:: JORDAN19 semantic presentation

REAL is set
NAT is non empty epsilon-transitive epsilon-connected ordinal V28() V33() V34() Element of K6(REAL)
K6(REAL) is non empty set
COMPLEX is set
omega is non empty epsilon-transitive epsilon-connected ordinal V28() V33() V34() set
K6(omega) is non empty V28() set
K6(NAT) is non empty V28() set
2 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
K7(2,2) is non empty set
K7(K7(2,2),2) is non empty set
K6(K7(K7(2,2),2)) is non empty set
1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
RAT is set
INT is set
K7(1,1) is non empty set
K6(K7(1,1)) is non empty set
K7(K7(1,1),1) is non empty set
K6(K7(K7(1,1),1)) is non empty set
K7(K7(1,1),REAL) is set
K6(K7(K7(1,1),REAL)) is non empty set
K7(REAL,REAL) is set
K7(K7(REAL,REAL),REAL) is set
K6(K7(K7(REAL,REAL),REAL)) is non empty set
K7(K7(2,2),REAL) is set
K6(K7(K7(2,2),REAL)) is non empty set
K6(K7(REAL,REAL)) is non empty set
TOP-REAL 2 is non empty non trivial TopSpace-like T_2 V85() V110() V111() V112() V113() V114() V115() V116() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL 2) is non empty non trivial functional set
K307( the carrier of (TOP-REAL 2)) is non empty functional FinSequence-membered M16( the carrier of (TOP-REAL 2))
K7( the carrier of (TOP-REAL 2),REAL) is set
K6(K7( the carrier of (TOP-REAL 2),REAL)) is non empty set
K6( the carrier of (TOP-REAL 2)) is non empty set
K7(COMPLEX,COMPLEX) is set
K6(K7(COMPLEX,COMPLEX)) is non empty set
K7(COMPLEX,REAL) is set
K6(K7(COMPLEX,REAL)) is non empty set
{} is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() real Function-like functional V28() V33() V35( {} ) FinSequence-membered ext-real non positive non negative set
the empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() real Function-like functional V28() V33() V35( {} ) FinSequence-membered ext-real non positive non negative set is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() real Function-like functional V28() V33() V35( {} ) FinSequence-membered ext-real non positive non negative set
3 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
K7(NAT, the carrier of (TOP-REAL 2)) is non empty V28() set
Seg 1 is non empty trivial V28() V35(1) Element of K6(NAT)
{1} is non empty trivial V35(1) set
Seg 2 is non empty V28() V35(2) Element of K6(NAT)
{1,2} is non empty set
Seg 3 is non empty V28() V35(3) Element of K6(NAT)
{1,2,3} is non empty set
4 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
proj1 is V15() V18( the carrier of (TOP-REAL 2)) V19( REAL ) Function-like V40( the carrier of (TOP-REAL 2), REAL ) V212( TOP-REAL 2) Element of K6(K7( the carrier of (TOP-REAL 2),REAL))
proj2 is V15() V18( the carrier of (TOP-REAL 2)) V19( REAL ) Function-like V40( the carrier of (TOP-REAL 2), REAL ) V212( TOP-REAL 2) Element of K6(K7( the carrier of (TOP-REAL 2),REAL))
0 is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() real Function-like functional V28() V33() V35( {} ) FinSequence-membered ext-real non positive non negative Element of NAT
K291( the carrier of (TOP-REAL 2)) is non empty Element of K6(K6( the carrier of (TOP-REAL 2)))
K6(K6( the carrier of (TOP-REAL 2))) is non empty set
K7(NAT,K291( the carrier of (TOP-REAL 2))) is non empty V28() set
K6(K7(NAT,K291( the carrier of (TOP-REAL 2)))) is non empty V28() set
C is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
C is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
(C) is V15() V18( NAT ) V19(K291( the carrier of (TOP-REAL 2))) Function-like V40( NAT ,K291( the carrier of (TOP-REAL 2))) Element of K6(K7(NAT,K291( the carrier of (TOP-REAL 2))))
Lim_inf (C) is functional Element of K6( the carrier of (TOP-REAL 2))
(C) is V15() V18( NAT ) V19(K291( the carrier of (TOP-REAL 2))) Function-like V40( NAT ,K291( the carrier of (TOP-REAL 2))) Element of K6(K7(NAT,K291( the carrier of (TOP-REAL 2))))
Lim_inf (C) is functional Element of K6( the carrier of (TOP-REAL 2))
p is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
C is V15() non empty-yielding V18( NAT ) V19(K307( the carrier of (TOP-REAL 2))) Function-like V28() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K307( the carrier of (TOP-REAL 2))
width C is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
0 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
len C is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(len C) div 2 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
((len C) div 2) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
Center C is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
[(Center C),p] is set
{(Center C),p} is non empty set
{(Center C)} is non empty trivial V35(1) set
{{(Center C),p},{(Center C)}} is non empty set
Indices C is set
C is non empty functional Element of K6( the carrier of (TOP-REAL 2))
N-bound C is V11() real ext-real Element of REAL
(TOP-REAL 2) | C is strict T_2 SubSpace of TOP-REAL 2
proj2 | C is V15() V18( the carrier of ((TOP-REAL 2) | C)) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | C), REAL ) V212((TOP-REAL 2) | C) Element of K6(K7( the carrier of ((TOP-REAL 2) | C),REAL))
the carrier of ((TOP-REAL 2) | C) is set
K7( the carrier of ((TOP-REAL 2) | C),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | C),REAL)) is non empty set
upper_bound (proj2 | C) is V11() real ext-real Element of REAL
(proj2 | C) .: the carrier of ((TOP-REAL 2) | C) is Element of K6(REAL)
upper_bound ((proj2 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
S-bound C is V11() real ext-real Element of REAL
lower_bound (proj2 | C) is V11() real ext-real Element of REAL
lower_bound ((proj2 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
W-bound C is V11() real ext-real Element of REAL
proj1 | C is V15() V18( the carrier of ((TOP-REAL 2) | C)) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | C), REAL ) V212((TOP-REAL 2) | C) Element of K6(K7( the carrier of ((TOP-REAL 2) | C),REAL))
lower_bound (proj1 | C) is V11() real ext-real Element of REAL
(proj1 | C) .: the carrier of ((TOP-REAL 2) | C) is Element of K6(REAL)
lower_bound ((proj1 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
E-bound C is V11() real ext-real Element of REAL
upper_bound (proj1 | C) is V11() real ext-real Element of REAL
upper_bound ((proj1 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
p is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
Gauge (C,p) is V15() non empty-yielding V18( NAT ) V19(K307( the carrier of (TOP-REAL 2))) Function-like V28() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column FinSequence of K307( the carrier of (TOP-REAL 2))
p9 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
width (Gauge (C,p)) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
[p9,(width (Gauge (C,p)))] is set
{p9,(width (Gauge (C,p)))} is non empty set
{p9} is non empty trivial V35(1) set
{{p9,(width (Gauge (C,p)))},{p9}} is non empty set
Indices (Gauge (C,p)) is set
(Gauge (C,p)) * (p9,(width (Gauge (C,p)))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (C,p)) * (p9,(width (Gauge (C,p))))) `2 is V11() real ext-real Element of REAL
(E-bound C) - (W-bound C) is V11() real ext-real Element of REAL
- (W-bound C) is V11() real ext-real set
(E-bound C) + (- (W-bound C)) is V11() real ext-real set
2 |^ p is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
((E-bound C) - (W-bound C)) / (2 |^ p) is V11() real ext-real Element of REAL
(2 |^ p) " is V11() real ext-real non negative set
((E-bound C) - (W-bound C)) * ((2 |^ p) ") is V11() real ext-real set
p9 - 2 is V11() real ext-real Element of REAL
- 2 is V11() real ext-real non positive set
p9 + (- 2) is V11() real ext-real set
(((E-bound C) - (W-bound C)) / (2 |^ p)) * (p9 - 2) is V11() real ext-real Element of REAL
(W-bound C) + ((((E-bound C) - (W-bound C)) / (2 |^ p)) * (p9 - 2)) is V11() real ext-real Element of REAL
(N-bound C) - (S-bound C) is V11() real ext-real Element of REAL
- (S-bound C) is V11() real ext-real set
(N-bound C) + (- (S-bound C)) is V11() real ext-real set
((N-bound C) - (S-bound C)) / (2 |^ p) is V11() real ext-real Element of REAL
((N-bound C) - (S-bound C)) * ((2 |^ p) ") is V11() real ext-real set
(width (Gauge (C,p))) - 2 is V11() real ext-real Element of REAL
(width (Gauge (C,p))) + (- 2) is V11() real ext-real set
(((N-bound C) - (S-bound C)) / (2 |^ p)) * ((width (Gauge (C,p))) - 2) is V11() real ext-real Element of REAL
(S-bound C) + ((((N-bound C) - (S-bound C)) / (2 |^ p)) * ((width (Gauge (C,p))) - 2)) is V11() real ext-real Element of REAL
|[((W-bound C) + ((((E-bound C) - (W-bound C)) / (2 |^ p)) * (p9 - 2))),((S-bound C) + ((((N-bound C) - (S-bound C)) / (2 |^ p)) * ((width (Gauge (C,p))) - 2)))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
|[((W-bound C) + ((((E-bound C) - (W-bound C)) / (2 |^ p)) * (p9 - 2))),((S-bound C) + ((((N-bound C) - (S-bound C)) / (2 |^ p)) * ((width (Gauge (C,p))) - 2)))]| `2 is V11() real ext-real Element of REAL
C is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
p is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
p + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
(p + 1) / p is V11() real ext-real non negative Element of REAL
p " is V11() real ext-real non negative set
(p + 1) * (p ") is V11() real ext-real non negative set
C + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
(C + 1) / C is V11() real ext-real non negative Element of REAL
C " is V11() real ext-real non negative set
(C + 1) * (C ") is V11() real ext-real non negative set
1 / p is V11() real ext-real non negative Element of REAL
1 * (p ") is V11() real ext-real non negative set
1 / C is V11() real ext-real non negative Element of REAL
1 * (C ") is V11() real ext-real non negative set
C / C is V11() real ext-real non negative Element of COMPLEX
C * (C ") is V11() real ext-real non negative set
(C / C) + (1 / C) is V11() real ext-real non negative Element of REAL
1 + (1 / C) is non empty V11() real ext-real positive non negative Element of REAL
p / p is V11() real ext-real non negative Element of COMPLEX
p * (p ") is V11() real ext-real non negative set
(p / p) + (1 / p) is V11() real ext-real non negative Element of REAL
1 + (1 / p) is non empty V11() real ext-real positive non negative Element of REAL
C is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
p is non empty functional closed bounded compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
Gauge (p,C) is V15() non empty-yielding V18( NAT ) V19(K307( the carrier of (TOP-REAL 2))) Function-like V28() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K307( the carrier of (TOP-REAL 2))
width (Gauge (p,C)) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
Center (Gauge (p,C)) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(Gauge (p,C)) * ((Center (Gauge (p,C))),(width (Gauge (p,C)))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
p9 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
s is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(Gauge (p,C)) * ((Center (Gauge (p,C))),s) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg (((Gauge (p,C)) * ((Center (Gauge (p,C))),(width (Gauge (p,C))))),((Gauge (p,C)) * ((Center (Gauge (p,C))),s))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
Gauge (p,p9) is V15() non empty-yielding V18( NAT ) V19(K307( the carrier of (TOP-REAL 2))) Function-like V28() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K307( the carrier of (TOP-REAL 2))
Center (Gauge (p,p9)) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
width (Gauge (p,p9)) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(Gauge (p,p9)) * ((Center (Gauge (p,p9))),(width (Gauge (p,p9)))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg (((Gauge (p,p9)) * ((Center (Gauge (p,p9))),(width (Gauge (p,p9))))),((Gauge (p,C)) * ((Center (Gauge (p,C))),s))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
N-bound p is V11() real ext-real Element of REAL
(TOP-REAL 2) | p is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | p is V15() V18( the carrier of ((TOP-REAL 2) | p)) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | p), REAL ) V212((TOP-REAL 2) | p) Element of K6(K7( the carrier of ((TOP-REAL 2) | p),REAL))
the carrier of ((TOP-REAL 2) | p) is set
K7( the carrier of ((TOP-REAL 2) | p),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | p),REAL)) is non empty set
upper_bound (proj2 | p) is V11() real ext-real Element of REAL
(proj2 | p) .: the carrier of ((TOP-REAL 2) | p) is Element of K6(REAL)
upper_bound ((proj2 | p) .: the carrier of ((TOP-REAL 2) | p)) is V11() real ext-real Element of REAL
S-bound p is V11() real ext-real Element of REAL
lower_bound (proj2 | p) is V11() real ext-real Element of REAL
lower_bound ((proj2 | p) .: the carrier of ((TOP-REAL 2) | p)) is V11() real ext-real Element of REAL
W-bound p is V11() real ext-real Element of REAL
proj1 | p is V15() V18( the carrier of ((TOP-REAL 2) | p)) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | p), REAL ) V212((TOP-REAL 2) | p) Element of K6(K7( the carrier of ((TOP-REAL 2) | p),REAL))
lower_bound (proj1 | p) is V11() real ext-real Element of REAL
(proj1 | p) .: the carrier of ((TOP-REAL 2) | p) is Element of K6(REAL)
lower_bound ((proj1 | p) .: the carrier of ((TOP-REAL 2) | p)) is V11() real ext-real Element of REAL
E-bound p is V11() real ext-real Element of REAL
upper_bound (proj1 | p) is V11() real ext-real Element of REAL
upper_bound ((proj1 | p) .: the carrier of ((TOP-REAL 2) | p)) is V11() real ext-real Element of REAL
len (Gauge (p,p9)) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
2 |^ p9 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(2 |^ p9) + 3 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
len (Gauge (p,C)) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
2 |^ C is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(2 |^ C) + 3 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
m9 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(N-bound p) - (S-bound p) is V11() real ext-real Element of REAL
- (S-bound p) is V11() real ext-real set
(N-bound p) + (- (S-bound p)) is V11() real ext-real set
((Gauge (p,p9)) * ((Center (Gauge (p,p9))),(width (Gauge (p,p9))))) `1 is V11() real ext-real Element of REAL
(Gauge (p,C)) * ((Center (Gauge (p,C))),m9) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * ((Center (Gauge (p,C))),m9)) `1 is V11() real ext-real Element of REAL
((Gauge (p,C)) * ((Center (Gauge (p,C))),s)) `1 is V11() real ext-real Element of REAL
[(Center (Gauge (p,C))),m9] is set
{(Center (Gauge (p,C))),m9} is non empty set
{(Center (Gauge (p,C)))} is non empty trivial V35(1) set
{{(Center (Gauge (p,C))),m9},{(Center (Gauge (p,C)))}} is non empty set
Indices (Gauge (p,C)) is set
((Gauge (p,C)) * ((Center (Gauge (p,C))),m9)) `2 is V11() real ext-real Element of REAL
(E-bound p) - (W-bound p) is V11() real ext-real Element of REAL
- (W-bound p) is V11() real ext-real set
(E-bound p) + (- (W-bound p)) is V11() real ext-real set
((E-bound p) - (W-bound p)) / (2 |^ C) is V11() real ext-real Element of REAL
(2 |^ C) " is V11() real ext-real non negative set
((E-bound p) - (W-bound p)) * ((2 |^ C) ") is V11() real ext-real set
(Center (Gauge (p,C))) - 2 is V11() real ext-real Element of REAL
(Center (Gauge (p,C))) + (- 2) is V11() real ext-real set
(((E-bound p) - (W-bound p)) / (2 |^ C)) * ((Center (Gauge (p,C))) - 2) is V11() real ext-real Element of REAL
(W-bound p) + ((((E-bound p) - (W-bound p)) / (2 |^ C)) * ((Center (Gauge (p,C))) - 2)) is V11() real ext-real Element of REAL
((N-bound p) - (S-bound p)) / (2 |^ C) is V11() real ext-real Element of REAL
((N-bound p) - (S-bound p)) * ((2 |^ C) ") is V11() real ext-real set
m9 - 2 is V11() real ext-real Element of REAL
m9 + (- 2) is V11() real ext-real set
(((N-bound p) - (S-bound p)) / (2 |^ C)) * (m9 - 2) is V11() real ext-real Element of REAL
(S-bound p) + ((((N-bound p) - (S-bound p)) / (2 |^ C)) * (m9 - 2)) is V11() real ext-real Element of REAL
|[((W-bound p) + ((((E-bound p) - (W-bound p)) / (2 |^ C)) * ((Center (Gauge (p,C))) - 2))),((S-bound p) + ((((N-bound p) - (S-bound p)) / (2 |^ C)) * (m9 - 2)))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
|[((W-bound p) + ((((E-bound p) - (W-bound p)) / (2 |^ C)) * ((Center (Gauge (p,C))) - 2))),((S-bound p) + ((((N-bound p) - (S-bound p)) / (2 |^ C)) * (m9 - 2)))]| `2 is V11() real ext-real Element of REAL
[(Center (Gauge (p,p9))),(width (Gauge (p,p9)))] is set
{(Center (Gauge (p,p9))),(width (Gauge (p,p9)))} is non empty set
{(Center (Gauge (p,p9)))} is non empty trivial V35(1) set
{{(Center (Gauge (p,p9))),(width (Gauge (p,p9)))},{(Center (Gauge (p,p9)))}} is non empty set
Indices (Gauge (p,p9)) is set
((Gauge (p,p9)) * ((Center (Gauge (p,p9))),(width (Gauge (p,p9))))) `2 is V11() real ext-real Element of REAL
((N-bound p) - (S-bound p)) / (2 |^ p9) is V11() real ext-real Element of REAL
(2 |^ p9) " is V11() real ext-real non negative set
((N-bound p) - (S-bound p)) * ((2 |^ p9) ") is V11() real ext-real set
(width (Gauge (p,p9))) - 2 is V11() real ext-real Element of REAL
(width (Gauge (p,p9))) + (- 2) is V11() real ext-real set
(((N-bound p) - (S-bound p)) / (2 |^ p9)) * ((width (Gauge (p,p9))) - 2) is V11() real ext-real Element of REAL
(S-bound p) + ((((N-bound p) - (S-bound p)) / (2 |^ p9)) * ((width (Gauge (p,p9))) - 2)) is V11() real ext-real Element of REAL
(2 |^ C) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
((2 |^ C) + 1) / (2 |^ C) is V11() real ext-real non negative Element of REAL
((2 |^ C) + 1) * ((2 |^ C) ") is V11() real ext-real non negative set
(2 |^ p9) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
((2 |^ p9) + 1) / (2 |^ p9) is V11() real ext-real non negative Element of REAL
((2 |^ p9) + 1) * ((2 |^ p9) ") is V11() real ext-real non negative set
((2 |^ C) + 3) - 2 is V11() real ext-real Element of REAL
((2 |^ C) + 3) + (- 2) is V11() real ext-real set
(m9 - 2) / (2 |^ C) is V11() real ext-real Element of REAL
(m9 - 2) * ((2 |^ C) ") is V11() real ext-real set
((width (Gauge (p,p9))) - 2) / (2 |^ p9) is V11() real ext-real Element of REAL
((width (Gauge (p,p9))) - 2) * ((2 |^ p9) ") is V11() real ext-real set
((N-bound p) - (S-bound p)) * ((m9 - 2) / (2 |^ C)) is V11() real ext-real Element of REAL
((N-bound p) - (S-bound p)) * (((width (Gauge (p,p9))) - 2) / (2 |^ p9)) is V11() real ext-real Element of REAL
((Gauge (p,C)) * ((Center (Gauge (p,C))),s)) `2 is V11() real ext-real Element of REAL
C is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
p is non empty functional closed connected bounded compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
Gauge (p,C) is V15() non empty-yielding V18( NAT ) V19(K307( the carrier of (TOP-REAL 2))) Function-like V28() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K307( the carrier of (TOP-REAL 2))
len (Gauge (p,C)) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
width (Gauge (p,C)) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
Cage (p,C) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like non constant V28() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the carrier of (TOP-REAL 2)
L~ (Cage (p,C)) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
Upper_Seq (p,C) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V28() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
L~ (Upper_Seq (p,C)) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
p9 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
s is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(Gauge (p,C)) * (p9,s) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(Gauge (p,C)) * (p9,(width (Gauge (p,C)))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg (((Gauge (p,C)) * (p9,(width (Gauge (p,C))))),((Gauge (p,C)) * (p9,s))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
SW-corner (L~ (Cage (p,C))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
W-bound (L~ (Cage (p,C))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (p,C))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ (Cage (p,C))) is V15() V18( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))), REAL ) V212((TOP-REAL 2) | (L~ (Cage (p,C)))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))),REAL))
the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))) is set
K7( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))),REAL)) is non empty set
lower_bound (proj1 | (L~ (Cage (p,C)))) is V11() real ext-real Element of REAL
(proj1 | (L~ (Cage (p,C)))) .: the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))) is Element of K6(REAL)
lower_bound ((proj1 | (L~ (Cage (p,C)))) .: the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C))))) is V11() real ext-real Element of REAL
S-bound (L~ (Cage (p,C))) is V11() real ext-real Element of REAL
proj2 | (L~ (Cage (p,C))) is V15() V18( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))), REAL ) V212((TOP-REAL 2) | (L~ (Cage (p,C)))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))),REAL))
lower_bound (proj2 | (L~ (Cage (p,C)))) is V11() real ext-real Element of REAL
(proj2 | (L~ (Cage (p,C)))) .: the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))) is Element of K6(REAL)
lower_bound ((proj2 | (L~ (Cage (p,C)))) .: the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Cage (p,C)))),(S-bound (L~ (Cage (p,C))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
Lower_Seq (p,C) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V28() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s))) is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
<*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> is non empty trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like constant V28() V35(1) FinSequence-like FinSubsequence-like special FinSequence of the carrier of (TOP-REAL 2)
<*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> ^ (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s)))) is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
<*(SW-corner (L~ (Cage (p,C))))*> is non empty trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like constant V28() V35(1) FinSequence-like FinSubsequence-like special FinSequence of the carrier of (TOP-REAL 2)
(<*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> ^ (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s))))) ^ <*(SW-corner (L~ (Cage (p,C))))*> is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len (Upper_Seq (p,C)) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
mid ((Upper_Seq (p,C)),2,(len (Upper_Seq (p,C)))) is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ (Lower_Seq (p,C)) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(L~ (Lower_Seq (p,C))) \/ (L~ (Upper_Seq (p,C))) is non empty functional Element of K6( the carrier of (TOP-REAL 2))
len (Lower_Seq (p,C)) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
((Gauge (p,C)) * (p9,(width (Gauge (p,C))))) `2 is V11() real ext-real Element of REAL
N-bound (L~ (Cage (p,C))) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ (Cage (p,C)))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (L~ (Cage (p,C)))) .: the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C))))) is V11() real ext-real Element of REAL
E-max (L~ (Cage (p,C))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
E-bound (L~ (Cage (p,C))) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ (Cage (p,C)))) is V11() real ext-real Element of REAL
upper_bound ((proj1 | (L~ (Cage (p,C)))) .: the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C))))) is V11() real ext-real Element of REAL
E-most (L~ (Cage (p,C))) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
SE-corner (L~ (Cage (p,C))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
|[(E-bound (L~ (Cage (p,C)))),(S-bound (L~ (Cage (p,C))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
NE-corner (L~ (Cage (p,C))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
|[(E-bound (L~ (Cage (p,C)))),(N-bound (L~ (Cage (p,C))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Cage (p,C)))),(NE-corner (L~ (Cage (p,C))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SE-corner (L~ (Cage (p,C)))),(NE-corner (L~ (Cage (p,C)))))) /\ (L~ (Cage (p,C))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (E-most (L~ (Cage (p,C)))) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Cage (p,C)))) is V15() V18( the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (p,C)))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (p,C))))), REAL ) V212((TOP-REAL 2) | (E-most (L~ (Cage (p,C))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (p,C))))),REAL))
the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (p,C))))) is set
K7( the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (p,C))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (p,C))))),REAL)) is non empty set
upper_bound (proj2 | (E-most (L~ (Cage (p,C))))) is V11() real ext-real Element of REAL
(proj2 | (E-most (L~ (Cage (p,C))))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (p,C))))) is Element of K6(REAL)
upper_bound ((proj2 | (E-most (L~ (Cage (p,C))))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (p,C)))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Cage (p,C)))),(upper_bound (proj2 | (E-most (L~ (Cage (p,C))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(Gauge (p,C)) * ((len (Gauge (p,C))),(width (Gauge (p,C)))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * ((len (Gauge (p,C))),(width (Gauge (p,C))))) `1 is V11() real ext-real Element of REAL
(E-max (L~ (Cage (p,C)))) `1 is V11() real ext-real Element of REAL
((Gauge (p,C)) * ((len (Gauge (p,C))),(width (Gauge (p,C))))) `2 is V11() real ext-real Element of REAL
(E-max (L~ (Cage (p,C)))) `2 is V11() real ext-real Element of REAL
((Gauge (p,C)) * (p9,s)) `1 is V11() real ext-real Element of REAL
((Gauge (p,C)) * (p9,s)) `2 is V11() real ext-real Element of REAL
(Gauge (p,C)) * ((len (Gauge (p,C))),s) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg (((Gauge (p,C)) * ((len (Gauge (p,C))),(width (Gauge (p,C))))),((Gauge (p,C)) * ((len (Gauge (p,C))),s))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
rng (Upper_Seq (p,C)) is functional Element of K6( the carrier of (TOP-REAL 2))
(Upper_Seq (p,C)) /. (len (Upper_Seq (p,C))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(Lower_Seq (p,C)) . (len (Lower_Seq (p,C))) is V15() Function-like set
W-min (L~ (Cage (p,C))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
W-most (L~ (Cage (p,C))) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
NW-corner (L~ (Cage (p,C))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
|[(W-bound (L~ (Cage (p,C)))),(N-bound (L~ (Cage (p,C))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (p,C)))),(NW-corner (L~ (Cage (p,C))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner (L~ (Cage (p,C)))),(NW-corner (L~ (Cage (p,C)))))) /\ (L~ (Cage (p,C))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (W-most (L~ (Cage (p,C)))) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Cage (p,C)))) is V15() V18( the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C)))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C))))), REAL ) V212((TOP-REAL 2) | (W-most (L~ (Cage (p,C))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C))))),REAL))
the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C))))) is set
K7( the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C))))),REAL)) is non empty set
lower_bound (proj2 | (W-most (L~ (Cage (p,C))))) is V11() real ext-real Element of REAL
(proj2 | (W-most (L~ (Cage (p,C))))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C))))) is Element of K6(REAL)
lower_bound ((proj2 | (W-most (L~ (Cage (p,C))))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C)))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Cage (p,C)))),(lower_bound (proj2 | (W-most (L~ (Cage (p,C))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
len (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s)))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
dom (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s)))) is Element of K6(NAT)
dom (Lower_Seq (p,C)) is non trivial Element of K6(NAT)
(L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s)))) /. (len (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s)))) . (len (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s))))) is V15() Function-like set
(Lower_Seq (p,C)) /. (len (Lower_Seq (p,C))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
len (<*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> ^ (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s))))) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
(<*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> ^ (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s))))) /. (len (<*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> ^ (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s)))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s)))) /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s)))) . 1 is V15() Function-like set
(L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s)))) ^ <*(SW-corner (L~ (Cage (p,C))))*> is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
((L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s)))) ^ <*(SW-corner (L~ (Cage (p,C))))*>) /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
1 + (len (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s))))) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
len ((<*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> ^ (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s))))) ^ <*(SW-corner (L~ (Cage (p,C))))*>) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
(len (<*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> ^ (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s)))))) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
(1 + (len (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s)))))) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
Rev ((<*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> ^ (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s))))) ^ <*(SW-corner (L~ (Cage (p,C))))*>) is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len (Rev ((<*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> ^ (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s))))) ^ <*(SW-corner (L~ (Cage (p,C))))*>)) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
{((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))} is non empty trivial functional V35(1) set
rng <*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> is trivial functional Element of K6( the carrier of (TOP-REAL 2))
len (Cage (p,C)) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
rng (Cage (p,C)) is non trivial functional Element of K6( the carrier of (TOP-REAL 2))
(SW-corner (L~ (Cage (p,C)))) `1 is V11() real ext-real Element of REAL
(SW-corner (L~ (Cage (p,C)))) `2 is V11() real ext-real Element of REAL
{ b₁ where b₁ is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2) : ( b₁ `1 = W-bound (L~ (Cage (p,C))) & b<sub>1</sub> `2 <= N-bound (L~ (Cage (p,C))) & S-bound (L~ (Cage (p,C))) <= b₁ `2 ) } is set
(W-min (L~ (Cage (p,C)))) `2 is V11() real ext-real Element of REAL
(W-min (L~ (Cage (p,C)))) `1 is V11() real ext-real Element of REAL
Index (((Gauge (p,C)) * (p9,s)),(Lower_Seq (p,C))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(Index (((Gauge (p,C)) * (p9,s)),(Lower_Seq (p,C)))) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
(Lower_Seq (p,C)) . ((Index (((Gauge (p,C)) * (p9,s)),(Lower_Seq (p,C)))) + 1) is V15() Function-like set
<*((Gauge (p,C)) * (p9,s))*> is non empty trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like constant V28() V35(1) FinSequence-like FinSubsequence-like special FinSequence of the carrier of (TOP-REAL 2)
mid ((Lower_Seq (p,C)),((Index (((Gauge (p,C)) * (p9,s)),(Lower_Seq (p,C)))) + 1),(len (Lower_Seq (p,C)))) is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
<*((Gauge (p,C)) * (p9,s))*> ^ (mid ((Lower_Seq (p,C)),((Index (((Gauge (p,C)) * (p9,s)),(Lower_Seq (p,C)))) + 1),(len (Lower_Seq (p,C))))) is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
rng (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s)))) is functional Element of K6( the carrier of (TOP-REAL 2))
rng <*((Gauge (p,C)) * (p9,s))*> is trivial functional Element of K6( the carrier of (TOP-REAL 2))
rng (mid ((Lower_Seq (p,C)),((Index (((Gauge (p,C)) * (p9,s)),(Lower_Seq (p,C)))) + 1),(len (Lower_Seq (p,C))))) is functional Element of K6( the carrier of (TOP-REAL 2))
(rng <*((Gauge (p,C)) * (p9,s))*>) \/ (rng (mid ((Lower_Seq (p,C)),((Index (((Gauge (p,C)) * (p9,s)),(Lower_Seq (p,C)))) + 1),(len (Lower_Seq (p,C)))))) is functional Element of K6( the carrier of (TOP-REAL 2))
{((Gauge (p,C)) * (p9,s))} is non empty trivial functional V35(1) set
{((Gauge (p,C)) * (p9,s))} \/ (rng (mid ((Lower_Seq (p,C)),((Index (((Gauge (p,C)) * (p9,s)),(Lower_Seq (p,C)))) + 1),(len (Lower_Seq (p,C)))))) is non empty set
N is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
N + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
(Cage (p,C)) /. N is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(Cage (p,C)) /. (N + 1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg (((Cage (p,C)) /. N),((Cage (p,C)) /. (N + 1))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
((Cage (p,C)) /. N) `1 is V11() real ext-real Element of REAL
((Cage (p,C)) /. (N + 1)) `1 is V11() real ext-real Element of REAL
(SW-corner (L~ (Cage (p,C)))) `1 is V11() real ext-real Element of REAL
(SW-corner (L~ (Cage (p,C)))) `2 is V11() real ext-real Element of REAL
((Cage (p,C)) /. N) `2 is V11() real ext-real Element of REAL
((Cage (p,C)) /. (N + 1)) `2 is V11() real ext-real Element of REAL
dom (Cage (p,C)) is non trivial Element of K6(NAT)
((Cage (p,C)) /. N) `2 is V11() real ext-real Element of REAL
((Cage (p,C)) /. (N + 1)) `2 is V11() real ext-real Element of REAL
(SW-corner (L~ (Cage (p,C)))) `2 is V11() real ext-real Element of REAL
(SW-corner (L~ (Cage (p,C)))) `1 is V11() real ext-real Element of REAL
((Cage (p,C)) /. N) `1 is V11() real ext-real Element of REAL
((Cage (p,C)) /. (N + 1)) `1 is V11() real ext-real Element of REAL
dom (Cage (p,C)) is non trivial Element of K6(NAT)
((Cage (p,C)) /. N) `1 is V11() real ext-real Element of REAL
((Cage (p,C)) /. (N + 1)) `1 is V11() real ext-real Element of REAL
((Cage (p,C)) /. N) `2 is V11() real ext-real Element of REAL
((Cage (p,C)) /. (N + 1)) `2 is V11() real ext-real Element of REAL
rng (Lower_Seq (p,C)) is functional Element of K6( the carrier of (TOP-REAL 2))
Index (((Gauge (p,C)) * (p9,s)),(Lower_Seq (p,C))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(Index (((Gauge (p,C)) * (p9,s)),(Lower_Seq (p,C)))) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
(Lower_Seq (p,C)) . ((Index (((Gauge (p,C)) * (p9,s)),(Lower_Seq (p,C)))) + 1) is V15() Function-like set
mid ((Lower_Seq (p,C)),((Index (((Gauge (p,C)) * (p9,s)),(Lower_Seq (p,C)))) + 1),(len (Lower_Seq (p,C)))) is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
rng (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s)))) is functional Element of K6( the carrier of (TOP-REAL 2))
rng (Lower_Seq (p,C)) is functional Element of K6( the carrier of (TOP-REAL 2))
Index (((Gauge (p,C)) * (p9,s)),(Lower_Seq (p,C))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(Index (((Gauge (p,C)) * (p9,s)),(Lower_Seq (p,C)))) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
(Lower_Seq (p,C)) . ((Index (((Gauge (p,C)) * (p9,s)),(Lower_Seq (p,C)))) + 1) is V15() Function-like set
rng (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s)))) is functional Element of K6( the carrier of (TOP-REAL 2))
rng (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s)))) is functional Element of K6( the carrier of (TOP-REAL 2))
(rng <*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*>) \/ (rng (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s))))) is functional Element of K6( the carrier of (TOP-REAL 2))
rng (<*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> ^ (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s))))) is functional Element of K6( the carrier of (TOP-REAL 2))
{(SW-corner (L~ (Cage (p,C))))} is non empty trivial functional V35(1) set
rng <*(SW-corner (L~ (Cage (p,C))))*> is trivial functional Element of K6( the carrier of (TOP-REAL 2))
rng (Lower_Seq (p,C)) is functional Element of K6( the carrier of (TOP-REAL 2))
{((Gauge (p,C)) * (p9,s))} is non empty trivial functional V35(1) set
<*((Gauge (p,C)) * (p9,s))*> is non empty trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like constant V28() V35(1) FinSequence-like FinSubsequence-like special FinSequence of the carrier of (TOP-REAL 2)
rng <*((Gauge (p,C)) * (p9,s))*> is trivial functional Element of K6( the carrier of (TOP-REAL 2))
Index (((Gauge (p,C)) * (p9,s)),(Lower_Seq (p,C))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(Index (((Gauge (p,C)) * (p9,s)),(Lower_Seq (p,C)))) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
mid ((Lower_Seq (p,C)),((Index (((Gauge (p,C)) * (p9,s)),(Lower_Seq (p,C)))) + 1),(len (Lower_Seq (p,C)))) is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
(Lower_Seq (p,C)) . ((Index (((Gauge (p,C)) * (p9,s)),(Lower_Seq (p,C)))) + 1) is V15() Function-like set
rng (mid ((Lower_Seq (p,C)),((Index (((Gauge (p,C)) * (p9,s)),(Lower_Seq (p,C)))) + 1),(len (Lower_Seq (p,C))))) is functional Element of K6( the carrier of (TOP-REAL 2))
(rng <*((Gauge (p,C)) * (p9,s))*>) \/ (rng (mid ((Lower_Seq (p,C)),((Index (((Gauge (p,C)) * (p9,s)),(Lower_Seq (p,C)))) + 1),(len (Lower_Seq (p,C)))))) is functional Element of K6( the carrier of (TOP-REAL 2))
<*((Gauge (p,C)) * (p9,s))*> ^ (mid ((Lower_Seq (p,C)),((Index (((Gauge (p,C)) * (p9,s)),(Lower_Seq (p,C)))) + 1),(len (Lower_Seq (p,C))))) is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
rng (<*((Gauge (p,C)) * (p9,s))*> ^ (mid ((Lower_Seq (p,C)),((Index (((Gauge (p,C)) * (p9,s)),(Lower_Seq (p,C)))) + 1),(len (Lower_Seq (p,C)))))) is functional Element of K6( the carrier of (TOP-REAL 2))
(Lower_Seq (p,C)) . ((Index (((Gauge (p,C)) * (p9,s)),(Lower_Seq (p,C)))) + 1) is V15() Function-like set
(Lower_Seq (p,C)) . ((Index (((Gauge (p,C)) * (p9,s)),(Lower_Seq (p,C)))) + 1) is V15() Function-like set
len <*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
<*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> /. (len <*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*>) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(<*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> /. (len <*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*>)) `1 is V11() real ext-real Element of REAL
<*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(<*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> /. 1) `1 is V11() real ext-real Element of REAL
((Gauge (p,C)) * (p9,(width (Gauge (p,C))))) `1 is V11() real ext-real Element of REAL
(Gauge (p,C)) * (p9,1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * (p9,1)) `1 is V11() real ext-real Element of REAL
((L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s)))) /. 1) `1 is V11() real ext-real Element of REAL
((<*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> ^ (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s))))) /. (len (<*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> ^ (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s))))))) `1 is V11() real ext-real Element of REAL
(SW-corner (L~ (Cage (p,C)))) `1 is V11() real ext-real Element of REAL
<*(SW-corner (L~ (Cage (p,C))))*> /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(<*(SW-corner (L~ (Cage (p,C))))*> /. 1) `1 is V11() real ext-real Element of REAL
2 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
len (mid ((Upper_Seq (p,C)),2,(len (Upper_Seq (p,C))))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
dom (Upper_Seq (p,C)) is non trivial Element of K6(NAT)
(Upper_Seq (p,C)) /. (len (Upper_Seq (p,C))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Upper_Seq (p,C)) /. (len (Upper_Seq (p,C)))) `1 is V11() real ext-real Element of REAL
(mid ((Upper_Seq (p,C)),2,(len (Upper_Seq (p,C))))) /. (len (mid ((Upper_Seq (p,C)),2,(len (Upper_Seq (p,C)))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((mid ((Upper_Seq (p,C)),2,(len (Upper_Seq (p,C))))) /. (len (mid ((Upper_Seq (p,C)),2,(len (Upper_Seq (p,C))))))) `1 is V11() real ext-real Element of REAL
(Upper_Seq (p,C)) /. (1 + 1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Upper_Seq (p,C)) /. (1 + 1)) `1 is V11() real ext-real Element of REAL
(mid ((Upper_Seq (p,C)),2,(len (Upper_Seq (p,C))))) /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((mid ((Upper_Seq (p,C)),2,(len (Upper_Seq (p,C))))) /. 1) `1 is V11() real ext-real Element of REAL
m is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
dom <*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> is non empty trivial V35(1) Element of K6(NAT)
<*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> . m is V15() Function-like set
<*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> /. m is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(Gauge (p,C)) * (1,(width (Gauge (p,C)))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * (1,(width (Gauge (p,C))))) `1 is V11() real ext-real Element of REAL
(<*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> /. m) `1 is V11() real ext-real Element of REAL
(Gauge (p,C)) * ((len (Gauge (p,C))),(width (Gauge (p,C)))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * ((len (Gauge (p,C))),(width (Gauge (p,C))))) `1 is V11() real ext-real Element of REAL
(<*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> /. m) `2 is V11() real ext-real Element of REAL
<*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> ^ ((L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s)))) ^ <*(SW-corner (L~ (Cage (p,C))))*>) is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
((<*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> ^ (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s))))) ^ <*(SW-corner (L~ (Cage (p,C))))*>) /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(((<*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> ^ (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s))))) ^ <*(SW-corner (L~ (Cage (p,C))))*>) /. 1) `2 is V11() real ext-real Element of REAL
(Rev ((<*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> ^ (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s))))) ^ <*(SW-corner (L~ (Cage (p,C))))*>)) /. (len ((<*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> ^ (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s))))) ^ <*(SW-corner (L~ (Cage (p,C))))*>)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Rev ((<*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> ^ (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s))))) ^ <*(SW-corner (L~ (Cage (p,C))))*>)) /. (len ((<*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> ^ (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s))))) ^ <*(SW-corner (L~ (Cage (p,C))))*>))) `2 is V11() real ext-real Element of REAL
(Rev ((<*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> ^ (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s))))) ^ <*(SW-corner (L~ (Cage (p,C))))*>)) /. (len (Rev ((<*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> ^ (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s))))) ^ <*(SW-corner (L~ (Cage (p,C))))*>))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Rev ((<*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> ^ (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s))))) ^ <*(SW-corner (L~ (Cage (p,C))))*>)) /. (len (Rev ((<*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> ^ (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s))))) ^ <*(SW-corner (L~ (Cage (p,C))))*>)))) `2 is V11() real ext-real Element of REAL
((<*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> ^ (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s))))) ^ <*(SW-corner (L~ (Cage (p,C))))*>) /. (len ((<*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> ^ (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s))))) ^ <*(SW-corner (L~ (Cage (p,C))))*>)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(((<*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> ^ (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s))))) ^ <*(SW-corner (L~ (Cage (p,C))))*>) /. (len ((<*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> ^ (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s))))) ^ <*(SW-corner (L~ (Cage (p,C))))*>))) `2 is V11() real ext-real Element of REAL
(Rev ((<*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> ^ (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s))))) ^ <*(SW-corner (L~ (Cage (p,C))))*>)) /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Rev ((<*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> ^ (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s))))) ^ <*(SW-corner (L~ (Cage (p,C))))*>)) /. 1) `2 is V11() real ext-real Element of REAL
L~ (mid ((Upper_Seq (p,C)),2,(len (Upper_Seq (p,C))))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
L~ (Rev ((<*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> ^ (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s))))) ^ <*(SW-corner (L~ (Cage (p,C))))*>)) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
L~ ((<*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> ^ (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s))))) ^ <*(SW-corner (L~ (Cage (p,C))))*>) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
m is set
L~ (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s)))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
L~ (<*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> ^ ((L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s)))) ^ <*(SW-corner (L~ (Cage (p,C))))*>)) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
LSeg (((Gauge (p,C)) * (p9,(width (Gauge (p,C))))),(((L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s)))) ^ <*(SW-corner (L~ (Cage (p,C))))*>) /. 1)) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
L~ ((L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s)))) ^ <*(SW-corner (L~ (Cage (p,C))))*>) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(LSeg (((Gauge (p,C)) * (p9,(width (Gauge (p,C))))),(((L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s)))) ^ <*(SW-corner (L~ (Cage (p,C))))*>) /. 1))) \/ (L~ ((L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s)))) ^ <*(SW-corner (L~ (Cage (p,C))))*>)) is non empty functional Element of K6( the carrier of (TOP-REAL 2))
LSeg (((L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s)))) /. (len (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s)))))),(SW-corner (L~ (Cage (p,C))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(L~ (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s))))) \/ (LSeg (((L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s)))) /. (len (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s)))))),(SW-corner (L~ (Cage (p,C)))))) is non empty functional Element of K6( the carrier of (TOP-REAL 2))
(LSeg (((Gauge (p,C)) * (p9,(width (Gauge (p,C))))),(((L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s)))) ^ <*(SW-corner (L~ (Cage (p,C))))*>) /. 1))) \/ ((L~ (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s))))) \/ (LSeg (((L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s)))) /. (len (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s)))))),(SW-corner (L~ (Cage (p,C))))))) is non empty functional Element of K6( the carrier of (TOP-REAL 2))
(Upper_Seq (p,C)) /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
<*((Gauge (p,C)) * (p9,(width (Gauge (p,C))))),((Gauge (p,C)) * (p9,s))*> is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() V35(2) FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ <*((Gauge (p,C)) * (p9,(width (Gauge (p,C))))),((Gauge (p,C)) * (p9,s))*> is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(L~ (Lower_Seq (p,C))) /\ (L~ (Upper_Seq (p,C))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
{(W-min (L~ (Cage (p,C)))),(E-max (L~ (Cage (p,C))))} is non empty functional set
(Lower_Seq (p,C)) . 1 is V15() Function-like set
(Lower_Seq (p,C)) /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
<*((Gauge (p,C)) * (p9,(width (Gauge (p,C))))),((Gauge (p,C)) * (p9,s))*> is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() V35(2) FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ <*((Gauge (p,C)) * (p9,(width (Gauge (p,C))))),((Gauge (p,C)) * (p9,s))*> is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
LSeg ((W-min (L~ (Cage (p,C)))),(SW-corner (L~ (Cage (p,C))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((W-min (L~ (Cage (p,C)))),(SW-corner (L~ (Cage (p,C)))))) /\ (L~ (Cage (p,C))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
{(W-min (L~ (Cage (p,C))))} is non empty trivial functional V35(1) set
<*((Gauge (p,C)) * (p9,(width (Gauge (p,C))))),((Gauge (p,C)) * (p9,s))*> is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() V35(2) FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ <*((Gauge (p,C)) * (p9,(width (Gauge (p,C))))),((Gauge (p,C)) * (p9,s))*> is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
<*((Gauge (p,C)) * (p9,(width (Gauge (p,C))))),((Gauge (p,C)) * (p9,s))*> is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() V35(2) FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ <*((Gauge (p,C)) * (p9,(width (Gauge (p,C))))),((Gauge (p,C)) * (p9,s))*> is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
<*((Gauge (p,C)) * (p9,(width (Gauge (p,C))))),((Gauge (p,C)) * (p9,s))*> is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() V35(2) FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ <*((Gauge (p,C)) * (p9,(width (Gauge (p,C))))),((Gauge (p,C)) * (p9,s))*> is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(Lower_Seq (p,C)) . (len (Lower_Seq (p,C))) is V15() Function-like set
W-min (L~ (Cage (p,C))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
W-most (L~ (Cage (p,C))) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
NW-corner (L~ (Cage (p,C))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
|[(W-bound (L~ (Cage (p,C)))),(N-bound (L~ (Cage (p,C))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (p,C)))),(NW-corner (L~ (Cage (p,C))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner (L~ (Cage (p,C)))),(NW-corner (L~ (Cage (p,C)))))) /\ (L~ (Cage (p,C))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (W-most (L~ (Cage (p,C)))) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Cage (p,C)))) is V15() V18( the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C)))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C))))), REAL ) V212((TOP-REAL 2) | (W-most (L~ (Cage (p,C))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C))))),REAL))
the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C))))) is set
K7( the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C))))),REAL)) is non empty set
lower_bound (proj2 | (W-most (L~ (Cage (p,C))))) is V11() real ext-real Element of REAL
(proj2 | (W-most (L~ (Cage (p,C))))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C))))) is Element of K6(REAL)
lower_bound ((proj2 | (W-most (L~ (Cage (p,C))))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C)))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Cage (p,C)))),(lower_bound (proj2 | (W-most (L~ (Cage (p,C))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
len (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s)))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
dom (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s)))) is Element of K6(NAT)
dom (Lower_Seq (p,C)) is non trivial Element of K6(NAT)
(L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s)))) /. (len (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s)))) . (len (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s))))) is V15() Function-like set
(Lower_Seq (p,C)) /. (len (Lower_Seq (p,C))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
len (<*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> ^ (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s))))) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
(<*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> ^ (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s))))) /. (len (<*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> ^ (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s)))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s)))) /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s)))) . 1 is V15() Function-like set
1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
1 + (len (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s))))) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
Rev (<*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> ^ (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s))))) is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len (Rev (<*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> ^ (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s)))))) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
rng (Lower_Seq (p,C)) is functional Element of K6( the carrier of (TOP-REAL 2))
{((Gauge (p,C)) * (p9,s))} is non empty trivial functional V35(1) set
<*((Gauge (p,C)) * (p9,s))*> is non empty trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like constant V28() V35(1) FinSequence-like FinSubsequence-like special FinSequence of the carrier of (TOP-REAL 2)
rng <*((Gauge (p,C)) * (p9,s))*> is trivial functional Element of K6( the carrier of (TOP-REAL 2))
Index (((Gauge (p,C)) * (p9,s)),(Lower_Seq (p,C))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(Index (((Gauge (p,C)) * (p9,s)),(Lower_Seq (p,C)))) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
mid ((Lower_Seq (p,C)),((Index (((Gauge (p,C)) * (p9,s)),(Lower_Seq (p,C)))) + 1),(len (Lower_Seq (p,C)))) is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
(Lower_Seq (p,C)) . ((Index (((Gauge (p,C)) * (p9,s)),(Lower_Seq (p,C)))) + 1) is V15() Function-like set
rng (mid ((Lower_Seq (p,C)),((Index (((Gauge (p,C)) * (p9,s)),(Lower_Seq (p,C)))) + 1),(len (Lower_Seq (p,C))))) is functional Element of K6( the carrier of (TOP-REAL 2))
(rng <*((Gauge (p,C)) * (p9,s))*>) \/ (rng (mid ((Lower_Seq (p,C)),((Index (((Gauge (p,C)) * (p9,s)),(Lower_Seq (p,C)))) + 1),(len (Lower_Seq (p,C)))))) is functional Element of K6( the carrier of (TOP-REAL 2))
