h ) } is set
LSeg ((NW-corner (L~ f)),(M /. 1)) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NW-corner (L~ f))) + (b₁ * (M /. 1))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(L~ M) \/ (LSeg ((NW-corner (L~ f)),(M /. 1))) is non empty Element of bool the carrier of (TOP-REAL 2)
h /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(h /. 1) `1 is V11() real ext-real Element of REAL
LSeg ((M /. 1),(NW-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (M /. 1)) + (b<sub>1</sub> * (NW-corner (L~ f)))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg ((M /. 1),(NW-corner (L~ f)))) /\ (L~ j) is Element of bool the carrier of (TOP-REAL 2)
(LSeg ((M /. 1),(NW-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
{(M /. 1)} is non empty trivial set
<*(NW-corner (L~ f))*> is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() V33(1) FinSequence-like FinSubsequence-like special FinSequence of the carrier of (TOP-REAL 2)
<*(NW-corner (L~ f))*> ^ M is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
<*(NE-corner (L~ f))*> is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() V33(1) FinSequence-like FinSubsequence-like special FinSequence of the carrier of (TOP-REAL 2)
(<*(NW-corner (L~ f))*> ^ M) ^ <*(NE-corner (L~ f))*> is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
dom (<*(NW-corner (L~ f))*> ^ M) is V137() V138() V139() V140() V141() V142() Element of bool NAT
g is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
g /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(<*(NW-corner (L~ f))*> ^ M) /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(g /. 1) `1 is V11() real ext-real Element of REAL
len g is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
len (<*(NW-corner (L~ f))*> ^ M) is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
len <*(NE-corner (L~ f))*> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
(len (<*(NW-corner (L~ f))*> ^ M)) + (len <*(NE-corner (L~ f))*>) is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
(len (<*(NW-corner (L~ f))*> ^ M)) + 1 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
g /. (len g) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(g /. (len g)) `1 is V11() real ext-real Element of REAL
len <*(NW-corner (L~ f))*> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
(len M) + (len <*(NW-corner (L~ f))*>) is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
(<*(NW-corner (L~ f))*> ^ M) /. (len (<*(NW-corner (L~ f))*> ^ M)) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
L~ (<*(NW-corner (L~ f))*> ^ M) is compact Element of bool the carrier of (TOP-REAL 2)
{ (LSeg ((<*(NW-corner (L~ f))*> ^ M),b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len (<*(NW-corner (L~ f))*> ^ M) ) } is set
union { (LSeg ((<*(NW-corner (L~ f))*> ^ M),b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len (<*(NW-corner (L~ f))*> ^ M) ) } is set
LSeg ((M /. 1),(NW-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (M /. 1)) + (b<sub>1</sub> * (NW-corner (L~ f)))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg ((M /. 1),(NW-corner (L~ f)))) /\ (L~ j) is Element of bool the carrier of (TOP-REAL 2)
(LSeg ((M /. 1),(NW-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
{(M /. 1)} is non empty trivial set
LSeg ((NW-corner (L~ f)),(M /. 1)) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (NW-corner (L~ f))) + (b<sub>1</sub> * (M /. 1))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(L~ M) \/ (LSeg ((NW-corner (L~ f)),(M /. 1))) is non empty Element of bool the carrier of (TOP-REAL 2)
LSeg (((<*(NW-corner (L~ f))*> ^ M) /. (len (<*(NW-corner (L~ f))*> ^ M))),(NE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * ((<*(NW-corner (L~ f))*> ^ M) /. (len (<*(NW-corner (L~ f))*> ^ M)))) + (b<sub>1</sub> * (NE-corner (L~ f)))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg (((<*(NW-corner (L~ f))*> ^ M) /. (len (<*(NW-corner (L~ f))*> ^ M))),(NE-corner (L~ f)))) /\ (L~ j) is Element of bool the carrier of (TOP-REAL 2)
(LSeg (((<*(NW-corner (L~ f))*> ^ M) /. (len (<*(NW-corner (L~ f))*> ^ M))),(NE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
{((<*(NW-corner (L~ f))*> ^ M) /. (len (<*(NW-corner (L~ f))*> ^ M)))} is non empty trivial set
L~ g is non empty compact Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (g,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len g ) } is set
union { (LSeg (g,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len g ) } is set
(L~ (<*(NW-corner (L~ f))*> ^ M)) \/ (LSeg (((<*(NW-corner (L~ f))*> ^ M) /. (len (<*(NW-corner (L~ f))*> ^ M))),(NE-corner (L~ f)))) is non empty Element of bool the carrier of (TOP-REAL 2)
f is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard () FinSequence of the carrier of (TOP-REAL 2)
f /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
L~ f is non empty compact being_simple_closed_curve Element of bool the carrier of (TOP-REAL 2)
len f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
{ (LSeg (f,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len f ) } is set
union { (LSeg (f,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len f ) } is set
N-min (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
N-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
NW-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
W-bound (L~ f) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ f) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
the carrier of ((TOP-REAL 2) | (L~ f)) is non empty set
[: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is set
lower_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
(proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K430(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
N-bound (L~ f) is V11() real ext-real Element of REAL
proj2 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
upper_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
(proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K429(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
NE-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
E-bound (L~ f) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
K429(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((NW-corner (L~ f)),(NE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (NW-corner (L~ f))) + (b<sub>1</sub> * (NE-corner (L~ f)))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg ((NW-corner (L~ f)),(NE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (N-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (N-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (N-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (N-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:] is set
lower_bound (proj1 | (N-most (L~ f))) is V11() real ext-real Element of REAL
(proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))) is V137() V138() V139() Element of bool REAL
K430(((proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (N-most (L~ f)))),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
N-max (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
upper_bound (proj1 | (N-most (L~ f))) is V11() real ext-real Element of REAL
K429(((proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))))) is V11() real ext-real Element of REAL
|[(upper_bound (proj1 | (N-most (L~ f)))),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
E-max (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
E-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
SE-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
S-bound (L~ f) is V11() real ext-real Element of REAL
lower_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
K430(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner (L~ f)),(NE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (SE-corner (L~ f))) + (b<sub>1</sub> * (NE-corner (L~ f)))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg ((SE-corner (L~ f)),(NE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (E-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (E-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (E-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (E-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (E-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (E-most (L~ f))),REAL:] is set
upper_bound (proj2 | (E-most (L~ f))) is V11() real ext-real Element of REAL
(proj2 | (E-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ f))) is V137() V138() V139() Element of bool REAL
K429(((proj2 | (E-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ f))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(upper_bound (proj2 | (E-most (L~ f))))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
(E-max (L~ f)) .. f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
(N-max (L~ f)) .. f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
S-max (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
S-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
SW-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
|[(W-bound (L~ f)),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner (L~ f)),(SE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (SW-corner (L~ f))) + (b<sub>1</sub> * (SE-corner (L~ f)))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg ((SW-corner (L~ f)),(SE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (S-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (S-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (S-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (S-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (S-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (S-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (S-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (S-most (L~ f))),REAL:] is set
upper_bound (proj1 | (S-most (L~ f))) is V11() real ext-real Element of REAL
(proj1 | (S-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (S-most (L~ f))) is V137() V138() V139() Element of bool REAL
K429(((proj1 | (S-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (S-most (L~ f))))) is V11() real ext-real Element of REAL
|[(upper_bound (proj1 | (S-most (L~ f)))),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
(S-max (L~ f)) .. f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
(N-min (L~ f)) .. f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
(N-min (L~ f)) `2 is V11() real ext-real Element of REAL
(S-max (L~ f)) `2 is V11() real ext-real Element of REAL
rng f is non empty non trivial Element of bool the carrier of (TOP-REAL 2)
dom f is non empty non trivial V137() V138() V139() V140() V141() V142() Element of bool NAT
f /. ((S-max (L~ f)) .. f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
f . ((S-max (L~ f)) .. f) is set
f /. (len f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
f /. ((N-max (L~ f)) .. f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
f . ((N-max (L~ f)) .. f) is set
mid (f,((S-max (L~ f)) .. f),((N-max (L~ f)) .. f)) is V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
M is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
M /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(M /. 1) `2 is V11() real ext-real Element of REAL
len M is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
M /. (len M) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(M /. (len M)) `2 is V11() real ext-real Element of REAL
f /. ((E-max (L~ f)) .. f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
f . ((E-max (L~ f)) .. f) is set
mid (f,1,((E-max (L~ f)) .. f)) is V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
h is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
len h is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
h /. (len h) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
L~ h is non empty compact Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (h,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len h ) } is set
union { (LSeg (h,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len h ) } is set
L~ M is non empty compact Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (M,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len M ) } is set
union { (LSeg (M,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len M ) } is set
h /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(h /. 1) `1 is V11() real ext-real Element of REAL
(h /. (len h)) `1 is V11() real ext-real Element of REAL
<*(NW-corner (L~ f))*> is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() V33(1) FinSequence-like FinSubsequence-like special FinSequence of the carrier of (TOP-REAL 2)
<*(NW-corner (L~ f))*> ^ h is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
g is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
len g is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
L~ g is non empty compact Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (g,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len g ) } is set
union { (LSeg (g,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len g ) } is set
h /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
LSeg ((NW-corner (L~ f)),(h /. 1)) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (NW-corner (L~ f))) + (b<sub>1</sub> * (h /. 1))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(L~ h) \/ (LSeg ((NW-corner (L~ f)),(h /. 1))) is non empty Element of bool the carrier of (TOP-REAL 2)
g /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(g /. 1) `1 is V11() real ext-real Element of REAL
((E-max (L~ f)) .. f) -' 1 is natural V11() real V37() ext-real non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
(((E-max (L~ f)) .. f) -' 1) + 1 is non empty natural V11() real V37() ext-real positive non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
1 + 1 is non empty natural V11() real V37() ext-real positive non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
dom h is non empty non trivial V137() V138() V139() V140() V141() V142() Element of bool NAT
len <*(NW-corner (L~ f))*> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
(len h) + (len <*(NW-corner (L~ f))*>) is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
g /. (len g) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(g /. (len g)) `1 is V11() real ext-real Element of REAL
LSeg ((h /. 1),(NW-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (h /. 1)) + (b<sub>1</sub> * (NW-corner (L~ f)))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg ((h /. 1),(NW-corner (L~ f)))) /\ (L~ M) is Element of bool the carrier of (TOP-REAL 2)
(LSeg ((h /. 1),(NW-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
{(h /. 1)} is non empty trivial set
f is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard () FinSequence of the carrier of (TOP-REAL 2)
f /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
L~ f is non empty compact being_simple_closed_curve Element of bool the carrier of (TOP-REAL 2)
len f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
{ (LSeg (f,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len f ) } is set
union { (LSeg (f,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len f ) } is set
N-min (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
N-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
NW-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
W-bound (L~ f) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ f) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
the carrier of ((TOP-REAL 2) | (L~ f)) is non empty set
[: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is set