<*((Gauge (p,C)) * (p9,s))*> ^ (mid ((Lower_Seq (p,C)),((Index (((Gauge (p,C)) * (p9,s)),(Lower_Seq (p,C)))) + 1),(len (Lower_Seq (p,C))))) is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
rng (<*((Gauge (p,C)) * (p9,s))*> ^ (mid ((Lower_Seq (p,C)),((Index (((Gauge (p,C)) * (p9,s)),(Lower_Seq (p,C)))) + 1),(len (Lower_Seq (p,C)))))) is functional Element of K6( the carrier of (TOP-REAL 2))
rng (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s)))) is functional Element of K6( the carrier of (TOP-REAL 2))
(Lower_Seq (p,C)) . ((Index (((Gauge (p,C)) * (p9,s)),(Lower_Seq (p,C)))) + 1) is V15() Function-like set
rng (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s)))) is functional Element of K6( the carrier of (TOP-REAL 2))
(Lower_Seq (p,C)) . ((Index (((Gauge (p,C)) * (p9,s)),(Lower_Seq (p,C)))) + 1) is V15() Function-like set
rng (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s)))) is functional Element of K6( the carrier of (TOP-REAL 2))
rng (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s)))) is functional Element of K6( the carrier of (TOP-REAL 2))
{((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))} is non empty trivial functional V35(1) set
rng <*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> is trivial functional Element of K6( the carrier of (TOP-REAL 2))
len <*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
<*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> /. (len <*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*>) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(<*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> /. (len <*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*>)) `1 is V11() real ext-real Element of REAL
<*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(<*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> /. 1) `1 is V11() real ext-real Element of REAL
((Gauge (p,C)) * (p9,(width (Gauge (p,C))))) `1 is V11() real ext-real Element of REAL
(Gauge (p,C)) * (p9,1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * (p9,1)) `1 is V11() real ext-real Element of REAL
((L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s)))) /. 1) `1 is V11() real ext-real Element of REAL
2 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
len (mid ((Upper_Seq (p,C)),2,(len (Upper_Seq (p,C))))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
dom (Upper_Seq (p,C)) is non trivial Element of K6(NAT)
(Upper_Seq (p,C)) /. (len (Upper_Seq (p,C))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Upper_Seq (p,C)) /. (len (Upper_Seq (p,C)))) `1 is V11() real ext-real Element of REAL
(mid ((Upper_Seq (p,C)),2,(len (Upper_Seq (p,C))))) /. (len (mid ((Upper_Seq (p,C)),2,(len (Upper_Seq (p,C)))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((mid ((Upper_Seq (p,C)),2,(len (Upper_Seq (p,C))))) /. (len (mid ((Upper_Seq (p,C)),2,(len (Upper_Seq (p,C))))))) `1 is V11() real ext-real Element of REAL
(Upper_Seq (p,C)) /. (1 + 1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Upper_Seq (p,C)) /. (1 + 1)) `1 is V11() real ext-real Element of REAL
(mid ((Upper_Seq (p,C)),2,(len (Upper_Seq (p,C))))) /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((mid ((Upper_Seq (p,C)),2,(len (Upper_Seq (p,C))))) /. 1) `1 is V11() real ext-real Element of REAL
p1 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
dom <*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> is non empty trivial V35(1) Element of K6(NAT)
<*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> . p1 is V15() Function-like set
<*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> /. p1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(Gauge (p,C)) * (1,(width (Gauge (p,C)))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * (1,(width (Gauge (p,C))))) `1 is V11() real ext-real Element of REAL
(<*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> /. p1) `1 is V11() real ext-real Element of REAL
(Gauge (p,C)) * ((len (Gauge (p,C))),(width (Gauge (p,C)))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * ((len (Gauge (p,C))),(width (Gauge (p,C))))) `1 is V11() real ext-real Element of REAL
(<*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> /. p1) `2 is V11() real ext-real Element of REAL
(<*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> ^ (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s))))) /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((<*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> ^ (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s))))) /. 1) `2 is V11() real ext-real Element of REAL
(Rev (<*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> ^ (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s)))))) /. (len (<*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> ^ (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s)))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Rev (<*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> ^ (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s)))))) /. (len (<*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> ^ (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s))))))) `2 is V11() real ext-real Element of REAL
(Rev (<*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> ^ (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s)))))) /. (len (Rev (<*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> ^ (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s))))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Rev (<*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> ^ (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s)))))) /. (len (Rev (<*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> ^ (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s)))))))) `2 is V11() real ext-real Element of REAL
((<*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> ^ (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s))))) /. (len (<*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> ^ (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s))))))) `2 is V11() real ext-real Element of REAL
(Rev (<*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> ^ (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s)))))) /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Rev (<*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> ^ (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s)))))) /. 1) `2 is V11() real ext-real Element of REAL
L~ (mid ((Upper_Seq (p,C)),2,(len (Upper_Seq (p,C))))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
L~ (Rev (<*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> ^ (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s)))))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
L~ (<*((Gauge (p,C)) * (p9,(width (Gauge (p,C)))))*> ^ (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s))))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
p1 is set
L~ (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s)))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
LSeg (((Gauge (p,C)) * (p9,(width (Gauge (p,C))))),((L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s)))) /. 1)) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg (((Gauge (p,C)) * (p9,(width (Gauge (p,C))))),((L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s)))) /. 1))) \/ (L~ (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s))))) is non empty functional Element of K6( the carrier of (TOP-REAL 2))
(Upper_Seq (p,C)) /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
<*((Gauge (p,C)) * (p9,(width (Gauge (p,C))))),((Gauge (p,C)) * (p9,s))*> is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() V35(2) FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ <*((Gauge (p,C)) * (p9,(width (Gauge (p,C))))),((Gauge (p,C)) * (p9,s))*> is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(L~ (Lower_Seq (p,C))) /\ (L~ (Upper_Seq (p,C))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
{(W-min (L~ (Cage (p,C)))),(E-max (L~ (Cage (p,C))))} is non empty functional set
(Lower_Seq (p,C)) . 1 is V15() Function-like set
(Lower_Seq (p,C)) /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
<*((Gauge (p,C)) * (p9,(width (Gauge (p,C))))),((Gauge (p,C)) * (p9,s))*> is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() V35(2) FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ <*((Gauge (p,C)) * (p9,(width (Gauge (p,C))))),((Gauge (p,C)) * (p9,s))*> is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
<*((Gauge (p,C)) * (p9,(width (Gauge (p,C))))),((Gauge (p,C)) * (p9,s))*> is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() V35(2) FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ <*((Gauge (p,C)) * (p9,(width (Gauge (p,C))))),((Gauge (p,C)) * (p9,s))*> is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
<*((Gauge (p,C)) * (p9,(width (Gauge (p,C))))),((Gauge (p,C)) * (p9,s))*> is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() V35(2) FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ <*((Gauge (p,C)) * (p9,(width (Gauge (p,C))))),((Gauge (p,C)) * (p9,s))*> is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(Lower_Seq (p,C)) . (len (Lower_Seq (p,C))) is V15() Function-like set
dom (Lower_Seq (p,C)) is non trivial Element of K6(NAT)
(Lower_Seq (p,C)) /. (len (Lower_Seq (p,C))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
W-min (L~ (Cage (p,C))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
W-most (L~ (Cage (p,C))) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
NW-corner (L~ (Cage (p,C))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
|[(W-bound (L~ (Cage (p,C)))),(N-bound (L~ (Cage (p,C))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (p,C)))),(NW-corner (L~ (Cage (p,C))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner (L~ (Cage (p,C)))),(NW-corner (L~ (Cage (p,C)))))) /\ (L~ (Cage (p,C))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (W-most (L~ (Cage (p,C)))) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Cage (p,C)))) is V15() V18( the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C)))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C))))), REAL ) V212((TOP-REAL 2) | (W-most (L~ (Cage (p,C))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C))))),REAL))
the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C))))) is set
K7( the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C))))),REAL)) is non empty set
lower_bound (proj2 | (W-most (L~ (Cage (p,C))))) is V11() real ext-real Element of REAL
(proj2 | (W-most (L~ (Cage (p,C))))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C))))) is Element of K6(REAL)
lower_bound ((proj2 | (W-most (L~ (Cage (p,C))))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C)))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Cage (p,C)))),(lower_bound (proj2 | (W-most (L~ (Cage (p,C))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
rng (Upper_Seq (p,C)) is functional Element of K6( the carrier of (TOP-REAL 2))
(Lower_Seq (p,C)) . (len (Lower_Seq (p,C))) is V15() Function-like set
W-min (L~ (Cage (p,C))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
W-most (L~ (Cage (p,C))) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
NW-corner (L~ (Cage (p,C))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
|[(W-bound (L~ (Cage (p,C)))),(N-bound (L~ (Cage (p,C))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (p,C)))),(NW-corner (L~ (Cage (p,C))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner (L~ (Cage (p,C)))),(NW-corner (L~ (Cage (p,C)))))) /\ (L~ (Cage (p,C))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (W-most (L~ (Cage (p,C)))) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Cage (p,C)))) is V15() V18( the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C)))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C))))), REAL ) V212((TOP-REAL 2) | (W-most (L~ (Cage (p,C))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C))))),REAL))
the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C))))) is set
K7( the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C))))),REAL)) is non empty set
lower_bound (proj2 | (W-most (L~ (Cage (p,C))))) is V11() real ext-real Element of REAL
(proj2 | (W-most (L~ (Cage (p,C))))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C))))) is Element of K6(REAL)
lower_bound ((proj2 | (W-most (L~ (Cage (p,C))))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C)))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Cage (p,C)))),(lower_bound (proj2 | (W-most (L~ (Cage (p,C))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
C is non empty functional closed connected bounded compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
p is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
Gauge (C,p) is V15() non empty-yielding V18( NAT ) V19(K307( the carrier of (TOP-REAL 2))) Function-like V28() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K307( the carrier of (TOP-REAL 2))
len (Gauge (C,p)) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
width (Gauge (C,p)) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
Cage (C,p) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like non constant V28() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the carrier of (TOP-REAL 2)
L~ (Cage (C,p)) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
Upper_Arc (L~ (Cage (C,p))) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
p9 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
s is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(Gauge (C,p)) * (p9,s) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(Gauge (C,p)) * (p9,(width (Gauge (C,p)))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg (((Gauge (C,p)) * (p9,(width (Gauge (C,p))))),((Gauge (C,p)) * (p9,s))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
Upper_Seq (C,p) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V28() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
L~ (Upper_Seq (C,p)) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
C is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
C + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
p is non empty functional closed connected bounded compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
Gauge (p,(C + 1)) is V15() non empty-yielding V18( NAT ) V19(K307( the carrier of (TOP-REAL 2))) Function-like V28() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K307( the carrier of (TOP-REAL 2))
Center (Gauge (p,(C + 1))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
Cage (p,(C + 1)) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like non constant V28() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the carrier of (TOP-REAL 2)
L~ (Cage (p,(C + 1))) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
Lower_Arc (L~ (Cage (p,(C + 1)))) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
width (Gauge (p,(C + 1))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
Gauge (p,1) is V15() non empty-yielding V18( NAT ) V19(K307( the carrier of (TOP-REAL 2))) Function-like V28() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K307( the carrier of (TOP-REAL 2))
Center (Gauge (p,1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
width (Gauge (p,1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(Gauge (p,1)) * ((Center (Gauge (p,1))),(width (Gauge (p,1)))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
Upper_Arc (L~ (Cage (p,(C + 1)))) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
p9 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(Gauge (p,(C + 1))) * ((Center (Gauge (p,(C + 1)))),p9) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg (((Gauge (p,1)) * ((Center (Gauge (p,1))),(width (Gauge (p,1))))),((Gauge (p,(C + 1))) * ((Center (Gauge (p,(C + 1)))),p9))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
len (Gauge (p,(C + 1))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(Gauge (p,(C + 1))) * ((Center (Gauge (p,(C + 1)))),(width (Gauge (p,(C + 1))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg (((Gauge (p,(C + 1))) * ((Center (Gauge (p,(C + 1)))),(width (Gauge (p,(C + 1)))))),((Gauge (p,(C + 1))) * ((Center (Gauge (p,(C + 1)))),p9))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
C is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
2 |^ C is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
p is non empty functional closed connected bounded compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
Gauge (p,C) is V15() non empty-yielding V18( NAT ) V19(K307( the carrier of (TOP-REAL 2))) Function-like V28() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K307( the carrier of (TOP-REAL 2))
N-bound p is V11() real ext-real Element of REAL
(TOP-REAL 2) | p is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | p is V15() V18( the carrier of ((TOP-REAL 2) | p)) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | p), REAL ) V212((TOP-REAL 2) | p) Element of K6(K7( the carrier of ((TOP-REAL 2) | p),REAL))
the carrier of ((TOP-REAL 2) | p) is set
K7( the carrier of ((TOP-REAL 2) | p),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | p),REAL)) is non empty set
upper_bound (proj2 | p) is V11() real ext-real Element of REAL
(proj2 | p) .: the carrier of ((TOP-REAL 2) | p) is Element of K6(REAL)
upper_bound ((proj2 | p) .: the carrier of ((TOP-REAL 2) | p)) is V11() real ext-real Element of REAL
S-bound p is V11() real ext-real Element of REAL
lower_bound (proj2 | p) is V11() real ext-real Element of REAL
lower_bound ((proj2 | p) .: the carrier of ((TOP-REAL 2) | p)) is V11() real ext-real Element of REAL
(N-bound p) - (S-bound p) is V11() real ext-real Element of REAL
- (S-bound p) is V11() real ext-real set
(N-bound p) + (- (S-bound p)) is V11() real ext-real set
((N-bound p) - (S-bound p)) / (2 |^ C) is V11() real ext-real Element of REAL
(2 |^ C) " is V11() real ext-real non negative set
((N-bound p) - (S-bound p)) * ((2 |^ C) ") is V11() real ext-real set
E-bound p is V11() real ext-real Element of REAL
proj1 | p is V15() V18( the carrier of ((TOP-REAL 2) | p)) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | p), REAL ) V212((TOP-REAL 2) | p) Element of K6(K7( the carrier of ((TOP-REAL 2) | p),REAL))
upper_bound (proj1 | p) is V11() real ext-real Element of REAL
(proj1 | p) .: the carrier of ((TOP-REAL 2) | p) is Element of K6(REAL)
upper_bound ((proj1 | p) .: the carrier of ((TOP-REAL 2) | p)) is V11() real ext-real Element of REAL
W-bound p is V11() real ext-real Element of REAL
lower_bound (proj1 | p) is V11() real ext-real Element of REAL
lower_bound ((proj1 | p) .: the carrier of ((TOP-REAL 2) | p)) is V11() real ext-real Element of REAL
(E-bound p) - (W-bound p) is V11() real ext-real Element of REAL
- (W-bound p) is V11() real ext-real set
(E-bound p) + (- (W-bound p)) is V11() real ext-real set
((E-bound p) - (W-bound p)) / (2 |^ C) is V11() real ext-real Element of REAL
((E-bound p) - (W-bound p)) * ((2 |^ C) ") is V11() real ext-real set
p9 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len p9 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
s is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
s + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
p9 /. s is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
p9 /. (s + 1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
dist ((p9 /. s),(p9 /. (s + 1))) is V11() real ext-real Element of REAL
Indices (Gauge (p,C)) is set
r is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
rr is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
[r,rr] is set
{r,rr} is non empty set
{r} is non empty trivial V35(1) set
{{r,rr},{r}} is non empty set
(Gauge (p,C)) * (r,rr) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
G is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
k1 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
[G,k1] is set
{G,k1} is non empty set
{G} is non empty trivial V35(1) set
{{G,k1},{G}} is non empty set
(Gauge (p,C)) * (G,k1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
rr + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
r + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
G + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
k1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
C is symmetric triangle MetrStruct
the carrier of C is set
p is V11() real ext-real set
2 * p is V11() real ext-real Element of REAL
p9 is Element of the carrier of C
r is Element of the carrier of C
Ball (r,p) is Element of K6( the carrier of C)
K6( the carrier of C) is non empty set
s is Element of the carrier of C
dist (p9,s) is V11() real ext-real Element of REAL
dist (p9,r) is V11() real ext-real Element of REAL
dist (r,s) is V11() real ext-real Element of REAL
(dist (p9,r)) + (dist (r,s)) is V11() real ext-real Element of REAL
p + p is V11() real ext-real set
C is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
p is non empty functional closed connected bounded compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
Cage (p,C) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like non constant V28() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the carrier of (TOP-REAL 2)
L~ (Cage (p,C)) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
N-bound (L~ (Cage (p,C))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (p,C))) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (L~ (Cage (p,C))) is V15() V18( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))), REAL ) V212((TOP-REAL 2) | (L~ (Cage (p,C)))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))),REAL))
the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))) is set
K7( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))),REAL)) is non empty set
upper_bound (proj2 | (L~ (Cage (p,C)))) is V11() real ext-real Element of REAL
(proj2 | (L~ (Cage (p,C)))) .: the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))) is Element of K6(REAL)
upper_bound ((proj2 | (L~ (Cage (p,C)))) .: the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C))))) is V11() real ext-real Element of REAL
N-bound p is V11() real ext-real Element of REAL
(TOP-REAL 2) | p is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | p is V15() V18( the carrier of ((TOP-REAL 2) | p)) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | p), REAL ) V212((TOP-REAL 2) | p) Element of K6(K7( the carrier of ((TOP-REAL 2) | p),REAL))
the carrier of ((TOP-REAL 2) | p) is set
K7( the carrier of ((TOP-REAL 2) | p),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | p),REAL)) is non empty set
upper_bound (proj2 | p) is V11() real ext-real Element of REAL
(proj2 | p) .: the carrier of ((TOP-REAL 2) | p) is Element of K6(REAL)
upper_bound ((proj2 | p) .: the carrier of ((TOP-REAL 2) | p)) is V11() real ext-real Element of REAL
2 |^ C is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
S-bound p is V11() real ext-real Element of REAL
lower_bound (proj2 | p) is V11() real ext-real Element of REAL
lower_bound ((proj2 | p) .: the carrier of ((TOP-REAL 2) | p)) is V11() real ext-real Element of REAL
(S-bound p) + 0 is V11() real ext-real Element of REAL
(N-bound p) - (S-bound p) is V11() real ext-real Element of REAL
- (S-bound p) is V11() real ext-real set
(N-bound p) + (- (S-bound p)) is V11() real ext-real set
((N-bound p) - (S-bound p)) / (2 |^ C) is V11() real ext-real Element of REAL
(2 |^ C) " is V11() real ext-real non negative set
((N-bound p) - (S-bound p)) * ((2 |^ C) ") is V11() real ext-real set
(N-bound p) - (N-bound p) is V11() real ext-real Element of REAL
- (N-bound p) is V11() real ext-real set
(N-bound p) + (- (N-bound p)) is V11() real ext-real set
(N-bound p) + (((N-bound p) - (S-bound p)) / (2 |^ C)) is V11() real ext-real Element of REAL
C is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
p is non empty functional closed connected bounded compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
Cage (p,C) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like non constant V28() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the carrier of (TOP-REAL 2)
L~ (Cage (p,C)) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
E-bound (L~ (Cage (p,C))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (p,C))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ (Cage (p,C))) is V15() V18( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))), REAL ) V212((TOP-REAL 2) | (L~ (Cage (p,C)))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))),REAL))
the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))) is set
K7( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))),REAL)) is non empty set
upper_bound (proj1 | (L~ (Cage (p,C)))) is V11() real ext-real Element of REAL
(proj1 | (L~ (Cage (p,C)))) .: the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))) is Element of K6(REAL)
upper_bound ((proj1 | (L~ (Cage (p,C)))) .: the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C))))) is V11() real ext-real Element of REAL
E-bound p is V11() real ext-real Element of REAL
(TOP-REAL 2) | p is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | p is V15() V18( the carrier of ((TOP-REAL 2) | p)) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | p), REAL ) V212((TOP-REAL 2) | p) Element of K6(K7( the carrier of ((TOP-REAL 2) | p),REAL))
the carrier of ((TOP-REAL 2) | p) is set
K7( the carrier of ((TOP-REAL 2) | p),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | p),REAL)) is non empty set
upper_bound (proj1 | p) is V11() real ext-real Element of REAL
(proj1 | p) .: the carrier of ((TOP-REAL 2) | p) is Element of K6(REAL)
upper_bound ((proj1 | p) .: the carrier of ((TOP-REAL 2) | p)) is V11() real ext-real Element of REAL
2 |^ C is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
W-bound p is V11() real ext-real Element of REAL
lower_bound (proj1 | p) is V11() real ext-real Element of REAL
lower_bound ((proj1 | p) .: the carrier of ((TOP-REAL 2) | p)) is V11() real ext-real Element of REAL
(W-bound p) + 0 is V11() real ext-real Element of REAL
(E-bound p) - (W-bound p) is V11() real ext-real Element of REAL
- (W-bound p) is V11() real ext-real set
(E-bound p) + (- (W-bound p)) is V11() real ext-real set
((E-bound p) - (W-bound p)) / (2 |^ C) is V11() real ext-real Element of REAL
(2 |^ C) " is V11() real ext-real non negative set
((E-bound p) - (W-bound p)) * ((2 |^ C) ") is V11() real ext-real set
(E-bound p) - (E-bound p) is V11() real ext-real Element of REAL
- (E-bound p) is V11() real ext-real set
(E-bound p) + (- (E-bound p)) is V11() real ext-real set
(E-bound p) + (((E-bound p) - (W-bound p)) / (2 |^ C)) is V11() real ext-real Element of REAL
C is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
p is non empty functional closed connected bounded compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
S-bound p is V11() real ext-real Element of REAL
(TOP-REAL 2) | p is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | p is V15() V18( the carrier of ((TOP-REAL 2) | p)) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | p), REAL ) V212((TOP-REAL 2) | p) Element of K6(K7( the carrier of ((TOP-REAL 2) | p),REAL))
the carrier of ((TOP-REAL 2) | p) is set
K7( the carrier of ((TOP-REAL 2) | p),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | p),REAL)) is non empty set
lower_bound (proj2 | p) is V11() real ext-real Element of REAL
(proj2 | p) .: the carrier of ((TOP-REAL 2) | p) is Element of K6(REAL)
lower_bound ((proj2 | p) .: the carrier of ((TOP-REAL 2) | p)) is V11() real ext-real Element of REAL
Cage (p,C) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like non constant V28() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the carrier of (TOP-REAL 2)
L~ (Cage (p,C)) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
S-bound (L~ (Cage (p,C))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (p,C))) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (L~ (Cage (p,C))) is V15() V18( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))), REAL ) V212((TOP-REAL 2) | (L~ (Cage (p,C)))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))),REAL))
the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))) is set
K7( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))),REAL)) is non empty set
lower_bound (proj2 | (L~ (Cage (p,C)))) is V11() real ext-real Element of REAL
(proj2 | (L~ (Cage (p,C)))) .: the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))) is Element of K6(REAL)
lower_bound ((proj2 | (L~ (Cage (p,C)))) .: the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C))))) is V11() real ext-real Element of REAL
2 |^ C is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
N-bound p is V11() real ext-real Element of REAL
upper_bound (proj2 | p) is V11() real ext-real Element of REAL
upper_bound ((proj2 | p) .: the carrier of ((TOP-REAL 2) | p)) is V11() real ext-real Element of REAL
(S-bound p) + 0 is V11() real ext-real Element of REAL
(N-bound p) - (S-bound p) is V11() real ext-real Element of REAL
- (S-bound p) is V11() real ext-real set
(N-bound p) + (- (S-bound p)) is V11() real ext-real set
((N-bound p) - (S-bound p)) / (2 |^ C) is V11() real ext-real Element of REAL
(2 |^ C) " is V11() real ext-real non negative set
((N-bound p) - (S-bound p)) * ((2 |^ C) ") is V11() real ext-real set
(S-bound p) - (S-bound p) is V11() real ext-real Element of REAL
(S-bound p) + (- (S-bound p)) is V11() real ext-real set
(S-bound p) - (((N-bound p) - (S-bound p)) / (2 |^ C)) is V11() real ext-real Element of REAL
- (((N-bound p) - (S-bound p)) / (2 |^ C)) is V11() real ext-real set
(S-bound p) + (- (((N-bound p) - (S-bound p)) / (2 |^ C))) is V11() real ext-real set
C is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
p is non empty functional closed connected bounded compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
W-bound p is V11() real ext-real Element of REAL
(TOP-REAL 2) | p is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | p is V15() V18( the carrier of ((TOP-REAL 2) | p)) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | p), REAL ) V212((TOP-REAL 2) | p) Element of K6(K7( the carrier of ((TOP-REAL 2) | p),REAL))
the carrier of ((TOP-REAL 2) | p) is set
K7( the carrier of ((TOP-REAL 2) | p),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | p),REAL)) is non empty set
lower_bound (proj1 | p) is V11() real ext-real Element of REAL
(proj1 | p) .: the carrier of ((TOP-REAL 2) | p) is Element of K6(REAL)
lower_bound ((proj1 | p) .: the carrier of ((TOP-REAL 2) | p)) is V11() real ext-real Element of REAL
Cage (p,C) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like non constant V28() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the carrier of (TOP-REAL 2)
L~ (Cage (p,C)) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
W-bound (L~ (Cage (p,C))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (p,C))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ (Cage (p,C))) is V15() V18( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))), REAL ) V212((TOP-REAL 2) | (L~ (Cage (p,C)))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))),REAL))
the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))) is set
K7( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))),REAL)) is non empty set
lower_bound (proj1 | (L~ (Cage (p,C)))) is V11() real ext-real Element of REAL
(proj1 | (L~ (Cage (p,C)))) .: the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))) is Element of K6(REAL)
lower_bound ((proj1 | (L~ (Cage (p,C)))) .: the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C))))) is V11() real ext-real Element of REAL
2 |^ C is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
E-bound p is V11() real ext-real Element of REAL
upper_bound (proj1 | p) is V11() real ext-real Element of REAL
upper_bound ((proj1 | p) .: the carrier of ((TOP-REAL 2) | p)) is V11() real ext-real Element of REAL
(W-bound p) + 0 is V11() real ext-real Element of REAL
(E-bound p) - (W-bound p) is V11() real ext-real Element of REAL
- (W-bound p) is V11() real ext-real set
(E-bound p) + (- (W-bound p)) is V11() real ext-real set
((E-bound p) - (W-bound p)) / (2 |^ C) is V11() real ext-real Element of REAL
(2 |^ C) " is V11() real ext-real non negative set
((E-bound p) - (W-bound p)) * ((2 |^ C) ") is V11() real ext-real set
(W-bound p) - (W-bound p) is V11() real ext-real Element of REAL
(W-bound p) + (- (W-bound p)) is V11() real ext-real set
(W-bound p) - (((E-bound p) - (W-bound p)) / (2 |^ C)) is V11() real ext-real Element of REAL
- (((E-bound p) - (W-bound p)) / (2 |^ C)) is V11() real ext-real set
(W-bound p) + (- (((E-bound p) - (W-bound p)) / (2 |^ C))) is V11() real ext-real set
C is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
p is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
Gauge (p,C) is V15() non empty-yielding V18( NAT ) V19(K307( the carrier of (TOP-REAL 2))) Function-like V28() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K307( the carrier of (TOP-REAL 2))
len (Gauge (p,C)) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
width (Gauge (p,C)) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
Upper_Seq (p,C) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V28() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
L~ (Upper_Seq (p,C)) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
Lower_Seq (p,C) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V28() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
L~ (Lower_Seq (p,C)) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
Upper_Arc p is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
p9 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
r is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
s is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(Gauge (p,C)) * (p9,r) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(Gauge (p,C)) * (p9,s) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,s))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,s)))) /\ (L~ (Upper_Seq (p,C))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
{((Gauge (p,C)) * (p9,r))} is non empty trivial functional V35(1) set
(LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,s)))) /\ (L~ (Lower_Seq (p,C))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
{((Gauge (p,C)) * (p9,s))} is non empty trivial functional V35(1) set
Cage (p,C) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like non constant V28() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the carrier of (TOP-REAL 2)
L~ (Cage (p,C)) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
W-min (L~ (Cage (p,C))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
W-bound (L~ (Cage (p,C))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (p,C))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ (Cage (p,C))) is V15() V18( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))), REAL ) V212((TOP-REAL 2) | (L~ (Cage (p,C)))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))),REAL))
the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))) is set
K7( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))),REAL)) is non empty set
lower_bound (proj1 | (L~ (Cage (p,C)))) is V11() real ext-real Element of REAL
(proj1 | (L~ (Cage (p,C)))) .: the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))) is Element of K6(REAL)
lower_bound ((proj1 | (L~ (Cage (p,C)))) .: the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C))))) is V11() real ext-real Element of REAL
W-most (L~ (Cage (p,C))) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
SW-corner (L~ (Cage (p,C))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
S-bound (L~ (Cage (p,C))) is V11() real ext-real Element of REAL
proj2 | (L~ (Cage (p,C))) is V15() V18( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))), REAL ) V212((TOP-REAL 2) | (L~ (Cage (p,C)))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))),REAL))
lower_bound (proj2 | (L~ (Cage (p,C)))) is V11() real ext-real Element of REAL
(proj2 | (L~ (Cage (p,C)))) .: the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))) is Element of K6(REAL)
lower_bound ((proj2 | (L~ (Cage (p,C)))) .: the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Cage (p,C)))),(S-bound (L~ (Cage (p,C))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
NW-corner (L~ (Cage (p,C))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
N-bound (L~ (Cage (p,C))) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ (Cage (p,C)))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (L~ (Cage (p,C)))) .: the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Cage (p,C)))),(N-bound (L~ (Cage (p,C))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (p,C)))),(NW-corner (L~ (Cage (p,C))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner (L~ (Cage (p,C)))),(NW-corner (L~ (Cage (p,C)))))) /\ (L~ (Cage (p,C))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (W-most (L~ (Cage (p,C)))) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Cage (p,C)))) is V15() V18( the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C)))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C))))), REAL ) V212((TOP-REAL 2) | (W-most (L~ (Cage (p,C))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C))))),REAL))
the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C))))) is set
K7( the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C))))),REAL)) is non empty set
lower_bound (proj2 | (W-most (L~ (Cage (p,C))))) is V11() real ext-real Element of REAL
(proj2 | (W-most (L~ (Cage (p,C))))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C))))) is Element of K6(REAL)
lower_bound ((proj2 | (W-most (L~ (Cage (p,C))))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C)))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Cage (p,C)))),(lower_bound (proj2 | (W-most (L~ (Cage (p,C))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
E-max (L~ (Cage (p,C))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
E-bound (L~ (Cage (p,C))) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ (Cage (p,C)))) is V11() real ext-real Element of REAL
upper_bound ((proj1 | (L~ (Cage (p,C)))) .: the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C))))) is V11() real ext-real Element of REAL
E-most (L~ (Cage (p,C))) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
SE-corner (L~ (Cage (p,C))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
|[(E-bound (L~ (Cage (p,C)))),(S-bound (L~ (Cage (p,C))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
NE-corner (L~ (Cage (p,C))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
|[(E-bound (L~ (Cage (p,C)))),(N-bound (L~ (Cage (p,C))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Cage (p,C)))),(NE-corner (L~ (Cage (p,C))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SE-corner (L~ (Cage (p,C)))),(NE-corner (L~ (Cage (p,C)))))) /\ (L~ (Cage (p,C))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (E-most (L~ (Cage (p,C)))) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Cage (p,C)))) is V15() V18( the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (p,C)))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (p,C))))), REAL ) V212((TOP-REAL 2) | (E-most (L~ (Cage (p,C))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (p,C))))),REAL))
the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (p,C))))) is set
K7( the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (p,C))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (p,C))))),REAL)) is non empty set
upper_bound (proj2 | (E-most (L~ (Cage (p,C))))) is V11() real ext-real Element of REAL
(proj2 | (E-most (L~ (Cage (p,C))))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (p,C))))) is Element of K6(REAL)
upper_bound ((proj2 | (E-most (L~ (Cage (p,C))))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (p,C)))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Cage (p,C)))),(upper_bound (proj2 | (E-most (L~ (Cage (p,C))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
[p9,s] is set
{p9,s} is non empty set
{p9} is non empty trivial V35(1) set
{{p9,s},{p9}} is non empty set
Indices (Gauge (p,C)) is set
[p9,r] is set
{p9,r} is non empty set
{{p9,r},{p9}} is non empty set
L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s))) is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
R_Cut ((Upper_Seq (p,C)),((Gauge (p,C)) * (p9,r))) is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len (Upper_Seq (p,C)) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
dom (Upper_Seq (p,C)) is non trivial Element of K6(NAT)
(Upper_Seq (p,C)) . 1 is V15() Function-like set
(Upper_Seq (p,C)) /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(W-min (L~ (Cage (p,C)))) `1 is V11() real ext-real Element of REAL
(Gauge (p,C)) * (1,r) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * (1,r)) `1 is V11() real ext-real Element of REAL
[1,r] is set
{1,r} is non empty set
{{1,r},{1}} is non empty set
1 + 2 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
len (Lower_Seq (p,C)) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
dom (Lower_Seq (p,C)) is non trivial Element of K6(NAT)
(Lower_Seq (p,C)) . (len (Lower_Seq (p,C))) is V15() Function-like set
(Lower_Seq (p,C)) /. (len (Lower_Seq (p,C))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
[(len (Gauge (p,C))),r] is set
{(len (Gauge (p,C))),r} is non empty set
{(len (Gauge (p,C)))} is non empty trivial V35(1) set
{{(len (Gauge (p,C))),r},{(len (Gauge (p,C)))}} is non empty set
(Lower_Seq (p,C)) . 1 is V15() Function-like set
(Lower_Seq (p,C)) /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(E-max (L~ (Cage (p,C)))) `1 is V11() real ext-real Element of REAL
(Gauge (p,C)) * ((len (Gauge (p,C))),r) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * ((len (Gauge (p,C))),r)) `1 is V11() real ext-real Element of REAL
1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
p19 is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V28() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
len p19 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
rng (Upper_Seq (p,C)) is functional Element of K6( the carrier of (TOP-REAL 2))
f is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V28() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
len f is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
rng (Lower_Seq (p,C)) is functional Element of K6( the carrier of (TOP-REAL 2))
i1 is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one non constant V28() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq s.c.c. FinSequence of the carrier of (TOP-REAL 2)
len i1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
dom i1 is non trivial Element of K6(NAT)
i1 /. (len i1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
i1 . (len i1) is V15() Function-like set
c1 is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one non constant V28() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq s.c.c. FinSequence of the carrier of (TOP-REAL 2)
len c1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
dom c1 is non trivial Element of K6(NAT)
c1 /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
c1 . 1 is V15() Function-like set
(len i1) - 1 is V11() real ext-real Element of REAL
- 1 is V11() real ext-real non positive set
(len i1) + (- 1) is V11() real ext-real set
c2 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
c2 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
(len i1) -' 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
LSeg (i1,c2) is functional Element of K6( the carrier of (TOP-REAL 2))
L~ i1 is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(LSeg (i1,c2)) /\ (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,s)))) is functional Element of K6( the carrier of (TOP-REAL 2))
i1 /. c2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((i1 /. c2),((Gauge (p,C)) * (p9,r))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
ii1 is set
LSeg (c1,1) is functional Element of K6( the carrier of (TOP-REAL 2))
L~ c1 is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(LSeg (c1,1)) /\ (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,s)))) is functional Element of K6( the carrier of (TOP-REAL 2))
c1 /. (1 + 1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg (((Gauge (p,C)) * (p9,s)),(c1 /. (1 + 1))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
ii1 is set
(LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,s)))) /\ (LSeg (c1,1)) is functional Element of K6( the carrier of (TOP-REAL 2))
i1 /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
c1 /. (len c1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
rng i1 is non trivial functional Element of K6( the carrier of (TOP-REAL 2))
rng c1 is non trivial functional Element of K6( the carrier of (TOP-REAL 2))
{(i1 /. 1)} is non empty trivial functional V35(1) set
(L~ i1) /\ (L~ c1) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
ii1 is set
[(len (Gauge (p,C))),s] is set
{(len (Gauge (p,C))),s} is non empty set
{{(len (Gauge (p,C))),s},{(len (Gauge (p,C)))}} is non empty set
ii1 is set
(L~ (Upper_Seq (p,C))) /\ (L~ (Lower_Seq (p,C))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
{(W-min (L~ (Cage (p,C)))),(E-max (L~ (Cage (p,C))))} is non empty functional set
(Gauge (p,C)) * ((len (Gauge (p,C))),s) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * ((len (Gauge (p,C))),s)) `1 is V11() real ext-real Element of REAL
i1 /. 2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * (p9,r)) `1 is V11() real ext-real Element of REAL
((Gauge (p,C)) * (p9,r)) .. (Upper_Seq (p,C)) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
mid ((Upper_Seq (p,C)),1,(((Gauge (p,C)) * (p9,r)) .. (Upper_Seq (p,C)))) is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
(Upper_Seq (p,C)) | (((Gauge (p,C)) * (p9,r)) .. (Upper_Seq (p,C))) is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V28() FinSequence-like FinSubsequence-like special unfolded s.n.c. FinSequence of the carrier of (TOP-REAL 2)
(Upper_Seq (p,C)) /. 2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
<*((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,s))*> is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() V35(2) FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
p2 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
dom <*((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,s))*> is non trivial V35(2) Element of K6(NAT)
<*((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,s))*> /. p2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(Gauge (p,C)) * (p9,1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * (p9,1)) `1 is V11() real ext-real Element of REAL
((Gauge (p,C)) * (p9,s)) `1 is V11() real ext-real Element of REAL
L~ <*((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,s))*> is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
<*((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,s))*> /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
len <*((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,s))*> is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
<*((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,s))*> /. (len <*((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,s))*>) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
p2 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ p2 is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
p2 /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
len p2 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
p2 /. (len p2) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
p2 is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V28() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
i1 ^' p2 is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
(i1 ^' p2) ^' c1 is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len (Cage (p,C)) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like non constant V28() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the carrier of (TOP-REAL 2)
len (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
len (i1 ^' p2) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
1 + 0 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
len ((i1 ^' p2) ^' c1) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
p2 /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(i1 ^' p2) /. (len (i1 ^' p2)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
<*((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,s))*> /. 2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg (p2,1) is functional Element of K6( the carrier of (TOP-REAL 2))
LSeg (i1,((len i1) -' 1)) is functional Element of K6( the carrier of (TOP-REAL 2))
(LSeg (i1,((len i1) -' 1))) /\ (LSeg (p2,1)) is functional Element of K6( the carrier of (TOP-REAL 2))
len p2 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
(LSeg (i1,c2)) /\ (LSeg (p2,1)) is functional Element of K6( the carrier of (TOP-REAL 2))
g is set
{(i1 /. (len i1))} is non empty trivial functional V35(1) set
2 + 0 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
(len p2) - 2 is V11() real ext-real Element of REAL
(len p2) + (- 2) is V11() real ext-real set
(len (i1 ^' p2)) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
((len (i1 ^' p2)) + 1) - 1 is V11() real ext-real Element of REAL
((len (i1 ^' p2)) + 1) + (- 1) is V11() real ext-real set
(len i1) + (len p2) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
((len i1) + (len p2)) - 1 is V11() real ext-real Element of REAL
((len i1) + (len p2)) + (- 1) is V11() real ext-real set
(len (i1 ^' p2)) - 1 is V11() real ext-real Element of REAL
(len (i1 ^' p2)) + (- 1) is V11() real ext-real set
(len i1) + ((len p2) - 2) is V11() real ext-real Element of REAL
(len p2) -' 2 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(len i1) + ((len p2) -' 2) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
(len (i1 ^' p2)) -' 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(len p2) - 1 is V11() real ext-real Element of REAL
(len p2) + (- 1) is V11() real ext-real set
(len p2) -' 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
((len p2) -' 2) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
((len p2) - 2) + 1 is V11() real ext-real Element of REAL
((len p2) - 1) + 1 is V11() real ext-real Element of REAL
LSeg (p2,((len p2) -' 1)) is functional Element of K6( the carrier of (TOP-REAL 2))
(LSeg (p2,((len p2) -' 1))) /\ (LSeg (c1,1)) is functional Element of K6( the carrier of (TOP-REAL 2))
g is set
((len p2) -' 1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
p2 /. (((len p2) -' 1) + 1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((i1 ^' p2),((len i1) + ((len p2) -' 2))) is functional Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((i1 ^' p2),((len i1) + ((len p2) -' 2)))) /\ (LSeg (c1,1)) is functional Element of K6( the carrier of (TOP-REAL 2))
{((i1 ^' p2) /. (len (i1 ^' p2)))} is non empty trivial functional V35(1) set
rng p2 is functional Element of K6( the carrier of (TOP-REAL 2))
L~ p2 is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
{(p2 /. 1)} is non empty trivial functional V35(1) set
(L~ i1) /\ (L~ p2) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
g is set
g is set
(L~ p2) /\ (L~ (Upper_Seq (p,C))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(rng i1) /\ (rng p2) is functional Element of K6( the carrier of (TOP-REAL 2))
p2 /. (len p2) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
{(p2 /. (len p2))} is non empty trivial functional V35(1) set
(L~ c1) /\ (L~ p2) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
g is set
g is set
(L~ p2) /\ (L~ (Lower_Seq (p,C))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
L~ (i1 ^' p2) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(L~ (i1 ^' p2)) /\ (L~ c1) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(L~ i1) \/ (L~ p2) is non empty functional Element of K6( the carrier of (TOP-REAL 2))
((L~ i1) \/ (L~ p2)) /\ (L~ c1) is functional Element of K6( the carrier of (TOP-REAL 2))
{(c1 /. 1)} is non empty trivial functional V35(1) set
{(i1 /. 1)} \/ {(c1 /. 1)} is non empty set
(i1 ^' p2) /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
{((i1 ^' p2) /. 1)} is non empty trivial functional V35(1) set
{((i1 ^' p2) /. 1)} \/ {(c1 /. 1)} is non empty set
{((i1 ^' p2) /. 1),(c1 /. 1)} is non empty functional set
W-min p is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
W-bound p is V11() real ext-real Element of REAL
(TOP-REAL 2) | p is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | p is V15() V18( the carrier of ((TOP-REAL 2) | p)) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | p), REAL ) V212((TOP-REAL 2) | p) Element of K6(K7( the carrier of ((TOP-REAL 2) | p),REAL))
the carrier of ((TOP-REAL 2) | p) is set
K7( the carrier of ((TOP-REAL 2) | p),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | p),REAL)) is non empty set
lower_bound (proj1 | p) is V11() real ext-real Element of REAL
(proj1 | p) .: the carrier of ((TOP-REAL 2) | p) is Element of K6(REAL)
lower_bound ((proj1 | p) .: the carrier of ((TOP-REAL 2) | p)) is V11() real ext-real Element of REAL
W-most p is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
SW-corner p is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
S-bound p is V11() real ext-real Element of REAL
proj2 | p is V15() V18( the carrier of ((TOP-REAL 2) | p)) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | p), REAL ) V212((TOP-REAL 2) | p) Element of K6(K7( the carrier of ((TOP-REAL 2) | p),REAL))
lower_bound (proj2 | p) is V11() real ext-real Element of REAL
(proj2 | p) .: the carrier of ((TOP-REAL 2) | p) is Element of K6(REAL)
lower_bound ((proj2 | p) .: the carrier of ((TOP-REAL 2) | p)) is V11() real ext-real Element of REAL
|[(W-bound p),(S-bound p)]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
NW-corner p is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
N-bound p is V11() real ext-real Element of REAL
upper_bound (proj2 | p) is V11() real ext-real Element of REAL
upper_bound ((proj2 | p) .: the carrier of ((TOP-REAL 2) | p)) is V11() real ext-real Element of REAL
|[(W-bound p),(N-bound p)]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner p),(NW-corner p)) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner p),(NW-corner p))) /\ p is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (W-most p) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (W-most p) is V15() V18( the carrier of ((TOP-REAL 2) | (W-most p))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (W-most p)), REAL ) V212((TOP-REAL 2) | (W-most p)) Element of K6(K7( the carrier of ((TOP-REAL 2) | (W-most p)),REAL))
the carrier of ((TOP-REAL 2) | (W-most p)) is set
K7( the carrier of ((TOP-REAL 2) | (W-most p)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (W-most p)),REAL)) is non empty set
lower_bound (proj2 | (W-most p)) is V11() real ext-real Element of REAL
(proj2 | (W-most p)) .: the carrier of ((TOP-REAL 2) | (W-most p)) is Element of K6(REAL)
lower_bound ((proj2 | (W-most p)) .: the carrier of ((TOP-REAL 2) | (W-most p))) is V11() real ext-real Element of REAL
|[(W-bound p),(lower_bound (proj2 | (W-most p)))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
E-max p is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
E-bound p is V11() real ext-real Element of REAL
upper_bound (proj1 | p) is V11() real ext-real Element of REAL
upper_bound ((proj1 | p) .: the carrier of ((TOP-REAL 2) | p)) is V11() real ext-real Element of REAL
E-most p is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
SE-corner p is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
|[(E-bound p),(S-bound p)]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
NE-corner p is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
|[(E-bound p),(N-bound p)]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner p),(NE-corner p)) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SE-corner p),(NE-corner p))) /\ p is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (E-most p) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (E-most p) is V15() V18( the carrier of ((TOP-REAL 2) | (E-most p))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (E-most p)), REAL ) V212((TOP-REAL 2) | (E-most p)) Element of K6(K7( the carrier of ((TOP-REAL 2) | (E-most p)),REAL))
the carrier of ((TOP-REAL 2) | (E-most p)) is set
K7( the carrier of ((TOP-REAL 2) | (E-most p)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (E-most p)),REAL)) is non empty set
upper_bound (proj2 | (E-most p)) is V11() real ext-real Element of REAL
(proj2 | (E-most p)) .: the carrier of ((TOP-REAL 2) | (E-most p)) is Element of K6(REAL)
upper_bound ((proj2 | (E-most p)) .: the carrier of ((TOP-REAL 2) | (E-most p))) is V11() real ext-real Element of REAL
|[(E-bound p),(upper_bound (proj2 | (E-most p)))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
rng (Cage (p,C)) is non trivial functional Element of K6( the carrier of (TOP-REAL 2))
(Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))) /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
W-max (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
W-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V15() V18( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))), REAL ) V212((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),REAL))
the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is set
K7( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),REAL)) is non empty set
lower_bound (proj1 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is V11() real ext-real Element of REAL
(proj1 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) .: the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is Element of K6(REAL)
lower_bound ((proj1 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) .: the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is V11() real ext-real Element of REAL
W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
SW-corner (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
S-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V11() real ext-real Element of REAL
proj2 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V15() V18( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))), REAL ) V212((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),REAL))
lower_bound (proj2 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is V11() real ext-real Element of REAL
(proj2 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) .: the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is Element of K6(REAL)
lower_bound ((proj2 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) .: the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),(S-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
NW-corner (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
N-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) .: the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),(N-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),(NW-corner (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),(NW-corner (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))))) /\ (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is V15() V18( the carrier of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))), REAL ) V212((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))),REAL))
the carrier of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is set
K7( the carrier of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))),REAL)) is non empty set
upper_bound (proj2 | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is V11() real ext-real Element of REAL
(proj2 | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is Element of K6(REAL)
upper_bound ((proj2 | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),(upper_bound (proj2 | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(W-max (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) .. (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
N-min (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
NE-corner (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
E-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is V11() real ext-real Element of REAL
upper_bound ((proj1 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) .: the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),(N-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((NW-corner (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),(NE-corner (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((NW-corner (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),(NE-corner (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))))) /\ (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is V15() V18( the carrier of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))), REAL ) V212((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))),REAL))
the carrier of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is set
K7( the carrier of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))),REAL)) is non empty set
lower_bound (proj1 | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is V11() real ext-real Element of REAL
(proj1 | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is Element of K6(REAL)
lower_bound ((proj1 | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))))),(N-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(N-min (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) .. (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
N-max (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
upper_bound (proj1 | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is V11() real ext-real Element of REAL
upper_bound ((proj1 | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))))) is V11() real ext-real Element of REAL
|[(upper_bound (proj1 | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))))),(N-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(N-max (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) .. (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(E-max (L~ (Cage (p,C)))) .. (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
g is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like non constant V28() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard FinSequence of the carrier of (TOP-REAL 2)
right_cell (g,1,(Gauge (p,C))) is functional Element of K6( the carrier of (TOP-REAL 2))
L~ g is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
(right_cell (g,1,(Gauge (p,C)))) \ (L~ g) is functional Element of K6( the carrier of (TOP-REAL 2))
RightComp g is non empty functional Element of K6( the carrier of (TOP-REAL 2))
(L~ (i1 ^' p2)) \/ (L~ c1) is non empty functional Element of K6( the carrier of (TOP-REAL 2))
((L~ i1) \/ (L~ p2)) \/ (L~ c1) is non empty functional Element of K6( the carrier of (TOP-REAL 2))
(L~ (Upper_Seq (p,C))) \/ (L~ (Lower_Seq (p,C))) is non empty functional Element of K6( the carrier of (TOP-REAL 2))
right_cell ((Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))),1) is functional Element of K6( the carrier of (TOP-REAL 2))
GoB (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))) is V15() non empty-yielding V18( NAT ) V19(K307( the carrier of (TOP-REAL 2))) Function-like V28() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K307( the carrier of (TOP-REAL 2))
right_cell ((Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))),1,(GoB (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is functional Element of K6( the carrier of (TOP-REAL 2))
GoB (Cage (p,C)) is V15() non empty-yielding V18( NAT ) V19(K307( the carrier of (TOP-REAL 2))) Function-like V28() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K307( the carrier of (TOP-REAL 2))
right_cell ((Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))),1,(GoB (Cage (p,C)))) is functional Element of K6( the carrier of (TOP-REAL 2))
right_cell ((Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))),1,(Gauge (p,C))) is functional Element of K6( the carrier of (TOP-REAL 2))
(Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))) -: (E-max (L~ (Cage (p,C)))) is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like special unfolded FinSequence of the carrier of (TOP-REAL 2)
right_cell (((Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))) -: (E-max (L~ (Cage (p,C))))),1,(Gauge (p,C))) is functional Element of K6( the carrier of (TOP-REAL 2))
right_cell ((Upper_Seq (p,C)),1,(Gauge (p,C))) is functional Element of K6( the carrier of (TOP-REAL 2))
right_cell ((R_Cut ((Upper_Seq (p,C)),((Gauge (p,C)) * (p9,r)))),1,(Gauge (p,C))) is functional Element of K6( the carrier of (TOP-REAL 2))
right_cell ((i1 ^' p2),1,(Gauge (p,C))) is functional Element of K6( the carrier of (TOP-REAL 2))
g /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
g /. 2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(i1 ^' p2) /. 2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(Upper_Seq (p,C)) ^' (Lower_Seq (p,C)) is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
((Upper_Seq (p,C)) ^' (Lower_Seq (p,C))) /. 2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))) /. 2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(L~ i1) \/ (L~ c1) is non empty functional Element of K6( the carrier of (TOP-REAL 2))
W-min ((L~ i1) \/ (L~ c1)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
W-bound ((L~ i1) \/ (L~ c1)) is V11() real ext-real Element of REAL
(TOP-REAL 2) | ((L~ i1) \/ (L~ c1)) is strict T_2 SubSpace of TOP-REAL 2
proj1 | ((L~ i1) \/ (L~ c1)) is V15() V18( the carrier of ((TOP-REAL 2) | ((L~ i1) \/ (L~ c1)))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | ((L~ i1) \/ (L~ c1))), REAL ) V212((TOP-REAL 2) | ((L~ i1) \/ (L~ c1))) Element of K6(K7( the carrier of ((TOP-REAL 2) | ((L~ i1) \/ (L~ c1))),REAL))
the carrier of ((TOP-REAL 2) | ((L~ i1) \/ (L~ c1))) is set
K7( the carrier of ((TOP-REAL 2) | ((L~ i1) \/ (L~ c1))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | ((L~ i1) \/ (L~ c1))),REAL)) is non empty set
lower_bound (proj1 | ((L~ i1) \/ (L~ c1))) is V11() real ext-real Element of REAL
(proj1 | ((L~ i1) \/ (L~ c1))) .: the carrier of ((TOP-REAL 2) | ((L~ i1) \/ (L~ c1))) is Element of K6(REAL)
lower_bound ((proj1 | ((L~ i1) \/ (L~ c1))) .: the carrier of ((TOP-REAL 2) | ((L~ i1) \/ (L~ c1)))) is V11() real ext-real Element of REAL
W-most ((L~ i1) \/ (L~ c1)) is functional Element of K6( the carrier of (TOP-REAL 2))
SW-corner ((L~ i1) \/ (L~ c1)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
S-bound ((L~ i1) \/ (L~ c1)) is V11() real ext-real Element of REAL
proj2 | ((L~ i1) \/ (L~ c1)) is V15() V18( the carrier of ((TOP-REAL 2) | ((L~ i1) \/ (L~ c1)))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | ((L~ i1) \/ (L~ c1))), REAL ) V212((TOP-REAL 2) | ((L~ i1) \/ (L~ c1))) Element of K6(K7( the carrier of ((TOP-REAL 2) | ((L~ i1) \/ (L~ c1))),REAL))
lower_bound (proj2 | ((L~ i1) \/ (L~ c1))) is V11() real ext-real Element of REAL
(proj2 | ((L~ i1) \/ (L~ c1))) .: the carrier of ((TOP-REAL 2) | ((L~ i1) \/ (L~ c1))) is Element of K6(REAL)
lower_bound ((proj2 | ((L~ i1) \/ (L~ c1))) .: the carrier of ((TOP-REAL 2) | ((L~ i1) \/ (L~ c1)))) is V11() real ext-real Element of REAL
|[(W-bound ((L~ i1) \/ (L~ c1))),(S-bound ((L~ i1) \/ (L~ c1)))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
NW-corner ((L~ i1) \/ (L~ c1)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
N-bound ((L~ i1) \/ (L~ c1)) is V11() real ext-real Element of REAL
upper_bound (proj2 | ((L~ i1) \/ (L~ c1))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | ((L~ i1) \/ (L~ c1))) .: the carrier of ((TOP-REAL 2) | ((L~ i1) \/ (L~ c1)))) is V11() real ext-real Element of REAL
|[(W-bound ((L~ i1) \/ (L~ c1))),(N-bound ((L~ i1) \/ (L~ c1)))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner ((L~ i1) \/ (L~ c1))),(NW-corner ((L~ i1) \/ (L~ c1)))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner ((L~ i1) \/ (L~ c1))),(NW-corner ((L~ i1) \/ (L~ c1))))) /\ ((L~ i1) \/ (L~ c1)) is functional Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (W-most ((L~ i1) \/ (L~ c1))) is strict T_2 SubSpace of TOP-REAL 2
proj2 | (W-most ((L~ i1) \/ (L~ c1))) is V15() V18( the carrier of ((TOP-REAL 2) | (W-most ((L~ i1) \/ (L~ c1))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (W-most ((L~ i1) \/ (L~ c1)))), REAL ) V212((TOP-REAL 2) | (W-most ((L~ i1) \/ (L~ c1)))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (W-most ((L~ i1) \/ (L~ c1)))),REAL))
the carrier of ((TOP-REAL 2) | (W-most ((L~ i1) \/ (L~ c1)))) is set
K7( the carrier of ((TOP-REAL 2) | (W-most ((L~ i1) \/ (L~ c1)))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (W-most ((L~ i1) \/ (L~ c1)))),REAL)) is non empty set
lower_bound (proj2 | (W-most ((L~ i1) \/ (L~ c1)))) is V11() real ext-real Element of REAL
(proj2 | (W-most ((L~ i1) \/ (L~ c1)))) .: the carrier of ((TOP-REAL 2) | (W-most ((L~ i1) \/ (L~ c1)))) is Element of K6(REAL)
lower_bound ((proj2 | (W-most ((L~ i1) \/ (L~ c1)))) .: the carrier of ((TOP-REAL 2) | (W-most ((L~ i1) \/ (L~ c1))))) is V11() real ext-real Element of REAL
|[(W-bound ((L~ i1) \/ (L~ c1))),(lower_bound (proj2 | (W-most ((L~ i1) \/ (L~ c1)))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(W-min ((L~ i1) \/ (L~ c1))) `1 is V11() real ext-real Element of REAL
W-bound (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,s)))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,s)))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,s)))) is V15() V18( the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,s)))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,s))))), REAL ) V212((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,s))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,s))))),REAL))
the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,s))))) is set
K7( the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,s))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,s))))),REAL)) is non empty set
lower_bound (proj1 | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,s))))) is V11() real ext-real Element of REAL
(proj1 | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,s))))) .: the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,s))))) is Element of K6(REAL)
lower_bound ((proj1 | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,s))))) .: the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,s)))))) is V11() real ext-real Element of REAL
W-bound (L~ p2) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ p2) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ p2) is V15() V18( the carrier of ((TOP-REAL 2) | (L~ p2))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ p2)), REAL ) V212((TOP-REAL 2) | (L~ p2)) Element of K6(K7( the carrier of ((TOP-REAL 2) | (L~ p2)),REAL))
the carrier of ((TOP-REAL 2) | (L~ p2)) is set
K7( the carrier of ((TOP-REAL 2) | (L~ p2)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (L~ p2)),REAL)) is non empty set
lower_bound (proj1 | (L~ p2)) is V11() real ext-real Element of REAL
(proj1 | (L~ p2)) .: the carrier of ((TOP-REAL 2) | (L~ p2)) is Element of K6(REAL)
lower_bound ((proj1 | (L~ p2)) .: the carrier of ((TOP-REAL 2) | (L~ p2))) is V11() real ext-real Element of REAL
((L~ i1) \/ (L~ c1)) \/ (L~ p2) is non empty functional Element of K6( the carrier of (TOP-REAL 2))
W-min (((L~ i1) \/ (L~ c1)) \/ (L~ p2)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
W-bound (((L~ i1) \/ (L~ c1)) \/ (L~ p2)) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (((L~ i1) \/ (L~ c1)) \/ (L~ p2)) is strict T_2 SubSpace of TOP-REAL 2
proj1 | (((L~ i1) \/ (L~ c1)) \/ (L~ p2)) is V15() V18( the carrier of ((TOP-REAL 2) | (((L~ i1) \/ (L~ c1)) \/ (L~ p2)))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (((L~ i1) \/ (L~ c1)) \/ (L~ p2))), REAL ) V212((TOP-REAL 2) | (((L~ i1) \/ (L~ c1)) \/ (L~ p2))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (((L~ i1) \/ (L~ c1)) \/ (L~ p2))),REAL))
the carrier of ((TOP-REAL 2) | (((L~ i1) \/ (L~ c1)) \/ (L~ p2))) is set
K7( the carrier of ((TOP-REAL 2) | (((L~ i1) \/ (L~ c1)) \/ (L~ p2))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (((L~ i1) \/ (L~ c1)) \/ (L~ p2))),REAL)) is non empty set
lower_bound (proj1 | (((L~ i1) \/ (L~ c1)) \/ (L~ p2))) is V11() real ext-real Element of REAL
(proj1 | (((L~ i1) \/ (L~ c1)) \/ (L~ p2))) .: the carrier of ((TOP-REAL 2) | (((L~ i1) \/ (L~ c1)) \/ (L~ p2))) is Element of K6(REAL)
lower_bound ((proj1 | (((L~ i1) \/ (L~ c1)) \/ (L~ p2))) .: the carrier of ((TOP-REAL 2) | (((L~ i1) \/ (L~ c1)) \/ (L~ p2)))) is V11() real ext-real Element of REAL
W-most (((L~ i1) \/ (L~ c1)) \/ (L~ p2)) is functional Element of K6( the carrier of (TOP-REAL 2))
SW-corner (((L~ i1) \/ (L~ c1)) \/ (L~ p2)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
S-bound (((L~ i1) \/ (L~ c1)) \/ (L~ p2)) is V11() real ext-real Element of REAL
proj2 | (((L~ i1) \/ (L~ c1)) \/ (L~ p2)) is V15() V18( the carrier of ((TOP-REAL 2) | (((L~ i1) \/ (L~ c1)) \/ (L~ p2)))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (((L~ i1) \/ (L~ c1)) \/ (L~ p2))), REAL ) V212((TOP-REAL 2) | (((L~ i1) \/ (L~ c1)) \/ (L~ p2))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (((L~ i1) \/ (L~ c1)) \/ (L~ p2))),REAL))
lower_bound (proj2 | (((L~ i1) \/ (L~ c1)) \/ (L~ p2))) is V11() real ext-real Element of REAL
(proj2 | (((L~ i1) \/ (L~ c1)) \/ (L~ p2))) .: the carrier of ((TOP-REAL 2) | (((L~ i1) \/ (L~ c1)) \/ (L~ p2))) is Element of K6(REAL)
lower_bound ((proj2 | (((L~ i1) \/ (L~ c1)) \/ (L~ p2))) .: the carrier of ((TOP-REAL 2) | (((L~ i1) \/ (L~ c1)) \/ (L~ p2)))) is V11() real ext-real Element of REAL
|[(W-bound (((L~ i1) \/ (L~ c1)) \/ (L~ p2))),(S-bound (((L~ i1) \/ (L~ c1)) \/ (L~ p2)))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
NW-corner (((L~ i1) \/ (L~ c1)) \/ (L~ p2)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
N-bound (((L~ i1) \/ (L~ c1)) \/ (L~ p2)) is V11() real ext-real Element of REAL
upper_bound (proj2 | (((L~ i1) \/ (L~ c1)) \/ (L~ p2))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (((L~ i1) \/ (L~ c1)) \/ (L~ p2))) .: the carrier of ((TOP-REAL 2) | (((L~ i1) \/ (L~ c1)) \/ (L~ p2)))) is V11() real ext-real Element of REAL
|[(W-bound (((L~ i1) \/ (L~ c1)) \/ (L~ p2))),(N-bound (((L~ i1) \/ (L~ c1)) \/ (L~ p2)))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner (((L~ i1) \/ (L~ c1)) \/ (L~ p2))),(NW-corner (((L~ i1) \/ (L~ c1)) \/ (L~ p2)))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner (((L~ i1) \/ (L~ c1)) \/ (L~ p2))),(NW-corner (((L~ i1) \/ (L~ c1)) \/ (L~ p2))))) /\ (((L~ i1) \/ (L~ c1)) \/ (L~ p2)) is functional Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (W-most (((L~ i1) \/ (L~ c1)) \/ (L~ p2))) is strict T_2 SubSpace of TOP-REAL 2
proj2 | (W-most (((L~ i1) \/ (L~ c1)) \/ (L~ p2))) is V15() V18( the carrier of ((TOP-REAL 2) | (W-most (((L~ i1) \/ (L~ c1)) \/ (L~ p2))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (W-most (((L~ i1) \/ (L~ c1)) \/ (L~ p2)))), REAL ) V212((TOP-REAL 2) | (W-most (((L~ i1) \/ (L~ c1)) \/ (L~ p2)))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (W-most (((L~ i1) \/ (L~ c1)) \/ (L~ p2)))),REAL))
the carrier of ((TOP-REAL 2) | (W-most (((L~ i1) \/ (L~ c1)) \/ (L~ p2)))) is set
K7( the carrier of ((TOP-REAL 2) | (W-most (((L~ i1) \/ (L~ c1)) \/ (L~ p2)))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (W-most (((L~ i1) \/ (L~ c1)) \/ (L~ p2)))),REAL)) is non empty set
lower_bound (proj2 | (W-most (((L~ i1) \/ (L~ c1)) \/ (L~ p2)))) is V11() real ext-real Element of REAL
(proj2 | (W-most (((L~ i1) \/ (L~ c1)) \/ (L~ p2)))) .: the carrier of ((TOP-REAL 2) | (W-most (((L~ i1) \/ (L~ c1)) \/ (L~ p2)))) is Element of K6(REAL)
lower_bound ((proj2 | (W-most (((L~ i1) \/ (L~ c1)) \/ (L~ p2)))) .: the carrier of ((TOP-REAL 2) | (W-most (((L~ i1) \/ (L~ c1)) \/ (L~ p2))))) is V11() real ext-real Element of REAL
|[(W-bound (((L~ i1) \/ (L~ c1)) \/ (L~ p2))),(lower_bound (proj2 | (W-most (((L~ i1) \/ (L~ c1)) \/ (L~ p2)))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
W-min (L~ g) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
W-bound (L~ g) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ g) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ g) is V15() V18( the carrier of ((TOP-REAL 2) | (L~ g))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ g)), REAL ) V212((TOP-REAL 2) | (L~ g)) Element of K6(K7( the carrier of ((TOP-REAL 2) | (L~ g)),REAL))
the carrier of ((TOP-REAL 2) | (L~ g)) is set
K7( the carrier of ((TOP-REAL 2) | (L~ g)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (L~ g)),REAL)) is non empty set
lower_bound (proj1 | (L~ g)) is V11() real ext-real Element of REAL
(proj1 | (L~ g)) .: the carrier of ((TOP-REAL 2) | (L~ g)) is Element of K6(REAL)
lower_bound ((proj1 | (L~ g)) .: the carrier of ((TOP-REAL 2) | (L~ g))) is V11() real ext-real Element of REAL
W-most (L~ g) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
SW-corner (L~ g) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
S-bound (L~ g) is V11() real ext-real Element of REAL
proj2 | (L~ g) is V15() V18( the carrier of ((TOP-REAL 2) | (L~ g))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ g)), REAL ) V212((TOP-REAL 2) | (L~ g)) Element of K6(K7( the carrier of ((TOP-REAL 2) | (L~ g)),REAL))
lower_bound (proj2 | (L~ g)) is V11() real ext-real Element of REAL
(proj2 | (L~ g)) .: the carrier of ((TOP-REAL 2) | (L~ g)) is Element of K6(REAL)
lower_bound ((proj2 | (L~ g)) .: the carrier of ((TOP-REAL 2) | (L~ g))) is V11() real ext-real Element of REAL
|[(W-bound (L~ g)),(S-bound (L~ g))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
NW-corner (L~ g) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
N-bound (L~ g) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ g)) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (L~ g)) .: the carrier of ((TOP-REAL 2) | (L~ g))) is V11() real ext-real Element of REAL
|[(W-bound (L~ g)),(N-bound (L~ g))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner (L~ g)),(NW-corner (L~ g))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner (L~ g)),(NW-corner (L~ g)))) /\ (L~ g) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (W-most (L~ g)) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (W-most (L~ g)) is V15() V18( the carrier of ((TOP-REAL 2) | (W-most (L~ g)))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (W-most (L~ g))), REAL ) V212((TOP-REAL 2) | (W-most (L~ g))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (W-most (L~ g))),REAL))
the carrier of ((TOP-REAL 2) | (W-most (L~ g))) is set
K7( the carrier of ((TOP-REAL 2) | (W-most (L~ g))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (W-most (L~ g))),REAL)) is non empty set
lower_bound (proj2 | (W-most (L~ g))) is V11() real ext-real Element of REAL
(proj2 | (W-most (L~ g))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ g))) is Element of K6(REAL)
lower_bound ((proj2 | (W-most (L~ g))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ g)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ g)),(lower_bound (proj2 | (W-most (L~ g))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
rng g is non trivial functional Element of K6( the carrier of (TOP-REAL 2))
dom g is non trivial Element of K6(NAT)
(g /. 2) `1 is V11() real ext-real Element of REAL
(W-min (L~ g)) `1 is V11() real ext-real Element of REAL
Rotate (g,(W-min (L~ g))) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like non constant V28() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard FinSequence of the carrier of (TOP-REAL 2)
(Rotate (g,(W-min (L~ g)))) /. 2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(Upper_Seq (p,C)) . (len (Upper_Seq (p,C))) is V15() Function-like set
(Upper_Seq (p,C)) /. (len (Upper_Seq (p,C))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
east_halfline (E-max p) is non empty functional connected V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
d2 is set
ii2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(east_halfline (E-max p)) /\ (L~ (Cage (p,C))) is functional Element of K6( the carrier of (TOP-REAL 2))
ii2 `1 is V11() real ext-real Element of REAL
d1 is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like non constant V28() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the carrier of (TOP-REAL 2)
L~ d1 is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
d2 is set
ii2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
ii2 `1 is V11() real ext-real Element of REAL
p9 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
(p9 + 1) - 1 is V11() real ext-real Element of REAL
(p9 + 1) + (- 1) is V11() real ext-real set
(len (Gauge (p,C))) - 1 is V11() real ext-real Element of REAL
(len (Gauge (p,C))) + (- 1) is V11() real ext-real set
(len (Gauge (p,C))) -' 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(Gauge (p,C)) * (((len (Gauge (p,C))) -' 1),1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * (((len (Gauge (p,C))) -' 1),1)) `1 is V11() real ext-real Element of REAL
(E-max p) `1 is V11() real ext-real Element of REAL
ii2 `2 is V11() real ext-real Element of REAL
(E-max p) `2 is V11() real ext-real Element of REAL
d2 is set
ii2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(east_halfline (E-max p)) /\ (L~ (Cage (p,C))) is functional Element of K6( the carrier of (TOP-REAL 2))
ii2 `1 is V11() real ext-real Element of REAL
(E-max p) `2 is V11() real ext-real Element of REAL
ii2 `2 is V11() real ext-real Element of REAL
Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like non constant V28() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the carrier of (TOP-REAL 2)
right_cell ((Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))),1) is functional Element of K6( the carrier of (TOP-REAL 2))
(Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))) -: (W-min (L~ (Cage (p,C)))) is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like special unfolded FinSequence of the carrier of (TOP-REAL 2)
LSeg ((Lower_Seq (p,C)),1) is functional Element of K6( the carrier of (TOP-REAL 2))
LSeg ((Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))),1) is functional Element of K6( the carrier of (TOP-REAL 2))
L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
len (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
GoB (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))) is V15() non empty-yielding V18( NAT ) V19(K307( the carrier of (TOP-REAL 2))) Function-like V28() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K307( the carrier of (TOP-REAL 2))
(Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))) /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
E-max (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
E-bound (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))) is V15() V18( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))), REAL ) V212((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))),REAL))
the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) is set
K7( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))),REAL)) is non empty set
upper_bound (proj1 | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) is V11() real ext-real Element of REAL
(proj1 | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) .: the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) is Element of K6(REAL)
upper_bound ((proj1 | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) .: the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) is V11() real ext-real Element of REAL
E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
SE-corner (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
S-bound (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))) is V11() real ext-real Element of REAL
proj2 | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))) is V15() V18( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))), REAL ) V212((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))),REAL))
lower_bound (proj2 | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) is V11() real ext-real Element of REAL
(proj2 | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) .: the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) is Element of K6(REAL)
lower_bound ((proj2 | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) .: the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))),(S-bound (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
NE-corner (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
N-bound (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) .: the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))),(N-bound (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))),(NE-corner (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SE-corner (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))),(NE-corner (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))))) /\ (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) is V15() V18( the carrier of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))), REAL ) V212((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))),REAL))
the carrier of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) is set
K7( the carrier of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))),REAL)) is non empty set
upper_bound (proj2 | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) is V11() real ext-real Element of REAL
(proj2 | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) is Element of K6(REAL)
upper_bound ((proj2 | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))),(upper_bound (proj2 | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))) /. (1 + 1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
Gij is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
Gji is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
Gji + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
[Gij,(Gji + 1)] is set
{Gij,(Gji + 1)} is non empty set
{Gij} is non empty trivial V35(1) set
{{Gij,(Gji + 1)},{Gij}} is non empty set
[Gij,Gji] is set
{Gij,Gji} is non empty set
{{Gij,Gji},{Gij}} is non empty set
(Gauge (p,C)) * (Gij,(Gji + 1)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(Gauge (p,C)) * (Gij,Gji) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
Gij9 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(Gauge (p,C)) * ((len (Gauge (p,C))),Gij9) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
[(len (Gauge (p,C))),Gij9] is set
{(len (Gauge (p,C))),Gij9} is non empty set
{{(len (Gauge (p,C))),Gij9},{(len (Gauge (p,C)))}} is non empty set
Gij + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
(Gji + 1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
Gij -' 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
cell ((Gauge (p,C)),(Gij -' 1),Gji) is functional Element of K6( the carrier of (TOP-REAL 2))
(Gij -' 1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
4 - 1 is V11() real ext-real Element of REAL
4 + (- 1) is V11() real ext-real set
Gij - 1 is V11() real ext-real Element of REAL
Gij + (- 1) is V11() real ext-real set
(Gauge (p,C)) * ((Gij -' 1),Gji) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * ((Gij -' 1),Gji)) `2 is V11() real ext-real Element of REAL
(Gauge (p,C)) * ((Gij -' 1),(Gji + 1)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * ((Gij -' 1),(Gji + 1))) `2 is V11() real ext-real Element of REAL
(Gauge (p,C)) * (1,Gji) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * (1,Gji)) `2 is V11() real ext-real Element of REAL
((Gauge (p,C)) * (Gij,Gji)) `2 is V11() real ext-real Element of REAL
(Gauge (p,C)) * (1,(Gji + 1)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * (1,(Gji + 1))) `2 is V11() real ext-real Element of REAL
((Gauge (p,C)) * (Gij,(Gji + 1))) `2 is V11() real ext-real Element of REAL
(Gauge (p,C)) * ((len (Gauge (p,C))),Gji) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * ((len (Gauge (p,C))),Gji)) `1 is V11() real ext-real Element of REAL
(Gauge (p,C)) * ((len (Gauge (p,C))),(Gji + 1)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * ((len (Gauge (p,C))),(Gji + 1))) `1 is V11() real ext-real Element of REAL
LSeg (((Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))) /. 1),((Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))) /. (1 + 1))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
Index (ii2,c1) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
LSeg (c1,(Index (ii2,c1))) is functional Element of K6( the carrier of (TOP-REAL 2))
((Gauge (p,C)) * (p9,s)) .. (Lower_Seq (p,C)) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
mid ((Lower_Seq (p,C)),(((Gauge (p,C)) * (p9,s)) .. (Lower_Seq (p,C))),(len (Lower_Seq (p,C)))) is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
Index (((Gauge (p,C)) * (p9,s)),(Lower_Seq (p,C))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(Index (((Gauge (p,C)) * (p9,s)),(Lower_Seq (p,C)))) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
Gji9 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative set
(Lower_Seq (p,C)) . Gji9 is V15() Function-like set
len (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s)))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(len (Lower_Seq (p,C))) - (Index (((Gauge (p,C)) * (p9,s)),(Lower_Seq (p,C)))) is V11() real ext-real Element of REAL
- (Index (((Gauge (p,C)) * (p9,s)),(Lower_Seq (p,C)))) is V11() real ext-real non positive set
(len (Lower_Seq (p,C))) + (- (Index (((Gauge (p,C)) * (p9,s)),(Lower_Seq (p,C))))) is V11() real ext-real set
(Index (ii2,c1)) + (((Gauge (p,C)) * (p9,s)) .. (Lower_Seq (p,C))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
((Index (ii2,c1)) + (((Gauge (p,C)) * (p9,s)) .. (Lower_Seq (p,C)))) -' 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
0 + (Index (((Gauge (p,C)) * (p9,s)),(Lower_Seq (p,C)))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(len (Lower_Seq (p,C))) -' (Index (((Gauge (p,C)) * (p9,s)),(Lower_Seq (p,C)))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(Index (ii2,c1)) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
((len (Lower_Seq (p,C))) -' (Index (((Gauge (p,C)) * (p9,s)),(Lower_Seq (p,C))))) - 1 is V11() real ext-real Element of REAL
((len (Lower_Seq (p,C))) -' (Index (((Gauge (p,C)) * (p9,s)),(Lower_Seq (p,C))))) + (- 1) is V11() real ext-real set
((len (Lower_Seq (p,C))) - (Index (((Gauge (p,C)) * (p9,s)),(Lower_Seq (p,C))))) - 1 is V11() real ext-real Element of REAL
((len (Lower_Seq (p,C))) - (Index (((Gauge (p,C)) * (p9,s)),(Lower_Seq (p,C))))) + (- 1) is V11() real ext-real set
(len (Lower_Seq (p,C))) - (((Gauge (p,C)) * (p9,s)) .. (Lower_Seq (p,C))) is V11() real ext-real Element of REAL
- (((Gauge (p,C)) * (p9,s)) .. (Lower_Seq (p,C))) is V11() real ext-real non positive set
(len (Lower_Seq (p,C))) + (- (((Gauge (p,C)) * (p9,s)) .. (Lower_Seq (p,C)))) is V11() real ext-real set
(len (Lower_Seq (p,C))) -' (((Gauge (p,C)) * (p9,s)) .. (Lower_Seq (p,C))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
((len (Lower_Seq (p,C))) -' (((Gauge (p,C)) * (p9,s)) .. (Lower_Seq (p,C)))) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
LSeg ((mid ((Lower_Seq (p,C)),(((Gauge (p,C)) * (p9,s)) .. (Lower_Seq (p,C))),(len (Lower_Seq (p,C))))),(Index (ii2,c1))) is functional Element of K6( the carrier of (TOP-REAL 2))
LSeg ((Lower_Seq (p,C)),(((Index (ii2,c1)) + (((Gauge (p,C)) * (p9,s)) .. (Lower_Seq (p,C)))) -' 1)) is functional Element of K6( the carrier of (TOP-REAL 2))
(1 + 1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
((1 + 1) + 1) - 1 is V11() real ext-real Element of REAL
((1 + 1) + 1) + (- 1) is V11() real ext-real set
((Index (ii2,c1)) + (((Gauge (p,C)) * (p9,s)) .. (Lower_Seq (p,C)))) - 1 is V11() real ext-real Element of REAL
((Index (ii2,c1)) + (((Gauge (p,C)) * (p9,s)) .. (Lower_Seq (p,C)))) + (- 1) is V11() real ext-real set
(LSeg ((Lower_Seq (p,C)),1)) /\ (LSeg ((Lower_Seq (p,C)),(((Index (ii2,c1)) + (((Gauge (p,C)) * (p9,s)) .. (Lower_Seq (p,C)))) -' 1))) is functional Element of K6( the carrier of (TOP-REAL 2))
(Lower_Seq (p,C)) /. 2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
{((Lower_Seq (p,C)) /. 2)} is non empty trivial functional V35(1) set
ii2 .. (Lower_Seq (p,C)) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(Gauge (p,C)) * ((len (Gauge (p,C))),s) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * ((len (Gauge (p,C))),s)) `1 is V11() real ext-real Element of REAL
(L~ d1) ` is non empty functional Element of K6( the carrier of (TOP-REAL 2))
d2 is functional Element of K6( the carrier of (TOP-REAL 2))
UBD (L~ d1) is non empty functional open connected Element of K6( the carrier of (TOP-REAL 2))
LeftComp d1 is non empty functional Element of K6( the carrier of (TOP-REAL 2))
C is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
p is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
Gauge (p,C) is V15() non empty-yielding V18( NAT ) V19(K307( the carrier of (TOP-REAL 2))) Function-like V28() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K307( the carrier of (TOP-REAL 2))
len (Gauge (p,C)) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
width (Gauge (p,C)) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
Upper_Seq (p,C) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V28() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
L~ (Upper_Seq (p,C)) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
Lower_Seq (p,C) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V28() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
L~ (Lower_Seq (p,C)) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
Lower_Arc p is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
p9 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
r is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
s is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(Gauge (p,C)) * (p9,r) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(Gauge (p,C)) * (p9,s) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,s))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,s)))) /\ (L~ (Upper_Seq (p,C))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
{((Gauge (p,C)) * (p9,r))} is non empty trivial functional V35(1) set
(LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,s)))) /\ (L~ (Lower_Seq (p,C))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
{((Gauge (p,C)) * (p9,s))} is non empty trivial functional V35(1) set
Cage (p,C) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like non constant V28() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the carrier of (TOP-REAL 2)
L~ (Cage (p,C)) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
W-min (L~ (Cage (p,C))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
W-bound (L~ (Cage (p,C))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (p,C))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ (Cage (p,C))) is V15() V18( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))), REAL ) V212((TOP-REAL 2) | (L~ (Cage (p,C)))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))),REAL))
the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))) is set
K7( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))),REAL)) is non empty set
lower_bound (proj1 | (L~ (Cage (p,C)))) is V11() real ext-real Element of REAL
(proj1 | (L~ (Cage (p,C)))) .: the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))) is Element of K6(REAL)
lower_bound ((proj1 | (L~ (Cage (p,C)))) .: the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C))))) is V11() real ext-real Element of REAL
W-most (L~ (Cage (p,C))) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
SW-corner (L~ (Cage (p,C))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
S-bound (L~ (Cage (p,C))) is V11() real ext-real Element of REAL
proj2 | (L~ (Cage (p,C))) is V15() V18( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))), REAL ) V212((TOP-REAL 2) | (L~ (Cage (p,C)))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))),REAL))
lower_bound (proj2 | (L~ (Cage (p,C)))) is V11() real ext-real Element of REAL
(proj2 | (L~ (Cage (p,C)))) .: the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))) is Element of K6(REAL)
lower_bound ((proj2 | (L~ (Cage (p,C)))) .: the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Cage (p,C)))),(S-bound (L~ (Cage (p,C))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
NW-corner (L~ (Cage (p,C))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
N-bound (L~ (Cage (p,C))) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ (Cage (p,C)))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (L~ (Cage (p,C)))) .: the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Cage (p,C)))),(N-bound (L~ (Cage (p,C))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (p,C)))),(NW-corner (L~ (Cage (p,C))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner (L~ (Cage (p,C)))),(NW-corner (L~ (Cage (p,C)))))) /\ (L~ (Cage (p,C))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (W-most (L~ (Cage (p,C)))) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Cage (p,C)))) is V15() V18( the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C)))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C))))), REAL ) V212((TOP-REAL 2) | (W-most (L~ (Cage (p,C))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C))))),REAL))
the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C))))) is set
K7( the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C))))),REAL)) is non empty set
lower_bound (proj2 | (W-most (L~ (Cage (p,C))))) is V11() real ext-real Element of REAL
(proj2 | (W-most (L~ (Cage (p,C))))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C))))) is Element of K6(REAL)
lower_bound ((proj2 | (W-most (L~ (Cage (p,C))))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C)))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Cage (p,C)))),(lower_bound (proj2 | (W-most (L~ (Cage (p,C))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
E-max (L~ (Cage (p,C))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
E-bound (L~ (Cage (p,C))) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ (Cage (p,C)))) is V11() real ext-real Element of REAL
upper_bound ((proj1 | (L~ (Cage (p,C)))) .: the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C))))) is V11() real ext-real Element of REAL
E-most (L~ (Cage (p,C))) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
SE-corner (L~ (Cage (p,C))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
|[(E-bound (L~ (Cage (p,C)))),(S-bound (L~ (Cage (p,C))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
NE-corner (L~ (Cage (p,C))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
|[(E-bound (L~ (Cage (p,C)))),(N-bound (L~ (Cage (p,C))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Cage (p,C)))),(NE-corner (L~ (Cage (p,C))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SE-corner (L~ (Cage (p,C)))),(NE-corner (L~ (Cage (p,C)))))) /\ (L~ (Cage (p,C))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (E-most (L~ (Cage (p,C)))) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Cage (p,C)))) is V15() V18( the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (p,C)))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (p,C))))), REAL ) V212((TOP-REAL 2) | (E-most (L~ (Cage (p,C))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (p,C))))),REAL))
the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (p,C))))) is set
K7( the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (p,C))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (p,C))))),REAL)) is non empty set
upper_bound (proj2 | (E-most (L~ (Cage (p,C))))) is V11() real ext-real Element of REAL
(proj2 | (E-most (L~ (Cage (p,C))))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (p,C))))) is Element of K6(REAL)
upper_bound ((proj2 | (E-most (L~ (Cage (p,C))))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (p,C)))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Cage (p,C)))),(upper_bound (proj2 | (E-most (L~ (Cage (p,C))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
[p9,s] is set
{p9,s} is non empty set
{p9} is non empty trivial V35(1) set
{{p9,s},{p9}} is non empty set
Indices (Gauge (p,C)) is set
[p9,r] is set
{p9,r} is non empty set
{{p9,r},{p9}} is non empty set
L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s))) is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
R_Cut ((Upper_Seq (p,C)),((Gauge (p,C)) * (p9,r))) is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len (Upper_Seq (p,C)) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
dom (Upper_Seq (p,C)) is non trivial Element of K6(NAT)
(Upper_Seq (p,C)) . 1 is V15() Function-like set
(Upper_Seq (p,C)) /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(W-min (L~ (Cage (p,C)))) `1 is V11() real ext-real Element of REAL
(Gauge (p,C)) * (1,r) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * (1,r)) `1 is V11() real ext-real Element of REAL
[1,r] is set
{1,r} is non empty set
{{1,r},{1}} is non empty set
1 + 2 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
len (Lower_Seq (p,C)) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
dom (Lower_Seq (p,C)) is non trivial Element of K6(NAT)
(Lower_Seq (p,C)) . (len (Lower_Seq (p,C))) is V15() Function-like set
(Lower_Seq (p,C)) /. (len (Lower_Seq (p,C))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
[(len (Gauge (p,C))),r] is set
{(len (Gauge (p,C))),r} is non empty set
{(len (Gauge (p,C)))} is non empty trivial V35(1) set
{{(len (Gauge (p,C))),r},{(len (Gauge (p,C)))}} is non empty set
(Lower_Seq (p,C)) . 1 is V15() Function-like set
(Lower_Seq (p,C)) /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(E-max (L~ (Cage (p,C)))) `1 is V11() real ext-real Element of REAL
(Gauge (p,C)) * ((len (Gauge (p,C))),r) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * ((len (Gauge (p,C))),r)) `1 is V11() real ext-real Element of REAL
1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
p19 is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V28() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
len p19 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
rng (Upper_Seq (p,C)) is functional Element of K6( the carrier of (TOP-REAL 2))
f is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V28() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
len f is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
rng (Lower_Seq (p,C)) is functional Element of K6( the carrier of (TOP-REAL 2))
i1 is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one non constant V28() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq s.c.c. FinSequence of the carrier of (TOP-REAL 2)
len i1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
dom i1 is non trivial Element of K6(NAT)
i1 /. (len i1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
i1 . (len i1) is V15() Function-like set
c1 is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one non constant V28() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq s.c.c. FinSequence of the carrier of (TOP-REAL 2)
len c1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
dom c1 is non trivial Element of K6(NAT)
c1 /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
c1 . 1 is V15() Function-like set
(len i1) - 1 is V11() real ext-real Element of REAL
- 1 is V11() real ext-real non positive set
(len i1) + (- 1) is V11() real ext-real set
c2 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
c2 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
(len i1) -' 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
LSeg (i1,c2) is functional Element of K6( the carrier of (TOP-REAL 2))
L~ i1 is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(LSeg (i1,c2)) /\ (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,s)))) is functional Element of K6( the carrier of (TOP-REAL 2))
i1 /. c2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((i1 /. c2),((Gauge (p,C)) * (p9,r))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
ii1 is set
LSeg (c1,1) is functional Element of K6( the carrier of (TOP-REAL 2))
L~ c1 is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(LSeg (c1,1)) /\ (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,s)))) is functional Element of K6( the carrier of (TOP-REAL 2))
c1 /. (1 + 1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg (((Gauge (p,C)) * (p9,s)),(c1 /. (1 + 1))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
ii1 is set
(LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,s)))) /\ (LSeg (c1,1)) is functional Element of K6( the carrier of (TOP-REAL 2))
i1 /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
c1 /. (len c1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
rng i1 is non trivial functional Element of K6( the carrier of (TOP-REAL 2))
rng c1 is non trivial functional Element of K6( the carrier of (TOP-REAL 2))
{(i1 /. 1)} is non empty trivial functional V35(1) set
(L~ i1) /\ (L~ c1) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
ii1 is set
[(len (Gauge (p,C))),s] is set
{(len (Gauge (p,C))),s} is non empty set
{{(len (Gauge (p,C))),s},{(len (Gauge (p,C)))}} is non empty set
ii1 is set
(L~ (Upper_Seq (p,C))) /\ (L~ (Lower_Seq (p,C))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
{(W-min (L~ (Cage (p,C)))),(E-max (L~ (Cage (p,C))))} is non empty functional set
(Gauge (p,C)) * ((len (Gauge (p,C))),s) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * ((len (Gauge (p,C))),s)) `1 is V11() real ext-real Element of REAL
i1 /. 2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * (p9,r)) `1 is V11() real ext-real Element of REAL
((Gauge (p,C)) * (p9,r)) .. (Upper_Seq (p,C)) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
mid ((Upper_Seq (p,C)),1,(((Gauge (p,C)) * (p9,r)) .. (Upper_Seq (p,C)))) is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
(Upper_Seq (p,C)) | (((Gauge (p,C)) * (p9,r)) .. (Upper_Seq (p,C))) is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V28() FinSequence-like FinSubsequence-like special unfolded s.n.c. FinSequence of the carrier of (TOP-REAL 2)
(Upper_Seq (p,C)) /. 2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
<*((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,s))*> is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() V35(2) FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
p2 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
dom <*((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,s))*> is non trivial V35(2) Element of K6(NAT)
<*((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,s))*> /. p2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(Gauge (p,C)) * (p9,1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * (p9,1)) `1 is V11() real ext-real Element of REAL
((Gauge (p,C)) * (p9,s)) `1 is V11() real ext-real Element of REAL
L~ <*((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,s))*> is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
<*((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,s))*> /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
len <*((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,s))*> is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
<*((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,s))*> /. (len <*((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,s))*>) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
p2 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ p2 is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
p2 /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
len p2 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
p2 /. (len p2) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
p2 is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V28() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
i1 ^' p2 is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
(i1 ^' p2) ^' c1 is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len (Cage (p,C)) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like non constant V28() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the carrier of (TOP-REAL 2)
len (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
len (i1 ^' p2) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
1 + 0 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
len ((i1 ^' p2) ^' c1) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
p2 /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(i1 ^' p2) /. (len (i1 ^' p2)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
<*((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,s))*> /. 2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg (p2,1) is functional Element of K6( the carrier of (TOP-REAL 2))
LSeg (i1,((len i1) -' 1)) is functional Element of K6( the carrier of (TOP-REAL 2))
(LSeg (i1,((len i1) -' 1))) /\ (LSeg (p2,1)) is functional Element of K6( the carrier of (TOP-REAL 2))
len p2 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
(LSeg (i1,c2)) /\ (LSeg (p2,1)) is functional Element of K6( the carrier of (TOP-REAL 2))
g is set
{(i1 /. (len i1))} is non empty trivial functional V35(1) set
2 + 0 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
(len p2) - 2 is V11() real ext-real Element of REAL