lower_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
(proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K430(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
N-bound (L~ f) is V11() real ext-real Element of REAL
proj2 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
upper_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
(proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K429(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
NE-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
E-bound (L~ f) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
K429(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((NW-corner (L~ f)),(NE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (NW-corner (L~ f))) + (b<sub>1</sub> * (NE-corner (L~ f)))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg ((NW-corner (L~ f)),(NE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (N-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (N-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (N-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (N-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:] is set
lower_bound (proj1 | (N-most (L~ f))) is V11() real ext-real Element of REAL
(proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))) is V137() V138() V139() Element of bool REAL
K430(((proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (N-most (L~ f)))),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
S-max (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
S-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
SW-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
S-bound (L~ f) is V11() real ext-real Element of REAL
lower_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
K430(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
SE-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
|[(E-bound (L~ f)),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner (L~ f)),(SE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (SW-corner (L~ f))) + (b<sub>1</sub> * (SE-corner (L~ f)))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg ((SW-corner (L~ f)),(SE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (S-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (S-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (S-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (S-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (S-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (S-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (S-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (S-most (L~ f))),REAL:] is set
upper_bound (proj1 | (S-most (L~ f))) is V11() real ext-real Element of REAL
(proj1 | (S-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (S-most (L~ f))) is V137() V138() V139() Element of bool REAL
K429(((proj1 | (S-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (S-most (L~ f))))) is V11() real ext-real Element of REAL
|[(upper_bound (proj1 | (S-most (L~ f)))),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
(S-max (L~ f)) .. f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
E-max (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
E-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
LSeg ((SE-corner (L~ f)),(NE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (SE-corner (L~ f))) + (b<sub>1</sub> * (NE-corner (L~ f)))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg ((SE-corner (L~ f)),(NE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (E-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (E-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (E-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (E-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (E-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (E-most (L~ f))),REAL:] is set
upper_bound (proj2 | (E-most (L~ f))) is V11() real ext-real Element of REAL
(proj2 | (E-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ f))) is V137() V138() V139() Element of bool REAL
K429(((proj2 | (E-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ f))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(upper_bound (proj2 | (E-most (L~ f))))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
(E-max (L~ f)) .. f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
N-max (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
upper_bound (proj1 | (N-most (L~ f))) is V11() real ext-real Element of REAL
K429(((proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))))) is V11() real ext-real Element of REAL
|[(upper_bound (proj1 | (N-most (L~ f)))),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
(N-max (L~ f)) `1 is V11() real ext-real Element of REAL
(N-min (L~ f)) `1 is V11() real ext-real Element of REAL
f /. 2 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(f /. 2) `2 is V11() real ext-real Element of REAL
(N-min (L~ f)) `2 is V11() real ext-real Element of REAL
E-min (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
lower_bound (proj2 | (E-most (L~ f))) is V11() real ext-real Element of REAL
K430(((proj2 | (E-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ f))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(lower_bound (proj2 | (E-most (L~ f))))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
(E-min (L~ f)) `2 is V11() real ext-real Element of REAL
rng f is non empty non trivial Element of bool the carrier of (TOP-REAL 2)
dom f is non empty non trivial V137() V138() V139() V140() V141() V142() Element of bool NAT
f /. ((S-max (L~ f)) .. f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
f . ((S-max (L~ f)) .. f) is set
(f /. ((S-max (L~ f)) .. f)) `2 is V11() real ext-real Element of REAL
(f /. 1) `2 is V11() real ext-real Element of REAL
mid (f,((S-max (L~ f)) .. f),2) is V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
j is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
j /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(j /. 1) `2 is V11() real ext-real Element of REAL
len j is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
j /. (len j) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
f /. ((E-max (L~ f)) .. f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
f . ((E-max (L~ f)) .. f) is set
f /. (len f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
((E-max (L~ f)) .. f) + 1 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
(len f) - ((E-max (L~ f)) .. f) is V11() real ext-real Element of REAL
(len f) -' ((E-max (L~ f)) .. f) is natural V11() real V37() ext-real non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
1 + 1 is non empty natural V11() real V37() ext-real positive non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
((len f) -' ((E-max (L~ f)) .. f)) + 1 is non empty natural V11() real V37() ext-real positive non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
(E-max (L~ f)) `2 is V11() real ext-real Element of REAL
mid (f,(len f),((E-max (L~ f)) .. f)) is V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
M is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
len M is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
M /. (len M) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
L~ M is non empty compact Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (M,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len M ) } is set
union { (LSeg (M,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len M ) } is set
L~ j is non empty compact Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (j,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len j ) } is set
union { (LSeg (j,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len j ) } is set
M /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(M /. 1) `1 is V11() real ext-real Element of REAL
(M /. (len M)) `1 is V11() real ext-real Element of REAL
<*(NW-corner (L~ f))*> is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() V33(1) FinSequence-like FinSubsequence-like special FinSequence of the carrier of (TOP-REAL 2)
<*(NW-corner (L~ f))*> ^ M is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
h is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
len h is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
L~ h is non empty compact Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (h,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len h ) } is set
union { (LSeg (h,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len h ) } is set
LSeg ((NW-corner (L~ f)),(M /. 1)) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NW-corner (L~ f))) + (b₁ * (M /. 1))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(L~ M) \/ (LSeg ((NW-corner (L~ f)),(M /. 1))) is non empty Element of bool the carrier of (TOP-REAL 2)
h /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(h /. 1) `1 is V11() real ext-real Element of REAL
LSeg ((M /. 1),(NW-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (M /. 1)) + (b<sub>1</sub> * (NW-corner (L~ f)))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg ((M /. 1),(NW-corner (L~ f)))) /\ (L~ j) is Element of bool the carrier of (TOP-REAL 2)
(LSeg ((M /. 1),(NW-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
{(M /. 1)} is non empty trivial set
dom M is non empty non trivial V137() V138() V139() V140() V141() V142() Element of bool NAT
len <*(NW-corner (L~ f))*> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
(len M) + (len <*(NW-corner (L~ f))*>) is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
h /. (len h) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(h /. (len h)) `1 is V11() real ext-real Element of REAL
f is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard FinSequence of the carrier of (TOP-REAL 2)
L~ f is non empty compact being_simple_closed_curve Element of bool the carrier of (TOP-REAL 2)
len f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
{ (LSeg (f,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
union { (LSeg (f,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
N-min (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
N-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
NW-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
W-bound (L~ f) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ f) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
the carrier of ((TOP-REAL 2) | (L~ f)) is non empty set
[: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is set
lower_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
(proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K430(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
N-bound (L~ f) is V11() real ext-real Element of REAL
proj2 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
upper_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
(proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K429(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
NE-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
E-bound (L~ f) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
K429(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((NW-corner (L~ f)),(NE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NW-corner (L~ f))) + (b₁ * (NE-corner (L~ f)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((NW-corner (L~ f)),(NE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (N-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (N-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (N-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (N-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:] is set
lower_bound (proj1 | (N-most (L~ f))) is V11() real ext-real Element of REAL
(proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))) is V137() V138() V139() Element of bool REAL
K430(((proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (N-most (L~ f)))),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((N-min (L~ f)),(NW-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (N-min (L~ f))) + (b₁ * (NW-corner (L~ f)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
E-max (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
E-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
SE-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
S-bound (L~ f) is V11() real ext-real Element of REAL
lower_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
K430(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner (L~ f)),(NE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SE-corner (L~ f))) + (b₁ * (NE-corner (L~ f)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((SE-corner (L~ f)),(NE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (E-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (E-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (E-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (E-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (E-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (E-most (L~ f))),REAL:] is set
upper_bound (proj2 | (E-most (L~ f))) is V11() real ext-real Element of REAL
(proj2 | (E-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ f))) is V137() V138() V139() Element of bool REAL
K429(((proj2 | (E-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ f))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(upper_bound (proj2 | (E-most (L~ f))))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((NE-corner (L~ f)),(E-max (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NE-corner (L~ f))) + (b₁ * (E-max (L~ f)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((N-min (L~ f)),(NW-corner (L~ f)))) /\ (LSeg ((NE-corner (L~ f)),(E-max (L~ f)))) is Element of bool the carrier of (TOP-REAL 2)
(NE-corner (L~ f)) `1 is V11() real ext-real Element of REAL
(E-max (L~ f)) `1 is V11() real ext-real Element of REAL
i1 is set
i2 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
i2 `1 is V11() real ext-real Element of REAL
(NW-corner (L~ f)) `1 is V11() real ext-real Element of REAL
(N-min (L~ f)) `1 is V11() real ext-real Element of REAL
N-max (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
upper_bound (proj1 | (N-most (L~ f))) is V11() real ext-real Element of REAL
K429(((proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))))) is V11() real ext-real Element of REAL
|[(upper_bound (proj1 | (N-most (L~ f)))),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
(N-max (L~ f)) `1 is V11() real ext-real Element of REAL
f is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard () FinSequence of the carrier of (TOP-REAL 2)
f /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
L~ f is non empty compact being_simple_closed_curve Element of bool the carrier of (TOP-REAL 2)
len f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
{ (LSeg (f,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
union { (LSeg (f,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
N-min (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
N-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
NW-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
W-bound (L~ f) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ f) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
the carrier of ((TOP-REAL 2) | (L~ f)) is non empty set
[: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is set
lower_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
(proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K430(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
N-bound (L~ f) is V11() real ext-real Element of REAL