(len p2) + (- 2) is V11() real ext-real set
(len (i1 ^' p2)) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
((len (i1 ^' p2)) + 1) - 1 is V11() real ext-real Element of REAL
((len (i1 ^' p2)) + 1) + (- 1) is V11() real ext-real set
(len i1) + (len p2) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
((len i1) + (len p2)) - 1 is V11() real ext-real Element of REAL
((len i1) + (len p2)) + (- 1) is V11() real ext-real set
(len (i1 ^' p2)) - 1 is V11() real ext-real Element of REAL
(len (i1 ^' p2)) + (- 1) is V11() real ext-real set
(len i1) + ((len p2) - 2) is V11() real ext-real Element of REAL
(len p2) -' 2 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(len i1) + ((len p2) -' 2) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
(len (i1 ^' p2)) -' 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(len p2) - 1 is V11() real ext-real Element of REAL
(len p2) + (- 1) is V11() real ext-real set
(len p2) -' 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
((len p2) -' 2) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
((len p2) - 2) + 1 is V11() real ext-real Element of REAL
((len p2) - 1) + 1 is V11() real ext-real Element of REAL
LSeg (p2,((len p2) -' 1)) is functional Element of K6( the carrier of (TOP-REAL 2))
(LSeg (p2,((len p2) -' 1))) /\ (LSeg (c1,1)) is functional Element of K6( the carrier of (TOP-REAL 2))
g is set
((len p2) -' 1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
p2 /. (((len p2) -' 1) + 1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((i1 ^' p2),((len i1) + ((len p2) -' 2))) is functional Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((i1 ^' p2),((len i1) + ((len p2) -' 2)))) /\ (LSeg (c1,1)) is functional Element of K6( the carrier of (TOP-REAL 2))
{((i1 ^' p2) /. (len (i1 ^' p2)))} is non empty trivial functional V35(1) set
rng p2 is functional Element of K6( the carrier of (TOP-REAL 2))
L~ p2 is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
{(p2 /. 1)} is non empty trivial functional V35(1) set
(L~ i1) /\ (L~ p2) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
g is set
g is set
(L~ p2) /\ (L~ (Upper_Seq (p,C))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(rng i1) /\ (rng p2) is functional Element of K6( the carrier of (TOP-REAL 2))
p2 /. (len p2) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
{(p2 /. (len p2))} is non empty trivial functional V35(1) set
(L~ c1) /\ (L~ p2) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
g is set
g is set
(L~ p2) /\ (L~ (Lower_Seq (p,C))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
L~ (i1 ^' p2) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(L~ (i1 ^' p2)) /\ (L~ c1) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(L~ i1) \/ (L~ p2) is non empty functional Element of K6( the carrier of (TOP-REAL 2))
((L~ i1) \/ (L~ p2)) /\ (L~ c1) is functional Element of K6( the carrier of (TOP-REAL 2))
{(c1 /. 1)} is non empty trivial functional V35(1) set
{(i1 /. 1)} \/ {(c1 /. 1)} is non empty set
(i1 ^' p2) /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
{((i1 ^' p2) /. 1)} is non empty trivial functional V35(1) set
{((i1 ^' p2) /. 1)} \/ {(c1 /. 1)} is non empty set
{((i1 ^' p2) /. 1),(c1 /. 1)} is non empty functional set
E-max p is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
E-bound p is V11() real ext-real Element of REAL
(TOP-REAL 2) | p is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | p is V15() V18( the carrier of ((TOP-REAL 2) | p)) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | p), REAL ) V212((TOP-REAL 2) | p) Element of K6(K7( the carrier of ((TOP-REAL 2) | p),REAL))
the carrier of ((TOP-REAL 2) | p) is set
K7( the carrier of ((TOP-REAL 2) | p),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | p),REAL)) is non empty set
upper_bound (proj1 | p) is V11() real ext-real Element of REAL
(proj1 | p) .: the carrier of ((TOP-REAL 2) | p) is Element of K6(REAL)
upper_bound ((proj1 | p) .: the carrier of ((TOP-REAL 2) | p)) is V11() real ext-real Element of REAL
E-most p is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
SE-corner p is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
S-bound p is V11() real ext-real Element of REAL
proj2 | p is V15() V18( the carrier of ((TOP-REAL 2) | p)) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | p), REAL ) V212((TOP-REAL 2) | p) Element of K6(K7( the carrier of ((TOP-REAL 2) | p),REAL))
lower_bound (proj2 | p) is V11() real ext-real Element of REAL
(proj2 | p) .: the carrier of ((TOP-REAL 2) | p) is Element of K6(REAL)
lower_bound ((proj2 | p) .: the carrier of ((TOP-REAL 2) | p)) is V11() real ext-real Element of REAL
|[(E-bound p),(S-bound p)]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
NE-corner p is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
N-bound p is V11() real ext-real Element of REAL
upper_bound (proj2 | p) is V11() real ext-real Element of REAL
upper_bound ((proj2 | p) .: the carrier of ((TOP-REAL 2) | p)) is V11() real ext-real Element of REAL
|[(E-bound p),(N-bound p)]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner p),(NE-corner p)) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SE-corner p),(NE-corner p))) /\ p is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (E-most p) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (E-most p) is V15() V18( the carrier of ((TOP-REAL 2) | (E-most p))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (E-most p)), REAL ) V212((TOP-REAL 2) | (E-most p)) Element of K6(K7( the carrier of ((TOP-REAL 2) | (E-most p)),REAL))
the carrier of ((TOP-REAL 2) | (E-most p)) is set
K7( the carrier of ((TOP-REAL 2) | (E-most p)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (E-most p)),REAL)) is non empty set
upper_bound (proj2 | (E-most p)) is V11() real ext-real Element of REAL
(proj2 | (E-most p)) .: the carrier of ((TOP-REAL 2) | (E-most p)) is Element of K6(REAL)
upper_bound ((proj2 | (E-most p)) .: the carrier of ((TOP-REAL 2) | (E-most p))) is V11() real ext-real Element of REAL
|[(E-bound p),(upper_bound (proj2 | (E-most p)))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
W-min p is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
W-bound p is V11() real ext-real Element of REAL
lower_bound (proj1 | p) is V11() real ext-real Element of REAL
lower_bound ((proj1 | p) .: the carrier of ((TOP-REAL 2) | p)) is V11() real ext-real Element of REAL
W-most p is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
SW-corner p is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
|[(W-bound p),(S-bound p)]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
NW-corner p is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
|[(W-bound p),(N-bound p)]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner p),(NW-corner p)) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner p),(NW-corner p))) /\ p is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (W-most p) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (W-most p) is V15() V18( the carrier of ((TOP-REAL 2) | (W-most p))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (W-most p)), REAL ) V212((TOP-REAL 2) | (W-most p)) Element of K6(K7( the carrier of ((TOP-REAL 2) | (W-most p)),REAL))
the carrier of ((TOP-REAL 2) | (W-most p)) is set
K7( the carrier of ((TOP-REAL 2) | (W-most p)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (W-most p)),REAL)) is non empty set
lower_bound (proj2 | (W-most p)) is V11() real ext-real Element of REAL
(proj2 | (W-most p)) .: the carrier of ((TOP-REAL 2) | (W-most p)) is Element of K6(REAL)
lower_bound ((proj2 | (W-most p)) .: the carrier of ((TOP-REAL 2) | (W-most p))) is V11() real ext-real Element of REAL
|[(W-bound p),(lower_bound (proj2 | (W-most p)))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
rng (Cage (p,C)) is non trivial functional Element of K6( the carrier of (TOP-REAL 2))
(Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))) /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
W-max (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
W-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V15() V18( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))), REAL ) V212((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),REAL))
the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is set
K7( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),REAL)) is non empty set
lower_bound (proj1 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is V11() real ext-real Element of REAL
(proj1 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) .: the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is Element of K6(REAL)
lower_bound ((proj1 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) .: the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is V11() real ext-real Element of REAL
W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
SW-corner (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
S-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V11() real ext-real Element of REAL
proj2 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V15() V18( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))), REAL ) V212((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),REAL))
lower_bound (proj2 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is V11() real ext-real Element of REAL
(proj2 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) .: the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is Element of K6(REAL)
lower_bound ((proj2 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) .: the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),(S-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
NW-corner (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
N-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) .: the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),(N-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),(NW-corner (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),(NW-corner (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))))) /\ (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is V15() V18( the carrier of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))), REAL ) V212((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))),REAL))
the carrier of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is set
K7( the carrier of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))),REAL)) is non empty set
upper_bound (proj2 | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is V11() real ext-real Element of REAL
(proj2 | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is Element of K6(REAL)
upper_bound ((proj2 | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),(upper_bound (proj2 | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(W-max (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) .. (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
N-min (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
NE-corner (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
E-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is V11() real ext-real Element of REAL
upper_bound ((proj1 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) .: the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),(N-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((NW-corner (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),(NE-corner (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((NW-corner (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),(NE-corner (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))))) /\ (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is V15() V18( the carrier of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))), REAL ) V212((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))),REAL))
the carrier of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is set
K7( the carrier of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))),REAL)) is non empty set
lower_bound (proj1 | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is V11() real ext-real Element of REAL
(proj1 | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is Element of K6(REAL)
lower_bound ((proj1 | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))))),(N-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(N-min (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) .. (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
N-max (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
upper_bound (proj1 | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is V11() real ext-real Element of REAL
upper_bound ((proj1 | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))))) is V11() real ext-real Element of REAL
|[(upper_bound (proj1 | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))))),(N-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(N-max (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) .. (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(E-max (L~ (Cage (p,C)))) .. (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
g is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like non constant V28() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard FinSequence of the carrier of (TOP-REAL 2)
right_cell (g,1,(Gauge (p,C))) is functional Element of K6( the carrier of (TOP-REAL 2))
L~ g is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
(right_cell (g,1,(Gauge (p,C)))) \ (L~ g) is functional Element of K6( the carrier of (TOP-REAL 2))
RightComp g is non empty functional Element of K6( the carrier of (TOP-REAL 2))
(L~ (i1 ^' p2)) \/ (L~ c1) is non empty functional Element of K6( the carrier of (TOP-REAL 2))
((L~ i1) \/ (L~ p2)) \/ (L~ c1) is non empty functional Element of K6( the carrier of (TOP-REAL 2))
(L~ (Upper_Seq (p,C))) \/ (L~ (Lower_Seq (p,C))) is non empty functional Element of K6( the carrier of (TOP-REAL 2))
right_cell ((Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))),1) is functional Element of K6( the carrier of (TOP-REAL 2))
GoB (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))) is V15() non empty-yielding V18( NAT ) V19(K307( the carrier of (TOP-REAL 2))) Function-like V28() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K307( the carrier of (TOP-REAL 2))
right_cell ((Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))),1,(GoB (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is functional Element of K6( the carrier of (TOP-REAL 2))
GoB (Cage (p,C)) is V15() non empty-yielding V18( NAT ) V19(K307( the carrier of (TOP-REAL 2))) Function-like V28() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K307( the carrier of (TOP-REAL 2))
right_cell ((Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))),1,(GoB (Cage (p,C)))) is functional Element of K6( the carrier of (TOP-REAL 2))
right_cell ((Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))),1,(Gauge (p,C))) is functional Element of K6( the carrier of (TOP-REAL 2))
(Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))) -: (E-max (L~ (Cage (p,C)))) is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like special unfolded FinSequence of the carrier of (TOP-REAL 2)
right_cell (((Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))) -: (E-max (L~ (Cage (p,C))))),1,(Gauge (p,C))) is functional Element of K6( the carrier of (TOP-REAL 2))
right_cell ((Upper_Seq (p,C)),1,(Gauge (p,C))) is functional Element of K6( the carrier of (TOP-REAL 2))
right_cell ((R_Cut ((Upper_Seq (p,C)),((Gauge (p,C)) * (p9,r)))),1,(Gauge (p,C))) is functional Element of K6( the carrier of (TOP-REAL 2))
right_cell ((i1 ^' p2),1,(Gauge (p,C))) is functional Element of K6( the carrier of (TOP-REAL 2))
g /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
g /. 2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(i1 ^' p2) /. 2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(Upper_Seq (p,C)) ^' (Lower_Seq (p,C)) is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
((Upper_Seq (p,C)) ^' (Lower_Seq (p,C))) /. 2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))) /. 2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(L~ i1) \/ (L~ c1) is non empty functional Element of K6( the carrier of (TOP-REAL 2))
W-min ((L~ i1) \/ (L~ c1)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
W-bound ((L~ i1) \/ (L~ c1)) is V11() real ext-real Element of REAL
(TOP-REAL 2) | ((L~ i1) \/ (L~ c1)) is strict T_2 SubSpace of TOP-REAL 2
proj1 | ((L~ i1) \/ (L~ c1)) is V15() V18( the carrier of ((TOP-REAL 2) | ((L~ i1) \/ (L~ c1)))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | ((L~ i1) \/ (L~ c1))), REAL ) V212((TOP-REAL 2) | ((L~ i1) \/ (L~ c1))) Element of K6(K7( the carrier of ((TOP-REAL 2) | ((L~ i1) \/ (L~ c1))),REAL))
the carrier of ((TOP-REAL 2) | ((L~ i1) \/ (L~ c1))) is set
K7( the carrier of ((TOP-REAL 2) | ((L~ i1) \/ (L~ c1))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | ((L~ i1) \/ (L~ c1))),REAL)) is non empty set
lower_bound (proj1 | ((L~ i1) \/ (L~ c1))) is V11() real ext-real Element of REAL
(proj1 | ((L~ i1) \/ (L~ c1))) .: the carrier of ((TOP-REAL 2) | ((L~ i1) \/ (L~ c1))) is Element of K6(REAL)
lower_bound ((proj1 | ((L~ i1) \/ (L~ c1))) .: the carrier of ((TOP-REAL 2) | ((L~ i1) \/ (L~ c1)))) is V11() real ext-real Element of REAL
W-most ((L~ i1) \/ (L~ c1)) is functional Element of K6( the carrier of (TOP-REAL 2))
SW-corner ((L~ i1) \/ (L~ c1)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
S-bound ((L~ i1) \/ (L~ c1)) is V11() real ext-real Element of REAL
proj2 | ((L~ i1) \/ (L~ c1)) is V15() V18( the carrier of ((TOP-REAL 2) | ((L~ i1) \/ (L~ c1)))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | ((L~ i1) \/ (L~ c1))), REAL ) V212((TOP-REAL 2) | ((L~ i1) \/ (L~ c1))) Element of K6(K7( the carrier of ((TOP-REAL 2) | ((L~ i1) \/ (L~ c1))),REAL))
lower_bound (proj2 | ((L~ i1) \/ (L~ c1))) is V11() real ext-real Element of REAL
(proj2 | ((L~ i1) \/ (L~ c1))) .: the carrier of ((TOP-REAL 2) | ((L~ i1) \/ (L~ c1))) is Element of K6(REAL)
lower_bound ((proj2 | ((L~ i1) \/ (L~ c1))) .: the carrier of ((TOP-REAL 2) | ((L~ i1) \/ (L~ c1)))) is V11() real ext-real Element of REAL
|[(W-bound ((L~ i1) \/ (L~ c1))),(S-bound ((L~ i1) \/ (L~ c1)))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
NW-corner ((L~ i1) \/ (L~ c1)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
N-bound ((L~ i1) \/ (L~ c1)) is V11() real ext-real Element of REAL
upper_bound (proj2 | ((L~ i1) \/ (L~ c1))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | ((L~ i1) \/ (L~ c1))) .: the carrier of ((TOP-REAL 2) | ((L~ i1) \/ (L~ c1)))) is V11() real ext-real Element of REAL
|[(W-bound ((L~ i1) \/ (L~ c1))),(N-bound ((L~ i1) \/ (L~ c1)))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner ((L~ i1) \/ (L~ c1))),(NW-corner ((L~ i1) \/ (L~ c1)))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner ((L~ i1) \/ (L~ c1))),(NW-corner ((L~ i1) \/ (L~ c1))))) /\ ((L~ i1) \/ (L~ c1)) is functional Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (W-most ((L~ i1) \/ (L~ c1))) is strict T_2 SubSpace of TOP-REAL 2
proj2 | (W-most ((L~ i1) \/ (L~ c1))) is V15() V18( the carrier of ((TOP-REAL 2) | (W-most ((L~ i1) \/ (L~ c1))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (W-most ((L~ i1) \/ (L~ c1)))), REAL ) V212((TOP-REAL 2) | (W-most ((L~ i1) \/ (L~ c1)))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (W-most ((L~ i1) \/ (L~ c1)))),REAL))
the carrier of ((TOP-REAL 2) | (W-most ((L~ i1) \/ (L~ c1)))) is set
K7( the carrier of ((TOP-REAL 2) | (W-most ((L~ i1) \/ (L~ c1)))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (W-most ((L~ i1) \/ (L~ c1)))),REAL)) is non empty set
lower_bound (proj2 | (W-most ((L~ i1) \/ (L~ c1)))) is V11() real ext-real Element of REAL
(proj2 | (W-most ((L~ i1) \/ (L~ c1)))) .: the carrier of ((TOP-REAL 2) | (W-most ((L~ i1) \/ (L~ c1)))) is Element of K6(REAL)
lower_bound ((proj2 | (W-most ((L~ i1) \/ (L~ c1)))) .: the carrier of ((TOP-REAL 2) | (W-most ((L~ i1) \/ (L~ c1))))) is V11() real ext-real Element of REAL
|[(W-bound ((L~ i1) \/ (L~ c1))),(lower_bound (proj2 | (W-most ((L~ i1) \/ (L~ c1)))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(W-min ((L~ i1) \/ (L~ c1))) `1 is V11() real ext-real Element of REAL
W-bound (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,s)))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,s)))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,s)))) is V15() V18( the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,s)))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,s))))), REAL ) V212((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,s))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,s))))),REAL))
the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,s))))) is set
K7( the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,s))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,s))))),REAL)) is non empty set
lower_bound (proj1 | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,s))))) is V11() real ext-real Element of REAL
(proj1 | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,s))))) .: the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,s))))) is Element of K6(REAL)
lower_bound ((proj1 | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,s))))) .: the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,s)))))) is V11() real ext-real Element of REAL
W-bound (L~ p2) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ p2) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ p2) is V15() V18( the carrier of ((TOP-REAL 2) | (L~ p2))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ p2)), REAL ) V212((TOP-REAL 2) | (L~ p2)) Element of K6(K7( the carrier of ((TOP-REAL 2) | (L~ p2)),REAL))
the carrier of ((TOP-REAL 2) | (L~ p2)) is set
K7( the carrier of ((TOP-REAL 2) | (L~ p2)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (L~ p2)),REAL)) is non empty set
lower_bound (proj1 | (L~ p2)) is V11() real ext-real Element of REAL
(proj1 | (L~ p2)) .: the carrier of ((TOP-REAL 2) | (L~ p2)) is Element of K6(REAL)
lower_bound ((proj1 | (L~ p2)) .: the carrier of ((TOP-REAL 2) | (L~ p2))) is V11() real ext-real Element of REAL
((L~ i1) \/ (L~ c1)) \/ (L~ p2) is non empty functional Element of K6( the carrier of (TOP-REAL 2))
W-min (((L~ i1) \/ (L~ c1)) \/ (L~ p2)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
W-bound (((L~ i1) \/ (L~ c1)) \/ (L~ p2)) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (((L~ i1) \/ (L~ c1)) \/ (L~ p2)) is strict T_2 SubSpace of TOP-REAL 2
proj1 | (((L~ i1) \/ (L~ c1)) \/ (L~ p2)) is V15() V18( the carrier of ((TOP-REAL 2) | (((L~ i1) \/ (L~ c1)) \/ (L~ p2)))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (((L~ i1) \/ (L~ c1)) \/ (L~ p2))), REAL ) V212((TOP-REAL 2) | (((L~ i1) \/ (L~ c1)) \/ (L~ p2))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (((L~ i1) \/ (L~ c1)) \/ (L~ p2))),REAL))
the carrier of ((TOP-REAL 2) | (((L~ i1) \/ (L~ c1)) \/ (L~ p2))) is set
K7( the carrier of ((TOP-REAL 2) | (((L~ i1) \/ (L~ c1)) \/ (L~ p2))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (((L~ i1) \/ (L~ c1)) \/ (L~ p2))),REAL)) is non empty set
lower_bound (proj1 | (((L~ i1) \/ (L~ c1)) \/ (L~ p2))) is V11() real ext-real Element of REAL
(proj1 | (((L~ i1) \/ (L~ c1)) \/ (L~ p2))) .: the carrier of ((TOP-REAL 2) | (((L~ i1) \/ (L~ c1)) \/ (L~ p2))) is Element of K6(REAL)
lower_bound ((proj1 | (((L~ i1) \/ (L~ c1)) \/ (L~ p2))) .: the carrier of ((TOP-REAL 2) | (((L~ i1) \/ (L~ c1)) \/ (L~ p2)))) is V11() real ext-real Element of REAL
W-most (((L~ i1) \/ (L~ c1)) \/ (L~ p2)) is functional Element of K6( the carrier of (TOP-REAL 2))
SW-corner (((L~ i1) \/ (L~ c1)) \/ (L~ p2)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
S-bound (((L~ i1) \/ (L~ c1)) \/ (L~ p2)) is V11() real ext-real Element of REAL
proj2 | (((L~ i1) \/ (L~ c1)) \/ (L~ p2)) is V15() V18( the carrier of ((TOP-REAL 2) | (((L~ i1) \/ (L~ c1)) \/ (L~ p2)))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (((L~ i1) \/ (L~ c1)) \/ (L~ p2))), REAL ) V212((TOP-REAL 2) | (((L~ i1) \/ (L~ c1)) \/ (L~ p2))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (((L~ i1) \/ (L~ c1)) \/ (L~ p2))),REAL))
lower_bound (proj2 | (((L~ i1) \/ (L~ c1)) \/ (L~ p2))) is V11() real ext-real Element of REAL
(proj2 | (((L~ i1) \/ (L~ c1)) \/ (L~ p2))) .: the carrier of ((TOP-REAL 2) | (((L~ i1) \/ (L~ c1)) \/ (L~ p2))) is Element of K6(REAL)
lower_bound ((proj2 | (((L~ i1) \/ (L~ c1)) \/ (L~ p2))) .: the carrier of ((TOP-REAL 2) | (((L~ i1) \/ (L~ c1)) \/ (L~ p2)))) is V11() real ext-real Element of REAL
|[(W-bound (((L~ i1) \/ (L~ c1)) \/ (L~ p2))),(S-bound (((L~ i1) \/ (L~ c1)) \/ (L~ p2)))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
NW-corner (((L~ i1) \/ (L~ c1)) \/ (L~ p2)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
N-bound (((L~ i1) \/ (L~ c1)) \/ (L~ p2)) is V11() real ext-real Element of REAL
upper_bound (proj2 | (((L~ i1) \/ (L~ c1)) \/ (L~ p2))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (((L~ i1) \/ (L~ c1)) \/ (L~ p2))) .: the carrier of ((TOP-REAL 2) | (((L~ i1) \/ (L~ c1)) \/ (L~ p2)))) is V11() real ext-real Element of REAL
|[(W-bound (((L~ i1) \/ (L~ c1)) \/ (L~ p2))),(N-bound (((L~ i1) \/ (L~ c1)) \/ (L~ p2)))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner (((L~ i1) \/ (L~ c1)) \/ (L~ p2))),(NW-corner (((L~ i1) \/ (L~ c1)) \/ (L~ p2)))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner (((L~ i1) \/ (L~ c1)) \/ (L~ p2))),(NW-corner (((L~ i1) \/ (L~ c1)) \/ (L~ p2))))) /\ (((L~ i1) \/ (L~ c1)) \/ (L~ p2)) is functional Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (W-most (((L~ i1) \/ (L~ c1)) \/ (L~ p2))) is strict T_2 SubSpace of TOP-REAL 2
proj2 | (W-most (((L~ i1) \/ (L~ c1)) \/ (L~ p2))) is V15() V18( the carrier of ((TOP-REAL 2) | (W-most (((L~ i1) \/ (L~ c1)) \/ (L~ p2))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (W-most (((L~ i1) \/ (L~ c1)) \/ (L~ p2)))), REAL ) V212((TOP-REAL 2) | (W-most (((L~ i1) \/ (L~ c1)) \/ (L~ p2)))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (W-most (((L~ i1) \/ (L~ c1)) \/ (L~ p2)))),REAL))
the carrier of ((TOP-REAL 2) | (W-most (((L~ i1) \/ (L~ c1)) \/ (L~ p2)))) is set
K7( the carrier of ((TOP-REAL 2) | (W-most (((L~ i1) \/ (L~ c1)) \/ (L~ p2)))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (W-most (((L~ i1) \/ (L~ c1)) \/ (L~ p2)))),REAL)) is non empty set
lower_bound (proj2 | (W-most (((L~ i1) \/ (L~ c1)) \/ (L~ p2)))) is V11() real ext-real Element of REAL
(proj2 | (W-most (((L~ i1) \/ (L~ c1)) \/ (L~ p2)))) .: the carrier of ((TOP-REAL 2) | (W-most (((L~ i1) \/ (L~ c1)) \/ (L~ p2)))) is Element of K6(REAL)
lower_bound ((proj2 | (W-most (((L~ i1) \/ (L~ c1)) \/ (L~ p2)))) .: the carrier of ((TOP-REAL 2) | (W-most (((L~ i1) \/ (L~ c1)) \/ (L~ p2))))) is V11() real ext-real Element of REAL
|[(W-bound (((L~ i1) \/ (L~ c1)) \/ (L~ p2))),(lower_bound (proj2 | (W-most (((L~ i1) \/ (L~ c1)) \/ (L~ p2)))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
W-min (L~ g) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
W-bound (L~ g) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ g) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ g) is V15() V18( the carrier of ((TOP-REAL 2) | (L~ g))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ g)), REAL ) V212((TOP-REAL 2) | (L~ g)) Element of K6(K7( the carrier of ((TOP-REAL 2) | (L~ g)),REAL))
the carrier of ((TOP-REAL 2) | (L~ g)) is set
K7( the carrier of ((TOP-REAL 2) | (L~ g)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (L~ g)),REAL)) is non empty set
lower_bound (proj1 | (L~ g)) is V11() real ext-real Element of REAL
(proj1 | (L~ g)) .: the carrier of ((TOP-REAL 2) | (L~ g)) is Element of K6(REAL)
lower_bound ((proj1 | (L~ g)) .: the carrier of ((TOP-REAL 2) | (L~ g))) is V11() real ext-real Element of REAL
W-most (L~ g) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
SW-corner (L~ g) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
S-bound (L~ g) is V11() real ext-real Element of REAL
proj2 | (L~ g) is V15() V18( the carrier of ((TOP-REAL 2) | (L~ g))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ g)), REAL ) V212((TOP-REAL 2) | (L~ g)) Element of K6(K7( the carrier of ((TOP-REAL 2) | (L~ g)),REAL))
lower_bound (proj2 | (L~ g)) is V11() real ext-real Element of REAL
(proj2 | (L~ g)) .: the carrier of ((TOP-REAL 2) | (L~ g)) is Element of K6(REAL)
lower_bound ((proj2 | (L~ g)) .: the carrier of ((TOP-REAL 2) | (L~ g))) is V11() real ext-real Element of REAL
|[(W-bound (L~ g)),(S-bound (L~ g))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
NW-corner (L~ g) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
N-bound (L~ g) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ g)) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (L~ g)) .: the carrier of ((TOP-REAL 2) | (L~ g))) is V11() real ext-real Element of REAL
|[(W-bound (L~ g)),(N-bound (L~ g))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner (L~ g)),(NW-corner (L~ g))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner (L~ g)),(NW-corner (L~ g)))) /\ (L~ g) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (W-most (L~ g)) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (W-most (L~ g)) is V15() V18( the carrier of ((TOP-REAL 2) | (W-most (L~ g)))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (W-most (L~ g))), REAL ) V212((TOP-REAL 2) | (W-most (L~ g))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (W-most (L~ g))),REAL))
the carrier of ((TOP-REAL 2) | (W-most (L~ g))) is set
K7( the carrier of ((TOP-REAL 2) | (W-most (L~ g))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (W-most (L~ g))),REAL)) is non empty set
lower_bound (proj2 | (W-most (L~ g))) is V11() real ext-real Element of REAL
(proj2 | (W-most (L~ g))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ g))) is Element of K6(REAL)
lower_bound ((proj2 | (W-most (L~ g))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ g)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ g)),(lower_bound (proj2 | (W-most (L~ g))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
rng g is non trivial functional Element of K6( the carrier of (TOP-REAL 2))
dom g is non trivial Element of K6(NAT)
(g /. 2) `1 is V11() real ext-real Element of REAL
(W-min (L~ g)) `1 is V11() real ext-real Element of REAL
Rotate (g,(W-min (L~ g))) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like non constant V28() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard FinSequence of the carrier of (TOP-REAL 2)
(Rotate (g,(W-min (L~ g)))) /. 2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(Upper_Seq (p,C)) . (len (Upper_Seq (p,C))) is V15() Function-like set
(Upper_Seq (p,C)) /. (len (Upper_Seq (p,C))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
east_halfline (E-max p) is non empty functional connected V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
d2 is set
ii2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(east_halfline (E-max p)) /\ (L~ (Cage (p,C))) is functional Element of K6( the carrier of (TOP-REAL 2))
ii2 `1 is V11() real ext-real Element of REAL
d1 is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like non constant V28() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the carrier of (TOP-REAL 2)
L~ d1 is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
d2 is set
ii2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
ii2 `1 is V11() real ext-real Element of REAL
p9 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
(p9 + 1) - 1 is V11() real ext-real Element of REAL
(p9 + 1) + (- 1) is V11() real ext-real set
(len (Gauge (p,C))) - 1 is V11() real ext-real Element of REAL
(len (Gauge (p,C))) + (- 1) is V11() real ext-real set
(len (Gauge (p,C))) -' 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(Gauge (p,C)) * (((len (Gauge (p,C))) -' 1),1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * (((len (Gauge (p,C))) -' 1),1)) `1 is V11() real ext-real Element of REAL
(E-max p) `1 is V11() real ext-real Element of REAL
ii2 `2 is V11() real ext-real Element of REAL
(E-max p) `2 is V11() real ext-real Element of REAL
d2 is set
ii2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(east_halfline (E-max p)) /\ (L~ (Cage (p,C))) is functional Element of K6( the carrier of (TOP-REAL 2))
ii2 `1 is V11() real ext-real Element of REAL
(E-max p) `2 is V11() real ext-real Element of REAL
ii2 `2 is V11() real ext-real Element of REAL
Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like non constant V28() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the carrier of (TOP-REAL 2)
right_cell ((Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))),1) is functional Element of K6( the carrier of (TOP-REAL 2))
(Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))) -: (W-min (L~ (Cage (p,C)))) is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like special unfolded FinSequence of the carrier of (TOP-REAL 2)
LSeg ((Lower_Seq (p,C)),1) is functional Element of K6( the carrier of (TOP-REAL 2))
LSeg ((Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))),1) is functional Element of K6( the carrier of (TOP-REAL 2))
L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
len (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
GoB (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))) is V15() non empty-yielding V18( NAT ) V19(K307( the carrier of (TOP-REAL 2))) Function-like V28() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K307( the carrier of (TOP-REAL 2))
(Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))) /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
E-max (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
E-bound (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))) is V15() V18( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))), REAL ) V212((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))),REAL))
the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) is set
K7( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))),REAL)) is non empty set
upper_bound (proj1 | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) is V11() real ext-real Element of REAL
(proj1 | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) .: the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) is Element of K6(REAL)
upper_bound ((proj1 | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) .: the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) is V11() real ext-real Element of REAL
E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
SE-corner (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
S-bound (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))) is V11() real ext-real Element of REAL
proj2 | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))) is V15() V18( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))), REAL ) V212((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))),REAL))
lower_bound (proj2 | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) is V11() real ext-real Element of REAL
(proj2 | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) .: the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) is Element of K6(REAL)
lower_bound ((proj2 | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) .: the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))),(S-bound (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
NE-corner (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
N-bound (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) .: the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))),(N-bound (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))),(NE-corner (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SE-corner (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))),(NE-corner (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))))) /\ (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) is V15() V18( the carrier of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))), REAL ) V212((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))),REAL))
the carrier of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) is set
K7( the carrier of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))),REAL)) is non empty set
upper_bound (proj2 | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) is V11() real ext-real Element of REAL
(proj2 | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) is Element of K6(REAL)
upper_bound ((proj2 | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))),(upper_bound (proj2 | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))) /. (1 + 1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
Gij is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
Gji is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
Gji + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
[Gij,(Gji + 1)] is set
{Gij,(Gji + 1)} is non empty set
{Gij} is non empty trivial V35(1) set
{{Gij,(Gji + 1)},{Gij}} is non empty set
[Gij,Gji] is set
{Gij,Gji} is non empty set
{{Gij,Gji},{Gij}} is non empty set
(Gauge (p,C)) * (Gij,(Gji + 1)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(Gauge (p,C)) * (Gij,Gji) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
Gij9 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(Gauge (p,C)) * ((len (Gauge (p,C))),Gij9) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
[(len (Gauge (p,C))),Gij9] is set
{(len (Gauge (p,C))),Gij9} is non empty set
{{(len (Gauge (p,C))),Gij9},{(len (Gauge (p,C)))}} is non empty set
Gij + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
(Gji + 1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
Gij -' 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
cell ((Gauge (p,C)),(Gij -' 1),Gji) is functional Element of K6( the carrier of (TOP-REAL 2))
(Gij -' 1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
4 - 1 is V11() real ext-real Element of REAL
4 + (- 1) is V11() real ext-real set
Gij - 1 is V11() real ext-real Element of REAL
Gij + (- 1) is V11() real ext-real set
(Gauge (p,C)) * ((Gij -' 1),Gji) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * ((Gij -' 1),Gji)) `2 is V11() real ext-real Element of REAL
(Gauge (p,C)) * ((Gij -' 1),(Gji + 1)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * ((Gij -' 1),(Gji + 1))) `2 is V11() real ext-real Element of REAL
(Gauge (p,C)) * (1,Gji) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * (1,Gji)) `2 is V11() real ext-real Element of REAL
((Gauge (p,C)) * (Gij,Gji)) `2 is V11() real ext-real Element of REAL
(Gauge (p,C)) * (1,(Gji + 1)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * (1,(Gji + 1))) `2 is V11() real ext-real Element of REAL
((Gauge (p,C)) * (Gij,(Gji + 1))) `2 is V11() real ext-real Element of REAL
(Gauge (p,C)) * ((len (Gauge (p,C))),Gji) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * ((len (Gauge (p,C))),Gji)) `1 is V11() real ext-real Element of REAL
(Gauge (p,C)) * ((len (Gauge (p,C))),(Gji + 1)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * ((len (Gauge (p,C))),(Gji + 1))) `1 is V11() real ext-real Element of REAL
LSeg (((Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))) /. 1),((Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))) /. (1 + 1))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
Index (ii2,c1) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
LSeg (c1,(Index (ii2,c1))) is functional Element of K6( the carrier of (TOP-REAL 2))
((Gauge (p,C)) * (p9,s)) .. (Lower_Seq (p,C)) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
mid ((Lower_Seq (p,C)),(((Gauge (p,C)) * (p9,s)) .. (Lower_Seq (p,C))),(len (Lower_Seq (p,C)))) is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
Index (((Gauge (p,C)) * (p9,s)),(Lower_Seq (p,C))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(Index (((Gauge (p,C)) * (p9,s)),(Lower_Seq (p,C)))) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
Gji9 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative set
(Lower_Seq (p,C)) . Gji9 is V15() Function-like set
len (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (p9,s)))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(len (Lower_Seq (p,C))) - (Index (((Gauge (p,C)) * (p9,s)),(Lower_Seq (p,C)))) is V11() real ext-real Element of REAL
- (Index (((Gauge (p,C)) * (p9,s)),(Lower_Seq (p,C)))) is V11() real ext-real non positive set
(len (Lower_Seq (p,C))) + (- (Index (((Gauge (p,C)) * (p9,s)),(Lower_Seq (p,C))))) is V11() real ext-real set
(Index (ii2,c1)) + (((Gauge (p,C)) * (p9,s)) .. (Lower_Seq (p,C))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
((Index (ii2,c1)) + (((Gauge (p,C)) * (p9,s)) .. (Lower_Seq (p,C)))) -' 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
0 + (Index (((Gauge (p,C)) * (p9,s)),(Lower_Seq (p,C)))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(len (Lower_Seq (p,C))) -' (Index (((Gauge (p,C)) * (p9,s)),(Lower_Seq (p,C)))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(Index (ii2,c1)) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
((len (Lower_Seq (p,C))) -' (Index (((Gauge (p,C)) * (p9,s)),(Lower_Seq (p,C))))) - 1 is V11() real ext-real Element of REAL
((len (Lower_Seq (p,C))) -' (Index (((Gauge (p,C)) * (p9,s)),(Lower_Seq (p,C))))) + (- 1) is V11() real ext-real set
((len (Lower_Seq (p,C))) - (Index (((Gauge (p,C)) * (p9,s)),(Lower_Seq (p,C))))) - 1 is V11() real ext-real Element of REAL
((len (Lower_Seq (p,C))) - (Index (((Gauge (p,C)) * (p9,s)),(Lower_Seq (p,C))))) + (- 1) is V11() real ext-real set
(len (Lower_Seq (p,C))) - (((Gauge (p,C)) * (p9,s)) .. (Lower_Seq (p,C))) is V11() real ext-real Element of REAL
- (((Gauge (p,C)) * (p9,s)) .. (Lower_Seq (p,C))) is V11() real ext-real non positive set
(len (Lower_Seq (p,C))) + (- (((Gauge (p,C)) * (p9,s)) .. (Lower_Seq (p,C)))) is V11() real ext-real set
(len (Lower_Seq (p,C))) -' (((Gauge (p,C)) * (p9,s)) .. (Lower_Seq (p,C))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
((len (Lower_Seq (p,C))) -' (((Gauge (p,C)) * (p9,s)) .. (Lower_Seq (p,C)))) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
LSeg ((mid ((Lower_Seq (p,C)),(((Gauge (p,C)) * (p9,s)) .. (Lower_Seq (p,C))),(len (Lower_Seq (p,C))))),(Index (ii2,c1))) is functional Element of K6( the carrier of (TOP-REAL 2))
LSeg ((Lower_Seq (p,C)),(((Index (ii2,c1)) + (((Gauge (p,C)) * (p9,s)) .. (Lower_Seq (p,C)))) -' 1)) is functional Element of K6( the carrier of (TOP-REAL 2))
(1 + 1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
((1 + 1) + 1) - 1 is V11() real ext-real Element of REAL
((1 + 1) + 1) + (- 1) is V11() real ext-real set
((Index (ii2,c1)) + (((Gauge (p,C)) * (p9,s)) .. (Lower_Seq (p,C)))) - 1 is V11() real ext-real Element of REAL
((Index (ii2,c1)) + (((Gauge (p,C)) * (p9,s)) .. (Lower_Seq (p,C)))) + (- 1) is V11() real ext-real set
(LSeg ((Lower_Seq (p,C)),1)) /\ (LSeg ((Lower_Seq (p,C)),(((Index (ii2,c1)) + (((Gauge (p,C)) * (p9,s)) .. (Lower_Seq (p,C)))) -' 1))) is functional Element of K6( the carrier of (TOP-REAL 2))
(Lower_Seq (p,C)) /. 2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
{((Lower_Seq (p,C)) /. 2)} is non empty trivial functional V35(1) set
ii2 .. (Lower_Seq (p,C)) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(Gauge (p,C)) * ((len (Gauge (p,C))),s) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * ((len (Gauge (p,C))),s)) `1 is V11() real ext-real Element of REAL
(L~ d1) ` is non empty functional Element of K6( the carrier of (TOP-REAL 2))
d2 is functional Element of K6( the carrier of (TOP-REAL 2))
UBD (L~ d1) is non empty functional open connected Element of K6( the carrier of (TOP-REAL 2))
LeftComp d1 is non empty functional Element of K6( the carrier of (TOP-REAL 2))
C is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
p is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
Gauge (p,C) is V15() non empty-yielding V18( NAT ) V19(K307( the carrier of (TOP-REAL 2))) Function-like V28() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K307( the carrier of (TOP-REAL 2))
len (Gauge (p,C)) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
width (Gauge (p,C)) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
Cage (p,C) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like non constant V28() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the carrier of (TOP-REAL 2)
L~ (Cage (p,C)) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
Lower_Arc (L~ (Cage (p,C))) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
Upper_Arc (L~ (Cage (p,C))) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
Upper_Arc p is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
p9 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
s is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
r is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(Gauge (p,C)) * (p9,s) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(Gauge (p,C)) * (p9,r) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg (((Gauge (p,C)) * (p9,s)),((Gauge (p,C)) * (p9,r))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg (((Gauge (p,C)) * (p9,s)),((Gauge (p,C)) * (p9,r)))) /\ (Lower_Arc (L~ (Cage (p,C)))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
{((Gauge (p,C)) * (p9,r))} is non empty trivial functional V35(1) set
(LSeg (((Gauge (p,C)) * (p9,s)),((Gauge (p,C)) * (p9,r)))) /\ (Upper_Arc (L~ (Cage (p,C)))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
{((Gauge (p,C)) * (p9,s))} is non empty trivial functional V35(1) set
Lower_Seq (p,C) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V28() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
L~ (Lower_Seq (p,C)) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
Upper_Seq (p,C) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V28() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
L~ (Upper_Seq (p,C)) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
C is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
p is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
Gauge (p,C) is V15() non empty-yielding V18( NAT ) V19(K307( the carrier of (TOP-REAL 2))) Function-like V28() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K307( the carrier of (TOP-REAL 2))
len (Gauge (p,C)) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
width (Gauge (p,C)) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
Cage (p,C) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like non constant V28() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the carrier of (TOP-REAL 2)
L~ (Cage (p,C)) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
Lower_Arc (L~ (Cage (p,C))) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
Upper_Arc (L~ (Cage (p,C))) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
Lower_Arc p is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
p9 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
s is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
r is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(Gauge (p,C)) * (p9,s) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(Gauge (p,C)) * (p9,r) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg (((Gauge (p,C)) * (p9,s)),((Gauge (p,C)) * (p9,r))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg (((Gauge (p,C)) * (p9,s)),((Gauge (p,C)) * (p9,r)))) /\ (Lower_Arc (L~ (Cage (p,C)))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
{((Gauge (p,C)) * (p9,r))} is non empty trivial functional V35(1) set
(LSeg (((Gauge (p,C)) * (p9,s)),((Gauge (p,C)) * (p9,r)))) /\ (Upper_Arc (L~ (Cage (p,C)))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
{((Gauge (p,C)) * (p9,s))} is non empty trivial functional V35(1) set
Lower_Seq (p,C) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V28() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
L~ (Lower_Seq (p,C)) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
Upper_Seq (p,C) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V28() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
L~ (Upper_Seq (p,C)) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
C is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
p is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
Gauge (p,C) is V15() non empty-yielding V18( NAT ) V19(K307( the carrier of (TOP-REAL 2))) Function-like V28() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K307( the carrier of (TOP-REAL 2))
len (Gauge (p,C)) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
width (Gauge (p,C)) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
Lower_Seq (p,C) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V28() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
L~ (Lower_Seq (p,C)) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
Upper_Seq (p,C) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V28() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
L~ (Upper_Seq (p,C)) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
Upper_Arc p is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
p9 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
s is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
r is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(Gauge (p,C)) * (p9,r) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(Gauge (p,C)) * (p9,s) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg (((Gauge (p,C)) * (p9,s)),((Gauge (p,C)) * (p9,r))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
rr is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
G is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(Gauge (p,C)) * (p9,rr) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(Gauge (p,C)) * (p9,G) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (p9,G))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (p9,G)))) /\ (L~ (Upper_Seq (p,C))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
{((Gauge (p,C)) * (p9,rr))} is non empty trivial functional V35(1) set
(LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (p9,G)))) /\ (L~ (Lower_Seq (p,C))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
{((Gauge (p,C)) * (p9,G))} is non empty trivial functional V35(1) set
C is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
p is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
Gauge (p,C) is V15() non empty-yielding V18( NAT ) V19(K307( the carrier of (TOP-REAL 2))) Function-like V28() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K307( the carrier of (TOP-REAL 2))
len (Gauge (p,C)) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
width (Gauge (p,C)) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
Lower_Seq (p,C) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V28() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
L~ (Lower_Seq (p,C)) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
Upper_Seq (p,C) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V28() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
L~ (Upper_Seq (p,C)) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
Lower_Arc p is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
p9 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
s is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
r is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(Gauge (p,C)) * (p9,r) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(Gauge (p,C)) * (p9,s) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg (((Gauge (p,C)) * (p9,s)),((Gauge (p,C)) * (p9,r))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
rr is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
G is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(Gauge (p,C)) * (p9,rr) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(Gauge (p,C)) * (p9,G) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (p9,G))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (p9,G)))) /\ (L~ (Upper_Seq (p,C))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
{((Gauge (p,C)) * (p9,rr))} is non empty trivial functional V35(1) set
(LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (p9,G)))) /\ (L~ (Lower_Seq (p,C))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
{((Gauge (p,C)) * (p9,G))} is non empty trivial functional V35(1) set
C is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
p is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
Gauge (p,C) is V15() non empty-yielding V18( NAT ) V19(K307( the carrier of (TOP-REAL 2))) Function-like V28() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K307( the carrier of (TOP-REAL 2))
len (Gauge (p,C)) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
width (Gauge (p,C)) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
Cage (p,C) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like non constant V28() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the carrier of (TOP-REAL 2)
L~ (Cage (p,C)) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
Lower_Arc (L~ (Cage (p,C))) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
Upper_Arc (L~ (Cage (p,C))) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
Upper_Arc p is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
p9 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
s is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
r is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(Gauge (p,C)) * (p9,r) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(Gauge (p,C)) * (p9,s) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg (((Gauge (p,C)) * (p9,s)),((Gauge (p,C)) * (p9,r))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
Lower_Seq (p,C) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V28() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
L~ (Lower_Seq (p,C)) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
Upper_Seq (p,C) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V28() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
L~ (Upper_Seq (p,C)) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
C is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
p is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
Gauge (p,C) is V15() non empty-yielding V18( NAT ) V19(K307( the carrier of (TOP-REAL 2))) Function-like V28() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K307( the carrier of (TOP-REAL 2))
len (Gauge (p,C)) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
width (Gauge (p,C)) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
Cage (p,C) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like non constant V28() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the carrier of (TOP-REAL 2)
L~ (Cage (p,C)) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
Lower_Arc (L~ (Cage (p,C))) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
Upper_Arc (L~ (Cage (p,C))) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
Lower_Arc p is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
p9 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
s is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
r is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(Gauge (p,C)) * (p9,r) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(Gauge (p,C)) * (p9,s) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg (((Gauge (p,C)) * (p9,s)),((Gauge (p,C)) * (p9,r))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
Lower_Seq (p,C) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V28() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
L~ (Lower_Seq (p,C)) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
Upper_Seq (p,C) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V28() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
L~ (Upper_Seq (p,C)) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
C is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
p is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
Gauge (p,C) is V15() non empty-yielding V18( NAT ) V19(K307( the carrier of (TOP-REAL 2))) Function-like V28() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K307( the carrier of (TOP-REAL 2))
len (Gauge (p,C)) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
width (Gauge (p,C)) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
Upper_Seq (p,C) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V28() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
L~ (Upper_Seq (p,C)) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
Lower_Seq (p,C) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V28() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
L~ (Lower_Seq (p,C)) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
Upper_Arc p is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
p9 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
s is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
r is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
rr is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(Gauge (p,C)) * (p9,r) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(Gauge (p,C)) * (p9,rr) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(Gauge (p,C)) * (s,rr) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) is non empty functional Element of K6( the carrier of (TOP-REAL 2))
((LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))))) /\ (L~ (Upper_Seq (p,C))) is functional Element of K6( the carrier of (TOP-REAL 2))
{((Gauge (p,C)) * (p9,r))} is non empty trivial functional V35(1) set
((LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))))) /\ (L~ (Lower_Seq (p,C))) is functional Element of K6( the carrier of (TOP-REAL 2))
{((Gauge (p,C)) * (s,rr))} is non empty trivial functional V35(1) set
Cage (p,C) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like non constant V28() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the carrier of (TOP-REAL 2)
L~ (Cage (p,C)) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
W-min (L~ (Cage (p,C))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
W-bound (L~ (Cage (p,C))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (p,C))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ (Cage (p,C))) is V15() V18( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))), REAL ) V212((TOP-REAL 2) | (L~ (Cage (p,C)))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))),REAL))
the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))) is set
K7( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))),REAL)) is non empty set
lower_bound (proj1 | (L~ (Cage (p,C)))) is V11() real ext-real Element of REAL
(proj1 | (L~ (Cage (p,C)))) .: the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))) is Element of K6(REAL)
lower_bound ((proj1 | (L~ (Cage (p,C)))) .: the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C))))) is V11() real ext-real Element of REAL
W-most (L~ (Cage (p,C))) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
SW-corner (L~ (Cage (p,C))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
S-bound (L~ (Cage (p,C))) is V11() real ext-real Element of REAL
proj2 | (L~ (Cage (p,C))) is V15() V18( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))), REAL ) V212((TOP-REAL 2) | (L~ (Cage (p,C)))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))),REAL))
lower_bound (proj2 | (L~ (Cage (p,C)))) is V11() real ext-real Element of REAL
(proj2 | (L~ (Cage (p,C)))) .: the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))) is Element of K6(REAL)
lower_bound ((proj2 | (L~ (Cage (p,C)))) .: the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Cage (p,C)))),(S-bound (L~ (Cage (p,C))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
NW-corner (L~ (Cage (p,C))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
N-bound (L~ (Cage (p,C))) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ (Cage (p,C)))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (L~ (Cage (p,C)))) .: the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Cage (p,C)))),(N-bound (L~ (Cage (p,C))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (p,C)))),(NW-corner (L~ (Cage (p,C))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner (L~ (Cage (p,C)))),(NW-corner (L~ (Cage (p,C)))))) /\ (L~ (Cage (p,C))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (W-most (L~ (Cage (p,C)))) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Cage (p,C)))) is V15() V18( the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C)))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C))))), REAL ) V212((TOP-REAL 2) | (W-most (L~ (Cage (p,C))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C))))),REAL))
the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C))))) is set
K7( the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C))))),REAL)) is non empty set
lower_bound (proj2 | (W-most (L~ (Cage (p,C))))) is V11() real ext-real Element of REAL
(proj2 | (W-most (L~ (Cage (p,C))))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C))))) is Element of K6(REAL)
lower_bound ((proj2 | (W-most (L~ (Cage (p,C))))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C)))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Cage (p,C)))),(lower_bound (proj2 | (W-most (L~ (Cage (p,C))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
E-max (L~ (Cage (p,C))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
E-bound (L~ (Cage (p,C))) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ (Cage (p,C)))) is V11() real ext-real Element of REAL
upper_bound ((proj1 | (L~ (Cage (p,C)))) .: the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C))))) is V11() real ext-real Element of REAL
E-most (L~ (Cage (p,C))) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
SE-corner (L~ (Cage (p,C))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
|[(E-bound (L~ (Cage (p,C)))),(S-bound (L~ (Cage (p,C))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
NE-corner (L~ (Cage (p,C))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
|[(E-bound (L~ (Cage (p,C)))),(N-bound (L~ (Cage (p,C))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Cage (p,C)))),(NE-corner (L~ (Cage (p,C))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SE-corner (L~ (Cage (p,C)))),(NE-corner (L~ (Cage (p,C)))))) /\ (L~ (Cage (p,C))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (E-most (L~ (Cage (p,C)))) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Cage (p,C)))) is V15() V18( the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (p,C)))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (p,C))))), REAL ) V212((TOP-REAL 2) | (E-most (L~ (Cage (p,C))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (p,C))))),REAL))
the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (p,C))))) is set
K7( the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (p,C))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (p,C))))),REAL)) is non empty set
upper_bound (proj2 | (E-most (L~ (Cage (p,C))))) is V11() real ext-real Element of REAL
(proj2 | (E-most (L~ (Cage (p,C))))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (p,C))))) is Element of K6(REAL)
upper_bound ((proj2 | (E-most (L~ (Cage (p,C))))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (p,C)))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Cage (p,C)))),(upper_bound (proj2 | (E-most (L~ (Cage (p,C))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
<*((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))*> is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() V35(3) FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ <*((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))*> is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))) is non empty functional Element of K6( the carrier of (TOP-REAL 2))
[p9,r] is set
{p9,r} is non empty set
{p9} is non empty trivial V35(1) set
{{p9,r},{p9}} is non empty set
Indices (Gauge (p,C)) is set
[s,rr] is set
{s,rr} is non empty set
{s} is non empty trivial V35(1) set
{{s,rr},{s}} is non empty set
[p9,rr] is set
{p9,rr} is non empty set
{{p9,rr},{p9}} is non empty set
R_Cut ((Upper_Seq (p,C)),((Gauge (p,C)) * (p9,r))) is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (s,rr))) is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len (Upper_Seq (p,C)) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
dom (Upper_Seq (p,C)) is non trivial Element of K6(NAT)
(Upper_Seq (p,C)) . 1 is V15() Function-like set
(Upper_Seq (p,C)) /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(W-min (L~ (Cage (p,C)))) `1 is V11() real ext-real Element of REAL
(Gauge (p,C)) * (1,rr) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * (1,rr)) `1 is V11() real ext-real Element of REAL
[1,rr] is set
{1,rr} is non empty set
{{1,rr},{1}} is non empty set
[1,r] is set
{1,r} is non empty set
{{1,r},{1}} is non empty set
1 + 2 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
len (Lower_Seq (p,C)) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
dom (Lower_Seq (p,C)) is non trivial Element of K6(NAT)
(Lower_Seq (p,C)) . (len (Lower_Seq (p,C))) is V15() Function-like set
(Lower_Seq (p,C)) /. (len (Lower_Seq (p,C))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
[(len (Gauge (p,C))),rr] is set
{(len (Gauge (p,C))),rr} is non empty set
{(len (Gauge (p,C)))} is non empty trivial V35(1) set
{{(len (Gauge (p,C))),rr},{(len (Gauge (p,C)))}} is non empty set
(Lower_Seq (p,C)) . 1 is V15() Function-like set
(Lower_Seq (p,C)) /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(E-max (L~ (Cage (p,C)))) `1 is V11() real ext-real Element of REAL
(Gauge (p,C)) * ((len (Gauge (p,C))),rr) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * ((len (Gauge (p,C))),rr)) `1 is V11() real ext-real Element of REAL
1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
c2 is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V28() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
len c2 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
rng (Upper_Seq (p,C)) is functional Element of K6( the carrier of (TOP-REAL 2))
ii1 is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V28() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
len ii1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
rng (Lower_Seq (p,C)) is functional Element of K6( the carrier of (TOP-REAL 2))
jj1 is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one non constant V28() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq s.c.c. FinSequence of the carrier of (TOP-REAL 2)
len jj1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
dom jj1 is non trivial Element of K6(NAT)
jj1 /. (len jj1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
jj1 . (len jj1) is V15() Function-like set
p2 is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one non constant V28() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq s.c.c. FinSequence of the carrier of (TOP-REAL 2)
len p2 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
dom p2 is non trivial Element of K6(NAT)
p2 /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
p2 . 1 is V15() Function-like set
(len jj1) - 1 is V11() real ext-real Element of REAL
- 1 is V11() real ext-real non positive set
(len jj1) + (- 1) is V11() real ext-real set
p2 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
p2 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
(len jj1) -' 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
LSeg (jj1,p2) is functional Element of K6( the carrier of (TOP-REAL 2))
L~ jj1 is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(LSeg (jj1,p2)) /\ (L~ <*((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))*>) is functional Element of K6( the carrier of (TOP-REAL 2))
jj1 /. p2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((jj1 /. p2),((Gauge (p,C)) * (p9,r))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
p29 is set
LSeg (p2,1) is functional Element of K6( the carrier of (TOP-REAL 2))
L~ p2 is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(LSeg (p2,1)) /\ (L~ <*((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))*>) is functional Element of K6( the carrier of (TOP-REAL 2))
p2 /. (1 + 1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg (((Gauge (p,C)) * (s,rr)),(p2 /. (1 + 1))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
p29 is set
(L~ <*((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))*>) /\ (LSeg (p2,1)) is functional Element of K6( the carrier of (TOP-REAL 2))
jj1 /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
p2 /. (len p2) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
rng jj1 is non trivial functional Element of K6( the carrier of (TOP-REAL 2))
rng p2 is non trivial functional Element of K6( the carrier of (TOP-REAL 2))
{(jj1 /. 1)} is non empty trivial functional V35(1) set
(L~ jj1) /\ (L~ p2) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
p29 is set
[(len (Gauge (p,C))),r] is set
{(len (Gauge (p,C))),r} is non empty set
{{(len (Gauge (p,C))),r},{(len (Gauge (p,C)))}} is non empty set
p29 is set
(L~ (Upper_Seq (p,C))) /\ (L~ (Lower_Seq (p,C))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
{(W-min (L~ (Cage (p,C)))),(E-max (L~ (Cage (p,C))))} is non empty functional set
(Gauge (p,C)) * ((len (Gauge (p,C))),r) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * ((len (Gauge (p,C))),r)) `1 is V11() real ext-real Element of REAL
jj1 /. 2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * (p9,r)) `1 is V11() real ext-real Element of REAL
(Gauge (p,C)) * (1,r) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * (1,r)) `1 is V11() real ext-real Element of REAL
((Gauge (p,C)) * (p9,r)) .. (Upper_Seq (p,C)) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
mid ((Upper_Seq (p,C)),1,(((Gauge (p,C)) * (p9,r)) .. (Upper_Seq (p,C)))) is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
(Upper_Seq (p,C)) | (((Gauge (p,C)) * (p9,r)) .. (Upper_Seq (p,C))) is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V28() FinSequence-like FinSubsequence-like special unfolded s.n.c. FinSequence of the carrier of (TOP-REAL 2)
(Upper_Seq (p,C)) /. 2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
i2 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
dom <*((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))*> is non trivial V35(3) Element of K6(NAT)
<*((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))*> /. i2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * (p9,rr)) `1 is V11() real ext-real Element of REAL
(Gauge (p,C)) * (p9,1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * (p9,1)) `1 is V11() real ext-real Element of REAL
((Gauge (p,C)) * (p9,rr)) `2 is V11() real ext-real Element of REAL
((Gauge (p,C)) * (1,rr)) `2 is V11() real ext-real Element of REAL
((Gauge (p,C)) * (s,rr)) `2 is V11() real ext-real Element of REAL
|[(((Gauge (p,C)) * (p9,r)) `1),(((Gauge (p,C)) * (s,rr)) `2)]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * (s,rr)) `1 is V11() real ext-real Element of REAL
((Gauge (p,C)) * (p9,r)) `2 is V11() real ext-real Element of REAL
<*((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))*> /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
len <*((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))*> is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
<*((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))*> /. (len <*((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))*>) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
i2 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ i2 is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
i2 /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
len i2 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
i2 /. (len i2) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
d1 is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V28() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
jj1 ^' d1 is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
(jj1 ^' d1) ^' p2 is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
W-bound (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) is V15() V18( the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))))), REAL ) V212((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))))),REAL))
the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))))) is set
K7( the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))))),REAL)) is non empty set
lower_bound (proj1 | (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))))) is V11() real ext-real Element of REAL
(proj1 | (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))))) .: the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))))) is Element of K6(REAL)
lower_bound ((proj1 | (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))))) .: the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))))) is V11() real ext-real Element of REAL
W-bound (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))) is V15() V18( the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr))))), REAL ) V212((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr))))),REAL))
the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr))))) is set
K7( the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr))))),REAL)) is non empty set
lower_bound (proj1 | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr))))) is V11() real ext-real Element of REAL
(proj1 | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr))))) .: the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr))))) is Element of K6(REAL)
lower_bound ((proj1 | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr))))) .: the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))))) is V11() real ext-real Element of REAL
W-bound ((LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr))))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | ((LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr))))) is strict T_2 SubSpace of TOP-REAL 2
proj1 | ((LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr))))) is V15() V18( the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr))))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))))), REAL ) V212((TOP-REAL 2) | ((LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))))),REAL))
the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))))) is set
K7( the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))))),REAL)) is non empty set
lower_bound (proj1 | ((LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))))) is V11() real ext-real Element of REAL
(proj1 | ((LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))))) .: the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))))) is Element of K6(REAL)
lower_bound ((proj1 | ((LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))))) .: the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr))))))) is V11() real ext-real Element of REAL
min ((W-bound (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))))),(W-bound (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))))) is V11() real ext-real set
L~ d1 is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
W-bound (L~ d1) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ d1) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ d1) is V15() V18( the carrier of ((TOP-REAL 2) | (L~ d1))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ d1)), REAL ) V212((TOP-REAL 2) | (L~ d1)) Element of K6(K7( the carrier of ((TOP-REAL 2) | (L~ d1)),REAL))
the carrier of ((TOP-REAL 2) | (L~ d1)) is set
K7( the carrier of ((TOP-REAL 2) | (L~ d1)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (L~ d1)),REAL)) is non empty set
lower_bound (proj1 | (L~ d1)) is V11() real ext-real Element of REAL
(proj1 | (L~ d1)) .: the carrier of ((TOP-REAL 2) | (L~ d1)) is Element of K6(REAL)
lower_bound ((proj1 | (L~ d1)) .: the carrier of ((TOP-REAL 2) | (L~ d1))) is V11() real ext-real Element of REAL
len (Cage (p,C)) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like non constant V28() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the carrier of (TOP-REAL 2)
len (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
len (jj1 ^' d1) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
1 + 0 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
len ((jj1 ^' d1) ^' p2) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
d1 /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(jj1 ^' d1) /. (len (jj1 ^' d1)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
<*((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))*> /. 3 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg (d1,1) is functional Element of K6( the carrier of (TOP-REAL 2))
LSeg (jj1,((len jj1) -' 1)) is functional Element of K6( the carrier of (TOP-REAL 2))
(LSeg (jj1,((len jj1) -' 1))) /\ (LSeg (d1,1)) is functional Element of K6( the carrier of (TOP-REAL 2))
2 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
len d1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
(LSeg (jj1,p2)) /\ (LSeg (d1,1)) is functional Element of K6( the carrier of (TOP-REAL 2))
ii2 is set
{(jj1 /. (len jj1))} is non empty trivial functional V35(1) set
(len d1) - 2 is V11() real ext-real Element of REAL
(len d1) + (- 2) is V11() real ext-real set
(len (jj1 ^' d1)) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
((len (jj1 ^' d1)) + 1) - 1 is V11() real ext-real Element of REAL
((len (jj1 ^' d1)) + 1) + (- 1) is V11() real ext-real set
(len jj1) + (len d1) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
((len jj1) + (len d1)) - 1 is V11() real ext-real Element of REAL
((len jj1) + (len d1)) + (- 1) is V11() real ext-real set
(len (jj1 ^' d1)) - 1 is V11() real ext-real Element of REAL
(len (jj1 ^' d1)) + (- 1) is V11() real ext-real set
(len jj1) + ((len d1) - 2) is V11() real ext-real Element of REAL
(len d1) -' 2 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(len jj1) + ((len d1) -' 2) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
(len (jj1 ^' d1)) -' 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(len d1) - 1 is V11() real ext-real Element of REAL
(len d1) + (- 1) is V11() real ext-real set
(len d1) -' 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
((len d1) -' 2) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
((len d1) - 2) + 1 is V11() real ext-real Element of REAL
((len d1) - 1) + 1 is V11() real ext-real Element of REAL
LSeg (d1,((len d1) -' 1)) is functional Element of K6( the carrier of (TOP-REAL 2))
(LSeg (d1,((len d1) -' 1))) /\ (LSeg (p2,1)) is functional Element of K6( the carrier of (TOP-REAL 2))
ii2 is set
((len d1) -' 1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
d1 /. (((len d1) -' 1) + 1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((jj1 ^' d1),((len jj1) + ((len d1) -' 2))) is functional Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((jj1 ^' d1),((len jj1) + ((len d1) -' 2)))) /\ (LSeg (p2,1)) is functional Element of K6( the carrier of (TOP-REAL 2))
{((jj1 ^' d1) /. (len (jj1 ^' d1)))} is non empty trivial functional V35(1) set
rng d1 is functional Element of K6( the carrier of (TOP-REAL 2))
{(d1 /. 1)} is non empty trivial functional V35(1) set
(L~ jj1) /\ (L~ d1) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
ii2 is set
ii2 is set
(rng jj1) /\ (rng d1) is functional Element of K6( the carrier of (TOP-REAL 2))
d1 /. (len d1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
{(d1 /. (len d1))} is non empty trivial functional V35(1) set
(L~ p2) /\ (L~ d1) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
ii2 is set
ii2 is set
L~ (jj1 ^' d1) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(L~ (jj1 ^' d1)) /\ (L~ p2) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(L~ jj1) \/ (L~ d1) is non empty functional Element of K6( the carrier of (TOP-REAL 2))
((L~ jj1) \/ (L~ d1)) /\ (L~ p2) is functional Element of K6( the carrier of (TOP-REAL 2))
{(p2 /. 1)} is non empty trivial functional V35(1) set
{(jj1 /. 1)} \/ {(p2 /. 1)} is non empty set
(jj1 ^' d1) /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
{((jj1 ^' d1) /. 1)} is non empty trivial functional V35(1) set
{((jj1 ^' d1) /. 1)} \/ {(p2 /. 1)} is non empty set
{((jj1 ^' d1) /. 1),(p2 /. 1)} is non empty functional set
W-min p is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
W-bound p is V11() real ext-real Element of REAL
(TOP-REAL 2) | p is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | p is V15() V18( the carrier of ((TOP-REAL 2) | p)) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | p), REAL ) V212((TOP-REAL 2) | p) Element of K6(K7( the carrier of ((TOP-REAL 2) | p),REAL))
the carrier of ((TOP-REAL 2) | p) is set
K7( the carrier of ((TOP-REAL 2) | p),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | p),REAL)) is non empty set
lower_bound (proj1 | p) is V11() real ext-real Element of REAL
(proj1 | p) .: the carrier of ((TOP-REAL 2) | p) is Element of K6(REAL)
lower_bound ((proj1 | p) .: the carrier of ((TOP-REAL 2) | p)) is V11() real ext-real Element of REAL
W-most p is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
SW-corner p is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
S-bound p is V11() real ext-real Element of REAL
proj2 | p is V15() V18( the carrier of ((TOP-REAL 2) | p)) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | p), REAL ) V212((TOP-REAL 2) | p) Element of K6(K7( the carrier of ((TOP-REAL 2) | p),REAL))
lower_bound (proj2 | p) is V11() real ext-real Element of REAL
(proj2 | p) .: the carrier of ((TOP-REAL 2) | p) is Element of K6(REAL)
lower_bound ((proj2 | p) .: the carrier of ((TOP-REAL 2) | p)) is V11() real ext-real Element of REAL
|[(W-bound p),(S-bound p)]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
NW-corner p is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
N-bound p is V11() real ext-real Element of REAL
upper_bound (proj2 | p) is V11() real ext-real Element of REAL
upper_bound ((proj2 | p) .: the carrier of ((TOP-REAL 2) | p)) is V11() real ext-real Element of REAL
|[(W-bound p),(N-bound p)]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner p),(NW-corner p)) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner p),(NW-corner p))) /\ p is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (W-most p) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (W-most p) is V15() V18( the carrier of ((TOP-REAL 2) | (W-most p))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (W-most p)), REAL ) V212((TOP-REAL 2) | (W-most p)) Element of K6(K7( the carrier of ((TOP-REAL 2) | (W-most p)),REAL))
the carrier of ((TOP-REAL 2) | (W-most p)) is set
K7( the carrier of ((TOP-REAL 2) | (W-most p)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (W-most p)),REAL)) is non empty set
lower_bound (proj2 | (W-most p)) is V11() real ext-real Element of REAL
(proj2 | (W-most p)) .: the carrier of ((TOP-REAL 2) | (W-most p)) is Element of K6(REAL)
lower_bound ((proj2 | (W-most p)) .: the carrier of ((TOP-REAL 2) | (W-most p))) is V11() real ext-real Element of REAL
|[(W-bound p),(lower_bound (proj2 | (W-most p)))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
E-max p is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
E-bound p is V11() real ext-real Element of REAL
upper_bound (proj1 | p) is V11() real ext-real Element of REAL
upper_bound ((proj1 | p) .: the carrier of ((TOP-REAL 2) | p)) is V11() real ext-real Element of REAL
E-most p is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
SE-corner p is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
|[(E-bound p),(S-bound p)]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
NE-corner p is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
|[(E-bound p),(N-bound p)]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner p),(NE-corner p)) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SE-corner p),(NE-corner p))) /\ p is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (E-most p) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (E-most p) is V15() V18( the carrier of ((TOP-REAL 2) | (E-most p))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (E-most p)), REAL ) V212((TOP-REAL 2) | (E-most p)) Element of K6(K7( the carrier of ((TOP-REAL 2) | (E-most p)),REAL))
the carrier of ((TOP-REAL 2) | (E-most p)) is set
K7( the carrier of ((TOP-REAL 2) | (E-most p)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (E-most p)),REAL)) is non empty set
upper_bound (proj2 | (E-most p)) is V11() real ext-real Element of REAL
(proj2 | (E-most p)) .: the carrier of ((TOP-REAL 2) | (E-most p)) is Element of K6(REAL)
upper_bound ((proj2 | (E-most p)) .: the carrier of ((TOP-REAL 2) | (E-most p))) is V11() real ext-real Element of REAL
|[(E-bound p),(upper_bound (proj2 | (E-most p)))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
rng (Cage (p,C)) is non trivial functional Element of K6( the carrier of (TOP-REAL 2))
(Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))) /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
W-max (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
W-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V15() V18( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))), REAL ) V212((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),REAL))
the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is set
K7( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),REAL)) is non empty set
lower_bound (proj1 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is V11() real ext-real Element of REAL
(proj1 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) .: the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is Element of K6(REAL)
lower_bound ((proj1 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) .: the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is V11() real ext-real Element of REAL
W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
SW-corner (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
S-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V11() real ext-real Element of REAL
proj2 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V15() V18( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))), REAL ) V212((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),REAL))
lower_bound (proj2 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is V11() real ext-real Element of REAL
(proj2 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) .: the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is Element of K6(REAL)
lower_bound ((proj2 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) .: the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),(S-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
NW-corner (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
N-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) .: the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),(N-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),(NW-corner (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),(NW-corner (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))))) /\ (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is V15() V18( the carrier of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))), REAL ) V212((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))),REAL))
the carrier of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is set
K7( the carrier of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))),REAL)) is non empty set
upper_bound (proj2 | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is V11() real ext-real Element of REAL
(proj2 | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is Element of K6(REAL)
upper_bound ((proj2 | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),(upper_bound (proj2 | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(W-max (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) .. (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
N-min (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
NE-corner (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
E-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is V11() real ext-real Element of REAL
upper_bound ((proj1 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) .: the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),(N-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((NW-corner (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),(NE-corner (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((NW-corner (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),(NE-corner (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))))) /\ (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is V15() V18( the carrier of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))), REAL ) V212((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))),REAL))
the carrier of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is set
K7( the carrier of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))),REAL)) is non empty set
lower_bound (proj1 | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is V11() real ext-real Element of REAL
(proj1 | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is Element of K6(REAL)
lower_bound ((proj1 | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))))),(N-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(N-min (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) .. (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
N-max (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
upper_bound (proj1 | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is V11() real ext-real Element of REAL
upper_bound ((proj1 | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))))) is V11() real ext-real Element of REAL
|[(upper_bound (proj1 | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))))),(N-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(N-max (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) .. (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(E-max (L~ (Cage (p,C)))) .. (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
ii2 is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like non constant V28() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard FinSequence of the carrier of (TOP-REAL 2)
right_cell (ii2,1,(Gauge (p,C))) is functional Element of K6( the carrier of (TOP-REAL 2))
L~ ii2 is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
(right_cell (ii2,1,(Gauge (p,C)))) \ (L~ ii2) is functional Element of K6( the carrier of (TOP-REAL 2))
RightComp ii2 is non empty functional Element of K6( the carrier of (TOP-REAL 2))
(L~ (jj1 ^' d1)) \/ (L~ p2) is non empty functional Element of K6( the carrier of (TOP-REAL 2))
((L~ jj1) \/ (L~ d1)) \/ (L~ p2) is non empty functional Element of K6( the carrier of (TOP-REAL 2))
(L~ (Upper_Seq (p,C))) \/ (L~ (Lower_Seq (p,C))) is non empty functional Element of K6( the carrier of (TOP-REAL 2))
right_cell ((Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))),1) is functional Element of K6( the carrier of (TOP-REAL 2))
GoB (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))) is V15() non empty-yielding V18( NAT ) V19(K307( the carrier of (TOP-REAL 2))) Function-like V28() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K307( the carrier of (TOP-REAL 2))
right_cell ((Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))),1,(GoB (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is functional Element of K6( the carrier of (TOP-REAL 2))
GoB (Cage (p,C)) is V15() non empty-yielding V18( NAT ) V19(K307( the carrier of (TOP-REAL 2))) Function-like V28() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K307( the carrier of (TOP-REAL 2))
right_cell ((Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))),1,(GoB (Cage (p,C)))) is functional Element of K6( the carrier of (TOP-REAL 2))
right_cell ((Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))),1,(Gauge (p,C))) is functional Element of K6( the carrier of (TOP-REAL 2))
(Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))) -: (E-max (L~ (Cage (p,C)))) is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like special unfolded FinSequence of the carrier of (TOP-REAL 2)
right_cell (((Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))) -: (E-max (L~ (Cage (p,C))))),1,(Gauge (p,C))) is functional Element of K6( the carrier of (TOP-REAL 2))
right_cell ((Upper_Seq (p,C)),1,(Gauge (p,C))) is functional Element of K6( the carrier of (TOP-REAL 2))
right_cell ((R_Cut ((Upper_Seq (p,C)),((Gauge (p,C)) * (p9,r)))),1,(Gauge (p,C))) is functional Element of K6( the carrier of (TOP-REAL 2))
right_cell ((jj1 ^' d1),1,(Gauge (p,C))) is functional Element of K6( the carrier of (TOP-REAL 2))
ii2 /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
ii2 /. 2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(jj1 ^' d1) /. 2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(Upper_Seq (p,C)) ^' (Lower_Seq (p,C)) is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
((Upper_Seq (p,C)) ^' (Lower_Seq (p,C))) /. 2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))) /. 2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(L~ jj1) \/ (L~ p2) is non empty functional Element of K6( the carrier of (TOP-REAL 2))
W-min ((L~ jj1) \/ (L~ p2)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
W-bound ((L~ jj1) \/ (L~ p2)) is V11() real ext-real Element of REAL
(TOP-REAL 2) | ((L~ jj1) \/ (L~ p2)) is strict T_2 SubSpace of TOP-REAL 2
proj1 | ((L~ jj1) \/ (L~ p2)) is V15() V18( the carrier of ((TOP-REAL 2) | ((L~ jj1) \/ (L~ p2)))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | ((L~ jj1) \/ (L~ p2))), REAL ) V212((TOP-REAL 2) | ((L~ jj1) \/ (L~ p2))) Element of K6(K7( the carrier of ((TOP-REAL 2) | ((L~ jj1) \/ (L~ p2))),REAL))
the carrier of ((TOP-REAL 2) | ((L~ jj1) \/ (L~ p2))) is set
K7( the carrier of ((TOP-REAL 2) | ((L~ jj1) \/ (L~ p2))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | ((L~ jj1) \/ (L~ p2))),REAL)) is non empty set
lower_bound (proj1 | ((L~ jj1) \/ (L~ p2))) is V11() real ext-real Element of REAL
(proj1 | ((L~ jj1) \/ (L~ p2))) .: the carrier of ((TOP-REAL 2) | ((L~ jj1) \/ (L~ p2))) is Element of K6(REAL)
lower_bound ((proj1 | ((L~ jj1) \/ (L~ p2))) .: the carrier of ((TOP-REAL 2) | ((L~ jj1) \/ (L~ p2)))) is V11() real ext-real Element of REAL
W-most ((L~ jj1) \/ (L~ p2)) is functional Element of K6( the carrier of (TOP-REAL 2))
SW-corner ((L~ jj1) \/ (L~ p2)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
S-bound ((L~ jj1) \/ (L~ p2)) is V11() real ext-real Element of REAL
proj2 | ((L~ jj1) \/ (L~ p2)) is V15() V18( the carrier of ((TOP-REAL 2) | ((L~ jj1) \/ (L~ p2)))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | ((L~ jj1) \/ (L~ p2))), REAL ) V212((TOP-REAL 2) | ((L~ jj1) \/ (L~ p2))) Element of K6(K7( the carrier of ((TOP-REAL 2) | ((L~ jj1) \/ (L~ p2))),REAL))
lower_bound (proj2 | ((L~ jj1) \/ (L~ p2))) is V11() real ext-real Element of REAL
(proj2 | ((L~ jj1) \/ (L~ p2))) .: the carrier of ((TOP-REAL 2) | ((L~ jj1) \/ (L~ p2))) is Element of K6(REAL)
lower_bound ((proj2 | ((L~ jj1) \/ (L~ p2))) .: the carrier of ((TOP-REAL 2) | ((L~ jj1) \/ (L~ p2)))) is V11() real ext-real Element of REAL
|[(W-bound ((L~ jj1) \/ (L~ p2))),(S-bound ((L~ jj1) \/ (L~ p2)))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
NW-corner ((L~ jj1) \/ (L~ p2)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
N-bound ((L~ jj1) \/ (L~ p2)) is V11() real ext-real Element of REAL
upper_bound (proj2 | ((L~ jj1) \/ (L~ p2))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | ((L~ jj1) \/ (L~ p2))) .: the carrier of ((TOP-REAL 2) | ((L~ jj1) \/ (L~ p2)))) is V11() real ext-real Element of REAL
|[(W-bound ((L~ jj1) \/ (L~ p2))),(N-bound ((L~ jj1) \/ (L~ p2)))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner ((L~ jj1) \/ (L~ p2))),(NW-corner ((L~ jj1) \/ (L~ p2)))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner ((L~ jj1) \/ (L~ p2))),(NW-corner ((L~ jj1) \/ (L~ p2))))) /\ ((L~ jj1) \/ (L~ p2)) is functional Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (W-most ((L~ jj1) \/ (L~ p2))) is strict T_2 SubSpace of TOP-REAL 2
proj2 | (W-most ((L~ jj1) \/ (L~ p2))) is V15() V18( the carrier of ((TOP-REAL 2) | (W-most ((L~ jj1) \/ (L~ p2))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (W-most ((L~ jj1) \/ (L~ p2)))), REAL ) V212((TOP-REAL 2) | (W-most ((L~ jj1) \/ (L~ p2)))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (W-most ((L~ jj1) \/ (L~ p2)))),REAL))
the carrier of ((TOP-REAL 2) | (W-most ((L~ jj1) \/ (L~ p2)))) is set
K7( the carrier of ((TOP-REAL 2) | (W-most ((L~ jj1) \/ (L~ p2)))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (W-most ((L~ jj1) \/ (L~ p2)))),REAL)) is non empty set
lower_bound (proj2 | (W-most ((L~ jj1) \/ (L~ p2)))) is V11() real ext-real Element of REAL
(proj2 | (W-most ((L~ jj1) \/ (L~ p2)))) .: the carrier of ((TOP-REAL 2) | (W-most ((L~ jj1) \/ (L~ p2)))) is Element of K6(REAL)
lower_bound ((proj2 | (W-most ((L~ jj1) \/ (L~ p2)))) .: the carrier of ((TOP-REAL 2) | (W-most ((L~ jj1) \/ (L~ p2))))) is V11() real ext-real Element of REAL
|[(W-bound ((L~ jj1) \/ (L~ p2))),(lower_bound (proj2 | (W-most ((L~ jj1) \/ (L~ p2)))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(W-min ((L~ jj1) \/ (L~ p2))) `1 is V11() real ext-real Element of REAL
((L~ jj1) \/ (L~ p2)) \/ (L~ d1) is non empty functional Element of K6( the carrier of (TOP-REAL 2))
W-min (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
W-bound (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)) is strict T_2 SubSpace of TOP-REAL 2
proj1 | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)) is V15() V18( the carrier of ((TOP-REAL 2) | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))), REAL ) V212((TOP-REAL 2) | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))),REAL))
the carrier of ((TOP-REAL 2) | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))) is set
K7( the carrier of ((TOP-REAL 2) | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))),REAL)) is non empty set
lower_bound (proj1 | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))) is V11() real ext-real Element of REAL
(proj1 | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))) .: the carrier of ((TOP-REAL 2) | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))) is Element of K6(REAL)
lower_bound ((proj1 | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))) .: the carrier of ((TOP-REAL 2) | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))) is V11() real ext-real Element of REAL
W-most (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)) is functional Element of K6( the carrier of (TOP-REAL 2))
SW-corner (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
S-bound (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)) is V11() real ext-real Element of REAL
proj2 | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)) is V15() V18( the carrier of ((TOP-REAL 2) | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))), REAL ) V212((TOP-REAL 2) | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))),REAL))
lower_bound (proj2 | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))) is V11() real ext-real Element of REAL
(proj2 | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))) .: the carrier of ((TOP-REAL 2) | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))) is Element of K6(REAL)
lower_bound ((proj2 | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))) .: the carrier of ((TOP-REAL 2) | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))) is V11() real ext-real Element of REAL
|[(W-bound (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))),(S-bound (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
NW-corner (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
N-bound (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)) is V11() real ext-real Element of REAL
upper_bound (proj2 | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))) .: the carrier of ((TOP-REAL 2) | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))) is V11() real ext-real Element of REAL
|[(W-bound (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))),(N-bound (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))),(NW-corner (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))),(NW-corner (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))))) /\ (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)) is functional Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (W-most (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))) is strict T_2 SubSpace of TOP-REAL 2
proj2 | (W-most (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))) is V15() V18( the carrier of ((TOP-REAL 2) | (W-most (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (W-most (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))), REAL ) V212((TOP-REAL 2) | (W-most (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (W-most (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))),REAL))
the carrier of ((TOP-REAL 2) | (W-most (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))) is set
K7( the carrier of ((TOP-REAL 2) | (W-most (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (W-most (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))),REAL)) is non empty set
lower_bound (proj2 | (W-most (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))) is V11() real ext-real Element of REAL
(proj2 | (W-most (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))) .: the carrier of ((TOP-REAL 2) | (W-most (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))) is Element of K6(REAL)
lower_bound ((proj2 | (W-most (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))) .: the carrier of ((TOP-REAL 2) | (W-most (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))))) is V11() real ext-real Element of REAL
|[(W-bound (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))),(lower_bound (proj2 | (W-most (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
W-min (L~ ii2) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
W-bound (L~ ii2) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ ii2) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ ii2) is V15() V18( the carrier of ((TOP-REAL 2) | (L~ ii2))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ ii2)), REAL ) V212((TOP-REAL 2) | (L~ ii2)) Element of K6(K7( the carrier of ((TOP-REAL 2) | (L~ ii2)),REAL))
the carrier of ((TOP-REAL 2) | (L~ ii2)) is set
K7( the carrier of ((TOP-REAL 2) | (L~ ii2)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (L~ ii2)),REAL)) is non empty set
lower_bound (proj1 | (L~ ii2)) is V11() real ext-real Element of REAL
(proj1 | (L~ ii2)) .: the carrier of ((TOP-REAL 2) | (L~ ii2)) is Element of K6(REAL)
lower_bound ((proj1 | (L~ ii2)) .: the carrier of ((TOP-REAL 2) | (L~ ii2))) is V11() real ext-real Element of REAL
W-most (L~ ii2) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
SW-corner (L~ ii2) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
S-bound (L~ ii2) is V11() real ext-real Element of REAL
proj2 | (L~ ii2) is V15() V18( the carrier of ((TOP-REAL 2) | (L~ ii2))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ ii2)), REAL ) V212((TOP-REAL 2) | (L~ ii2)) Element of K6(K7( the carrier of ((TOP-REAL 2) | (L~ ii2)),REAL))
lower_bound (proj2 | (L~ ii2)) is V11() real ext-real Element of REAL
(proj2 | (L~ ii2)) .: the carrier of ((TOP-REAL 2) | (L~ ii2)) is Element of K6(REAL)
lower_bound ((proj2 | (L~ ii2)) .: the carrier of ((TOP-REAL 2) | (L~ ii2))) is V11() real ext-real Element of REAL
|[(W-bound (L~ ii2)),(S-bound (L~ ii2))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
NW-corner (L~ ii2) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
N-bound (L~ ii2) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ ii2)) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (L~ ii2)) .: the carrier of ((TOP-REAL 2) | (L~ ii2))) is V11() real ext-real Element of REAL
|[(W-bound (L~ ii2)),(N-bound (L~ ii2))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner (L~ ii2)),(NW-corner (L~ ii2))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner (L~ ii2)),(NW-corner (L~ ii2)))) /\ (L~ ii2) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (W-most (L~ ii2)) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (W-most (L~ ii2)) is V15() V18( the carrier of ((TOP-REAL 2) | (W-most (L~ ii2)))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (W-most (L~ ii2))), REAL ) V212((TOP-REAL 2) | (W-most (L~ ii2))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (W-most (L~ ii2))),REAL))
the carrier of ((TOP-REAL 2) | (W-most (L~ ii2))) is set
K7( the carrier of ((TOP-REAL 2) | (W-most (L~ ii2))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (W-most (L~ ii2))),REAL)) is non empty set
lower_bound (proj2 | (W-most (L~ ii2))) is V11() real ext-real Element of REAL
(proj2 | (W-most (L~ ii2))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ ii2))) is Element of K6(REAL)
lower_bound ((proj2 | (W-most (L~ ii2))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ ii2)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ ii2)),(lower_bound (proj2 | (W-most (L~ ii2))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
rng ii2 is non trivial functional Element of K6( the carrier of (TOP-REAL 2))
dom ii2 is non trivial Element of K6(NAT)
(ii2 /. 2) `1 is V11() real ext-real Element of REAL
(W-min (L~ ii2)) `1 is V11() real ext-real Element of REAL
Rotate (ii2,(W-min (L~ ii2))) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like non constant V28() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard FinSequence of the carrier of (TOP-REAL 2)
(Rotate (ii2,(W-min (L~ ii2)))) /. 2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(Upper_Seq (p,C)) . (len (Upper_Seq (p,C))) is V15() Function-like set
(Upper_Seq (p,C)) /. (len (Upper_Seq (p,C))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
east_halfline (E-max p) is non empty functional connected V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
Gji is set
Gij9 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(east_halfline (E-max p)) /\ (L~ (Cage (p,C))) is functional Element of K6( the carrier of (TOP-REAL 2))
Gij9 `1 is V11() real ext-real Element of REAL
Gij is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like non constant V28() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the carrier of (TOP-REAL 2)
L~ Gij is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
Gji is set
Gij9 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
Gij9 `1 is V11() real ext-real Element of REAL
Gij9 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
Gij9 `1 is V11() real ext-real Element of REAL
Gij9 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
Gij9 `1 is V11() real ext-real Element of REAL
Gij9 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
Gij9 `1 is V11() real ext-real Element of REAL
s + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
(len (Gauge (p,C))) - 1 is V11() real ext-real Element of REAL
(len (Gauge (p,C))) + (- 1) is V11() real ext-real set
(len (Gauge (p,C))) -' 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(Gauge (p,C)) * (((len (Gauge (p,C))) -' 1),1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * (((len (Gauge (p,C))) -' 1),1)) `1 is V11() real ext-real Element of REAL
(E-max p) `1 is V11() real ext-real Element of REAL
Gij9 `2 is V11() real ext-real Element of REAL
(E-max p) `2 is V11() real ext-real Element of REAL
Gji is set
Gij9 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(east_halfline (E-max p)) /\ (L~ (Cage (p,C))) is functional Element of K6( the carrier of (TOP-REAL 2))
Gij9 `1 is V11() real ext-real Element of REAL
(E-max p) `2 is V11() real ext-real Element of REAL
Gij9 `2 is V11() real ext-real Element of REAL
Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like non constant V28() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the carrier of (TOP-REAL 2)
right_cell ((Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))),1) is functional Element of K6( the carrier of (TOP-REAL 2))
(Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))) -: (W-min (L~ (Cage (p,C)))) is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like special unfolded FinSequence of the carrier of (TOP-REAL 2)
LSeg ((Lower_Seq (p,C)),1) is functional Element of K6( the carrier of (TOP-REAL 2))
LSeg ((Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))),1) is functional Element of K6( the carrier of (TOP-REAL 2))
L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
len (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
GoB (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))) is V15() non empty-yielding V18( NAT ) V19(K307( the carrier of (TOP-REAL 2))) Function-like V28() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K307( the carrier of (TOP-REAL 2))
(Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))) /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
E-max (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
E-bound (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))) is V15() V18( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))), REAL ) V212((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))),REAL))
the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) is set
K7( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))),REAL)) is non empty set
upper_bound (proj1 | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) is V11() real ext-real Element of REAL