proj2 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
upper_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
(proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K429(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
NE-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
E-bound (L~ f) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
K429(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((NW-corner (L~ f)),(NE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NW-corner (L~ f))) + (b₁ * (NE-corner (L~ f)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((NW-corner (L~ f)),(NE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (N-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (N-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (N-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (N-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:] is set
lower_bound (proj1 | (N-most (L~ f))) is V11() real ext-real Element of REAL
(proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))) is V137() V138() V139() Element of bool REAL
K430(((proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (N-most (L~ f)))),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
E-min (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
E-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
SE-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
S-bound (L~ f) is V11() real ext-real Element of REAL
lower_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
K430(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner (L~ f)),(NE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SE-corner (L~ f))) + (b₁ * (NE-corner (L~ f)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((SE-corner (L~ f)),(NE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (E-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (E-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (E-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (E-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (E-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (E-most (L~ f))),REAL:] is set
lower_bound (proj2 | (E-most (L~ f))) is V11() real ext-real Element of REAL
(proj2 | (E-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ f))) is V137() V138() V139() Element of bool REAL
K430(((proj2 | (E-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ f))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(lower_bound (proj2 | (E-most (L~ f))))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
(E-min (L~ f)) .. f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
E-max (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
upper_bound (proj2 | (E-most (L~ f))) is V11() real ext-real Element of REAL
K429(((proj2 | (E-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ f))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(upper_bound (proj2 | (E-most (L~ f))))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
(E-max (L~ f)) .. f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
S-max (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
S-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
SW-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
|[(W-bound (L~ f)),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner (L~ f)),(SE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SW-corner (L~ f))) + (b₁ * (SE-corner (L~ f)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((SW-corner (L~ f)),(SE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (S-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (S-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (S-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (S-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (S-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (S-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (S-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (S-most (L~ f))),REAL:] is set
upper_bound (proj1 | (S-most (L~ f))) is V11() real ext-real Element of REAL
(proj1 | (S-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (S-most (L~ f))) is V137() V138() V139() Element of bool REAL
K429(((proj1 | (S-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (S-most (L~ f))))) is V11() real ext-real Element of REAL
|[(upper_bound (proj1 | (S-most (L~ f)))),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
(S-max (L~ f)) .. f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
rng f is non empty non trivial Element of bool the carrier of (TOP-REAL 2)
dom f is non empty non trivial V137() V138() V139() V140() V141() V142() Element of bool NAT
f /. ((E-min (L~ f)) .. f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
f . ((E-min (L~ f)) .. f) is set
N-max (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
upper_bound (proj1 | (N-most (L~ f))) is V11() real ext-real Element of REAL
K429(((proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))))) is V11() real ext-real Element of REAL
|[(upper_bound (proj1 | (N-most (L~ f)))),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
(N-max (L~ f)) `1 is V11() real ext-real Element of REAL
(N-min (L~ f)) `1 is V11() real ext-real Element of REAL
(E-min (L~ f)) `1 is V11() real ext-real Element of REAL
(S-max (L~ f)) `2 is V11() real ext-real Element of REAL
(N-min (L~ f)) `2 is V11() real ext-real Element of REAL
f /. ((E-max (L~ f)) .. f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
f . ((E-max (L~ f)) .. f) is set
(E-max (L~ f)) `2 is V11() real ext-real Element of REAL
(E-min (L~ f)) `2 is V11() real ext-real Element of REAL
mid (f,1,((E-min (L~ f)) .. f)) is V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
M is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
M /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
mid (f,((S-max (L~ f)) .. f),((E-max (L~ f)) .. f)) is V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
h is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
len h is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
h /. (len h) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
f /. ((S-max (L~ f)) .. f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
f . ((S-max (L~ f)) .. f) is set
h /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(h /. 1) `2 is V11() real ext-real Element of REAL
len M is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
M /. (len M) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(M /. (len M)) `1 is V11() real ext-real Element of REAL
1 + 1 is non empty natural V11() real V37() ext-real positive non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
((E-min (L~ f)) .. f) -' 1 is natural V11() real V37() ext-real non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
(((E-min (L~ f)) .. f) -' 1) + 1 is non empty natural V11() real V37() ext-real positive non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
f /. (len f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
L~ M is non empty compact Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (M,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len M ) } is set
union { (LSeg (M,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len M ) } is set
L~ h is non empty compact Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (h,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len h ) } is set
union { (LSeg (h,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len h ) } is set
(M /. 1) `1 is V11() real ext-real Element of REAL
(h /. (len h)) `2 is V11() real ext-real Element of REAL
<*(NW-corner (L~ f))*> is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() V33(1) FinSequence-like FinSubsequence-like special FinSequence of the carrier of (TOP-REAL 2)
<*(NW-corner (L~ f))*> ^ M is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
g is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
len g is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
L~ g is non empty compact Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (g,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len g ) } is set
union { (LSeg (g,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len g ) } is set
LSeg ((NW-corner (L~ f)),(M /. 1)) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (NW-corner (L~ f))) + (b<sub>1</sub> * (M /. 1))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(L~ M) \/ (LSeg ((NW-corner (L~ f)),(M /. 1))) is non empty Element of bool the carrier of (TOP-REAL 2)
(h /. (len h)) `2 is V11() real ext-real Element of REAL
g /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(g /. 1) `1 is V11() real ext-real Element of REAL
dom M is non empty non trivial V137() V138() V139() V140() V141() V142() Element of bool NAT
len <*(NW-corner (L~ f))*> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
(len M) + (len <*(NW-corner (L~ f))*>) is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
g /. (len g) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(g /. (len g)) `1 is V11() real ext-real Element of REAL
LSeg ((M /. 1),(NW-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (M /. 1)) + (b₁ * (NW-corner (L~ f)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((M /. 1),(NW-corner (L~ f)))) /\ (L~ h) is Element of bool the carrier of (TOP-REAL 2)
(LSeg ((M /. 1),(NW-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
{(M /. 1)} is non empty trivial set
<*(NE-corner (L~ f))*> is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() V33(1) FinSequence-like FinSubsequence-like special FinSequence of the carrier of (TOP-REAL 2)
h ^ <*(NE-corner (L~ f))*> is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
g is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
len g is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
LSeg ((h /. (len h)),(NE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (h /. (len h))) + (b₁ * (NE-corner (L~ f)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((h /. (len h)),(NE-corner (L~ f)))) /\ (L~ M) is Element of bool the carrier of (TOP-REAL 2)
(LSeg ((h /. (len h)),(NE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
{(h /. (len h))} is non empty trivial set
L~ g is non empty compact Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (g,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len g ) } is set
union { (LSeg (g,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len g ) } is set
LSeg ((NE-corner (L~ f)),(h /. (len h))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NE-corner (L~ f))) + (b₁ * (h /. (len h)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(L~ h) \/ (LSeg ((NE-corner (L~ f)),(h /. (len h)))) is non empty Element of bool the carrier of (TOP-REAL 2)
len <*(NE-corner (L~ f))*> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
(len h) + (len <*(NE-corner (L~ f))*>) is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
(len h) + 1 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
g /. (len g) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(g /. (len g)) `2 is V11() real ext-real Element of REAL
(M /. 1) `1 is V11() real ext-real Element of REAL
dom h is non empty non trivial V137() V138() V139() V140() V141() V142() Element of bool NAT
g /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(g /. 1) `2 is V11() real ext-real Element of REAL
<*(NE-corner (L~ f))*> is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() V33(1) FinSequence-like FinSubsequence-like special FinSequence of the carrier of (TOP-REAL 2)
h ^ <*(NE-corner (L~ f))*> is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
<*(NW-corner (L~ f))*> is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() V33(1) FinSequence-like FinSubsequence-like special FinSequence of the carrier of (TOP-REAL 2)
<*(NW-corner (L~ f))*> ^ M is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
g is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
len g is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
g is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
len g is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
L~ g is non empty compact Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (g,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len g ) } is set
union { (LSeg (g,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len g ) } is set
LSeg ((NE-corner (L~ f)),(h /. (len h))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (NE-corner (L~ f))) + (b<sub>1</sub> * (h /. (len h)))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(L~ h) \/ (LSeg ((NE-corner (L~ f)),(h /. (len h)))) is non empty Element of bool the carrier of (TOP-REAL 2)
LSeg ((M /. 1),(NW-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (M /. 1)) + (b<sub>1</sub> * (NW-corner (L~ f)))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg ((M /. 1),(NW-corner (L~ f)))) /\ (LSeg ((NE-corner (L~ f)),(h /. (len h)))) is Element of bool the carrier of (TOP-REAL 2)
(LSeg ((M /. 1),(NW-corner (L~ f)))) /\ (L~ g) is Element of bool the carrier of (TOP-REAL 2)
(LSeg ((M /. 1),(NW-corner (L~ f)))) /\ (L~ h) is Element of bool the carrier of (TOP-REAL 2)
((LSeg ((M /. 1),(NW-corner (L~ f)))) /\ (L~ h)) \/ {} is set
(LSeg ((M /. 1),(NW-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
{(M /. 1)} is non empty trivial set
g /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(g /. 1) `1 is V11() real ext-real Element of REAL
dom M is non empty non trivial V137() V138() V139() V140() V141() V142() Element of bool NAT
len <*(NW-corner (L~ f))*> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
(len M) + (len <*(NW-corner (L~ f))*>) is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
g /. (len g) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(g /. (len g)) `1 is V11() real ext-real Element of REAL
len <*(NE-corner (L~ f))*> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
(len h) + (len <*(NE-corner (L~ f))*>) is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
(len h) + 1 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
g /. (len g) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(g /. (len g)) `2 is V11() real ext-real Element of REAL
LSeg ((h /. (len h)),(NE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (h /. (len h))) + (b₁ * (NE-corner (L~ f)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((h /. (len h)),(NE-corner (L~ f)))) /\ (L~ M) is Element of bool the carrier of (TOP-REAL 2)
(LSeg ((h /. (len h)),(NE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
{(h /. (len h))} is non empty trivial set
dom h is non empty non trivial V137() V138() V139() V140() V141() V142() Element of bool NAT
g /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(g /. 1) `2 is V11() real ext-real Element of REAL
L~ g is non empty compact Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (g,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len g ) } is set
union { (LSeg (g,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len g ) } is set
LSeg ((NW-corner (L~ f)),(M /. 1)) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (NW-corner (L~ f))) + (b<sub>1</sub> * (M /. 1))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(L~ M) \/ (LSeg ((NW-corner (L~ f)),(M /. 1))) is non empty Element of bool the carrier of (TOP-REAL 2)
f is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard () FinSequence of the carrier of (TOP-REAL 2)
f /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
L~ f is non empty compact being_simple_closed_curve Element of bool the carrier of (TOP-REAL 2)
len f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