(proj1 | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) .: the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) is Element of K6(REAL)
upper_bound ((proj1 | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) .: the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) is V11() real ext-real Element of REAL
E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
SE-corner (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
S-bound (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))) is V11() real ext-real Element of REAL
proj2 | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))) is V15() V18( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))), REAL ) V212((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))),REAL))
lower_bound (proj2 | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) is V11() real ext-real Element of REAL
(proj2 | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) .: the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) is Element of K6(REAL)
lower_bound ((proj2 | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) .: the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))),(S-bound (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
NE-corner (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
N-bound (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) .: the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))),(N-bound (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))),(NE-corner (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SE-corner (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))),(NE-corner (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))))) /\ (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) is V15() V18( the carrier of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))), REAL ) V212((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))),REAL))
the carrier of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) is set
K7( the carrier of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))),REAL)) is non empty set
upper_bound (proj2 | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) is V11() real ext-real Element of REAL
(proj2 | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) is Element of K6(REAL)
upper_bound ((proj2 | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))),(upper_bound (proj2 | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))) /. (1 + 1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
x is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
x9 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
x9 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
[x,(x9 + 1)] is set
{x,(x9 + 1)} is non empty set
{x} is non empty trivial V35(1) set
{{x,(x9 + 1)},{x}} is non empty set
[x,x9] is set
{x,x9} is non empty set
{{x,x9},{x}} is non empty set
(Gauge (p,C)) * (x,(x9 + 1)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(Gauge (p,C)) * (x,x9) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
jj2 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(Gauge (p,C)) * ((len (Gauge (p,C))),jj2) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
[(len (Gauge (p,C))),jj2] is set
{(len (Gauge (p,C))),jj2} is non empty set
{{(len (Gauge (p,C))),jj2},{(len (Gauge (p,C)))}} is non empty set
x + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
(x9 + 1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
x -' 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
cell ((Gauge (p,C)),(x -' 1),x9) is functional Element of K6( the carrier of (TOP-REAL 2))
(x -' 1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
4 - 1 is V11() real ext-real Element of REAL
4 + (- 1) is V11() real ext-real set
x - 1 is V11() real ext-real Element of REAL
x + (- 1) is V11() real ext-real set
(Gauge (p,C)) * ((x -' 1),x9) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * ((x -' 1),x9)) `2 is V11() real ext-real Element of REAL
(Gauge (p,C)) * ((x -' 1),(x9 + 1)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * ((x -' 1),(x9 + 1))) `2 is V11() real ext-real Element of REAL
(Gauge (p,C)) * (1,x9) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * (1,x9)) `2 is V11() real ext-real Element of REAL
((Gauge (p,C)) * (x,x9)) `2 is V11() real ext-real Element of REAL
(Gauge (p,C)) * (1,(x9 + 1)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * (1,(x9 + 1))) `2 is V11() real ext-real Element of REAL
((Gauge (p,C)) * (x,(x9 + 1))) `2 is V11() real ext-real Element of REAL
(Gauge (p,C)) * ((len (Gauge (p,C))),x9) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * ((len (Gauge (p,C))),x9)) `1 is V11() real ext-real Element of REAL
(Gauge (p,C)) * ((len (Gauge (p,C))),(x9 + 1)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * ((len (Gauge (p,C))),(x9 + 1))) `1 is V11() real ext-real Element of REAL
LSeg (((Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))) /. 1),((Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))) /. (1 + 1))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
Index (Gij9,p2) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
LSeg (p2,(Index (Gij9,p2))) is functional Element of K6( the carrier of (TOP-REAL 2))
((Gauge (p,C)) * (s,rr)) .. (Lower_Seq (p,C)) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
mid ((Lower_Seq (p,C)),(((Gauge (p,C)) * (s,rr)) .. (Lower_Seq (p,C))),(len (Lower_Seq (p,C)))) is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
Index (((Gauge (p,C)) * (s,rr)),(Lower_Seq (p,C))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(Index (((Gauge (p,C)) * (s,rr)),(Lower_Seq (p,C)))) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
t is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative set
(Lower_Seq (p,C)) . t is V15() Function-like set
len (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (s,rr)))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(len (Lower_Seq (p,C))) - (Index (((Gauge (p,C)) * (s,rr)),(Lower_Seq (p,C)))) is V11() real ext-real Element of REAL
- (Index (((Gauge (p,C)) * (s,rr)),(Lower_Seq (p,C)))) is V11() real ext-real non positive set
(len (Lower_Seq (p,C))) + (- (Index (((Gauge (p,C)) * (s,rr)),(Lower_Seq (p,C))))) is V11() real ext-real set
(Index (Gij9,p2)) + (((Gauge (p,C)) * (s,rr)) .. (Lower_Seq (p,C))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
((Index (Gij9,p2)) + (((Gauge (p,C)) * (s,rr)) .. (Lower_Seq (p,C)))) -' 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
0 + (Index (((Gauge (p,C)) * (s,rr)),(Lower_Seq (p,C)))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(len (Lower_Seq (p,C))) -' (Index (((Gauge (p,C)) * (s,rr)),(Lower_Seq (p,C)))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(Index (Gij9,p2)) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
((len (Lower_Seq (p,C))) -' (Index (((Gauge (p,C)) * (s,rr)),(Lower_Seq (p,C))))) - 1 is V11() real ext-real Element of REAL
((len (Lower_Seq (p,C))) -' (Index (((Gauge (p,C)) * (s,rr)),(Lower_Seq (p,C))))) + (- 1) is V11() real ext-real set
((len (Lower_Seq (p,C))) - (Index (((Gauge (p,C)) * (s,rr)),(Lower_Seq (p,C))))) - 1 is V11() real ext-real Element of REAL
((len (Lower_Seq (p,C))) - (Index (((Gauge (p,C)) * (s,rr)),(Lower_Seq (p,C))))) + (- 1) is V11() real ext-real set
(len (Lower_Seq (p,C))) - (((Gauge (p,C)) * (s,rr)) .. (Lower_Seq (p,C))) is V11() real ext-real Element of REAL
- (((Gauge (p,C)) * (s,rr)) .. (Lower_Seq (p,C))) is V11() real ext-real non positive set
(len (Lower_Seq (p,C))) + (- (((Gauge (p,C)) * (s,rr)) .. (Lower_Seq (p,C)))) is V11() real ext-real set
(len (Lower_Seq (p,C))) -' (((Gauge (p,C)) * (s,rr)) .. (Lower_Seq (p,C))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
((len (Lower_Seq (p,C))) -' (((Gauge (p,C)) * (s,rr)) .. (Lower_Seq (p,C)))) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
LSeg ((mid ((Lower_Seq (p,C)),(((Gauge (p,C)) * (s,rr)) .. (Lower_Seq (p,C))),(len (Lower_Seq (p,C))))),(Index (Gij9,p2))) is functional Element of K6( the carrier of (TOP-REAL 2))
LSeg ((Lower_Seq (p,C)),(((Index (Gij9,p2)) + (((Gauge (p,C)) * (s,rr)) .. (Lower_Seq (p,C)))) -' 1)) is functional Element of K6( the carrier of (TOP-REAL 2))
(1 + 1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
((1 + 1) + 1) - 1 is V11() real ext-real Element of REAL
((1 + 1) + 1) + (- 1) is V11() real ext-real set
((Index (Gij9,p2)) + (((Gauge (p,C)) * (s,rr)) .. (Lower_Seq (p,C)))) - 1 is V11() real ext-real Element of REAL
((Index (Gij9,p2)) + (((Gauge (p,C)) * (s,rr)) .. (Lower_Seq (p,C)))) + (- 1) is V11() real ext-real set
(LSeg ((Lower_Seq (p,C)),1)) /\ (LSeg ((Lower_Seq (p,C)),(((Index (Gij9,p2)) + (((Gauge (p,C)) * (s,rr)) .. (Lower_Seq (p,C)))) -' 1))) is functional Element of K6( the carrier of (TOP-REAL 2))
(Lower_Seq (p,C)) /. 2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
{((Lower_Seq (p,C)) /. 2)} is non empty trivial functional V35(1) set
Gij9 .. (Lower_Seq (p,C)) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(Gauge (p,C)) * ((len (Gauge (p,C))),r) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * ((len (Gauge (p,C))),r)) `1 is V11() real ext-real Element of REAL
(L~ Gij) ` is non empty functional Element of K6( the carrier of (TOP-REAL 2))
Gji is functional Element of K6( the carrier of (TOP-REAL 2))
UBD (L~ Gij) is non empty functional open connected Element of K6( the carrier of (TOP-REAL 2))
LeftComp Gij is non empty functional Element of K6( the carrier of (TOP-REAL 2))
((Gauge (p,C)) * (s,rr)) `1 is V11() real ext-real Element of REAL
{((Gauge (p,C)) * (p9,rr))} is non empty trivial functional V35(1) set
((Gauge (p,C)) * (p9,r)) `2 is V11() real ext-real Element of REAL
{((Gauge (p,C)) * (p9,rr))} is non empty trivial functional V35(1) set
((Gauge (p,C)) * (s,rr)) `1 is V11() real ext-real Element of REAL
((Gauge (p,C)) * (p9,r)) `2 is V11() real ext-real Element of REAL
C is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
p is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
Gauge (p,C) is V15() non empty-yielding V18( NAT ) V19(K307( the carrier of (TOP-REAL 2))) Function-like V28() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K307( the carrier of (TOP-REAL 2))
len (Gauge (p,C)) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
width (Gauge (p,C)) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
Upper_Seq (p,C) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V28() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
L~ (Upper_Seq (p,C)) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
Lower_Seq (p,C) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V28() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
L~ (Lower_Seq (p,C)) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
Lower_Arc p is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
p9 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
s is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
r is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
rr is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(Gauge (p,C)) * (p9,r) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(Gauge (p,C)) * (p9,rr) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(Gauge (p,C)) * (s,rr) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) is non empty functional Element of K6( the carrier of (TOP-REAL 2))
((LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))))) /\ (L~ (Upper_Seq (p,C))) is functional Element of K6( the carrier of (TOP-REAL 2))
{((Gauge (p,C)) * (p9,r))} is non empty trivial functional V35(1) set
((LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))))) /\ (L~ (Lower_Seq (p,C))) is functional Element of K6( the carrier of (TOP-REAL 2))
{((Gauge (p,C)) * (s,rr))} is non empty trivial functional V35(1) set
Cage (p,C) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like non constant V28() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the carrier of (TOP-REAL 2)
L~ (Cage (p,C)) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
W-min (L~ (Cage (p,C))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
W-bound (L~ (Cage (p,C))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (p,C))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ (Cage (p,C))) is V15() V18( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))), REAL ) V212((TOP-REAL 2) | (L~ (Cage (p,C)))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))),REAL))
the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))) is set
K7( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))),REAL)) is non empty set
lower_bound (proj1 | (L~ (Cage (p,C)))) is V11() real ext-real Element of REAL
(proj1 | (L~ (Cage (p,C)))) .: the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))) is Element of K6(REAL)
lower_bound ((proj1 | (L~ (Cage (p,C)))) .: the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C))))) is V11() real ext-real Element of REAL
W-most (L~ (Cage (p,C))) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
SW-corner (L~ (Cage (p,C))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
S-bound (L~ (Cage (p,C))) is V11() real ext-real Element of REAL
proj2 | (L~ (Cage (p,C))) is V15() V18( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))), REAL ) V212((TOP-REAL 2) | (L~ (Cage (p,C)))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))),REAL))
lower_bound (proj2 | (L~ (Cage (p,C)))) is V11() real ext-real Element of REAL
(proj2 | (L~ (Cage (p,C)))) .: the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))) is Element of K6(REAL)
lower_bound ((proj2 | (L~ (Cage (p,C)))) .: the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Cage (p,C)))),(S-bound (L~ (Cage (p,C))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
NW-corner (L~ (Cage (p,C))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
N-bound (L~ (Cage (p,C))) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ (Cage (p,C)))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (L~ (Cage (p,C)))) .: the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Cage (p,C)))),(N-bound (L~ (Cage (p,C))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (p,C)))),(NW-corner (L~ (Cage (p,C))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner (L~ (Cage (p,C)))),(NW-corner (L~ (Cage (p,C)))))) /\ (L~ (Cage (p,C))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (W-most (L~ (Cage (p,C)))) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Cage (p,C)))) is V15() V18( the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C)))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C))))), REAL ) V212((TOP-REAL 2) | (W-most (L~ (Cage (p,C))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C))))),REAL))
the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C))))) is set
K7( the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C))))),REAL)) is non empty set
lower_bound (proj2 | (W-most (L~ (Cage (p,C))))) is V11() real ext-real Element of REAL
(proj2 | (W-most (L~ (Cage (p,C))))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C))))) is Element of K6(REAL)
lower_bound ((proj2 | (W-most (L~ (Cage (p,C))))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C)))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Cage (p,C)))),(lower_bound (proj2 | (W-most (L~ (Cage (p,C))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
E-max (L~ (Cage (p,C))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
E-bound (L~ (Cage (p,C))) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ (Cage (p,C)))) is V11() real ext-real Element of REAL
upper_bound ((proj1 | (L~ (Cage (p,C)))) .: the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C))))) is V11() real ext-real Element of REAL
E-most (L~ (Cage (p,C))) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
SE-corner (L~ (Cage (p,C))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
|[(E-bound (L~ (Cage (p,C)))),(S-bound (L~ (Cage (p,C))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
NE-corner (L~ (Cage (p,C))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
|[(E-bound (L~ (Cage (p,C)))),(N-bound (L~ (Cage (p,C))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Cage (p,C)))),(NE-corner (L~ (Cage (p,C))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SE-corner (L~ (Cage (p,C)))),(NE-corner (L~ (Cage (p,C)))))) /\ (L~ (Cage (p,C))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (E-most (L~ (Cage (p,C)))) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Cage (p,C)))) is V15() V18( the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (p,C)))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (p,C))))), REAL ) V212((TOP-REAL 2) | (E-most (L~ (Cage (p,C))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (p,C))))),REAL))
the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (p,C))))) is set
K7( the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (p,C))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (p,C))))),REAL)) is non empty set
upper_bound (proj2 | (E-most (L~ (Cage (p,C))))) is V11() real ext-real Element of REAL
(proj2 | (E-most (L~ (Cage (p,C))))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (p,C))))) is Element of K6(REAL)
upper_bound ((proj2 | (E-most (L~ (Cage (p,C))))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (p,C)))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Cage (p,C)))),(upper_bound (proj2 | (E-most (L~ (Cage (p,C))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
<*((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))*> is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() V35(3) FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ <*((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))*> is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))) is non empty functional Element of K6( the carrier of (TOP-REAL 2))
[p9,r] is set
{p9,r} is non empty set
{p9} is non empty trivial V35(1) set
{{p9,r},{p9}} is non empty set
Indices (Gauge (p,C)) is set
[s,rr] is set
{s,rr} is non empty set
{s} is non empty trivial V35(1) set
{{s,rr},{s}} is non empty set
[p9,rr] is set
{p9,rr} is non empty set
{{p9,rr},{p9}} is non empty set
R_Cut ((Upper_Seq (p,C)),((Gauge (p,C)) * (p9,r))) is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (s,rr))) is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len (Upper_Seq (p,C)) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
dom (Upper_Seq (p,C)) is non trivial Element of K6(NAT)
(Upper_Seq (p,C)) . 1 is V15() Function-like set
(Upper_Seq (p,C)) /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(W-min (L~ (Cage (p,C)))) `1 is V11() real ext-real Element of REAL
(Gauge (p,C)) * (1,rr) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * (1,rr)) `1 is V11() real ext-real Element of REAL
[1,rr] is set
{1,rr} is non empty set
{{1,rr},{1}} is non empty set
[1,r] is set
{1,r} is non empty set
{{1,r},{1}} is non empty set
1 + 2 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
len (Lower_Seq (p,C)) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
dom (Lower_Seq (p,C)) is non trivial Element of K6(NAT)
(Lower_Seq (p,C)) . (len (Lower_Seq (p,C))) is V15() Function-like set
(Lower_Seq (p,C)) /. (len (Lower_Seq (p,C))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
[(len (Gauge (p,C))),rr] is set
{(len (Gauge (p,C))),rr} is non empty set
{(len (Gauge (p,C)))} is non empty trivial V35(1) set
{{(len (Gauge (p,C))),rr},{(len (Gauge (p,C)))}} is non empty set
(Lower_Seq (p,C)) . 1 is V15() Function-like set
(Lower_Seq (p,C)) /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(E-max (L~ (Cage (p,C)))) `1 is V11() real ext-real Element of REAL
(Gauge (p,C)) * ((len (Gauge (p,C))),rr) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * ((len (Gauge (p,C))),rr)) `1 is V11() real ext-real Element of REAL
1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
c2 is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V28() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
len c2 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
rng (Upper_Seq (p,C)) is functional Element of K6( the carrier of (TOP-REAL 2))
ii1 is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V28() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
len ii1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
rng (Lower_Seq (p,C)) is functional Element of K6( the carrier of (TOP-REAL 2))
jj1 is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one non constant V28() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq s.c.c. FinSequence of the carrier of (TOP-REAL 2)
len jj1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
dom jj1 is non trivial Element of K6(NAT)
jj1 /. (len jj1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
jj1 . (len jj1) is V15() Function-like set
p2 is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one non constant V28() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq s.c.c. FinSequence of the carrier of (TOP-REAL 2)
len p2 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
dom p2 is non trivial Element of K6(NAT)
p2 /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
p2 . 1 is V15() Function-like set
(len jj1) - 1 is V11() real ext-real Element of REAL
- 1 is V11() real ext-real non positive set
(len jj1) + (- 1) is V11() real ext-real set
p2 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
p2 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
(len jj1) -' 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
LSeg (jj1,p2) is functional Element of K6( the carrier of (TOP-REAL 2))
L~ jj1 is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(LSeg (jj1,p2)) /\ (L~ <*((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))*>) is functional Element of K6( the carrier of (TOP-REAL 2))
jj1 /. p2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((jj1 /. p2),((Gauge (p,C)) * (p9,r))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
p29 is set
LSeg (p2,1) is functional Element of K6( the carrier of (TOP-REAL 2))
L~ p2 is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(LSeg (p2,1)) /\ (L~ <*((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))*>) is functional Element of K6( the carrier of (TOP-REAL 2))
p2 /. (1 + 1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg (((Gauge (p,C)) * (s,rr)),(p2 /. (1 + 1))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
p29 is set
(L~ <*((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))*>) /\ (LSeg (p2,1)) is functional Element of K6( the carrier of (TOP-REAL 2))
jj1 /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
p2 /. (len p2) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
rng jj1 is non trivial functional Element of K6( the carrier of (TOP-REAL 2))
rng p2 is non trivial functional Element of K6( the carrier of (TOP-REAL 2))
{(jj1 /. 1)} is non empty trivial functional V35(1) set
(L~ jj1) /\ (L~ p2) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
p29 is set
[(len (Gauge (p,C))),r] is set
{(len (Gauge (p,C))),r} is non empty set
{{(len (Gauge (p,C))),r},{(len (Gauge (p,C)))}} is non empty set
p29 is set
(L~ (Upper_Seq (p,C))) /\ (L~ (Lower_Seq (p,C))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
{(W-min (L~ (Cage (p,C)))),(E-max (L~ (Cage (p,C))))} is non empty functional set
(Gauge (p,C)) * ((len (Gauge (p,C))),r) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * ((len (Gauge (p,C))),r)) `1 is V11() real ext-real Element of REAL
jj1 /. 2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * (p9,r)) `1 is V11() real ext-real Element of REAL
(Gauge (p,C)) * (1,r) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * (1,r)) `1 is V11() real ext-real Element of REAL
((Gauge (p,C)) * (p9,r)) .. (Upper_Seq (p,C)) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
mid ((Upper_Seq (p,C)),1,(((Gauge (p,C)) * (p9,r)) .. (Upper_Seq (p,C)))) is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
(Upper_Seq (p,C)) | (((Gauge (p,C)) * (p9,r)) .. (Upper_Seq (p,C))) is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V28() FinSequence-like FinSubsequence-like special unfolded s.n.c. FinSequence of the carrier of (TOP-REAL 2)
(Upper_Seq (p,C)) /. 2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
i2 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
dom <*((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))*> is non trivial V35(3) Element of K6(NAT)
<*((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))*> /. i2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * (p9,rr)) `1 is V11() real ext-real Element of REAL
(Gauge (p,C)) * (p9,1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * (p9,1)) `1 is V11() real ext-real Element of REAL
((Gauge (p,C)) * (p9,rr)) `2 is V11() real ext-real Element of REAL
((Gauge (p,C)) * (1,rr)) `2 is V11() real ext-real Element of REAL
((Gauge (p,C)) * (s,rr)) `2 is V11() real ext-real Element of REAL
|[(((Gauge (p,C)) * (p9,r)) `1),(((Gauge (p,C)) * (s,rr)) `2)]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * (s,rr)) `1 is V11() real ext-real Element of REAL
((Gauge (p,C)) * (p9,r)) `2 is V11() real ext-real Element of REAL
<*((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))*> /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
len <*((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))*> is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
<*((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))*> /. (len <*((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))*>) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
i2 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ i2 is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
i2 /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
len i2 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
i2 /. (len i2) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
d1 is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V28() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
jj1 ^' d1 is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
(jj1 ^' d1) ^' p2 is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
W-bound (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) is V15() V18( the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))))), REAL ) V212((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))))),REAL))
the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))))) is set
K7( the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))))),REAL)) is non empty set
lower_bound (proj1 | (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))))) is V11() real ext-real Element of REAL
(proj1 | (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))))) .: the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))))) is Element of K6(REAL)
lower_bound ((proj1 | (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))))) .: the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))))) is V11() real ext-real Element of REAL
W-bound (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))) is V15() V18( the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr))))), REAL ) V212((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr))))),REAL))
the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr))))) is set
K7( the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr))))),REAL)) is non empty set
lower_bound (proj1 | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr))))) is V11() real ext-real Element of REAL
(proj1 | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr))))) .: the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr))))) is Element of K6(REAL)
lower_bound ((proj1 | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr))))) .: the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))))) is V11() real ext-real Element of REAL
W-bound ((LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr))))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | ((LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr))))) is strict T_2 SubSpace of TOP-REAL 2
proj1 | ((LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr))))) is V15() V18( the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr))))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))))), REAL ) V212((TOP-REAL 2) | ((LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))))),REAL))
the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))))) is set
K7( the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))))),REAL)) is non empty set
lower_bound (proj1 | ((LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))))) is V11() real ext-real Element of REAL
(proj1 | ((LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))))) .: the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))))) is Element of K6(REAL)
lower_bound ((proj1 | ((LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))))) .: the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr))))))) is V11() real ext-real Element of REAL
min ((W-bound (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))))),(W-bound (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))))) is V11() real ext-real set
L~ d1 is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
W-bound (L~ d1) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ d1) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ d1) is V15() V18( the carrier of ((TOP-REAL 2) | (L~ d1))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ d1)), REAL ) V212((TOP-REAL 2) | (L~ d1)) Element of K6(K7( the carrier of ((TOP-REAL 2) | (L~ d1)),REAL))
the carrier of ((TOP-REAL 2) | (L~ d1)) is set
K7( the carrier of ((TOP-REAL 2) | (L~ d1)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (L~ d1)),REAL)) is non empty set
lower_bound (proj1 | (L~ d1)) is V11() real ext-real Element of REAL
(proj1 | (L~ d1)) .: the carrier of ((TOP-REAL 2) | (L~ d1)) is Element of K6(REAL)
lower_bound ((proj1 | (L~ d1)) .: the carrier of ((TOP-REAL 2) | (L~ d1))) is V11() real ext-real Element of REAL
len (Cage (p,C)) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like non constant V28() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the carrier of (TOP-REAL 2)
len (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
len (jj1 ^' d1) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
1 + 0 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
len ((jj1 ^' d1) ^' p2) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
d1 /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(jj1 ^' d1) /. (len (jj1 ^' d1)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
<*((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))*> /. 3 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg (d1,1) is functional Element of K6( the carrier of (TOP-REAL 2))
LSeg (jj1,((len jj1) -' 1)) is functional Element of K6( the carrier of (TOP-REAL 2))
(LSeg (jj1,((len jj1) -' 1))) /\ (LSeg (d1,1)) is functional Element of K6( the carrier of (TOP-REAL 2))
2 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
len d1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
(LSeg (jj1,p2)) /\ (LSeg (d1,1)) is functional Element of K6( the carrier of (TOP-REAL 2))
ii2 is set
{(jj1 /. (len jj1))} is non empty trivial functional V35(1) set
(len d1) - 2 is V11() real ext-real Element of REAL
(len d1) + (- 2) is V11() real ext-real set
(len (jj1 ^' d1)) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
((len (jj1 ^' d1)) + 1) - 1 is V11() real ext-real Element of REAL
((len (jj1 ^' d1)) + 1) + (- 1) is V11() real ext-real set
(len jj1) + (len d1) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
((len jj1) + (len d1)) - 1 is V11() real ext-real Element of REAL
((len jj1) + (len d1)) + (- 1) is V11() real ext-real set
(len (jj1 ^' d1)) - 1 is V11() real ext-real Element of REAL
(len (jj1 ^' d1)) + (- 1) is V11() real ext-real set
(len jj1) + ((len d1) - 2) is V11() real ext-real Element of REAL
(len d1) -' 2 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(len jj1) + ((len d1) -' 2) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
(len (jj1 ^' d1)) -' 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(len d1) - 1 is V11() real ext-real Element of REAL
(len d1) + (- 1) is V11() real ext-real set
(len d1) -' 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
((len d1) -' 2) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
((len d1) - 2) + 1 is V11() real ext-real Element of REAL
((len d1) - 1) + 1 is V11() real ext-real Element of REAL
LSeg (d1,((len d1) -' 1)) is functional Element of K6( the carrier of (TOP-REAL 2))
(LSeg (d1,((len d1) -' 1))) /\ (LSeg (p2,1)) is functional Element of K6( the carrier of (TOP-REAL 2))
ii2 is set
((len d1) -' 1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
d1 /. (((len d1) -' 1) + 1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((jj1 ^' d1),((len jj1) + ((len d1) -' 2))) is functional Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((jj1 ^' d1),((len jj1) + ((len d1) -' 2)))) /\ (LSeg (p2,1)) is functional Element of K6( the carrier of (TOP-REAL 2))
{((jj1 ^' d1) /. (len (jj1 ^' d1)))} is non empty trivial functional V35(1) set
rng d1 is functional Element of K6( the carrier of (TOP-REAL 2))
{(d1 /. 1)} is non empty trivial functional V35(1) set
(L~ jj1) /\ (L~ d1) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
ii2 is set
ii2 is set
(rng jj1) /\ (rng d1) is functional Element of K6( the carrier of (TOP-REAL 2))
d1 /. (len d1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
{(d1 /. (len d1))} is non empty trivial functional V35(1) set
(L~ p2) /\ (L~ d1) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
ii2 is set
ii2 is set
L~ (jj1 ^' d1) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(L~ (jj1 ^' d1)) /\ (L~ p2) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(L~ jj1) \/ (L~ d1) is non empty functional Element of K6( the carrier of (TOP-REAL 2))
((L~ jj1) \/ (L~ d1)) /\ (L~ p2) is functional Element of K6( the carrier of (TOP-REAL 2))
{(p2 /. 1)} is non empty trivial functional V35(1) set
{(jj1 /. 1)} \/ {(p2 /. 1)} is non empty set
(jj1 ^' d1) /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
{((jj1 ^' d1) /. 1)} is non empty trivial functional V35(1) set
{((jj1 ^' d1) /. 1)} \/ {(p2 /. 1)} is non empty set
{((jj1 ^' d1) /. 1),(p2 /. 1)} is non empty functional set
E-max p is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
E-bound p is V11() real ext-real Element of REAL
(TOP-REAL 2) | p is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | p is V15() V18( the carrier of ((TOP-REAL 2) | p)) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | p), REAL ) V212((TOP-REAL 2) | p) Element of K6(K7( the carrier of ((TOP-REAL 2) | p),REAL))
the carrier of ((TOP-REAL 2) | p) is set
K7( the carrier of ((TOP-REAL 2) | p),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | p),REAL)) is non empty set
upper_bound (proj1 | p) is V11() real ext-real Element of REAL
(proj1 | p) .: the carrier of ((TOP-REAL 2) | p) is Element of K6(REAL)
upper_bound ((proj1 | p) .: the carrier of ((TOP-REAL 2) | p)) is V11() real ext-real Element of REAL
E-most p is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
SE-corner p is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
S-bound p is V11() real ext-real Element of REAL
proj2 | p is V15() V18( the carrier of ((TOP-REAL 2) | p)) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | p), REAL ) V212((TOP-REAL 2) | p) Element of K6(K7( the carrier of ((TOP-REAL 2) | p),REAL))
lower_bound (proj2 | p) is V11() real ext-real Element of REAL
(proj2 | p) .: the carrier of ((TOP-REAL 2) | p) is Element of K6(REAL)
lower_bound ((proj2 | p) .: the carrier of ((TOP-REAL 2) | p)) is V11() real ext-real Element of REAL
|[(E-bound p),(S-bound p)]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
NE-corner p is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
N-bound p is V11() real ext-real Element of REAL
upper_bound (proj2 | p) is V11() real ext-real Element of REAL
upper_bound ((proj2 | p) .: the carrier of ((TOP-REAL 2) | p)) is V11() real ext-real Element of REAL
|[(E-bound p),(N-bound p)]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner p),(NE-corner p)) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SE-corner p),(NE-corner p))) /\ p is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (E-most p) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (E-most p) is V15() V18( the carrier of ((TOP-REAL 2) | (E-most p))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (E-most p)), REAL ) V212((TOP-REAL 2) | (E-most p)) Element of K6(K7( the carrier of ((TOP-REAL 2) | (E-most p)),REAL))
the carrier of ((TOP-REAL 2) | (E-most p)) is set
K7( the carrier of ((TOP-REAL 2) | (E-most p)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (E-most p)),REAL)) is non empty set
upper_bound (proj2 | (E-most p)) is V11() real ext-real Element of REAL
(proj2 | (E-most p)) .: the carrier of ((TOP-REAL 2) | (E-most p)) is Element of K6(REAL)
upper_bound ((proj2 | (E-most p)) .: the carrier of ((TOP-REAL 2) | (E-most p))) is V11() real ext-real Element of REAL
|[(E-bound p),(upper_bound (proj2 | (E-most p)))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
W-min p is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
W-bound p is V11() real ext-real Element of REAL
lower_bound (proj1 | p) is V11() real ext-real Element of REAL
lower_bound ((proj1 | p) .: the carrier of ((TOP-REAL 2) | p)) is V11() real ext-real Element of REAL
W-most p is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
SW-corner p is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
|[(W-bound p),(S-bound p)]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
NW-corner p is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
|[(W-bound p),(N-bound p)]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner p),(NW-corner p)) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner p),(NW-corner p))) /\ p is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (W-most p) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (W-most p) is V15() V18( the carrier of ((TOP-REAL 2) | (W-most p))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (W-most p)), REAL ) V212((TOP-REAL 2) | (W-most p)) Element of K6(K7( the carrier of ((TOP-REAL 2) | (W-most p)),REAL))
the carrier of ((TOP-REAL 2) | (W-most p)) is set
K7( the carrier of ((TOP-REAL 2) | (W-most p)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (W-most p)),REAL)) is non empty set
lower_bound (proj2 | (W-most p)) is V11() real ext-real Element of REAL
(proj2 | (W-most p)) .: the carrier of ((TOP-REAL 2) | (W-most p)) is Element of K6(REAL)
lower_bound ((proj2 | (W-most p)) .: the carrier of ((TOP-REAL 2) | (W-most p))) is V11() real ext-real Element of REAL
|[(W-bound p),(lower_bound (proj2 | (W-most p)))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
rng (Cage (p,C)) is non trivial functional Element of K6( the carrier of (TOP-REAL 2))
(Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))) /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
W-max (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
W-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V15() V18( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))), REAL ) V212((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),REAL))
the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is set
K7( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),REAL)) is non empty set
lower_bound (proj1 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is V11() real ext-real Element of REAL
(proj1 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) .: the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is Element of K6(REAL)
lower_bound ((proj1 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) .: the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is V11() real ext-real Element of REAL
W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
SW-corner (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
S-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V11() real ext-real Element of REAL
proj2 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V15() V18( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))), REAL ) V212((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),REAL))
lower_bound (proj2 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is V11() real ext-real Element of REAL
(proj2 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) .: the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is Element of K6(REAL)
lower_bound ((proj2 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) .: the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),(S-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
NW-corner (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
N-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) .: the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),(N-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),(NW-corner (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),(NW-corner (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))))) /\ (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is V15() V18( the carrier of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))), REAL ) V212((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))),REAL))
the carrier of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is set
K7( the carrier of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))),REAL)) is non empty set
upper_bound (proj2 | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is V11() real ext-real Element of REAL
(proj2 | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is Element of K6(REAL)
upper_bound ((proj2 | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),(upper_bound (proj2 | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(W-max (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) .. (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
N-min (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
NE-corner (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
E-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is V11() real ext-real Element of REAL
upper_bound ((proj1 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) .: the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),(N-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((NW-corner (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),(NE-corner (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((NW-corner (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),(NE-corner (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))))) /\ (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is V15() V18( the carrier of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))), REAL ) V212((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))),REAL))
the carrier of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is set
K7( the carrier of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))),REAL)) is non empty set
lower_bound (proj1 | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is V11() real ext-real Element of REAL
(proj1 | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is Element of K6(REAL)
lower_bound ((proj1 | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))))),(N-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(N-min (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) .. (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
N-max (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
upper_bound (proj1 | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is V11() real ext-real Element of REAL
upper_bound ((proj1 | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))))) is V11() real ext-real Element of REAL
|[(upper_bound (proj1 | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))))),(N-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(N-max (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) .. (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(E-max (L~ (Cage (p,C)))) .. (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
ii2 is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like non constant V28() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard FinSequence of the carrier of (TOP-REAL 2)
right_cell (ii2,1,(Gauge (p,C))) is functional Element of K6( the carrier of (TOP-REAL 2))
L~ ii2 is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
(right_cell (ii2,1,(Gauge (p,C)))) \ (L~ ii2) is functional Element of K6( the carrier of (TOP-REAL 2))
RightComp ii2 is non empty functional Element of K6( the carrier of (TOP-REAL 2))
(L~ (jj1 ^' d1)) \/ (L~ p2) is non empty functional Element of K6( the carrier of (TOP-REAL 2))
((L~ jj1) \/ (L~ d1)) \/ (L~ p2) is non empty functional Element of K6( the carrier of (TOP-REAL 2))
(L~ (Upper_Seq (p,C))) \/ (L~ (Lower_Seq (p,C))) is non empty functional Element of K6( the carrier of (TOP-REAL 2))
right_cell ((Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))),1) is functional Element of K6( the carrier of (TOP-REAL 2))
GoB (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))) is V15() non empty-yielding V18( NAT ) V19(K307( the carrier of (TOP-REAL 2))) Function-like V28() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K307( the carrier of (TOP-REAL 2))
right_cell ((Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))),1,(GoB (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is functional Element of K6( the carrier of (TOP-REAL 2))
GoB (Cage (p,C)) is V15() non empty-yielding V18( NAT ) V19(K307( the carrier of (TOP-REAL 2))) Function-like V28() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K307( the carrier of (TOP-REAL 2))
right_cell ((Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))),1,(GoB (Cage (p,C)))) is functional Element of K6( the carrier of (TOP-REAL 2))
right_cell ((Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))),1,(Gauge (p,C))) is functional Element of K6( the carrier of (TOP-REAL 2))
(Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))) -: (E-max (L~ (Cage (p,C)))) is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like special unfolded FinSequence of the carrier of (TOP-REAL 2)
right_cell (((Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))) -: (E-max (L~ (Cage (p,C))))),1,(Gauge (p,C))) is functional Element of K6( the carrier of (TOP-REAL 2))
right_cell ((Upper_Seq (p,C)),1,(Gauge (p,C))) is functional Element of K6( the carrier of (TOP-REAL 2))
right_cell ((R_Cut ((Upper_Seq (p,C)),((Gauge (p,C)) * (p9,r)))),1,(Gauge (p,C))) is functional Element of K6( the carrier of (TOP-REAL 2))
right_cell ((jj1 ^' d1),1,(Gauge (p,C))) is functional Element of K6( the carrier of (TOP-REAL 2))
ii2 /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
ii2 /. 2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(jj1 ^' d1) /. 2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(Upper_Seq (p,C)) ^' (Lower_Seq (p,C)) is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
((Upper_Seq (p,C)) ^' (Lower_Seq (p,C))) /. 2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))) /. 2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(L~ jj1) \/ (L~ p2) is non empty functional Element of K6( the carrier of (TOP-REAL 2))
W-min ((L~ jj1) \/ (L~ p2)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
W-bound ((L~ jj1) \/ (L~ p2)) is V11() real ext-real Element of REAL
(TOP-REAL 2) | ((L~ jj1) \/ (L~ p2)) is strict T_2 SubSpace of TOP-REAL 2
proj1 | ((L~ jj1) \/ (L~ p2)) is V15() V18( the carrier of ((TOP-REAL 2) | ((L~ jj1) \/ (L~ p2)))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | ((L~ jj1) \/ (L~ p2))), REAL ) V212((TOP-REAL 2) | ((L~ jj1) \/ (L~ p2))) Element of K6(K7( the carrier of ((TOP-REAL 2) | ((L~ jj1) \/ (L~ p2))),REAL))
the carrier of ((TOP-REAL 2) | ((L~ jj1) \/ (L~ p2))) is set
K7( the carrier of ((TOP-REAL 2) | ((L~ jj1) \/ (L~ p2))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | ((L~ jj1) \/ (L~ p2))),REAL)) is non empty set
lower_bound (proj1 | ((L~ jj1) \/ (L~ p2))) is V11() real ext-real Element of REAL
(proj1 | ((L~ jj1) \/ (L~ p2))) .: the carrier of ((TOP-REAL 2) | ((L~ jj1) \/ (L~ p2))) is Element of K6(REAL)
lower_bound ((proj1 | ((L~ jj1) \/ (L~ p2))) .: the carrier of ((TOP-REAL 2) | ((L~ jj1) \/ (L~ p2)))) is V11() real ext-real Element of REAL
W-most ((L~ jj1) \/ (L~ p2)) is functional Element of K6( the carrier of (TOP-REAL 2))
SW-corner ((L~ jj1) \/ (L~ p2)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
S-bound ((L~ jj1) \/ (L~ p2)) is V11() real ext-real Element of REAL
proj2 | ((L~ jj1) \/ (L~ p2)) is V15() V18( the carrier of ((TOP-REAL 2) | ((L~ jj1) \/ (L~ p2)))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | ((L~ jj1) \/ (L~ p2))), REAL ) V212((TOP-REAL 2) | ((L~ jj1) \/ (L~ p2))) Element of K6(K7( the carrier of ((TOP-REAL 2) | ((L~ jj1) \/ (L~ p2))),REAL))
lower_bound (proj2 | ((L~ jj1) \/ (L~ p2))) is V11() real ext-real Element of REAL
(proj2 | ((L~ jj1) \/ (L~ p2))) .: the carrier of ((TOP-REAL 2) | ((L~ jj1) \/ (L~ p2))) is Element of K6(REAL)
lower_bound ((proj2 | ((L~ jj1) \/ (L~ p2))) .: the carrier of ((TOP-REAL 2) | ((L~ jj1) \/ (L~ p2)))) is V11() real ext-real Element of REAL
|[(W-bound ((L~ jj1) \/ (L~ p2))),(S-bound ((L~ jj1) \/ (L~ p2)))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
NW-corner ((L~ jj1) \/ (L~ p2)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
N-bound ((L~ jj1) \/ (L~ p2)) is V11() real ext-real Element of REAL
upper_bound (proj2 | ((L~ jj1) \/ (L~ p2))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | ((L~ jj1) \/ (L~ p2))) .: the carrier of ((TOP-REAL 2) | ((L~ jj1) \/ (L~ p2)))) is V11() real ext-real Element of REAL
|[(W-bound ((L~ jj1) \/ (L~ p2))),(N-bound ((L~ jj1) \/ (L~ p2)))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner ((L~ jj1) \/ (L~ p2))),(NW-corner ((L~ jj1) \/ (L~ p2)))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner ((L~ jj1) \/ (L~ p2))),(NW-corner ((L~ jj1) \/ (L~ p2))))) /\ ((L~ jj1) \/ (L~ p2)) is functional Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (W-most ((L~ jj1) \/ (L~ p2))) is strict T_2 SubSpace of TOP-REAL 2
proj2 | (W-most ((L~ jj1) \/ (L~ p2))) is V15() V18( the carrier of ((TOP-REAL 2) | (W-most ((L~ jj1) \/ (L~ p2))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (W-most ((L~ jj1) \/ (L~ p2)))), REAL ) V212((TOP-REAL 2) | (W-most ((L~ jj1) \/ (L~ p2)))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (W-most ((L~ jj1) \/ (L~ p2)))),REAL))
the carrier of ((TOP-REAL 2) | (W-most ((L~ jj1) \/ (L~ p2)))) is set
K7( the carrier of ((TOP-REAL 2) | (W-most ((L~ jj1) \/ (L~ p2)))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (W-most ((L~ jj1) \/ (L~ p2)))),REAL)) is non empty set
lower_bound (proj2 | (W-most ((L~ jj1) \/ (L~ p2)))) is V11() real ext-real Element of REAL
(proj2 | (W-most ((L~ jj1) \/ (L~ p2)))) .: the carrier of ((TOP-REAL 2) | (W-most ((L~ jj1) \/ (L~ p2)))) is Element of K6(REAL)
lower_bound ((proj2 | (W-most ((L~ jj1) \/ (L~ p2)))) .: the carrier of ((TOP-REAL 2) | (W-most ((L~ jj1) \/ (L~ p2))))) is V11() real ext-real Element of REAL
|[(W-bound ((L~ jj1) \/ (L~ p2))),(lower_bound (proj2 | (W-most ((L~ jj1) \/ (L~ p2)))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(W-min ((L~ jj1) \/ (L~ p2))) `1 is V11() real ext-real Element of REAL
((L~ jj1) \/ (L~ p2)) \/ (L~ d1) is non empty functional Element of K6( the carrier of (TOP-REAL 2))
W-min (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
W-bound (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)) is strict T_2 SubSpace of TOP-REAL 2
proj1 | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)) is V15() V18( the carrier of ((TOP-REAL 2) | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))), REAL ) V212((TOP-REAL 2) | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))),REAL))
the carrier of ((TOP-REAL 2) | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))) is set
K7( the carrier of ((TOP-REAL 2) | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))),REAL)) is non empty set
lower_bound (proj1 | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))) is V11() real ext-real Element of REAL
(proj1 | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))) .: the carrier of ((TOP-REAL 2) | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))) is Element of K6(REAL)
lower_bound ((proj1 | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))) .: the carrier of ((TOP-REAL 2) | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))) is V11() real ext-real Element of REAL
W-most (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)) is functional Element of K6( the carrier of (TOP-REAL 2))
SW-corner (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
S-bound (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)) is V11() real ext-real Element of REAL
proj2 | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)) is V15() V18( the carrier of ((TOP-REAL 2) | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))), REAL ) V212((TOP-REAL 2) | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))),REAL))
lower_bound (proj2 | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))) is V11() real ext-real Element of REAL
(proj2 | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))) .: the carrier of ((TOP-REAL 2) | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))) is Element of K6(REAL)
lower_bound ((proj2 | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))) .: the carrier of ((TOP-REAL 2) | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))) is V11() real ext-real Element of REAL
|[(W-bound (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))),(S-bound (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
NW-corner (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
N-bound (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)) is V11() real ext-real Element of REAL
upper_bound (proj2 | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))) .: the carrier of ((TOP-REAL 2) | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))) is V11() real ext-real Element of REAL
|[(W-bound (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))),(N-bound (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))),(NW-corner (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))),(NW-corner (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))))) /\ (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)) is functional Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (W-most (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))) is strict T_2 SubSpace of TOP-REAL 2