{ (LSeg (f,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len f ) } is set
union { (LSeg (f,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len f ) } is set
N-min (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
N-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
NW-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
W-bound (L~ f) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ f) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
the carrier of ((TOP-REAL 2) | (L~ f)) is non empty set
[: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is set
lower_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
(proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K430(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
N-bound (L~ f) is V11() real ext-real Element of REAL
proj2 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
upper_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
(proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K429(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
NE-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
E-bound (L~ f) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
K429(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((NW-corner (L~ f)),(NE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (NW-corner (L~ f))) + (b<sub>1</sub> * (NE-corner (L~ f)))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg ((NW-corner (L~ f)),(NE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (N-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (N-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (N-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (N-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:] is set
lower_bound (proj1 | (N-most (L~ f))) is V11() real ext-real Element of REAL
(proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))) is V137() V138() V139() Element of bool REAL
K430(((proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (N-most (L~ f)))),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
E-min (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
E-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
SE-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
S-bound (L~ f) is V11() real ext-real Element of REAL
lower_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
K430(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner (L~ f)),(NE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (SE-corner (L~ f))) + (b<sub>1</sub> * (NE-corner (L~ f)))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg ((SE-corner (L~ f)),(NE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (E-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (E-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (E-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (E-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (E-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (E-most (L~ f))),REAL:] is set
lower_bound (proj2 | (E-most (L~ f))) is V11() real ext-real Element of REAL
(proj2 | (E-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ f))) is V137() V138() V139() Element of bool REAL
K430(((proj2 | (E-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ f))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(lower_bound (proj2 | (E-most (L~ f))))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
S-max (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
S-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
SW-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
|[(W-bound (L~ f)),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner (L~ f)),(SE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (SW-corner (L~ f))) + (b<sub>1</sub> * (SE-corner (L~ f)))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg ((SW-corner (L~ f)),(SE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (S-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (S-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (S-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (S-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (S-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (S-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (S-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (S-most (L~ f))),REAL:] is set
upper_bound (proj1 | (S-most (L~ f))) is V11() real ext-real Element of REAL
(proj1 | (S-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (S-most (L~ f))) is V137() V138() V139() Element of bool REAL
K429(((proj1 | (S-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (S-most (L~ f))))) is V11() real ext-real Element of REAL
|[(upper_bound (proj1 | (S-most (L~ f)))),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
(S-max (L~ f)) .. f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
(E-min (L~ f)) .. f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
f /. 2 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(f /. 2) `2 is V11() real ext-real Element of REAL
(N-min (L~ f)) `2 is V11() real ext-real Element of REAL
rng f is non empty non trivial Element of bool the carrier of (TOP-REAL 2)
dom f is non empty non trivial V137() V138() V139() V140() V141() V142() Element of bool NAT
f /. ((S-max (L~ f)) .. f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
f . ((S-max (L~ f)) .. f) is set
(f /. ((S-max (L~ f)) .. f)) `2 is V11() real ext-real Element of REAL
(f /. 1) `2 is V11() real ext-real Element of REAL
mid (f,((S-max (L~ f)) .. f),2) is V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
j is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
j /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(j /. 1) `2 is V11() real ext-real Element of REAL
len j is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
j /. (len j) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
N-max (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
upper_bound (proj1 | (N-most (L~ f))) is V11() real ext-real Element of REAL
K429(((proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))))) is V11() real ext-real Element of REAL
|[(upper_bound (proj1 | (N-most (L~ f)))),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
(N-max (L~ f)) `1 is V11() real ext-real Element of REAL
(N-min (L~ f)) `1 is V11() real ext-real Element of REAL
(E-min (L~ f)) `1 is V11() real ext-real Element of REAL
f /. ((E-min (L~ f)) .. f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
f . ((E-min (L~ f)) .. f) is set
f /. (len f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
((E-min (L~ f)) .. f) + 1 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
(len f) - ((E-min (L~ f)) .. f) is V11() real ext-real Element of REAL
(len f) -' ((E-min (L~ f)) .. f) is natural V11() real V37() ext-real non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
1 + 1 is non empty natural V11() real V37() ext-real positive non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
((len f) -' ((E-min (L~ f)) .. f)) + 1 is non empty natural V11() real V37() ext-real positive non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
mid (f,(len f),((E-min (L~ f)) .. f)) is V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
M is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
len M is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
M /. (len M) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
L~ M is non empty compact Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (M,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len M ) } is set
union { (LSeg (M,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len M ) } is set
L~ j is non empty compact Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (j,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len j ) } is set
union { (LSeg (j,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len j ) } is set
M /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(M /. 1) `1 is V11() real ext-real Element of REAL
(M /. (len M)) `1 is V11() real ext-real Element of REAL
<*(NW-corner (L~ f))*> is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() V33(1) FinSequence-like FinSubsequence-like special FinSequence of the carrier of (TOP-REAL 2)
<*(NW-corner (L~ f))*> ^ M is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
h is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
len h is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
L~ h is non empty compact Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (h,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len h ) } is set
union { (LSeg (h,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len h ) } is set
LSeg ((NW-corner (L~ f)),(M /. 1)) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (NW-corner (L~ f))) + (b<sub>1</sub> * (M /. 1))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(L~ M) \/ (LSeg ((NW-corner (L~ f)),(M /. 1))) is non empty Element of bool the carrier of (TOP-REAL 2)
h /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(h /. 1) `1 is V11() real ext-real Element of REAL
LSeg ((M /. 1),(NW-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (M /. 1)) + (b₁ * (NW-corner (L~ f)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((M /. 1),(NW-corner (L~ f)))) /\ (L~ j) is Element of bool the carrier of (TOP-REAL 2)
(LSeg ((M /. 1),(NW-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
{(M /. 1)} is non empty trivial set
dom M is non empty non trivial V137() V138() V139() V140() V141() V142() Element of bool NAT
len <*(NW-corner (L~ f))*> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
(len M) + (len <*(NW-corner (L~ f))*>) is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
h /. (len h) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(h /. (len h)) `1 is V11() real ext-real Element of REAL
f is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard () FinSequence of the carrier of (TOP-REAL 2)
f /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
L~ f is non empty compact being_simple_closed_curve Element of bool the carrier of (TOP-REAL 2)
len f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
{ (LSeg (f,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len f ) } is set
union { (LSeg (f,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len f ) } is set
N-min (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
N-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
NW-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
W-bound (L~ f) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ f) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
the carrier of ((TOP-REAL 2) | (L~ f)) is non empty set
[: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is set
lower_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
(proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K430(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
N-bound (L~ f) is V11() real ext-real Element of REAL
proj2 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
upper_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
(proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K429(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
NE-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
E-bound (L~ f) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
K429(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((NW-corner (L~ f)),(NE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (NW-corner (L~ f))) + (b<sub>1</sub> * (NE-corner (L~ f)))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg ((NW-corner (L~ f)),(NE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (N-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (N-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (N-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (N-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:] is set
lower_bound (proj1 | (N-most (L~ f))) is V11() real ext-real Element of REAL
(proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))) is V137() V138() V139() Element of bool REAL
K430(((proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (N-most (L~ f)))),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
S-min (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
S-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
SW-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
S-bound (L~ f) is V11() real ext-real Element of REAL
lower_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
K430(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
SE-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
|[(E-bound (L~ f)),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner (L~ f)),(SE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (SW-corner (L~ f))) + (b<sub>1</sub> * (SE-corner (L~ f)))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg ((SW-corner (L~ f)),(SE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (S-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (S-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (S-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (S-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (S-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (S-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (S-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (S-most (L~ f))),REAL:] is set
lower_bound (proj1 | (S-most (L~ f))) is V11() real ext-real Element of REAL
(proj1 | (S-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (S-most (L~ f))) is V137() V138() V139() Element of bool REAL
K430(((proj1 | (S-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (S-most (L~ f))))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (S-most (L~ f)))),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
(S-min (L~ f)) .. f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
S-max (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
upper_bound (proj1 | (S-most (L~ f))) is V11() real ext-real Element of REAL
K429(((proj1 | (S-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (S-most (L~ f))))) is V11() real ext-real Element of REAL
|[(upper_bound (proj1 | (S-most (L~ f)))),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
(S-max (L~ f)) .. f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
N-max (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
upper_bound (proj1 | (N-most (L~ f))) is V11() real ext-real Element of REAL
K429(((proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))))) is V11() real ext-real Element of REAL
|[(upper_bound (proj1 | (N-most (L~ f)))),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
(N-max (L~ f)) .. f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
f /. (len f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
rng f is non empty non trivial Element of bool the carrier of (TOP-REAL 2)
dom f is non empty non trivial V137() V138() V139() V140() V141() V142() Element of bool NAT
f /. ((S-max (L~ f)) .. f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
f . ((S-max (L~ f)) .. f) is set
(N-min (L~ f)) `2 is V11() real ext-real Element of REAL
(S-max (L~ f)) `2 is V11() real ext-real Element of REAL
((S-max (L~ f)) .. f) + 1 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
(len f) - ((S-max (L~ f)) .. f) is V11() real ext-real Element of REAL
(len f) -' ((S-max (L~ f)) .. f) is natural V11() real V37() ext-real non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
1 + 1 is non empty natural V11() real V37() ext-real positive non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
((len f) -' ((S-max (L~ f)) .. f)) + 1 is non empty natural V11() real V37() ext-real positive non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
mid (f,(len f),((S-max (L~ f)) .. f)) is V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
f /. ((N-max (L~ f)) .. f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
f . ((N-max (L~ f)) .. f) is set
(f /. ((N-max (L~ f)) .. f)) `2 is V11() real ext-real Element of REAL
M is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
M /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
len M is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
M /. (len M) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
L~ M is non empty compact Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (M,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len M ) } is set
union { (LSeg (M,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len M ) } is set
dom M is non empty non trivial V137() V138() V139() V140() V141() V142() Element of bool NAT
mid (f,((S-min (L~ f)) .. f),((N-max (L~ f)) .. f)) is V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
f /. ((S-min (L~ f)) .. f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
f . ((S-min (L~ f)) .. f) is set
h is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
h /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(h /. 1) `2 is V11() real ext-real Element of REAL
len h is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
h /. (len h) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
L~ h is non empty compact Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (h,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len h ) } is set
union { (LSeg (h,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len h ) } is set
(M /. 1) `1 is V11() real ext-real Element of REAL
(M /. (len M)) `1 is V11() real ext-real Element of REAL
<*(SE-corner (L~ f))*> is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() V33(1) FinSequence-like FinSubsequence-like special FinSequence of the carrier of (TOP-REAL 2)
M ^ <*(SE-corner (L~ f))*> is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
g is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
len g is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
L~ g is non empty compact Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (g,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len g ) } is set
union { (LSeg (g,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len g ) } is set
LSeg ((M /. (len M)),(SE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (M /. (len M))) + (b<sub>1</sub> * (SE-corner (L~ f)))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(L~ M) \/ (LSeg ((M /. (len M)),(SE-corner (L~ f)))) is non empty Element of bool the carrier of (TOP-REAL 2)
len <*(SE-corner (L~ f))*> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
(len M) + (len <*(SE-corner (L~ f))*>) is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
(len M) + 1 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
g /. (len g) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(g /. (len g)) `1 is V11() real ext-real Element of REAL
(LSeg ((M /. (len M)),(SE-corner (L~ f)))) /\ (L~ h) is Element of bool the carrier of (TOP-REAL 2)
(LSeg ((M /. (len M)),(SE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
{(M /. (len M))} is non empty trivial set
g /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(g /. 1) `1 is V11() real ext-real Element of REAL
<*(NW-corner (L~ f))*> is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() V33(1) FinSequence-like FinSubsequence-like special FinSequence of the carrier of (TOP-REAL 2)
<*(NW-corner (L~ f))*> ^ M is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
g is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
len g is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
len <*(NW-corner (L~ f))*> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
(len M) + (len <*(NW-corner (L~ f))*>) is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
g /. (len g) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(g /. (len g)) `1 is V11() real ext-real Element of REAL
L~ g is non empty compact Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (g,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len g ) } is set
union { (LSeg (g,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len g ) } is set
LSeg ((NW-corner (L~ f)),(M /. 1)) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NW-corner (L~ f))) + (b₁ * (M /. 1))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(L~ M) \/ (LSeg ((NW-corner (L~ f)),(M /. 1))) is non empty Element of bool the carrier of (TOP-REAL 2)
g /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(g /. 1) `1 is V11() real ext-real Element of REAL
LSeg ((M /. 1),(NW-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (M /. 1)) + (b<sub>1</sub> * (NW-corner (L~ f)))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg ((M /. 1),(NW-corner (L~ f)))) /\ (L~ h) is Element of bool the carrier of (TOP-REAL 2)
(LSeg ((M /. 1),(NW-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
{(M /. 1)} is non empty trivial set
<*(NW-corner (L~ f))*> is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() V33(1) FinSequence-like FinSubsequence-like special FinSequence of the carrier of (TOP-REAL 2)
<*(NW-corner (L~ f))*> ^ M is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
<*(SE-corner (L~ f))*> is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() V33(1) FinSequence-like FinSubsequence-like special FinSequence of the carrier of (TOP-REAL 2)
(<*(NW-corner (L~ f))*> ^ M) ^ <*(SE-corner (L~ f))*> is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
dom (<*(NW-corner (L~ f))*> ^ M) is V137() V138() V139() V140() V141() V142() Element of bool NAT
g is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
g /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(<*(NW-corner (L~ f))*> ^ M) /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(g /. 1) `1 is V11() real ext-real Element of REAL
len g is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
len (<*(NW-corner (L~ f))*> ^ M) is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
len <*(SE-corner (L~ f))*> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
(len (<*(NW-corner (L~ f))*> ^ M)) + (len <*(SE-corner (L~ f))*>) is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
(len (<*(NW-corner (L~ f))*> ^ M)) + 1 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
g /. (len g) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(g /. (len g)) `1 is V11() real ext-real Element of REAL
len <*(NW-corner (L~ f))*> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
(len M) + (len <*(NW-corner (L~ f))*>) is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
(<*(NW-corner (L~ f))*> ^ M) /. (len (<*(NW-corner (L~ f))*> ^ M)) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
L~ (<*(NW-corner (L~ f))*> ^ M) is compact Element of bool the carrier of (TOP-REAL 2)
{ (LSeg ((<*(NW-corner (L~ f))*> ^ M),b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len (<*(NW-corner (L~ f))*> ^ M) ) } is set
union { (LSeg ((<*(NW-corner (L~ f))*> ^ M),b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len (<*(NW-corner (L~ f))*> ^ M) ) } is set
LSeg ((M /. 1),(NW-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (M /. 1)) + (b<sub>1</sub> * (NW-corner (L~ f)))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg ((M /. 1),(NW-corner (L~ f)))) /\ (L~ h) is Element of bool the carrier of (TOP-REAL 2)
(LSeg ((M /. 1),(NW-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
{(M /. 1)} is non empty trivial set
LSeg ((NW-corner (L~ f)),(M /. 1)) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (NW-corner (L~ f))) + (b<sub>1</sub> * (M /. 1))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(L~ M) \/ (LSeg ((NW-corner (L~ f)),(M /. 1))) is non empty Element of bool the carrier of (TOP-REAL 2)
LSeg (((<*(NW-corner (L~ f))*> ^ M) /. (len (<*(NW-corner (L~ f))*> ^ M))),(SE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * ((<*(NW-corner (L~ f))*> ^ M) /. (len (<*(NW-corner (L~ f))*> ^ M)))) + (b<sub>1</sub> * (SE-corner (L~ f)))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg (((<*(NW-corner (L~ f))*> ^ M) /. (len (<*(NW-corner (L~ f))*> ^ M))),(SE-corner (L~ f)))) /\ (L~ h) is Element of bool the carrier of (TOP-REAL 2)
(LSeg (((<*(NW-corner (L~ f))*> ^ M) /. (len (<*(NW-corner (L~ f))*> ^ M))),(SE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
{((<*(NW-corner (L~ f))*> ^ M) /. (len (<*(NW-corner (L~ f))*> ^ M)))} is non empty trivial set
L~ g is non empty compact Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (g,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len g ) } is set
union { (LSeg (g,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len g ) } is set
(L~ (<*(NW-corner (L~ f))*> ^ M)) \/ (LSeg (((<*(NW-corner (L~ f))*> ^ M) /. (len (<*(NW-corner (L~ f))*> ^ M))),(SE-corner (L~ f)))) is non empty Element of bool the carrier of (TOP-REAL 2)
f is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard () FinSequence of the carrier of (TOP-REAL 2)
f /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
L~ f is non empty compact being_simple_closed_curve Element of bool the carrier of (TOP-REAL 2)
len f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
{ (LSeg (f,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len f ) } is set
union { (LSeg (f,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len f ) } is set
N-min (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
N-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
NW-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
W-bound (L~ f) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ f) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
the carrier of ((TOP-REAL 2) | (L~ f)) is non empty set
[: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is set
lower_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
(proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K430(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
N-bound (L~ f) is V11() real ext-real Element of REAL
proj2 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
upper_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
(proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K429(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
NE-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
E-bound (L~ f) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
K429(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((NW-corner (L~ f)),(NE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (NW-corner (L~ f))) + (b<sub>1</sub> * (NE-corner (L~ f)))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg ((NW-corner (L~ f)),(NE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (N-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (N-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (N-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (N-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:] is set
lower_bound (proj1 | (N-most (L~ f))) is V11() real ext-real Element of REAL
(proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))) is V137() V138() V139() Element of bool REAL
K430(((proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (N-most (L~ f)))),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
S-min (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
S-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
SW-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
S-bound (L~ f) is V11() real ext-real Element of REAL
lower_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
K430(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
SE-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
|[(E-bound (L~ f)),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner (L~ f)),(SE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (SW-corner (L~ f))) + (b<sub>1</sub> * (SE-corner (L~ f)))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg ((SW-corner (L~ f)),(SE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (S-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (S-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (S-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (S-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (S-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (S-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (S-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (S-most (L~ f))),REAL:] is set
lower_bound (proj1 | (S-most (L~ f))) is V11() real ext-real Element of REAL
(proj1 | (S-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (S-most (L~ f))) is V137() V138() V139() Element of bool REAL
K430(((proj1 | (S-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (S-most (L~ f))))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (S-most (L~ f)))),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
(S-min (L~ f)) .. f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
E-min (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
E-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
LSeg ((SE-corner (L~ f)),(NE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (SE-corner (L~ f))) + (b<sub>1</sub> * (NE-corner (L~ f)))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg ((SE-corner (L~ f)),(NE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (E-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (E-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (E-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (E-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (E-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (E-most (L~ f))),REAL:] is set
lower_bound (proj2 | (E-most (L~ f))) is V11() real ext-real Element of REAL
(proj2 | (E-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ f))) is V137() V138() V139() Element of bool REAL
K430(((proj2 | (E-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ f))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(lower_bound (proj2 | (E-most (L~ f))))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
(E-min (L~ f)) .. f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
S-max (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
upper_bound (proj1 | (S-most (L~ f))) is V11() real ext-real Element of REAL
K429(((proj1 | (S-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (S-most (L~ f))))) is V11() real ext-real Element of REAL
|[(upper_bound (proj1 | (S-most (L~ f)))),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
(S-max (L~ f)) .. f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
f is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard () FinSequence of the carrier of (TOP-REAL 2)
f /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
L~ f is non empty compact being_simple_closed_curve Element of bool the carrier of (TOP-REAL 2)
len f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
{ (LSeg (f,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len f ) } is set
union { (LSeg (f,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len f ) } is set
N-min (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
N-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
NW-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
W-bound (L~ f) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ f) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
the carrier of ((TOP-REAL 2) | (L~ f)) is non empty set
[: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is set
lower_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
(proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K430(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
N-bound (L~ f) is V11() real ext-real Element of REAL
proj2 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
upper_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
(proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K429(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
NE-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
E-bound (L~ f) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
K429(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((NW-corner (L~ f)),(NE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (NW-corner (L~ f))) + (b<sub>1</sub> * (NE-corner (L~ f)))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg ((NW-corner (L~ f)),(NE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (N-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (N-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (N-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (N-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:] is set
lower_bound (proj1 | (N-most (L~ f))) is V11() real ext-real Element of REAL
(proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))) is V137() V138() V139() Element of bool REAL
K430(((proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (N-most (L~ f)))),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
W-max (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
W-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
SW-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
S-bound (L~ f) is V11() real ext-real Element of REAL
lower_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
K430(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner (L~ f)),(NW-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (SW-corner (L~ f))) + (b<sub>1</sub> * (NW-corner (L~ f)))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg ((SW-corner (L~ f)),(NW-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (W-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (W-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (W-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (W-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (W-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (W-most (L~ f))),REAL:] is set
upper_bound (proj2 | (W-most (L~ f))) is V11() real ext-real Element of REAL
(proj2 | (W-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ f))) is V137() V138() V139() Element of bool REAL
K429(((proj2 | (W-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ f))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(upper_bound (proj2 | (W-most (L~ f))))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
(W-max (L~ f)) .. f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
E-min (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
E-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
SE-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
|[(E-bound (L~ f)),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner (L~ f)),(NE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (SE-corner (L~ f))) + (b<sub>1</sub> * (NE-corner (L~ f)))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg ((SE-corner (L~ f)),(NE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (E-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (E-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (E-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (E-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (E-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (E-most (L~ f))),REAL:] is set
lower_bound (proj2 | (E-most (L~ f))) is V11() real ext-real Element of REAL
(proj2 | (E-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ f))) is V137() V138() V139() Element of bool REAL
K430(((proj2 | (E-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ f))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(lower_bound (proj2 | (E-most (L~ f))))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
(E-min (L~ f)) .. f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
S-min (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
S-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
LSeg ((SW-corner (L~ f)),(SE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (SW-corner (L~ f))) + (b<sub>1</sub> * (SE-corner (L~ f)))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg ((SW-corner (L~ f)),(SE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (S-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (S-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (S-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (S-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (S-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (S-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (S-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (S-most (L~ f))),REAL:] is set
lower_bound (proj1 | (S-most (L~ f))) is V11() real ext-real Element of REAL
(proj1 | (S-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (S-most (L~ f))) is V137() V138() V139() Element of bool REAL
K430(((proj1 | (S-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (S-most (L~ f))))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (S-most (L~ f)))),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
(S-min (L~ f)) .. f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
f /. (len f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
N-max (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
upper_bound (proj1 | (N-most (L~ f))) is V11() real ext-real Element of REAL
K429(((proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))))) is V11() real ext-real Element of REAL
|[(upper_bound (proj1 | (N-most (L~ f)))),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
(N-max (L~ f)) `1 is V11() real ext-real Element of REAL
(N-min (L~ f)) `1 is V11() real ext-real Element of REAL
(E-min (L~ f)) `1 is V11() real ext-real Element of REAL
(N-min (L~ f)) `2 is V11() real ext-real Element of REAL
(S-min (L~ f)) `2 is V11() real ext-real Element of REAL
rng f is non empty non trivial Element of bool the carrier of (TOP-REAL 2)
dom f is non empty non trivial V137() V138() V139() V140() V141() V142() Element of bool NAT
f /. ((E-min (L~ f)) .. f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
f . ((E-min (L~ f)) .. f) is set
f /. ((W-max (L~ f)) .. f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
f . ((W-max (L~ f)) .. f) is set
(W-max (L~ f)) `1 is V11() real ext-real Element of REAL
f /. ((S-min (L~ f)) .. f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
f . ((S-min (L~ f)) .. f) is set
mid (f,((S-min (L~ f)) .. f),(len f)) is V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
M is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
len M is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
M /. (len M) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(M /. (len M)) `2 is V11() real ext-real Element of REAL
mid (f,((W-max (L~ f)) .. f),((E-min (L~ f)) .. f)) is V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
h is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
len h is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
h /. (len h) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(h /. (len h)) `1 is V11() real ext-real Element of REAL
h /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(h /. 1) `1 is V11() real ext-real Element of REAL
M /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(M /. 1) `2 is V11() real ext-real Element of REAL
L~ h is non empty compact Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (h,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len h ) } is set
union { (LSeg (h,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len h ) } is set
L~ M is non empty compact Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (M,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len M ) } is set
union { (LSeg (M,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len M ) } is set
f is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard () FinSequence of the carrier of (TOP-REAL 2)
f /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
L~ f is non empty compact being_simple_closed_curve Element of bool the carrier of (TOP-REAL 2)
len f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
{ (LSeg (f,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len f ) } is set
union { (LSeg (f,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len f ) } is set
N-min (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
N-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
NW-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
W-bound (L~ f) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ f) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
the carrier of ((TOP-REAL 2) | (L~ f)) is non empty set
[: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is set
lower_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
(proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K430(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
N-bound (L~ f) is V11() real ext-real Element of REAL
proj2 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
upper_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
(proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K429(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
NE-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
E-bound (L~ f) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
K429(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((NW-corner (L~ f)),(NE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (NW-corner (L~ f))) + (b<sub>1</sub> * (NE-corner (L~ f)))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg ((NW-corner (L~ f)),(NE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (N-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (N-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (N-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (N-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:] is set
lower_bound (proj1 | (N-most (L~ f))) is V11() real ext-real Element of REAL
(proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))) is V137() V138() V139() Element of bool REAL
K430(((proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (N-most (L~ f)))),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
W-min (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
W-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
SW-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
S-bound (L~ f) is V11() real ext-real Element of REAL
lower_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
K430(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner (L~ f)),(NW-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (SW-corner (L~ f))) + (b<sub>1</sub> * (NW-corner (L~ f)))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg ((SW-corner (L~ f)),(NW-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (W-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (W-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (W-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (W-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (W-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (W-most (L~ f))),REAL:] is set
lower_bound (proj2 | (W-most (L~ f))) is V11() real ext-real Element of REAL
(proj2 | (W-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ f))) is V137() V138() V139() Element of bool REAL
K430(((proj2 | (W-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ f))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(lower_bound (proj2 | (W-most (L~ f))))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
(W-min (L~ f)) .. f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
E-min (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
E-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
SE-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
|[(E-bound (L~ f)),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner (L~ f)),(NE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (SE-corner (L~ f))) + (b<sub>1</sub> * (NE-corner (L~ f)))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg ((SE-corner (L~ f)),(NE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (E-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (E-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (E-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (E-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (E-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (E-most (L~ f))),REAL:] is set
lower_bound (proj2 | (E-most (L~ f))) is V11() real ext-real Element of REAL
(proj2 | (E-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ f))) is V137() V138() V139() Element of bool REAL
K430(((proj2 | (E-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ f))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(lower_bound (proj2 | (E-most (L~ f))))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
(E-min (L~ f)) .. f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
S-min (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
S-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
LSeg ((SW-corner (L~ f)),(SE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (SW-corner (L~ f))) + (b<sub>1</sub> * (SE-corner (L~ f)))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg ((SW-corner (L~ f)),(SE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (S-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (S-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (S-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (S-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (S-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (S-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (S-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (S-most (L~ f))),REAL:] is set
lower_bound (proj1 | (S-most (L~ f))) is V11() real ext-real Element of REAL
(proj1 | (S-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (S-most (L~ f))) is V137() V138() V139() Element of bool REAL
K430(((proj1 | (S-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (S-most (L~ f))))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (S-most (L~ f)))),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
(S-min (L~ f)) .. f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
f /. (len f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
N-max (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
upper_bound (proj1 | (N-most (L~ f))) is V11() real ext-real Element of REAL
K429(((proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))))) is V11() real ext-real Element of REAL
|[(upper_bound (proj1 | (N-most (L~ f)))),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
(N-max (L~ f)) `1 is V11() real ext-real Element of REAL
(N-min (L~ f)) `1 is V11() real ext-real Element of REAL
(E-min (L~ f)) `1 is V11() real ext-real Element of REAL
(N-min (L~ f)) `2 is V11() real ext-real Element of REAL
(S-min (L~ f)) `2 is V11() real ext-real Element of REAL
rng f is non empty non trivial Element of bool the carrier of (TOP-REAL 2)
dom f is non empty non trivial V137() V138() V139() V140() V141() V142() Element of bool NAT
f /. ((E-min (L~ f)) .. f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
f . ((E-min (L~ f)) .. f) is set
f /. ((W-min (L~ f)) .. f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
f . ((W-min (L~ f)) .. f) is set
(W-min (L~ f)) `1 is V11() real ext-real Element of REAL
f /. ((S-min (L~ f)) .. f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
f . ((S-min (L~ f)) .. f) is set
mid (f,((S-min (L~ f)) .. f),(len f)) is V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
M is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
len M is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
M /. (len M) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(M /. (len M)) `2 is V11() real ext-real Element of REAL
mid (f,((W-min (L~ f)) .. f),((E-min (L~ f)) .. f)) is V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
h is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
len h is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
h /. (len h) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(h /. (len h)) `1 is V11() real ext-real Element of REAL
M /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(M /. 1) `2 is V11() real ext-real Element of REAL
W-max (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
upper_bound (proj2 | (W-most (L~ f))) is V11() real ext-real Element of REAL
K429(((proj2 | (W-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ f))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(upper_bound (proj2 | (W-most (L~ f))))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
(W-max (L~ f)) `2 is V11() real ext-real Element of REAL
L~ h is non empty compact Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (h,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len h ) } is set
union { (LSeg (h,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len h ) } is set
L~ M is non empty compact Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (M,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len M ) } is set
union { (LSeg (M,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len M ) } is set
h /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(h /. 1) `1 is V11() real ext-real Element of REAL
f is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard () FinSequence of the carrier of (TOP-REAL 2)
f /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
L~ f is non empty compact being_simple_closed_curve Element of bool the carrier of (TOP-REAL 2)
len f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
{ (LSeg (f,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
union { (LSeg (f,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
N-min (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
N-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
NW-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
W-bound (L~ f) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ f) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
the carrier of ((TOP-REAL 2) | (L~ f)) is non empty set
[: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is set
lower_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
(proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K430(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
N-bound (L~ f) is V11() real ext-real Element of REAL
proj2 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
upper_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
(proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K429(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
NE-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
E-bound (L~ f) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
K429(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((NW-corner (L~ f)),(NE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NW-corner (L~ f))) + (b₁ * (NE-corner (L~ f)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((NW-corner (L~ f)),(NE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (N-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (N-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (N-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (N-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:] is set
lower_bound (proj1 | (N-most (L~ f))) is V11() real ext-real Element of REAL
(proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))) is V137() V138() V139() Element of bool REAL
K430(((proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (N-most (L~ f)))),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
S-min (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
S-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
SW-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
S-bound (L~ f) is V11() real ext-real Element of REAL
lower_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
K430(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
SE-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
|[(E-bound (L~ f)),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner (L~ f)),(SE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SW-corner (L~ f))) + (b₁ * (SE-corner (L~ f)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((SW-corner (L~ f)),(SE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (S-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (S-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (S-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (S-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (S-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (S-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (S-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (S-most (L~ f))),REAL:] is set
lower_bound (proj1 | (S-most (L~ f))) is V11() real ext-real Element of REAL
(proj1 | (S-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (S-most (L~ f))) is V137() V138() V139() Element of bool REAL
K430(((proj1 | (S-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (S-most (L~ f))))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (S-most (L~ f)))),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
W-min (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
W-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
LSeg ((SW-corner (L~ f)),(NW-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SW-corner (L~ f))) + (b₁ * (NW-corner (L~ f)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((SW-corner (L~ f)),(NW-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (W-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (W-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (W-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (W-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (W-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (W-most (L~ f))),REAL:] is set
lower_bound (proj2 | (W-most (L~ f))) is V11() real ext-real Element of REAL
(proj2 | (W-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ f))) is V137() V138() V139() Element of bool REAL
K430(((proj2 | (W-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ f))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(lower_bound (proj2 | (W-most (L~ f))))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
(W-min (L~ f)) .. f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
(S-min (L~ f)) .. f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
E-min (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
E-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
LSeg ((SE-corner (L~ f)),(NE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SE-corner (L~ f))) + (b₁ * (NE-corner (L~ f)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((SE-corner (L~ f)),(NE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (E-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (E-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (E-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (E-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (E-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (E-most (L~ f))),REAL:] is set
lower_bound (proj2 | (E-most (L~ f))) is V11() real ext-real Element of REAL
(proj2 | (E-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ f))) is V137() V138() V139() Element of bool REAL
K430(((proj2 | (E-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ f))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(lower_bound (proj2 | (E-most (L~ f))))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
(E-min (L~ f)) .. f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
f /. (len f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
N-max (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
upper_bound (proj1 | (N-most (L~ f))) is V11() real ext-real Element of REAL
K429(((proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))))) is V11() real ext-real Element of REAL
|[(upper_bound (proj1 | (N-most (L~ f)))),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
(N-max (L~ f)) `1 is V11() real ext-real Element of REAL
(N-min (L~ f)) `1 is V11() real ext-real Element of REAL
(E-min (L~ f)) `1 is V11() real ext-real Element of REAL
rng f is non empty non trivial Element of bool the carrier of (TOP-REAL 2)
dom f is non empty non trivial V137() V138() V139() V140() V141() V142() Element of bool NAT
f /. ((E-min (L~ f)) .. f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
f . ((E-min (L~ f)) .. f) is set
(N-min (L~ f)) `2 is V11() real ext-real Element of REAL
(S-min (L~ f)) `2 is V11() real ext-real Element of REAL
f /. ((S-min (L~ f)) .. f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
f . ((S-min (L~ f)) .. f) is set
mid (f,((S-min (L~ f)) .. f),(len f)) is V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
M is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
len M is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
M /. (len M) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(M /. (len M)) `2 is V11() real ext-real Element of REAL
M /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(M /. 1) `2 is V11() real ext-real Element of REAL
mid (f,((W-min (L~ f)) .. f),((E-min (L~ f)) .. f)) is V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
h is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
len h is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
h /. (len h) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(h /. (len h)) `1 is V11() real ext-real Element of REAL
f /. ((W-min (L~ f)) .. f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
f . ((W-min (L~ f)) .. f) is set
h /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(h /. 1) `1 is V11() real ext-real Element of REAL
L~ h is non empty compact Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (h,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len h ) } is set
union { (LSeg (h,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len h ) } is set
L~ M is non empty compact Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (M,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len M ) } is set
union { (LSeg (M,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len M ) } is set
f is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard () FinSequence of the carrier of (TOP-REAL 2)
f /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
L~ f is non empty compact being_simple_closed_curve Element of bool the carrier of (TOP-REAL 2)
len f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
{ (LSeg (f,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len f ) } is set
union { (LSeg (f,b<sub>1</sub>)) where b<sub>1</sub> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> + 1 <= len f ) } is set
N-min (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
N-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
NW-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
W-bound (L~ f) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ f) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
the carrier of ((TOP-REAL 2) | (L~ f)) is non empty set
[: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is set
lower_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
(proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K430(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
N-bound (L~ f) is V11() real ext-real Element of REAL
proj2 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
upper_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
(proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K429(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
NE-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
E-bound (L~ f) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
K429(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((NW-corner (L~ f)),(NE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (NW-corner (L~ f))) + (b<sub>1</sub> * (NE-corner (L~ f)))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg ((NW-corner (L~ f)),(NE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (N-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (N-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (N-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (N-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:] is set
lower_bound (proj1 | (N-most (L~ f))) is V11() real ext-real Element of REAL
(proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))) is V137() V138() V139() Element of bool REAL
K430(((proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (N-most (L~ f)))),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
W-max (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
W-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
SW-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
S-bound (L~ f) is V11() real ext-real Element of REAL
lower_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
K430(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner (L~ f)),(NW-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (SW-corner (L~ f))) + (b<sub>1</sub> * (NW-corner (L~ f)))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg ((SW-corner (L~ f)),(NW-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (W-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (W-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (W-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (W-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (W-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (W-most (L~ f))),REAL:] is set
upper_bound (proj2 | (W-most (L~ f))) is V11() real ext-real Element of REAL
(proj2 | (W-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ f))) is V137() V138() V139() Element of bool REAL
K429(((proj2 | (W-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ f))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(upper_bound (proj2 | (W-most (L~ f))))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
(W-max (L~ f)) .. f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
W-min (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
lower_bound (proj2 | (W-most (L~ f))) is V11() real ext-real Element of REAL
K430(((proj2 | (W-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ f))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(lower_bound (proj2 | (W-most (L~ f))))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
(W-min (L~ f)) .. f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
E-min (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
E-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
SE-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
|[(E-bound (L~ f)),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner (L~ f)),(NE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (SE-corner (L~ f))) + (b<sub>1</sub> * (NE-corner (L~ f)))) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg ((SE-corner (L~ f)),(NE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (E-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (E-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (E-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (E-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (E-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (E-most (L~ f))),REAL:] is set
lower_bound (proj2 | (E-most (L~ f))) is V11() real ext-real Element of REAL
(proj2 | (E-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ f))) is V137() V138() V139() Element of bool REAL
K430(((proj2 | (E-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ f))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(lower_bound (proj2 | (E-most (L~ f))))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
(E-min (L~ f)) .. f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
rng f is non empty non trivial Element of bool the carrier of (TOP-REAL 2)
dom f is non empty non trivial V137() V138() V139() V140() V141() V142() Element of bool NAT
f /. ((E-min (L~ f)) .. f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
f . ((E-min (L~ f)) .. f) is set
(f /. ((E-min (L~ f)) .. f)) `1 is V11() real ext-real Element of REAL
f /. (len f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
f /. ((W-min (L~ f)) .. f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
f . ((W-min (L~ f)) .. f) is set
(N-min (L~ f)) `2 is V11() real ext-real Element of REAL
(W-max (L~ f)) `2 is V11() real ext-real Element of REAL
((W-min (L~ f)) .. f) + 1 is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
(len f) - ((W-min (L~ f)) .. f) is V11() real ext-real Element of REAL
(len f) -' ((W-min (L~ f)) .. f) is natural V11() real V37() ext-real non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
1 + 1 is non empty natural V11() real V37() ext-real positive non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
((len f) -' ((W-min (L~ f)) .. f)) + 1 is non empty natural V11() real V37() ext-real positive non negative V90() V137() V138() V139() V140() V141() V142() Element of NAT
mid (f,((W-min (L~ f)) .. f),(len f)) is V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
M is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
M /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
len M is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
M /. (len M) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
N-max (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
upper_bound (proj1 | (N-most (L~ f))) is V11() real ext-real Element of REAL
K429(((proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))))) is V11() real ext-real Element of REAL
|[(upper_bound (proj1 | (N-most (L~ f)))),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
(N-max (L~ f)) `1 is V11() real ext-real Element of REAL
(N-min (L~ f)) `1 is V11() real ext-real Element of REAL
(E-min (L~ f)) `1 is V11() real ext-real Element of REAL
mid (f,((W-max (L~ f)) .. f),((E-min (L~ f)) .. f)) is V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
f /. ((W-max (L~ f)) .. f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
f . ((W-max (L~ f)) .. f) is set
h is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
h /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(h /. 1) `1 is V11() real ext-real Element of REAL
len h is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
h /. (len h) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
L~ M is non empty compact Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (M,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len M ) } is set
union { (LSeg (M,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len M ) } is set
L~ h is non empty compact Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (h,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len h ) } is set
union { (LSeg (h,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len h ) } is set
(M /. (len M)) `2 is V11() real ext-real Element of REAL
(M /. 1) `2 is V11() real ext-real Element of REAL
<*(SW-corner (L~ f))*> is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() V33(1) FinSequence-like FinSubsequence-like special FinSequence of the carrier of (TOP-REAL 2)
<*(SW-corner (L~ f))*> ^ M is non empty V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
g is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
g /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(g /. 1) `2 is V11() real ext-real Element of REAL
dom M is non empty non trivial V137() V138() V139() V140() V141() V142() Element of bool NAT
len g is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
len <*(SW-corner (L~ f))*> is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
(len M) + (len <*(SW-corner (L~ f))*>) is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
g /. (len g) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
(g /. (len g)) `2 is V11() real ext-real Element of REAL
LSeg ((M /. 1),(SW-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (M /. 1)) + (b₁ * (SW-corner (L~ f)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((M /. 1),(SW-corner (L~ f)))) /\ (L~ h) is Element of bool the carrier of (TOP-REAL 2)
(LSeg ((M /. 1),(SW-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
{(M /. 1)} is non empty trivial set
L~ g is non empty compact Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (g,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len g ) } is set
union { (LSeg (g,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len g ) } is set
LSeg ((SW-corner (L~ f)),(M /. 1)) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SW-corner (L~ f))) + (b₁ * (M /. 1))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(L~ M) \/ (LSeg ((SW-corner (L~ f)),(M /. 1))) is non empty Element of bool the carrier of (TOP-REAL 2)
f is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard () FinSequence of the carrier of (TOP-REAL 2)
f /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
L~ f is non empty compact being_simple_closed_curve Element of bool the carrier of (TOP-REAL 2)
len f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
{ (LSeg (f,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
union { (LSeg (f,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
N-min (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
N-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
NW-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
W-bound (L~ f) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ f) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
the carrier of ((TOP-REAL 2) | (L~ f)) is non empty set
[: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is set
lower_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
(proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K430(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
N-bound (L~ f) is V11() real ext-real Element of REAL
proj2 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
upper_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
(proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K429(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
NE-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
E-bound (L~ f) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
K429(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((NW-corner (L~ f)),(NE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NW-corner (L~ f))) + (b₁ * (NE-corner (L~ f)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((NW-corner (L~ f)),(NE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (N-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (N-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (N-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (N-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:] is set
lower_bound (proj1 | (N-most (L~ f))) is V11() real ext-real Element of REAL
(proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))) is V137() V138() V139() Element of bool REAL
K430(((proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (N-most (L~ f)))),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
W-min (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
W-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
SW-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
S-bound (L~ f) is V11() real ext-real Element of REAL
lower_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
K430(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner (L~ f)),(NW-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SW-corner (L~ f))) + (b₁ * (NW-corner (L~ f)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((SW-corner (L~ f)),(NW-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (W-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (W-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (W-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (W-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (W-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (W-most (L~ f))),REAL:] is set
lower_bound (proj2 | (W-most (L~ f))) is V11() real ext-real Element of REAL
(proj2 | (W-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ f))) is V137() V138() V139() Element of bool REAL
K430(((proj2 | (W-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ f))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(lower_bound (proj2 | (W-most (L~ f))))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
(W-min (L~ f)) .. f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
W-max (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
upper_bound (proj2 | (W-most (L~ f))) is V11() real ext-real Element of REAL
K429(((proj2 | (W-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ f))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(upper_bound (proj2 | (W-most (L~ f))))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
rng f is non empty non trivial Element of bool the carrier of (TOP-REAL 2)
f /. (len f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
dom f is non empty non trivial V137() V138() V139() V140() V141() V142() Element of bool NAT
f /. ((W-min (L~ f)) .. f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
f . ((W-min (L~ f)) .. f) is set
(W-max (L~ f)) .. f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
dom f is non empty non trivial V137() V138() V139() V140() V141() V142() Element of bool NAT
f is non empty non trivial V13() V16( NAT ) V17( the carrier of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard FinSequence of the carrier of (TOP-REAL 2)
f /. 1 is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
L~ f is non empty compact being_simple_closed_curve Element of bool the carrier of (TOP-REAL 2)
len f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
{ (LSeg (f,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
union { (LSeg (f,b₁)) where b₁ is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
N-min (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
N-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
NW-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
W-bound (L~ f) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ f) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
the carrier of ((TOP-REAL 2) | (L~ f)) is non empty set
[: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:] is set
lower_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
(proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K430(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
N-bound (L~ f) is V11() real ext-real Element of REAL
proj2 | (L~ f) is V13() V16( the carrier of ((TOP-REAL 2) | (L~ f))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ f)), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ f)),REAL:]
upper_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
(proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)) is non empty V137() V138() V139() Element of bool REAL
K429(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
NE-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
E-bound (L~ f) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ f)) is V11() real ext-real Element of REAL
K429(((proj1 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ f)),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((NW-corner (L~ f)),(NE-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NW-corner (L~ f))) + (b₁ * (NE-corner (L~ f)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((NW-corner (L~ f)),(NE-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (N-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (N-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (N-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (N-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ f))),REAL:] is set
lower_bound (proj1 | (N-most (L~ f))) is V11() real ext-real Element of REAL
(proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))) is V137() V138() V139() Element of bool REAL
K430(((proj1 | (N-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ f))))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (N-most (L~ f)))),(N-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
W-max (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
W-most (L~ f) is Element of bool the carrier of (TOP-REAL 2)
SW-corner (L~ f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
S-bound (L~ f) is V11() real ext-real Element of REAL
lower_bound (proj2 | (L~ f)) is V11() real ext-real Element of REAL
K430(((proj2 | (L~ f)) .: the carrier of ((TOP-REAL 2) | (L~ f)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(S-bound (L~ f))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner (L~ f)),(NW-corner (L~ f))) is non empty compact V218( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SW-corner (L~ f))) + (b₁ * (NW-corner (L~ f)))) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((SW-corner (L~ f)),(NW-corner (L~ f)))) /\ (L~ f) is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ f)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ f)) is V13() V16( the carrier of ((TOP-REAL 2) | (W-most (L~ f)))) V17( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (W-most (L~ f))), REAL ) V127() V128() V129() Element of bool [: the carrier of ((TOP-REAL 2) | (W-most (L~ f))),REAL:]
the carrier of ((TOP-REAL 2) | (W-most (L~ f))) is set
[: the carrier of ((TOP-REAL 2) | (W-most (L~ f))),REAL:] is V127() V128() V129() set
bool [: the carrier of ((TOP-REAL 2) | (W-most (L~ f))),REAL:] is set
upper_bound (proj2 | (W-most (L~ f))) is V11() real ext-real Element of REAL
(proj2 | (W-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ f))) is V137() V138() V139() Element of bool REAL
K429(((proj2 | (W-most (L~ f))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ f))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ f)),(upper_bound (proj2 | (W-most (L~ f))))]| is non empty V13() V16( NAT ) Function-like V26() V33(2) FinSequence-like FinSubsequence-like V127() V128() V129() Element of the carrier of (TOP-REAL 2)
(W-max (L~ f)) .. f is natural V11() real V37() ext-real V90() V137() V138() V139() V140() V141() V142() Element of NAT
f /. (len f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
rng f is non empty non trivial Element of bool the carrier of (TOP-REAL 2)
dom f is non empty non trivial V137() V138() V139() V140() V141() V142() Element of bool NAT
f /. ((W-max (L~ f)) .. f) is V33(2) FinSequence-like V129() Element of the carrier of (TOP-REAL 2)
f . ((W-max (L~ f)) .. f) is set