proj2 | (W-most (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))) is V15() V18( the carrier of ((TOP-REAL 2) | (W-most (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (W-most (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))), REAL ) V212((TOP-REAL 2) | (W-most (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (W-most (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))),REAL))
the carrier of ((TOP-REAL 2) | (W-most (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))) is set
K7( the carrier of ((TOP-REAL 2) | (W-most (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (W-most (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))),REAL)) is non empty set
lower_bound (proj2 | (W-most (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))) is V11() real ext-real Element of REAL
(proj2 | (W-most (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))) .: the carrier of ((TOP-REAL 2) | (W-most (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))) is Element of K6(REAL)
lower_bound ((proj2 | (W-most (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))) .: the carrier of ((TOP-REAL 2) | (W-most (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))))) is V11() real ext-real Element of REAL
|[(W-bound (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))),(lower_bound (proj2 | (W-most (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
W-min (L~ ii2) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
W-bound (L~ ii2) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ ii2) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ ii2) is V15() V18( the carrier of ((TOP-REAL 2) | (L~ ii2))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ ii2)), REAL ) V212((TOP-REAL 2) | (L~ ii2)) Element of K6(K7( the carrier of ((TOP-REAL 2) | (L~ ii2)),REAL))
the carrier of ((TOP-REAL 2) | (L~ ii2)) is set
K7( the carrier of ((TOP-REAL 2) | (L~ ii2)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (L~ ii2)),REAL)) is non empty set
lower_bound (proj1 | (L~ ii2)) is V11() real ext-real Element of REAL
(proj1 | (L~ ii2)) .: the carrier of ((TOP-REAL 2) | (L~ ii2)) is Element of K6(REAL)
lower_bound ((proj1 | (L~ ii2)) .: the carrier of ((TOP-REAL 2) | (L~ ii2))) is V11() real ext-real Element of REAL
W-most (L~ ii2) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
SW-corner (L~ ii2) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
S-bound (L~ ii2) is V11() real ext-real Element of REAL
proj2 | (L~ ii2) is V15() V18( the carrier of ((TOP-REAL 2) | (L~ ii2))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ ii2)), REAL ) V212((TOP-REAL 2) | (L~ ii2)) Element of K6(K7( the carrier of ((TOP-REAL 2) | (L~ ii2)),REAL))
lower_bound (proj2 | (L~ ii2)) is V11() real ext-real Element of REAL
(proj2 | (L~ ii2)) .: the carrier of ((TOP-REAL 2) | (L~ ii2)) is Element of K6(REAL)
lower_bound ((proj2 | (L~ ii2)) .: the carrier of ((TOP-REAL 2) | (L~ ii2))) is V11() real ext-real Element of REAL
|[(W-bound (L~ ii2)),(S-bound (L~ ii2))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
NW-corner (L~ ii2) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
N-bound (L~ ii2) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ ii2)) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (L~ ii2)) .: the carrier of ((TOP-REAL 2) | (L~ ii2))) is V11() real ext-real Element of REAL
|[(W-bound (L~ ii2)),(N-bound (L~ ii2))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner (L~ ii2)),(NW-corner (L~ ii2))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner (L~ ii2)),(NW-corner (L~ ii2)))) /\ (L~ ii2) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (W-most (L~ ii2)) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (W-most (L~ ii2)) is V15() V18( the carrier of ((TOP-REAL 2) | (W-most (L~ ii2)))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (W-most (L~ ii2))), REAL ) V212((TOP-REAL 2) | (W-most (L~ ii2))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (W-most (L~ ii2))),REAL))
the carrier of ((TOP-REAL 2) | (W-most (L~ ii2))) is set
K7( the carrier of ((TOP-REAL 2) | (W-most (L~ ii2))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (W-most (L~ ii2))),REAL)) is non empty set
lower_bound (proj2 | (W-most (L~ ii2))) is V11() real ext-real Element of REAL
(proj2 | (W-most (L~ ii2))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ ii2))) is Element of K6(REAL)
lower_bound ((proj2 | (W-most (L~ ii2))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ ii2)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ ii2)),(lower_bound (proj2 | (W-most (L~ ii2))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
rng ii2 is non trivial functional Element of K6( the carrier of (TOP-REAL 2))
dom ii2 is non trivial Element of K6(NAT)
(ii2 /. 2) `1 is V11() real ext-real Element of REAL
(W-min (L~ ii2)) `1 is V11() real ext-real Element of REAL
Rotate (ii2,(W-min (L~ ii2))) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like non constant V28() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard FinSequence of the carrier of (TOP-REAL 2)
(Rotate (ii2,(W-min (L~ ii2)))) /. 2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(Upper_Seq (p,C)) . (len (Upper_Seq (p,C))) is V15() Function-like set
(Upper_Seq (p,C)) /. (len (Upper_Seq (p,C))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
east_halfline (E-max p) is non empty functional connected V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
Gji is set
Gij9 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(east_halfline (E-max p)) /\ (L~ (Cage (p,C))) is functional Element of K6( the carrier of (TOP-REAL 2))
Gij9 `1 is V11() real ext-real Element of REAL
Gij is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like non constant V28() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the carrier of (TOP-REAL 2)
L~ Gij is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
Gji is set
Gij9 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
Gij9 `1 is V11() real ext-real Element of REAL
Gij9 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
Gij9 `1 is V11() real ext-real Element of REAL
Gij9 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
Gij9 `1 is V11() real ext-real Element of REAL
Gij9 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
Gij9 `1 is V11() real ext-real Element of REAL
s + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
(len (Gauge (p,C))) - 1 is V11() real ext-real Element of REAL
(len (Gauge (p,C))) + (- 1) is V11() real ext-real set
(len (Gauge (p,C))) -' 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(Gauge (p,C)) * (((len (Gauge (p,C))) -' 1),1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * (((len (Gauge (p,C))) -' 1),1)) `1 is V11() real ext-real Element of REAL
(E-max p) `1 is V11() real ext-real Element of REAL
Gij9 `2 is V11() real ext-real Element of REAL
(E-max p) `2 is V11() real ext-real Element of REAL
Gji is set
Gij9 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(east_halfline (E-max p)) /\ (L~ (Cage (p,C))) is functional Element of K6( the carrier of (TOP-REAL 2))
Gij9 `1 is V11() real ext-real Element of REAL
(E-max p) `2 is V11() real ext-real Element of REAL
Gij9 `2 is V11() real ext-real Element of REAL
Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like non constant V28() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the carrier of (TOP-REAL 2)
right_cell ((Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))),1) is functional Element of K6( the carrier of (TOP-REAL 2))
(Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))) -: (W-min (L~ (Cage (p,C)))) is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like special unfolded FinSequence of the carrier of (TOP-REAL 2)
LSeg ((Lower_Seq (p,C)),1) is functional Element of K6( the carrier of (TOP-REAL 2))
LSeg ((Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))),1) is functional Element of K6( the carrier of (TOP-REAL 2))
L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
len (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
GoB (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))) is V15() non empty-yielding V18( NAT ) V19(K307( the carrier of (TOP-REAL 2))) Function-like V28() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K307( the carrier of (TOP-REAL 2))
(Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))) /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
E-max (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
E-bound (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))) is V15() V18( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))), REAL ) V212((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))),REAL))
the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) is set
K7( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))),REAL)) is non empty set
upper_bound (proj1 | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) is V11() real ext-real Element of REAL
(proj1 | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) .: the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) is Element of K6(REAL)
upper_bound ((proj1 | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) .: the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) is V11() real ext-real Element of REAL
E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
SE-corner (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
S-bound (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))) is V11() real ext-real Element of REAL
proj2 | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))) is V15() V18( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))), REAL ) V212((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))),REAL))
lower_bound (proj2 | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) is V11() real ext-real Element of REAL
(proj2 | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) .: the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) is Element of K6(REAL)
lower_bound ((proj2 | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) .: the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))),(S-bound (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
NE-corner (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
N-bound (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) .: the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))),(N-bound (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))),(NE-corner (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SE-corner (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))),(NE-corner (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))))) /\ (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) is V15() V18( the carrier of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))), REAL ) V212((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))),REAL))
the carrier of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) is set
K7( the carrier of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))),REAL)) is non empty set
upper_bound (proj2 | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) is V11() real ext-real Element of REAL
(proj2 | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) is Element of K6(REAL)
upper_bound ((proj2 | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))),(upper_bound (proj2 | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))) /. (1 + 1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
x is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
x9 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
x9 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
[x,(x9 + 1)] is set
{x,(x9 + 1)} is non empty set
{x} is non empty trivial V35(1) set
{{x,(x9 + 1)},{x}} is non empty set
[x,x9] is set
{x,x9} is non empty set
{{x,x9},{x}} is non empty set
(Gauge (p,C)) * (x,(x9 + 1)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(Gauge (p,C)) * (x,x9) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
jj2 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(Gauge (p,C)) * ((len (Gauge (p,C))),jj2) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
[(len (Gauge (p,C))),jj2] is set
{(len (Gauge (p,C))),jj2} is non empty set
{{(len (Gauge (p,C))),jj2},{(len (Gauge (p,C)))}} is non empty set
x + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
(x9 + 1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
x -' 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
cell ((Gauge (p,C)),(x -' 1),x9) is functional Element of K6( the carrier of (TOP-REAL 2))
(x -' 1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
4 - 1 is V11() real ext-real Element of REAL
4 + (- 1) is V11() real ext-real set
x - 1 is V11() real ext-real Element of REAL
x + (- 1) is V11() real ext-real set
(Gauge (p,C)) * ((x -' 1),x9) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * ((x -' 1),x9)) `2 is V11() real ext-real Element of REAL
(Gauge (p,C)) * ((x -' 1),(x9 + 1)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * ((x -' 1),(x9 + 1))) `2 is V11() real ext-real Element of REAL
(Gauge (p,C)) * (1,x9) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * (1,x9)) `2 is V11() real ext-real Element of REAL
((Gauge (p,C)) * (x,x9)) `2 is V11() real ext-real Element of REAL
(Gauge (p,C)) * (1,(x9 + 1)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * (1,(x9 + 1))) `2 is V11() real ext-real Element of REAL
((Gauge (p,C)) * (x,(x9 + 1))) `2 is V11() real ext-real Element of REAL
(Gauge (p,C)) * ((len (Gauge (p,C))),x9) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * ((len (Gauge (p,C))),x9)) `1 is V11() real ext-real Element of REAL
(Gauge (p,C)) * ((len (Gauge (p,C))),(x9 + 1)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * ((len (Gauge (p,C))),(x9 + 1))) `1 is V11() real ext-real Element of REAL
LSeg (((Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))) /. 1),((Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))) /. (1 + 1))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
Index (Gij9,p2) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
LSeg (p2,(Index (Gij9,p2))) is functional Element of K6( the carrier of (TOP-REAL 2))
((Gauge (p,C)) * (s,rr)) .. (Lower_Seq (p,C)) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
mid ((Lower_Seq (p,C)),(((Gauge (p,C)) * (s,rr)) .. (Lower_Seq (p,C))),(len (Lower_Seq (p,C)))) is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
Index (((Gauge (p,C)) * (s,rr)),(Lower_Seq (p,C))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(Index (((Gauge (p,C)) * (s,rr)),(Lower_Seq (p,C)))) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
t is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative set
(Lower_Seq (p,C)) . t is V15() Function-like set
len (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (s,rr)))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(len (Lower_Seq (p,C))) - (Index (((Gauge (p,C)) * (s,rr)),(Lower_Seq (p,C)))) is V11() real ext-real Element of REAL
- (Index (((Gauge (p,C)) * (s,rr)),(Lower_Seq (p,C)))) is V11() real ext-real non positive set
(len (Lower_Seq (p,C))) + (- (Index (((Gauge (p,C)) * (s,rr)),(Lower_Seq (p,C))))) is V11() real ext-real set
(Index (Gij9,p2)) + (((Gauge (p,C)) * (s,rr)) .. (Lower_Seq (p,C))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
((Index (Gij9,p2)) + (((Gauge (p,C)) * (s,rr)) .. (Lower_Seq (p,C)))) -' 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
0 + (Index (((Gauge (p,C)) * (s,rr)),(Lower_Seq (p,C)))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(len (Lower_Seq (p,C))) -' (Index (((Gauge (p,C)) * (s,rr)),(Lower_Seq (p,C)))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(Index (Gij9,p2)) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
((len (Lower_Seq (p,C))) -' (Index (((Gauge (p,C)) * (s,rr)),(Lower_Seq (p,C))))) - 1 is V11() real ext-real Element of REAL
((len (Lower_Seq (p,C))) -' (Index (((Gauge (p,C)) * (s,rr)),(Lower_Seq (p,C))))) + (- 1) is V11() real ext-real set
((len (Lower_Seq (p,C))) - (Index (((Gauge (p,C)) * (s,rr)),(Lower_Seq (p,C))))) - 1 is V11() real ext-real Element of REAL
((len (Lower_Seq (p,C))) - (Index (((Gauge (p,C)) * (s,rr)),(Lower_Seq (p,C))))) + (- 1) is V11() real ext-real set
(len (Lower_Seq (p,C))) - (((Gauge (p,C)) * (s,rr)) .. (Lower_Seq (p,C))) is V11() real ext-real Element of REAL
- (((Gauge (p,C)) * (s,rr)) .. (Lower_Seq (p,C))) is V11() real ext-real non positive set
(len (Lower_Seq (p,C))) + (- (((Gauge (p,C)) * (s,rr)) .. (Lower_Seq (p,C)))) is V11() real ext-real set
(len (Lower_Seq (p,C))) -' (((Gauge (p,C)) * (s,rr)) .. (Lower_Seq (p,C))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
((len (Lower_Seq (p,C))) -' (((Gauge (p,C)) * (s,rr)) .. (Lower_Seq (p,C)))) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
LSeg ((mid ((Lower_Seq (p,C)),(((Gauge (p,C)) * (s,rr)) .. (Lower_Seq (p,C))),(len (Lower_Seq (p,C))))),(Index (Gij9,p2))) is functional Element of K6( the carrier of (TOP-REAL 2))
LSeg ((Lower_Seq (p,C)),(((Index (Gij9,p2)) + (((Gauge (p,C)) * (s,rr)) .. (Lower_Seq (p,C)))) -' 1)) is functional Element of K6( the carrier of (TOP-REAL 2))
(1 + 1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
((1 + 1) + 1) - 1 is V11() real ext-real Element of REAL
((1 + 1) + 1) + (- 1) is V11() real ext-real set
((Index (Gij9,p2)) + (((Gauge (p,C)) * (s,rr)) .. (Lower_Seq (p,C)))) - 1 is V11() real ext-real Element of REAL
((Index (Gij9,p2)) + (((Gauge (p,C)) * (s,rr)) .. (Lower_Seq (p,C)))) + (- 1) is V11() real ext-real set
(LSeg ((Lower_Seq (p,C)),1)) /\ (LSeg ((Lower_Seq (p,C)),(((Index (Gij9,p2)) + (((Gauge (p,C)) * (s,rr)) .. (Lower_Seq (p,C)))) -' 1))) is functional Element of K6( the carrier of (TOP-REAL 2))
(Lower_Seq (p,C)) /. 2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
{((Lower_Seq (p,C)) /. 2)} is non empty trivial functional V35(1) set
Gij9 .. (Lower_Seq (p,C)) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(Gauge (p,C)) * ((len (Gauge (p,C))),r) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * ((len (Gauge (p,C))),r)) `1 is V11() real ext-real Element of REAL
(L~ Gij) ` is non empty functional Element of K6( the carrier of (TOP-REAL 2))
Gji is functional Element of K6( the carrier of (TOP-REAL 2))
UBD (L~ Gij) is non empty functional open connected Element of K6( the carrier of (TOP-REAL 2))
LeftComp Gij is non empty functional Element of K6( the carrier of (TOP-REAL 2))
((Gauge (p,C)) * (s,rr)) `1 is V11() real ext-real Element of REAL
{((Gauge (p,C)) * (p9,rr))} is non empty trivial functional V35(1) set
((Gauge (p,C)) * (p9,r)) `2 is V11() real ext-real Element of REAL
{((Gauge (p,C)) * (p9,rr))} is non empty trivial functional V35(1) set
((Gauge (p,C)) * (s,rr)) `1 is V11() real ext-real Element of REAL
((Gauge (p,C)) * (p9,r)) `2 is V11() real ext-real Element of REAL
C is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
p is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
Gauge (p,C) is V15() non empty-yielding V18( NAT ) V19(K307( the carrier of (TOP-REAL 2))) Function-like V28() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K307( the carrier of (TOP-REAL 2))
len (Gauge (p,C)) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
width (Gauge (p,C)) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
Upper_Seq (p,C) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V28() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
L~ (Upper_Seq (p,C)) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
Lower_Seq (p,C) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V28() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
L~ (Lower_Seq (p,C)) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
Upper_Arc p is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
s is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
p9 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
r is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
rr is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(Gauge (p,C)) * (p9,r) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(Gauge (p,C)) * (p9,rr) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(Gauge (p,C)) * (s,rr) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) is non empty functional Element of K6( the carrier of (TOP-REAL 2))
((LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))))) /\ (L~ (Upper_Seq (p,C))) is functional Element of K6( the carrier of (TOP-REAL 2))
{((Gauge (p,C)) * (p9,r))} is non empty trivial functional V35(1) set
((LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))))) /\ (L~ (Lower_Seq (p,C))) is functional Element of K6( the carrier of (TOP-REAL 2))
{((Gauge (p,C)) * (s,rr))} is non empty trivial functional V35(1) set
Cage (p,C) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like non constant V28() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the carrier of (TOP-REAL 2)
L~ (Cage (p,C)) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
W-min (L~ (Cage (p,C))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
W-bound (L~ (Cage (p,C))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (p,C))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ (Cage (p,C))) is V15() V18( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))), REAL ) V212((TOP-REAL 2) | (L~ (Cage (p,C)))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))),REAL))
the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))) is set
K7( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))),REAL)) is non empty set
lower_bound (proj1 | (L~ (Cage (p,C)))) is V11() real ext-real Element of REAL
(proj1 | (L~ (Cage (p,C)))) .: the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))) is Element of K6(REAL)
lower_bound ((proj1 | (L~ (Cage (p,C)))) .: the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C))))) is V11() real ext-real Element of REAL
W-most (L~ (Cage (p,C))) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
SW-corner (L~ (Cage (p,C))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
S-bound (L~ (Cage (p,C))) is V11() real ext-real Element of REAL
proj2 | (L~ (Cage (p,C))) is V15() V18( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))), REAL ) V212((TOP-REAL 2) | (L~ (Cage (p,C)))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))),REAL))
lower_bound (proj2 | (L~ (Cage (p,C)))) is V11() real ext-real Element of REAL
(proj2 | (L~ (Cage (p,C)))) .: the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))) is Element of K6(REAL)
lower_bound ((proj2 | (L~ (Cage (p,C)))) .: the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Cage (p,C)))),(S-bound (L~ (Cage (p,C))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
NW-corner (L~ (Cage (p,C))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
N-bound (L~ (Cage (p,C))) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ (Cage (p,C)))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (L~ (Cage (p,C)))) .: the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Cage (p,C)))),(N-bound (L~ (Cage (p,C))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (p,C)))),(NW-corner (L~ (Cage (p,C))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner (L~ (Cage (p,C)))),(NW-corner (L~ (Cage (p,C)))))) /\ (L~ (Cage (p,C))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (W-most (L~ (Cage (p,C)))) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Cage (p,C)))) is V15() V18( the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C)))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C))))), REAL ) V212((TOP-REAL 2) | (W-most (L~ (Cage (p,C))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C))))),REAL))
the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C))))) is set
K7( the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C))))),REAL)) is non empty set
lower_bound (proj2 | (W-most (L~ (Cage (p,C))))) is V11() real ext-real Element of REAL
(proj2 | (W-most (L~ (Cage (p,C))))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C))))) is Element of K6(REAL)
lower_bound ((proj2 | (W-most (L~ (Cage (p,C))))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C)))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Cage (p,C)))),(lower_bound (proj2 | (W-most (L~ (Cage (p,C))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
E-max (L~ (Cage (p,C))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
E-bound (L~ (Cage (p,C))) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ (Cage (p,C)))) is V11() real ext-real Element of REAL
upper_bound ((proj1 | (L~ (Cage (p,C)))) .: the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C))))) is V11() real ext-real Element of REAL
E-most (L~ (Cage (p,C))) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
SE-corner (L~ (Cage (p,C))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
|[(E-bound (L~ (Cage (p,C)))),(S-bound (L~ (Cage (p,C))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
NE-corner (L~ (Cage (p,C))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
|[(E-bound (L~ (Cage (p,C)))),(N-bound (L~ (Cage (p,C))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Cage (p,C)))),(NE-corner (L~ (Cage (p,C))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SE-corner (L~ (Cage (p,C)))),(NE-corner (L~ (Cage (p,C)))))) /\ (L~ (Cage (p,C))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (E-most (L~ (Cage (p,C)))) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Cage (p,C)))) is V15() V18( the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (p,C)))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (p,C))))), REAL ) V212((TOP-REAL 2) | (E-most (L~ (Cage (p,C))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (p,C))))),REAL))
the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (p,C))))) is set
K7( the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (p,C))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (p,C))))),REAL)) is non empty set
upper_bound (proj2 | (E-most (L~ (Cage (p,C))))) is V11() real ext-real Element of REAL
(proj2 | (E-most (L~ (Cage (p,C))))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (p,C))))) is Element of K6(REAL)
upper_bound ((proj2 | (E-most (L~ (Cage (p,C))))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (p,C)))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Cage (p,C)))),(upper_bound (proj2 | (E-most (L~ (Cage (p,C))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
<*((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))*> is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() V35(3) FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ <*((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))*> is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))) is non empty functional Element of K6( the carrier of (TOP-REAL 2))
[p9,r] is set
{p9,r} is non empty set
{p9} is non empty trivial V35(1) set
{{p9,r},{p9}} is non empty set
Indices (Gauge (p,C)) is set
[s,rr] is set
{s,rr} is non empty set
{s} is non empty trivial V35(1) set
{{s,rr},{s}} is non empty set
[p9,rr] is set
{p9,rr} is non empty set
{{p9,rr},{p9}} is non empty set
R_Cut ((Upper_Seq (p,C)),((Gauge (p,C)) * (p9,r))) is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (s,rr))) is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len (Upper_Seq (p,C)) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
dom (Upper_Seq (p,C)) is non trivial Element of K6(NAT)
(Upper_Seq (p,C)) . 1 is V15() Function-like set
(Upper_Seq (p,C)) /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(W-min (L~ (Cage (p,C)))) `1 is V11() real ext-real Element of REAL
(Gauge (p,C)) * (1,rr) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * (1,rr)) `1 is V11() real ext-real Element of REAL
[1,rr] is set
{1,rr} is non empty set
{{1,rr},{1}} is non empty set
1 + 2 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
len (Lower_Seq (p,C)) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
dom (Lower_Seq (p,C)) is non trivial Element of K6(NAT)
(Lower_Seq (p,C)) . (len (Lower_Seq (p,C))) is V15() Function-like set
(Lower_Seq (p,C)) /. (len (Lower_Seq (p,C))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
[(len (Gauge (p,C))),rr] is set
{(len (Gauge (p,C))),rr} is non empty set
{(len (Gauge (p,C)))} is non empty trivial V35(1) set
{{(len (Gauge (p,C))),rr},{(len (Gauge (p,C)))}} is non empty set
(Lower_Seq (p,C)) . 1 is V15() Function-like set
(Lower_Seq (p,C)) /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(E-max (L~ (Cage (p,C)))) `1 is V11() real ext-real Element of REAL
(Gauge (p,C)) * ((len (Gauge (p,C))),rr) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * ((len (Gauge (p,C))),rr)) `1 is V11() real ext-real Element of REAL
1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
c2 is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V28() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
len c2 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
rng (Upper_Seq (p,C)) is functional Element of K6( the carrier of (TOP-REAL 2))
ii1 is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V28() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
len ii1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
rng (Lower_Seq (p,C)) is functional Element of K6( the carrier of (TOP-REAL 2))
jj1 is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one non constant V28() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq s.c.c. FinSequence of the carrier of (TOP-REAL 2)
len jj1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
dom jj1 is non trivial Element of K6(NAT)
jj1 /. (len jj1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
jj1 . (len jj1) is V15() Function-like set
p2 is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one non constant V28() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq s.c.c. FinSequence of the carrier of (TOP-REAL 2)
len p2 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
dom p2 is non trivial Element of K6(NAT)
p2 /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
p2 . 1 is V15() Function-like set
(len jj1) - 1 is V11() real ext-real Element of REAL
- 1 is V11() real ext-real non positive set
(len jj1) + (- 1) is V11() real ext-real set
p2 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
p2 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
(len jj1) -' 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
LSeg (jj1,p2) is functional Element of K6( the carrier of (TOP-REAL 2))
L~ jj1 is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(LSeg (jj1,p2)) /\ (L~ <*((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))*>) is functional Element of K6( the carrier of (TOP-REAL 2))
jj1 /. p2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((jj1 /. p2),((Gauge (p,C)) * (p9,r))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
p29 is set
LSeg (p2,1) is functional Element of K6( the carrier of (TOP-REAL 2))
L~ p2 is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(LSeg (p2,1)) /\ (L~ <*((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))*>) is functional Element of K6( the carrier of (TOP-REAL 2))
p2 /. (1 + 1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg (((Gauge (p,C)) * (s,rr)),(p2 /. (1 + 1))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
p29 is set
(L~ <*((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))*>) /\ (LSeg (p2,1)) is functional Element of K6( the carrier of (TOP-REAL 2))
jj1 /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
p2 /. (len p2) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
rng jj1 is non trivial functional Element of K6( the carrier of (TOP-REAL 2))
rng p2 is non trivial functional Element of K6( the carrier of (TOP-REAL 2))
{(jj1 /. 1)} is non empty trivial functional V35(1) set
(L~ jj1) /\ (L~ p2) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
p29 is set
[(len (Gauge (p,C))),r] is set
{(len (Gauge (p,C))),r} is non empty set
{{(len (Gauge (p,C))),r},{(len (Gauge (p,C)))}} is non empty set
p29 is set
(L~ (Upper_Seq (p,C))) /\ (L~ (Lower_Seq (p,C))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
{(W-min (L~ (Cage (p,C)))),(E-max (L~ (Cage (p,C))))} is non empty functional set
(Gauge (p,C)) * ((len (Gauge (p,C))),r) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * ((len (Gauge (p,C))),r)) `1 is V11() real ext-real Element of REAL
jj1 /. 2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * (s,rr)) `1 is V11() real ext-real Element of REAL
((Gauge (p,C)) * (p9,r)) .. (Upper_Seq (p,C)) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
mid ((Upper_Seq (p,C)),1,(((Gauge (p,C)) * (p9,r)) .. (Upper_Seq (p,C)))) is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
(Upper_Seq (p,C)) | (((Gauge (p,C)) * (p9,r)) .. (Upper_Seq (p,C))) is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V28() FinSequence-like FinSubsequence-like special unfolded s.n.c. FinSequence of the carrier of (TOP-REAL 2)
(Upper_Seq (p,C)) /. 2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
i2 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
dom <*((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))*> is non trivial V35(3) Element of K6(NAT)
<*((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))*> /. i2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * (p9,rr)) `1 is V11() real ext-real Element of REAL
(Gauge (p,C)) * (p9,1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * (p9,1)) `1 is V11() real ext-real Element of REAL
((Gauge (p,C)) * (p9,r)) `1 is V11() real ext-real Element of REAL
((Gauge (p,C)) * (p9,rr)) `2 is V11() real ext-real Element of REAL
((Gauge (p,C)) * (1,rr)) `2 is V11() real ext-real Element of REAL
((Gauge (p,C)) * (s,rr)) `2 is V11() real ext-real Element of REAL
|[(((Gauge (p,C)) * (p9,r)) `1),(((Gauge (p,C)) * (s,rr)) `2)]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * (p9,r)) `2 is V11() real ext-real Element of REAL
<*((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))*> /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
len <*((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))*> is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
<*((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))*> /. (len <*((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))*>) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
i2 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ i2 is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
i2 /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
len i2 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
i2 /. (len i2) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
d1 is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V28() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
jj1 ^' d1 is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
(jj1 ^' d1) ^' p2 is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
W-bound (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) is V15() V18( the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))))), REAL ) V212((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))))),REAL))
the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))))) is set
K7( the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))))),REAL)) is non empty set
lower_bound (proj1 | (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))))) is V11() real ext-real Element of REAL
(proj1 | (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))))) .: the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))))) is Element of K6(REAL)
lower_bound ((proj1 | (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))))) .: the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))))) is V11() real ext-real Element of REAL
W-bound (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))) is V15() V18( the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr))))), REAL ) V212((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr))))),REAL))
the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr))))) is set
K7( the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr))))),REAL)) is non empty set
lower_bound (proj1 | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr))))) is V11() real ext-real Element of REAL
(proj1 | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr))))) .: the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr))))) is Element of K6(REAL)
lower_bound ((proj1 | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr))))) .: the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))))) is V11() real ext-real Element of REAL
W-bound ((LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr))))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | ((LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr))))) is strict T_2 SubSpace of TOP-REAL 2
proj1 | ((LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr))))) is V15() V18( the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr))))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))))), REAL ) V212((TOP-REAL 2) | ((LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))))),REAL))
the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))))) is set
K7( the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))))),REAL)) is non empty set
lower_bound (proj1 | ((LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))))) is V11() real ext-real Element of REAL
(proj1 | ((LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))))) .: the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))))) is Element of K6(REAL)
lower_bound ((proj1 | ((LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))))) .: the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr))))))) is V11() real ext-real Element of REAL
min ((W-bound (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))))),(W-bound (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))))) is V11() real ext-real set
L~ d1 is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
W-bound (L~ d1) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ d1) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ d1) is V15() V18( the carrier of ((TOP-REAL 2) | (L~ d1))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ d1)), REAL ) V212((TOP-REAL 2) | (L~ d1)) Element of K6(K7( the carrier of ((TOP-REAL 2) | (L~ d1)),REAL))
the carrier of ((TOP-REAL 2) | (L~ d1)) is set
K7( the carrier of ((TOP-REAL 2) | (L~ d1)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (L~ d1)),REAL)) is non empty set
lower_bound (proj1 | (L~ d1)) is V11() real ext-real Element of REAL
(proj1 | (L~ d1)) .: the carrier of ((TOP-REAL 2) | (L~ d1)) is Element of K6(REAL)
lower_bound ((proj1 | (L~ d1)) .: the carrier of ((TOP-REAL 2) | (L~ d1))) is V11() real ext-real Element of REAL
len (Cage (p,C)) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like non constant V28() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the carrier of (TOP-REAL 2)
len (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
len (jj1 ^' d1) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
1 + 0 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
len ((jj1 ^' d1) ^' p2) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
d1 /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(jj1 ^' d1) /. (len (jj1 ^' d1)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
<*((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))*> /. 3 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg (d1,1) is functional Element of K6( the carrier of (TOP-REAL 2))
LSeg (jj1,((len jj1) -' 1)) is functional Element of K6( the carrier of (TOP-REAL 2))
(LSeg (jj1,((len jj1) -' 1))) /\ (LSeg (d1,1)) is functional Element of K6( the carrier of (TOP-REAL 2))
2 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
len d1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
(LSeg (jj1,p2)) /\ (LSeg (d1,1)) is functional Element of K6( the carrier of (TOP-REAL 2))
ii2 is set
{(jj1 /. (len jj1))} is non empty trivial functional V35(1) set
(len d1) - 2 is V11() real ext-real Element of REAL
(len d1) + (- 2) is V11() real ext-real set
(len (jj1 ^' d1)) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
((len (jj1 ^' d1)) + 1) - 1 is V11() real ext-real Element of REAL
((len (jj1 ^' d1)) + 1) + (- 1) is V11() real ext-real set
(len jj1) + (len d1) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
((len jj1) + (len d1)) - 1 is V11() real ext-real Element of REAL
((len jj1) + (len d1)) + (- 1) is V11() real ext-real set
(len (jj1 ^' d1)) - 1 is V11() real ext-real Element of REAL
(len (jj1 ^' d1)) + (- 1) is V11() real ext-real set
(len jj1) + ((len d1) - 2) is V11() real ext-real Element of REAL
(len d1) -' 2 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(len jj1) + ((len d1) -' 2) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
(len (jj1 ^' d1)) -' 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(len d1) - 1 is V11() real ext-real Element of REAL
(len d1) + (- 1) is V11() real ext-real set
(len d1) -' 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
((len d1) -' 2) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
((len d1) - 2) + 1 is V11() real ext-real Element of REAL
((len d1) - 1) + 1 is V11() real ext-real Element of REAL
LSeg (d1,((len d1) -' 1)) is functional Element of K6( the carrier of (TOP-REAL 2))
(LSeg (d1,((len d1) -' 1))) /\ (LSeg (p2,1)) is functional Element of K6( the carrier of (TOP-REAL 2))
ii2 is set
((len d1) -' 1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
d1 /. (((len d1) -' 1) + 1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((jj1 ^' d1),((len jj1) + ((len d1) -' 2))) is functional Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((jj1 ^' d1),((len jj1) + ((len d1) -' 2)))) /\ (LSeg (p2,1)) is functional Element of K6( the carrier of (TOP-REAL 2))
{((jj1 ^' d1) /. (len (jj1 ^' d1)))} is non empty trivial functional V35(1) set
rng d1 is functional Element of K6( the carrier of (TOP-REAL 2))
{(d1 /. 1)} is non empty trivial functional V35(1) set
(L~ jj1) /\ (L~ d1) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
ii2 is set
ii2 is set
(rng jj1) /\ (rng d1) is functional Element of K6( the carrier of (TOP-REAL 2))
d1 /. (len d1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
{(d1 /. (len d1))} is non empty trivial functional V35(1) set
(L~ p2) /\ (L~ d1) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
ii2 is set
ii2 is set
L~ (jj1 ^' d1) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(L~ (jj1 ^' d1)) /\ (L~ p2) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(L~ jj1) \/ (L~ d1) is non empty functional Element of K6( the carrier of (TOP-REAL 2))
((L~ jj1) \/ (L~ d1)) /\ (L~ p2) is functional Element of K6( the carrier of (TOP-REAL 2))
{(p2 /. 1)} is non empty trivial functional V35(1) set
{(jj1 /. 1)} \/ {(p2 /. 1)} is non empty set
(jj1 ^' d1) /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
{((jj1 ^' d1) /. 1)} is non empty trivial functional V35(1) set
{((jj1 ^' d1) /. 1)} \/ {(p2 /. 1)} is non empty set
{((jj1 ^' d1) /. 1),(p2 /. 1)} is non empty functional set
W-min p is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
W-bound p is V11() real ext-real Element of REAL
(TOP-REAL 2) | p is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | p is V15() V18( the carrier of ((TOP-REAL 2) | p)) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | p), REAL ) V212((TOP-REAL 2) | p) Element of K6(K7( the carrier of ((TOP-REAL 2) | p),REAL))
the carrier of ((TOP-REAL 2) | p) is set
K7( the carrier of ((TOP-REAL 2) | p),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | p),REAL)) is non empty set
lower_bound (proj1 | p) is V11() real ext-real Element of REAL
(proj1 | p) .: the carrier of ((TOP-REAL 2) | p) is Element of K6(REAL)
lower_bound ((proj1 | p) .: the carrier of ((TOP-REAL 2) | p)) is V11() real ext-real Element of REAL
W-most p is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
SW-corner p is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
S-bound p is V11() real ext-real Element of REAL
proj2 | p is V15() V18( the carrier of ((TOP-REAL 2) | p)) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | p), REAL ) V212((TOP-REAL 2) | p) Element of K6(K7( the carrier of ((TOP-REAL 2) | p),REAL))
lower_bound (proj2 | p) is V11() real ext-real Element of REAL
(proj2 | p) .: the carrier of ((TOP-REAL 2) | p) is Element of K6(REAL)
lower_bound ((proj2 | p) .: the carrier of ((TOP-REAL 2) | p)) is V11() real ext-real Element of REAL
|[(W-bound p),(S-bound p)]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
NW-corner p is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
N-bound p is V11() real ext-real Element of REAL
upper_bound (proj2 | p) is V11() real ext-real Element of REAL
upper_bound ((proj2 | p) .: the carrier of ((TOP-REAL 2) | p)) is V11() real ext-real Element of REAL
|[(W-bound p),(N-bound p)]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner p),(NW-corner p)) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner p),(NW-corner p))) /\ p is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (W-most p) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (W-most p) is V15() V18( the carrier of ((TOP-REAL 2) | (W-most p))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (W-most p)), REAL ) V212((TOP-REAL 2) | (W-most p)) Element of K6(K7( the carrier of ((TOP-REAL 2) | (W-most p)),REAL))
the carrier of ((TOP-REAL 2) | (W-most p)) is set
K7( the carrier of ((TOP-REAL 2) | (W-most p)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (W-most p)),REAL)) is non empty set
lower_bound (proj2 | (W-most p)) is V11() real ext-real Element of REAL
(proj2 | (W-most p)) .: the carrier of ((TOP-REAL 2) | (W-most p)) is Element of K6(REAL)
lower_bound ((proj2 | (W-most p)) .: the carrier of ((TOP-REAL 2) | (W-most p))) is V11() real ext-real Element of REAL
|[(W-bound p),(lower_bound (proj2 | (W-most p)))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
E-max p is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
E-bound p is V11() real ext-real Element of REAL
upper_bound (proj1 | p) is V11() real ext-real Element of REAL
upper_bound ((proj1 | p) .: the carrier of ((TOP-REAL 2) | p)) is V11() real ext-real Element of REAL
E-most p is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
SE-corner p is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
|[(E-bound p),(S-bound p)]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
NE-corner p is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
|[(E-bound p),(N-bound p)]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner p),(NE-corner p)) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SE-corner p),(NE-corner p))) /\ p is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (E-most p) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (E-most p) is V15() V18( the carrier of ((TOP-REAL 2) | (E-most p))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (E-most p)), REAL ) V212((TOP-REAL 2) | (E-most p)) Element of K6(K7( the carrier of ((TOP-REAL 2) | (E-most p)),REAL))
the carrier of ((TOP-REAL 2) | (E-most p)) is set
K7( the carrier of ((TOP-REAL 2) | (E-most p)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (E-most p)),REAL)) is non empty set
upper_bound (proj2 | (E-most p)) is V11() real ext-real Element of REAL
(proj2 | (E-most p)) .: the carrier of ((TOP-REAL 2) | (E-most p)) is Element of K6(REAL)
upper_bound ((proj2 | (E-most p)) .: the carrier of ((TOP-REAL 2) | (E-most p))) is V11() real ext-real Element of REAL
|[(E-bound p),(upper_bound (proj2 | (E-most p)))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
rng (Cage (p,C)) is non trivial functional Element of K6( the carrier of (TOP-REAL 2))
(Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))) /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
W-max (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
W-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V15() V18( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))), REAL ) V212((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),REAL))
the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is set
K7( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),REAL)) is non empty set
lower_bound (proj1 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is V11() real ext-real Element of REAL
(proj1 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) .: the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is Element of K6(REAL)
lower_bound ((proj1 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) .: the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is V11() real ext-real Element of REAL
W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
SW-corner (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
S-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V11() real ext-real Element of REAL
proj2 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V15() V18( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))), REAL ) V212((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),REAL))
lower_bound (proj2 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is V11() real ext-real Element of REAL
(proj2 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) .: the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is Element of K6(REAL)
lower_bound ((proj2 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) .: the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),(S-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
NW-corner (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
N-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) .: the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),(N-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),(NW-corner (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),(NW-corner (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))))) /\ (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is V15() V18( the carrier of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))), REAL ) V212((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))),REAL))
the carrier of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is set
K7( the carrier of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))),REAL)) is non empty set
upper_bound (proj2 | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is V11() real ext-real Element of REAL
(proj2 | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is Element of K6(REAL)
upper_bound ((proj2 | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),(upper_bound (proj2 | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(W-max (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) .. (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
N-min (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
NE-corner (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
E-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is V11() real ext-real Element of REAL
upper_bound ((proj1 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) .: the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),(N-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((NW-corner (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),(NE-corner (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((NW-corner (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),(NE-corner (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))))) /\ (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is V15() V18( the carrier of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))), REAL ) V212((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))),REAL))
the carrier of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is set
K7( the carrier of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))),REAL)) is non empty set
lower_bound (proj1 | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is V11() real ext-real Element of REAL
(proj1 | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is Element of K6(REAL)
lower_bound ((proj1 | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))))),(N-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(N-min (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) .. (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
N-max (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
upper_bound (proj1 | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is V11() real ext-real Element of REAL
upper_bound ((proj1 | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))))) is V11() real ext-real Element of REAL
|[(upper_bound (proj1 | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))))),(N-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(N-max (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) .. (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(E-max (L~ (Cage (p,C)))) .. (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
ii2 is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like non constant V28() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard FinSequence of the carrier of (TOP-REAL 2)
right_cell (ii2,1,(Gauge (p,C))) is functional Element of K6( the carrier of (TOP-REAL 2))
L~ ii2 is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
(right_cell (ii2,1,(Gauge (p,C)))) \ (L~ ii2) is functional Element of K6( the carrier of (TOP-REAL 2))
RightComp ii2 is non empty functional Element of K6( the carrier of (TOP-REAL 2))
(L~ (jj1 ^' d1)) \/ (L~ p2) is non empty functional Element of K6( the carrier of (TOP-REAL 2))
((L~ jj1) \/ (L~ d1)) \/ (L~ p2) is non empty functional Element of K6( the carrier of (TOP-REAL 2))
(L~ (Upper_Seq (p,C))) \/ (L~ (Lower_Seq (p,C))) is non empty functional Element of K6( the carrier of (TOP-REAL 2))
right_cell ((Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))),1) is functional Element of K6( the carrier of (TOP-REAL 2))
GoB (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))) is V15() non empty-yielding V18( NAT ) V19(K307( the carrier of (TOP-REAL 2))) Function-like V28() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K307( the carrier of (TOP-REAL 2))
right_cell ((Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))),1,(GoB (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is functional Element of K6( the carrier of (TOP-REAL 2))
GoB (Cage (p,C)) is V15() non empty-yielding V18( NAT ) V19(K307( the carrier of (TOP-REAL 2))) Function-like V28() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K307( the carrier of (TOP-REAL 2))
right_cell ((Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))),1,(GoB (Cage (p,C)))) is functional Element of K6( the carrier of (TOP-REAL 2))
right_cell ((Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))),1,(Gauge (p,C))) is functional Element of K6( the carrier of (TOP-REAL 2))
(Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))) -: (E-max (L~ (Cage (p,C)))) is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like special unfolded FinSequence of the carrier of (TOP-REAL 2)
right_cell (((Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))) -: (E-max (L~ (Cage (p,C))))),1,(Gauge (p,C))) is functional Element of K6( the carrier of (TOP-REAL 2))
right_cell ((Upper_Seq (p,C)),1,(Gauge (p,C))) is functional Element of K6( the carrier of (TOP-REAL 2))
right_cell ((R_Cut ((Upper_Seq (p,C)),((Gauge (p,C)) * (p9,r)))),1,(Gauge (p,C))) is functional Element of K6( the carrier of (TOP-REAL 2))
right_cell ((jj1 ^' d1),1,(Gauge (p,C))) is functional Element of K6( the carrier of (TOP-REAL 2))
ii2 /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
ii2 /. 2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(jj1 ^' d1) /. 2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(Upper_Seq (p,C)) ^' (Lower_Seq (p,C)) is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
((Upper_Seq (p,C)) ^' (Lower_Seq (p,C))) /. 2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))) /. 2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(L~ jj1) \/ (L~ p2) is non empty functional Element of K6( the carrier of (TOP-REAL 2))
W-min ((L~ jj1) \/ (L~ p2)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
W-bound ((L~ jj1) \/ (L~ p2)) is V11() real ext-real Element of REAL
(TOP-REAL 2) | ((L~ jj1) \/ (L~ p2)) is strict T_2 SubSpace of TOP-REAL 2
proj1 | ((L~ jj1) \/ (L~ p2)) is V15() V18( the carrier of ((TOP-REAL 2) | ((L~ jj1) \/ (L~ p2)))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | ((L~ jj1) \/ (L~ p2))), REAL ) V212((TOP-REAL 2) | ((L~ jj1) \/ (L~ p2))) Element of K6(K7( the carrier of ((TOP-REAL 2) | ((L~ jj1) \/ (L~ p2))),REAL))
the carrier of ((TOP-REAL 2) | ((L~ jj1) \/ (L~ p2))) is set
K7( the carrier of ((TOP-REAL 2) | ((L~ jj1) \/ (L~ p2))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | ((L~ jj1) \/ (L~ p2))),REAL)) is non empty set
lower_bound (proj1 | ((L~ jj1) \/ (L~ p2))) is V11() real ext-real Element of REAL
(proj1 | ((L~ jj1) \/ (L~ p2))) .: the carrier of ((TOP-REAL 2) | ((L~ jj1) \/ (L~ p2))) is Element of K6(REAL)
lower_bound ((proj1 | ((L~ jj1) \/ (L~ p2))) .: the carrier of ((TOP-REAL 2) | ((L~ jj1) \/ (L~ p2)))) is V11() real ext-real Element of REAL
W-most ((L~ jj1) \/ (L~ p2)) is functional Element of K6( the carrier of (TOP-REAL 2))
SW-corner ((L~ jj1) \/ (L~ p2)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
S-bound ((L~ jj1) \/ (L~ p2)) is V11() real ext-real Element of REAL
proj2 | ((L~ jj1) \/ (L~ p2)) is V15() V18( the carrier of ((TOP-REAL 2) | ((L~ jj1) \/ (L~ p2)))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | ((L~ jj1) \/ (L~ p2))), REAL ) V212((TOP-REAL 2) | ((L~ jj1) \/ (L~ p2))) Element of K6(K7( the carrier of ((TOP-REAL 2) | ((L~ jj1) \/ (L~ p2))),REAL))
lower_bound (proj2 | ((L~ jj1) \/ (L~ p2))) is V11() real ext-real Element of REAL
(proj2 | ((L~ jj1) \/ (L~ p2))) .: the carrier of ((TOP-REAL 2) | ((L~ jj1) \/ (L~ p2))) is Element of K6(REAL)
lower_bound ((proj2 | ((L~ jj1) \/ (L~ p2))) .: the carrier of ((TOP-REAL 2) | ((L~ jj1) \/ (L~ p2)))) is V11() real ext-real Element of REAL
|[(W-bound ((L~ jj1) \/ (L~ p2))),(S-bound ((L~ jj1) \/ (L~ p2)))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
NW-corner ((L~ jj1) \/ (L~ p2)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
N-bound ((L~ jj1) \/ (L~ p2)) is V11() real ext-real Element of REAL
upper_bound (proj2 | ((L~ jj1) \/ (L~ p2))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | ((L~ jj1) \/ (L~ p2))) .: the carrier of ((TOP-REAL 2) | ((L~ jj1) \/ (L~ p2)))) is V11() real ext-real Element of REAL
|[(W-bound ((L~ jj1) \/ (L~ p2))),(N-bound ((L~ jj1) \/ (L~ p2)))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner ((L~ jj1) \/ (L~ p2))),(NW-corner ((L~ jj1) \/ (L~ p2)))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner ((L~ jj1) \/ (L~ p2))),(NW-corner ((L~ jj1) \/ (L~ p2))))) /\ ((L~ jj1) \/ (L~ p2)) is functional Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (W-most ((L~ jj1) \/ (L~ p2))) is strict T_2 SubSpace of TOP-REAL 2
proj2 | (W-most ((L~ jj1) \/ (L~ p2))) is V15() V18( the carrier of ((TOP-REAL 2) | (W-most ((L~ jj1) \/ (L~ p2))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (W-most ((L~ jj1) \/ (L~ p2)))), REAL ) V212((TOP-REAL 2) | (W-most ((L~ jj1) \/ (L~ p2)))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (W-most ((L~ jj1) \/ (L~ p2)))),REAL))
the carrier of ((TOP-REAL 2) | (W-most ((L~ jj1) \/ (L~ p2)))) is set
K7( the carrier of ((TOP-REAL 2) | (W-most ((L~ jj1) \/ (L~ p2)))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (W-most ((L~ jj1) \/ (L~ p2)))),REAL)) is non empty set
lower_bound (proj2 | (W-most ((L~ jj1) \/ (L~ p2)))) is V11() real ext-real Element of REAL
(proj2 | (W-most ((L~ jj1) \/ (L~ p2)))) .: the carrier of ((TOP-REAL 2) | (W-most ((L~ jj1) \/ (L~ p2)))) is Element of K6(REAL)
lower_bound ((proj2 | (W-most ((L~ jj1) \/ (L~ p2)))) .: the carrier of ((TOP-REAL 2) | (W-most ((L~ jj1) \/ (L~ p2))))) is V11() real ext-real Element of REAL
|[(W-bound ((L~ jj1) \/ (L~ p2))),(lower_bound (proj2 | (W-most ((L~ jj1) \/ (L~ p2)))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(W-min ((L~ jj1) \/ (L~ p2))) `1 is V11() real ext-real Element of REAL
((L~ jj1) \/ (L~ p2)) \/ (L~ d1) is non empty functional Element of K6( the carrier of (TOP-REAL 2))
W-min (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
W-bound (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)) is strict T_2 SubSpace of TOP-REAL 2
proj1 | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)) is V15() V18( the carrier of ((TOP-REAL 2) | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))), REAL ) V212((TOP-REAL 2) | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))),REAL))
the carrier of ((TOP-REAL 2) | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))) is set
K7( the carrier of ((TOP-REAL 2) | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))),REAL)) is non empty set
lower_bound (proj1 | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))) is V11() real ext-real Element of REAL
(proj1 | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))) .: the carrier of ((TOP-REAL 2) | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))) is Element of K6(REAL)
lower_bound ((proj1 | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))) .: the carrier of ((TOP-REAL 2) | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))) is V11() real ext-real Element of REAL
W-most (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)) is functional Element of K6( the carrier of (TOP-REAL 2))
SW-corner (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
S-bound (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)) is V11() real ext-real Element of REAL
proj2 | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)) is V15() V18( the carrier of ((TOP-REAL 2) | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))), REAL ) V212((TOP-REAL 2) | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))),REAL))
lower_bound (proj2 | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))) is V11() real ext-real Element of REAL
(proj2 | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))) .: the carrier of ((TOP-REAL 2) | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))) is Element of K6(REAL)
lower_bound ((proj2 | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))) .: the carrier of ((TOP-REAL 2) | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))) is V11() real ext-real Element of REAL
|[(W-bound (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))),(S-bound (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
NW-corner (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
N-bound (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)) is V11() real ext-real Element of REAL
upper_bound (proj2 | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))) .: the carrier of ((TOP-REAL 2) | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))) is V11() real ext-real Element of REAL
|[(W-bound (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))),(N-bound (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))),(NW-corner (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))),(NW-corner (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))))) /\ (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)) is functional Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (W-most (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))) is strict T_2 SubSpace of TOP-REAL 2
proj2 | (W-most (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))) is V15() V18( the carrier of ((TOP-REAL 2) | (W-most (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (W-most (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))), REAL ) V212((TOP-REAL 2) | (W-most (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (W-most (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))),REAL))
the carrier of ((TOP-REAL 2) | (W-most (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))) is set
K7( the carrier of ((TOP-REAL 2) | (W-most (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (W-most (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))),REAL)) is non empty set
lower_bound (proj2 | (W-most (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))) is V11() real ext-real Element of REAL
(proj2 | (W-most (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))) .: the carrier of ((TOP-REAL 2) | (W-most (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))) is Element of K6(REAL)
lower_bound ((proj2 | (W-most (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))) .: the carrier of ((TOP-REAL 2) | (W-most (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))))) is V11() real ext-real Element of REAL
|[(W-bound (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))),(lower_bound (proj2 | (W-most (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
W-min (L~ ii2) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
W-bound (L~ ii2) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ ii2) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ ii2) is V15() V18( the carrier of ((TOP-REAL 2) | (L~ ii2))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ ii2)), REAL ) V212((TOP-REAL 2) | (L~ ii2)) Element of K6(K7( the carrier of ((TOP-REAL 2) | (L~ ii2)),REAL))
the carrier of ((TOP-REAL 2) | (L~ ii2)) is set
K7( the carrier of ((TOP-REAL 2) | (L~ ii2)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (L~ ii2)),REAL)) is non empty set
lower_bound (proj1 | (L~ ii2)) is V11() real ext-real Element of REAL
(proj1 | (L~ ii2)) .: the carrier of ((TOP-REAL 2) | (L~ ii2)) is Element of K6(REAL)
lower_bound ((proj1 | (L~ ii2)) .: the carrier of ((TOP-REAL 2) | (L~ ii2))) is V11() real ext-real Element of REAL
W-most (L~ ii2) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
SW-corner (L~ ii2) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
S-bound (L~ ii2) is V11() real ext-real Element of REAL
proj2 | (L~ ii2) is V15() V18( the carrier of ((TOP-REAL 2) | (L~ ii2))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ ii2)), REAL ) V212((TOP-REAL 2) | (L~ ii2)) Element of K6(K7( the carrier of ((TOP-REAL 2) | (L~ ii2)),REAL))
lower_bound (proj2 | (L~ ii2)) is V11() real ext-real Element of REAL
(proj2 | (L~ ii2)) .: the carrier of ((TOP-REAL 2) | (L~ ii2)) is Element of K6(REAL)
lower_bound ((proj2 | (L~ ii2)) .: the carrier of ((TOP-REAL 2) | (L~ ii2))) is V11() real ext-real Element of REAL
|[(W-bound (L~ ii2)),(S-bound (L~ ii2))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
NW-corner (L~ ii2) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
N-bound (L~ ii2) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ ii2)) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (L~ ii2)) .: the carrier of ((TOP-REAL 2) | (L~ ii2))) is V11() real ext-real Element of REAL
|[(W-bound (L~ ii2)),(N-bound (L~ ii2))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner (L~ ii2)),(NW-corner (L~ ii2))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner (L~ ii2)),(NW-corner (L~ ii2)))) /\ (L~ ii2) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (W-most (L~ ii2)) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (W-most (L~ ii2)) is V15() V18( the carrier of ((TOP-REAL 2) | (W-most (L~ ii2)))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (W-most (L~ ii2))), REAL ) V212((TOP-REAL 2) | (W-most (L~ ii2))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (W-most (L~ ii2))),REAL))
the carrier of ((TOP-REAL 2) | (W-most (L~ ii2))) is set
K7( the carrier of ((TOP-REAL 2) | (W-most (L~ ii2))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (W-most (L~ ii2))),REAL)) is non empty set
lower_bound (proj2 | (W-most (L~ ii2))) is V11() real ext-real Element of REAL
(proj2 | (W-most (L~ ii2))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ ii2))) is Element of K6(REAL)
lower_bound ((proj2 | (W-most (L~ ii2))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ ii2)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ ii2)),(lower_bound (proj2 | (W-most (L~ ii2))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
rng ii2 is non trivial functional Element of K6( the carrier of (TOP-REAL 2))
dom ii2 is non trivial Element of K6(NAT)
(ii2 /. 2) `1 is V11() real ext-real Element of REAL
(W-min (L~ ii2)) `1 is V11() real ext-real Element of REAL
Rotate (ii2,(W-min (L~ ii2))) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like non constant V28() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard FinSequence of the carrier of (TOP-REAL 2)
(Rotate (ii2,(W-min (L~ ii2)))) /. 2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(Upper_Seq (p,C)) . (len (Upper_Seq (p,C))) is V15() Function-like set
(Upper_Seq (p,C)) /. (len (Upper_Seq (p,C))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
east_halfline (E-max p) is non empty functional connected V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
Gji is set
Gij9 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(east_halfline (E-max p)) /\ (L~ (Cage (p,C))) is functional Element of K6( the carrier of (TOP-REAL 2))
Gij9 `1 is V11() real ext-real Element of REAL
Gij is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like non constant V28() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the carrier of (TOP-REAL 2)
L~ Gij is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
Gji is set
Gij9 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
Gij9 `1 is V11() real ext-real Element of REAL
Gij9 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
Gij9 `1 is V11() real ext-real Element of REAL
Gij9 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
Gij9 `1 is V11() real ext-real Element of REAL
Gij9 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
Gij9 `1 is V11() real ext-real Element of REAL
p9 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
(len (Gauge (p,C))) - 1 is V11() real ext-real Element of REAL
(len (Gauge (p,C))) + (- 1) is V11() real ext-real set
(len (Gauge (p,C))) -' 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(Gauge (p,C)) * (((len (Gauge (p,C))) -' 1),1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * (((len (Gauge (p,C))) -' 1),1)) `1 is V11() real ext-real Element of REAL
(E-max p) `1 is V11() real ext-real Element of REAL
Gij9 `2 is V11() real ext-real Element of REAL
(E-max p) `2 is V11() real ext-real Element of REAL
Gji is set
Gij9 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(east_halfline (E-max p)) /\ (L~ (Cage (p,C))) is functional Element of K6( the carrier of (TOP-REAL 2))
Gij9 `1 is V11() real ext-real Element of REAL
(E-max p) `2 is V11() real ext-real Element of REAL
Gij9 `2 is V11() real ext-real Element of REAL
Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like non constant V28() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the carrier of (TOP-REAL 2)
right_cell ((Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))),1) is functional Element of K6( the carrier of (TOP-REAL 2))
(Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))) -: (W-min (L~ (Cage (p,C)))) is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like special unfolded FinSequence of the carrier of (TOP-REAL 2)
LSeg ((Lower_Seq (p,C)),1) is functional Element of K6( the carrier of (TOP-REAL 2))
LSeg ((Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))),1) is functional Element of K6( the carrier of (TOP-REAL 2))
L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
len (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
GoB (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))) is V15() non empty-yielding V18( NAT ) V19(K307( the carrier of (TOP-REAL 2))) Function-like V28() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K307( the carrier of (TOP-REAL 2))
(Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))) /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
E-max (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
E-bound (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))) is V15() V18( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))), REAL ) V212((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))),REAL))
the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) is set
K7( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))),REAL)) is non empty set
upper_bound (proj1 | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) is V11() real ext-real Element of REAL
(proj1 | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) .: the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) is Element of K6(REAL)
upper_bound ((proj1 | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) .: the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) is V11() real ext-real Element of REAL
E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
SE-corner (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
S-bound (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))) is V11() real ext-real Element of REAL
proj2 | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))) is V15() V18( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))), REAL ) V212((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))),REAL))
lower_bound (proj2 | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) is V11() real ext-real Element of REAL
(proj2 | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) .: the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) is Element of K6(REAL)
lower_bound ((proj2 | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) .: the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))),(S-bound (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
NE-corner (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
N-bound (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) .: the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))),(N-bound (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))),(NE-corner (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SE-corner (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))),(NE-corner (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))))) /\ (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) is V15() V18( the carrier of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))), REAL ) V212((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))),REAL))
the carrier of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) is set
K7( the carrier of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))),REAL)) is non empty set
upper_bound (proj2 | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) is V11() real ext-real Element of REAL
(proj2 | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) is Element of K6(REAL)
upper_bound ((proj2 | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))),(upper_bound (proj2 | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))) /. (1 + 1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
x is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
x9 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
x9 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
[x,(x9 + 1)] is set
{x,(x9 + 1)} is non empty set
{x} is non empty trivial V35(1) set
{{x,(x9 + 1)},{x}} is non empty set
[x,x9] is set
{x,x9} is non empty set
{{x,x9},{x}} is non empty set
(Gauge (p,C)) * (x,(x9 + 1)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(Gauge (p,C)) * (x,x9) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
jj2 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(Gauge (p,C)) * ((len (Gauge (p,C))),jj2) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
[(len (Gauge (p,C))),jj2] is set
{(len (Gauge (p,C))),jj2} is non empty set
{{(len (Gauge (p,C))),jj2},{(len (Gauge (p,C)))}} is non empty set
x + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
(x9 + 1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
x -' 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
cell ((Gauge (p,C)),(x -' 1),x9) is functional Element of K6( the carrier of (TOP-REAL 2))
(x -' 1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
4 - 1 is V11() real ext-real Element of REAL
4 + (- 1) is V11() real ext-real set
x - 1 is V11() real ext-real Element of REAL
x + (- 1) is V11() real ext-real set
(Gauge (p,C)) * ((x -' 1),x9) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * ((x -' 1),x9)) `2 is V11() real ext-real Element of REAL
(Gauge (p,C)) * ((x -' 1),(x9 + 1)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * ((x -' 1),(x9 + 1))) `2 is V11() real ext-real Element of REAL
(Gauge (p,C)) * (1,x9) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * (1,x9)) `2 is V11() real ext-real Element of REAL
((Gauge (p,C)) * (x,x9)) `2 is V11() real ext-real Element of REAL
(Gauge (p,C)) * (1,(x9 + 1)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * (1,(x9 + 1))) `2 is V11() real ext-real Element of REAL
((Gauge (p,C)) * (x,(x9 + 1))) `2 is V11() real ext-real Element of REAL
(Gauge (p,C)) * ((len (Gauge (p,C))),x9) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * ((len (Gauge (p,C))),x9)) `1 is V11() real ext-real Element of REAL
(Gauge (p,C)) * ((len (Gauge (p,C))),(x9 + 1)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * ((len (Gauge (p,C))),(x9 + 1))) `1 is V11() real ext-real Element of REAL
LSeg (((Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))) /. 1),((Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))) /. (1 + 1))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
Index (Gij9,p2) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
LSeg (p2,(Index (Gij9,p2))) is functional Element of K6( the carrier of (TOP-REAL 2))
((Gauge (p,C)) * (s,rr)) .. (Lower_Seq (p,C)) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
mid ((Lower_Seq (p,C)),(((Gauge (p,C)) * (s,rr)) .. (Lower_Seq (p,C))),(len (Lower_Seq (p,C)))) is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
Index (((Gauge (p,C)) * (s,rr)),(Lower_Seq (p,C))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(Index (((Gauge (p,C)) * (s,rr)),(Lower_Seq (p,C)))) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
t is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative set
(Lower_Seq (p,C)) . t is V15() Function-like set
len (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (s,rr)))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(len (Lower_Seq (p,C))) - (Index (((Gauge (p,C)) * (s,rr)),(Lower_Seq (p,C)))) is V11() real ext-real Element of REAL
- (Index (((Gauge (p,C)) * (s,rr)),(Lower_Seq (p,C)))) is V11() real ext-real non positive set
(len (Lower_Seq (p,C))) + (- (Index (((Gauge (p,C)) * (s,rr)),(Lower_Seq (p,C))))) is V11() real ext-real set
(Index (Gij9,p2)) + (((Gauge (p,C)) * (s,rr)) .. (Lower_Seq (p,C))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
((Index (Gij9,p2)) + (((Gauge (p,C)) * (s,rr)) .. (Lower_Seq (p,C)))) -' 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
0 + (Index (((Gauge (p,C)) * (s,rr)),(Lower_Seq (p,C)))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(len (Lower_Seq (p,C))) -' (Index (((Gauge (p,C)) * (s,rr)),(Lower_Seq (p,C)))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(Index (Gij9,p2)) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
((len (Lower_Seq (p,C))) -' (Index (((Gauge (p,C)) * (s,rr)),(Lower_Seq (p,C))))) - 1 is V11() real ext-real Element of REAL
((len (Lower_Seq (p,C))) -' (Index (((Gauge (p,C)) * (s,rr)),(Lower_Seq (p,C))))) + (- 1) is V11() real ext-real set
((len (Lower_Seq (p,C))) - (Index (((Gauge (p,C)) * (s,rr)),(Lower_Seq (p,C))))) - 1 is V11() real ext-real Element of REAL
((len (Lower_Seq (p,C))) - (Index (((Gauge (p,C)) * (s,rr)),(Lower_Seq (p,C))))) + (- 1) is V11() real ext-real set
(len (Lower_Seq (p,C))) - (((Gauge (p,C)) * (s,rr)) .. (Lower_Seq (p,C))) is V11() real ext-real Element of REAL
- (((Gauge (p,C)) * (s,rr)) .. (Lower_Seq (p,C))) is V11() real ext-real non positive set
(len (Lower_Seq (p,C))) + (- (((Gauge (p,C)) * (s,rr)) .. (Lower_Seq (p,C)))) is V11() real ext-real set
(len (Lower_Seq (p,C))) -' (((Gauge (p,C)) * (s,rr)) .. (Lower_Seq (p,C))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
((len (Lower_Seq (p,C))) -' (((Gauge (p,C)) * (s,rr)) .. (Lower_Seq (p,C)))) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
LSeg ((mid ((Lower_Seq (p,C)),(((Gauge (p,C)) * (s,rr)) .. (Lower_Seq (p,C))),(len (Lower_Seq (p,C))))),(Index (Gij9,p2))) is functional Element of K6( the carrier of (TOP-REAL 2))
LSeg ((Lower_Seq (p,C)),(((Index (Gij9,p2)) + (((Gauge (p,C)) * (s,rr)) .. (Lower_Seq (p,C)))) -' 1)) is functional Element of K6( the carrier of (TOP-REAL 2))
(1 + 1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
((1 + 1) + 1) - 1 is V11() real ext-real Element of REAL
((1 + 1) + 1) + (- 1) is V11() real ext-real set
((Index (Gij9,p2)) + (((Gauge (p,C)) * (s,rr)) .. (Lower_Seq (p,C)))) - 1 is V11() real ext-real Element of REAL
((Index (Gij9,p2)) + (((Gauge (p,C)) * (s,rr)) .. (Lower_Seq (p,C)))) + (- 1) is V11() real ext-real set
(LSeg ((Lower_Seq (p,C)),1)) /\ (LSeg ((Lower_Seq (p,C)),(((Index (Gij9,p2)) + (((Gauge (p,C)) * (s,rr)) .. (Lower_Seq (p,C)))) -' 1))) is functional Element of K6( the carrier of (TOP-REAL 2))
(Lower_Seq (p,C)) /. 2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
{((Lower_Seq (p,C)) /. 2)} is non empty trivial functional V35(1) set
Gij9 .. (Lower_Seq (p,C)) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(Gauge (p,C)) * ((len (Gauge (p,C))),r) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * ((len (Gauge (p,C))),r)) `1 is V11() real ext-real Element of REAL
(L~ Gij) ` is non empty functional Element of K6( the carrier of (TOP-REAL 2))
Gji is functional Element of K6( the carrier of (TOP-REAL 2))
UBD (L~ Gij) is non empty functional open connected Element of K6( the carrier of (TOP-REAL 2))
LeftComp Gij is non empty functional Element of K6( the carrier of (TOP-REAL 2))
{((Gauge (p,C)) * (p9,rr))} is non empty trivial functional V35(1) set
((Gauge (p,C)) * (p9,r)) `2 is V11() real ext-real Element of REAL
{((Gauge (p,C)) * (p9,rr))} is non empty trivial functional V35(1) set
((Gauge (p,C)) * (p9,r)) `2 is V11() real ext-real Element of REAL
C is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
p is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
Gauge (p,C) is V15() non empty-yielding V18( NAT ) V19(K307( the carrier of (TOP-REAL 2))) Function-like V28() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K307( the carrier of (TOP-REAL 2))
len (Gauge (p,C)) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
width (Gauge (p,C)) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
Upper_Seq (p,C) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V28() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
L~ (Upper_Seq (p,C)) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
Lower_Seq (p,C) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V28() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
L~ (Lower_Seq (p,C)) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
Lower_Arc p is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
s is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
p9 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
r is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
rr is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(Gauge (p,C)) * (p9,r) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(Gauge (p,C)) * (p9,rr) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(Gauge (p,C)) * (s,rr) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) is non empty functional Element of K6( the carrier of (TOP-REAL 2))
((LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))))) /\ (L~ (Upper_Seq (p,C))) is functional Element of K6( the carrier of (TOP-REAL 2))
{((Gauge (p,C)) * (p9,r))} is non empty trivial functional V35(1) set
((LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))))) /\ (L~ (Lower_Seq (p,C))) is functional Element of K6( the carrier of (TOP-REAL 2))
{((Gauge (p,C)) * (s,rr))} is non empty trivial functional V35(1) set
Cage (p,C) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like non constant V28() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the carrier of (TOP-REAL 2)
L~ (Cage (p,C)) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
W-min (L~ (Cage (p,C))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
W-bound (L~ (Cage (p,C))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (p,C))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ (Cage (p,C))) is V15() V18( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))), REAL ) V212((TOP-REAL 2) | (L~ (Cage (p,C)))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))),REAL))
the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))) is set
K7( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))),REAL)) is non empty set
lower_bound (proj1 | (L~ (Cage (p,C)))) is V11() real ext-real Element of REAL
(proj1 | (L~ (Cage (p,C)))) .: the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))) is Element of K6(REAL)
lower_bound ((proj1 | (L~ (Cage (p,C)))) .: the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C))))) is V11() real ext-real Element of REAL
W-most (L~ (Cage (p,C))) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
SW-corner (L~ (Cage (p,C))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
S-bound (L~ (Cage (p,C))) is V11() real ext-real Element of REAL
proj2 | (L~ (Cage (p,C))) is V15() V18( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))), REAL ) V212((TOP-REAL 2) | (L~ (Cage (p,C)))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))),REAL))
lower_bound (proj2 | (L~ (Cage (p,C)))) is V11() real ext-real Element of REAL
(proj2 | (L~ (Cage (p,C)))) .: the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C)))) is Element of K6(REAL)
lower_bound ((proj2 | (L~ (Cage (p,C)))) .: the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Cage (p,C)))),(S-bound (L~ (Cage (p,C))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
NW-corner (L~ (Cage (p,C))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
N-bound (L~ (Cage (p,C))) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ (Cage (p,C)))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (L~ (Cage (p,C)))) .: the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Cage (p,C)))),(N-bound (L~ (Cage (p,C))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (p,C)))),(NW-corner (L~ (Cage (p,C))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner (L~ (Cage (p,C)))),(NW-corner (L~ (Cage (p,C)))))) /\ (L~ (Cage (p,C))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (W-most (L~ (Cage (p,C)))) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Cage (p,C)))) is V15() V18( the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C)))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C))))), REAL ) V212((TOP-REAL 2) | (W-most (L~ (Cage (p,C))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C))))),REAL))
the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C))))) is set
K7( the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C))))),REAL)) is non empty set
lower_bound (proj2 | (W-most (L~ (Cage (p,C))))) is V11() real ext-real Element of REAL
(proj2 | (W-most (L~ (Cage (p,C))))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C))))) is Element of K6(REAL)
lower_bound ((proj2 | (W-most (L~ (Cage (p,C))))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (p,C)))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Cage (p,C)))),(lower_bound (proj2 | (W-most (L~ (Cage (p,C))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
E-max (L~ (Cage (p,C))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
E-bound (L~ (Cage (p,C))) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ (Cage (p,C)))) is V11() real ext-real Element of REAL
upper_bound ((proj1 | (L~ (Cage (p,C)))) .: the carrier of ((TOP-REAL 2) | (L~ (Cage (p,C))))) is V11() real ext-real Element of REAL
E-most (L~ (Cage (p,C))) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
SE-corner (L~ (Cage (p,C))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
|[(E-bound (L~ (Cage (p,C)))),(S-bound (L~ (Cage (p,C))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
NE-corner (L~ (Cage (p,C))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
|[(E-bound (L~ (Cage (p,C)))),(N-bound (L~ (Cage (p,C))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Cage (p,C)))),(NE-corner (L~ (Cage (p,C))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SE-corner (L~ (Cage (p,C)))),(NE-corner (L~ (Cage (p,C)))))) /\ (L~ (Cage (p,C))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (E-most (L~ (Cage (p,C)))) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Cage (p,C)))) is V15() V18( the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (p,C)))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (p,C))))), REAL ) V212((TOP-REAL 2) | (E-most (L~ (Cage (p,C))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (p,C))))),REAL))
the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (p,C))))) is set
K7( the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (p,C))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (p,C))))),REAL)) is non empty set
upper_bound (proj2 | (E-most (L~ (Cage (p,C))))) is V11() real ext-real Element of REAL
(proj2 | (E-most (L~ (Cage (p,C))))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (p,C))))) is Element of K6(REAL)
upper_bound ((proj2 | (E-most (L~ (Cage (p,C))))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (p,C)))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Cage (p,C)))),(upper_bound (proj2 | (E-most (L~ (Cage (p,C))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
<*((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))*> is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() V35(3) FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ <*((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))*> is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))) is non empty functional Element of K6( the carrier of (TOP-REAL 2))
[p9,r] is set
{p9,r} is non empty set
{p9} is non empty trivial V35(1) set
{{p9,r},{p9}} is non empty set
Indices (Gauge (p,C)) is set
[s,rr] is set
{s,rr} is non empty set
{s} is non empty trivial V35(1) set
{{s,rr},{s}} is non empty set
[p9,rr] is set
{p9,rr} is non empty set
{{p9,rr},{p9}} is non empty set
R_Cut ((Upper_Seq (p,C)),((Gauge (p,C)) * (p9,r))) is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (s,rr))) is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len (Upper_Seq (p,C)) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
dom (Upper_Seq (p,C)) is non trivial Element of K6(NAT)
(Upper_Seq (p,C)) . 1 is V15() Function-like set
(Upper_Seq (p,C)) /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(W-min (L~ (Cage (p,C)))) `1 is V11() real ext-real Element of REAL
(Gauge (p,C)) * (1,rr) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * (1,rr)) `1 is V11() real ext-real Element of REAL
[1,rr] is set
{1,rr} is non empty set
{{1,rr},{1}} is non empty set
1 + 2 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
len (Lower_Seq (p,C)) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
dom (Lower_Seq (p,C)) is non trivial Element of K6(NAT)
(Lower_Seq (p,C)) . (len (Lower_Seq (p,C))) is V15() Function-like set
(Lower_Seq (p,C)) /. (len (Lower_Seq (p,C))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
[(len (Gauge (p,C))),rr] is set
{(len (Gauge (p,C))),rr} is non empty set
{(len (Gauge (p,C)))} is non empty trivial V35(1) set
{{(len (Gauge (p,C))),rr},{(len (Gauge (p,C)))}} is non empty set
(Lower_Seq (p,C)) . 1 is V15() Function-like set
(Lower_Seq (p,C)) /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(E-max (L~ (Cage (p,C)))) `1 is V11() real ext-real Element of REAL
(Gauge (p,C)) * ((len (Gauge (p,C))),rr) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * ((len (Gauge (p,C))),rr)) `1 is V11() real ext-real Element of REAL
1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
c2 is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V28() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
len c2 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
rng (Upper_Seq (p,C)) is functional Element of K6( the carrier of (TOP-REAL 2))
ii1 is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V28() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
len ii1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
rng (Lower_Seq (p,C)) is functional Element of K6( the carrier of (TOP-REAL 2))
jj1 is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one non constant V28() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq s.c.c. FinSequence of the carrier of (TOP-REAL 2)
len jj1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
dom jj1 is non trivial Element of K6(NAT)
jj1 /. (len jj1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
jj1 . (len jj1) is V15() Function-like set
p2 is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one non constant V28() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq s.c.c. FinSequence of the carrier of (TOP-REAL 2)
len p2 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
dom p2 is non trivial Element of K6(NAT)
p2 /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
p2 . 1 is V15() Function-like set
(len jj1) - 1 is V11() real ext-real Element of REAL
- 1 is V11() real ext-real non positive set
(len jj1) + (- 1) is V11() real ext-real set
p2 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
p2 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
(len jj1) -' 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
LSeg (jj1,p2) is functional Element of K6( the carrier of (TOP-REAL 2))
L~ jj1 is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(LSeg (jj1,p2)) /\ (L~ <*((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))*>) is functional Element of K6( the carrier of (TOP-REAL 2))
jj1 /. p2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((jj1 /. p2),((Gauge (p,C)) * (p9,r))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
p29 is set
LSeg (p2,1) is functional Element of K6( the carrier of (TOP-REAL 2))
L~ p2 is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(LSeg (p2,1)) /\ (L~ <*((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))*>) is functional Element of K6( the carrier of (TOP-REAL 2))
p2 /. (1 + 1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg (((Gauge (p,C)) * (s,rr)),(p2 /. (1 + 1))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
p29 is set
(L~ <*((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))*>) /\ (LSeg (p2,1)) is functional Element of K6( the carrier of (TOP-REAL 2))
jj1 /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
p2 /. (len p2) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
rng jj1 is non trivial functional Element of K6( the carrier of (TOP-REAL 2))
rng p2 is non trivial functional Element of K6( the carrier of (TOP-REAL 2))
{(jj1 /. 1)} is non empty trivial functional V35(1) set
(L~ jj1) /\ (L~ p2) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
p29 is set
[(len (Gauge (p,C))),r] is set
{(len (Gauge (p,C))),r} is non empty set
{{(len (Gauge (p,C))),r},{(len (Gauge (p,C)))}} is non empty set
p29 is set
(L~ (Upper_Seq (p,C))) /\ (L~ (Lower_Seq (p,C))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
{(W-min (L~ (Cage (p,C)))),(E-max (L~ (Cage (p,C))))} is non empty functional set
(Gauge (p,C)) * ((len (Gauge (p,C))),r) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * ((len (Gauge (p,C))),r)) `1 is V11() real ext-real Element of REAL
jj1 /. 2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * (s,rr)) `1 is V11() real ext-real Element of REAL
((Gauge (p,C)) * (p9,r)) .. (Upper_Seq (p,C)) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
mid ((Upper_Seq (p,C)),1,(((Gauge (p,C)) * (p9,r)) .. (Upper_Seq (p,C)))) is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
(Upper_Seq (p,C)) | (((Gauge (p,C)) * (p9,r)) .. (Upper_Seq (p,C))) is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V28() FinSequence-like FinSubsequence-like special unfolded s.n.c. FinSequence of the carrier of (TOP-REAL 2)
(Upper_Seq (p,C)) /. 2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
i2 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
dom <*((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))*> is non trivial V35(3) Element of K6(NAT)
<*((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))*> /. i2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * (p9,rr)) `1 is V11() real ext-real Element of REAL
(Gauge (p,C)) * (p9,1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * (p9,1)) `1 is V11() real ext-real Element of REAL
((Gauge (p,C)) * (p9,r)) `1 is V11() real ext-real Element of REAL
((Gauge (p,C)) * (p9,rr)) `2 is V11() real ext-real Element of REAL
((Gauge (p,C)) * (1,rr)) `2 is V11() real ext-real Element of REAL
((Gauge (p,C)) * (s,rr)) `2 is V11() real ext-real Element of REAL
|[(((Gauge (p,C)) * (p9,r)) `1),(((Gauge (p,C)) * (s,rr)) `2)]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * (p9,r)) `2 is V11() real ext-real Element of REAL
<*((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))*> /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
len <*((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))*> is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
<*((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))*> /. (len <*((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))*>) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
i2 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ i2 is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
i2 /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
len i2 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
i2 /. (len i2) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
d1 is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V28() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
jj1 ^' d1 is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
(jj1 ^' d1) ^' p2 is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
W-bound (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) is V15() V18( the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))))), REAL ) V212((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))))),REAL))
the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))))) is set
K7( the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))))),REAL)) is non empty set
lower_bound (proj1 | (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))))) is V11() real ext-real Element of REAL
(proj1 | (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))))) .: the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))))) is Element of K6(REAL)
lower_bound ((proj1 | (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))))) .: the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))))) is V11() real ext-real Element of REAL
W-bound (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))) is V15() V18( the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr))))), REAL ) V212((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr))))),REAL))
the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr))))) is set
K7( the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr))))),REAL)) is non empty set
lower_bound (proj1 | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr))))) is V11() real ext-real Element of REAL
(proj1 | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr))))) .: the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr))))) is Element of K6(REAL)
lower_bound ((proj1 | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr))))) .: the carrier of ((TOP-REAL 2) | (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))))) is V11() real ext-real Element of REAL
W-bound ((LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr))))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | ((LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr))))) is strict T_2 SubSpace of TOP-REAL 2
proj1 | ((LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr))))) is V15() V18( the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr))))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))))), REAL ) V212((TOP-REAL 2) | ((LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))))),REAL))
the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))))) is set
K7( the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))))),REAL)) is non empty set
lower_bound (proj1 | ((LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))))) is V11() real ext-real Element of REAL
(proj1 | ((LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))))) .: the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))))) is Element of K6(REAL)
lower_bound ((proj1 | ((LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))))) .: the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr)))) \/ (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr))))))) is V11() real ext-real Element of REAL
min ((W-bound (LSeg (((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))))),(W-bound (LSeg (((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)))))) is V11() real ext-real set
L~ d1 is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
W-bound (L~ d1) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ d1) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ d1) is V15() V18( the carrier of ((TOP-REAL 2) | (L~ d1))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ d1)), REAL ) V212((TOP-REAL 2) | (L~ d1)) Element of K6(K7( the carrier of ((TOP-REAL 2) | (L~ d1)),REAL))
the carrier of ((TOP-REAL 2) | (L~ d1)) is set
K7( the carrier of ((TOP-REAL 2) | (L~ d1)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (L~ d1)),REAL)) is non empty set
lower_bound (proj1 | (L~ d1)) is V11() real ext-real Element of REAL
(proj1 | (L~ d1)) .: the carrier of ((TOP-REAL 2) | (L~ d1)) is Element of K6(REAL)
lower_bound ((proj1 | (L~ d1)) .: the carrier of ((TOP-REAL 2) | (L~ d1))) is V11() real ext-real Element of REAL
len (Cage (p,C)) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like non constant V28() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the carrier of (TOP-REAL 2)
len (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
len (jj1 ^' d1) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
1 + 0 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
len ((jj1 ^' d1) ^' p2) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
d1 /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(jj1 ^' d1) /. (len (jj1 ^' d1)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
<*((Gauge (p,C)) * (p9,r)),((Gauge (p,C)) * (p9,rr)),((Gauge (p,C)) * (s,rr))*> /. 3 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg (d1,1) is functional Element of K6( the carrier of (TOP-REAL 2))
LSeg (jj1,((len jj1) -' 1)) is functional Element of K6( the carrier of (TOP-REAL 2))
(LSeg (jj1,((len jj1) -' 1))) /\ (LSeg (d1,1)) is functional Element of K6( the carrier of (TOP-REAL 2))
2 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
len d1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
(LSeg (jj1,p2)) /\ (LSeg (d1,1)) is functional Element of K6( the carrier of (TOP-REAL 2))
ii2 is set
{(jj1 /. (len jj1))} is non empty trivial functional V35(1) set
(len d1) - 2 is V11() real ext-real Element of REAL
(len d1) + (- 2) is V11() real ext-real set
(len (jj1 ^' d1)) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
((len (jj1 ^' d1)) + 1) - 1 is V11() real ext-real Element of REAL
((len (jj1 ^' d1)) + 1) + (- 1) is V11() real ext-real set
(len jj1) + (len d1) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
((len jj1) + (len d1)) - 1 is V11() real ext-real Element of REAL
((len jj1) + (len d1)) + (- 1) is V11() real ext-real set
(len (jj1 ^' d1)) - 1 is V11() real ext-real Element of REAL
(len (jj1 ^' d1)) + (- 1) is V11() real ext-real set
(len jj1) + ((len d1) - 2) is V11() real ext-real Element of REAL
(len d1) -' 2 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(len jj1) + ((len d1) -' 2) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
(len (jj1 ^' d1)) -' 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(len d1) - 1 is V11() real ext-real Element of REAL
(len d1) + (- 1) is V11() real ext-real set
(len d1) -' 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
((len d1) -' 2) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
((len d1) - 2) + 1 is V11() real ext-real Element of REAL
((len d1) - 1) + 1 is V11() real ext-real Element of REAL
LSeg (d1,((len d1) -' 1)) is functional Element of K6( the carrier of (TOP-REAL 2))
(LSeg (d1,((len d1) -' 1))) /\ (LSeg (p2,1)) is functional Element of K6( the carrier of (TOP-REAL 2))
ii2 is set
((len d1) -' 1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
d1 /. (((len d1) -' 1) + 1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((jj1 ^' d1),((len jj1) + ((len d1) -' 2))) is functional Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((jj1 ^' d1),((len jj1) + ((len d1) -' 2)))) /\ (LSeg (p2,1)) is functional Element of K6( the carrier of (TOP-REAL 2))
{((jj1 ^' d1) /. (len (jj1 ^' d1)))} is non empty trivial functional V35(1) set
rng d1 is functional Element of K6( the carrier of (TOP-REAL 2))
{(d1 /. 1)} is non empty trivial functional V35(1) set
(L~ jj1) /\ (L~ d1) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
ii2 is set
ii2 is set
(rng jj1) /\ (rng d1) is functional Element of K6( the carrier of (TOP-REAL 2))
d1 /. (len d1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
{(d1 /. (len d1))} is non empty trivial functional V35(1) set
(L~ p2) /\ (L~ d1) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
ii2 is set
ii2 is set
L~ (jj1 ^' d1) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(L~ (jj1 ^' d1)) /\ (L~ p2) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(L~ jj1) \/ (L~ d1) is non empty functional Element of K6( the carrier of (TOP-REAL 2))
((L~ jj1) \/ (L~ d1)) /\ (L~ p2) is functional Element of K6( the carrier of (TOP-REAL 2))
{(p2 /. 1)} is non empty trivial functional V35(1) set
{(jj1 /. 1)} \/ {(p2 /. 1)} is non empty set
(jj1 ^' d1) /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
{((jj1 ^' d1) /. 1)} is non empty trivial functional V35(1) set
{((jj1 ^' d1) /. 1)} \/ {(p2 /. 1)} is non empty set
{((jj1 ^' d1) /. 1),(p2 /. 1)} is non empty functional set
E-max p is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
E-bound p is V11() real ext-real Element of REAL
(TOP-REAL 2) | p is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | p is V15() V18( the carrier of ((TOP-REAL 2) | p)) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | p), REAL ) V212((TOP-REAL 2) | p) Element of K6(K7( the carrier of ((TOP-REAL 2) | p),REAL))
the carrier of ((TOP-REAL 2) | p) is set
K7( the carrier of ((TOP-REAL 2) | p),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | p),REAL)) is non empty set
upper_bound (proj1 | p) is V11() real ext-real Element of REAL
(proj1 | p) .: the carrier of ((TOP-REAL 2) | p) is Element of K6(REAL)
upper_bound ((proj1 | p) .: the carrier of ((TOP-REAL 2) | p)) is V11() real ext-real Element of REAL
E-most p is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
SE-corner p is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
S-bound p is V11() real ext-real Element of REAL
proj2 | p is V15() V18( the carrier of ((TOP-REAL 2) | p)) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | p), REAL ) V212((TOP-REAL 2) | p) Element of K6(K7( the carrier of ((TOP-REAL 2) | p),REAL))
lower_bound (proj2 | p) is V11() real ext-real Element of REAL
(proj2 | p) .: the carrier of ((TOP-REAL 2) | p) is Element of K6(REAL)
lower_bound ((proj2 | p) .: the carrier of ((TOP-REAL 2) | p)) is V11() real ext-real Element of REAL
|[(E-bound p),(S-bound p)]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
NE-corner p is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
N-bound p is V11() real ext-real Element of REAL
upper_bound (proj2 | p) is V11() real ext-real Element of REAL
upper_bound ((proj2 | p) .: the carrier of ((TOP-REAL 2) | p)) is V11() real ext-real Element of REAL
|[(E-bound p),(N-bound p)]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner p),(NE-corner p)) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SE-corner p),(NE-corner p))) /\ p is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (E-most p) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (E-most p) is V15() V18( the carrier of ((TOP-REAL 2) | (E-most p))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (E-most p)), REAL ) V212((TOP-REAL 2) | (E-most p)) Element of K6(K7( the carrier of ((TOP-REAL 2) | (E-most p)),REAL))
the carrier of ((TOP-REAL 2) | (E-most p)) is set
K7( the carrier of ((TOP-REAL 2) | (E-most p)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (E-most p)),REAL)) is non empty set
upper_bound (proj2 | (E-most p)) is V11() real ext-real Element of REAL
(proj2 | (E-most p)) .: the carrier of ((TOP-REAL 2) | (E-most p)) is Element of K6(REAL)
upper_bound ((proj2 | (E-most p)) .: the carrier of ((TOP-REAL 2) | (E-most p))) is V11() real ext-real Element of REAL
|[(E-bound p),(upper_bound (proj2 | (E-most p)))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
W-min p is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
W-bound p is V11() real ext-real Element of REAL
lower_bound (proj1 | p) is V11() real ext-real Element of REAL
lower_bound ((proj1 | p) .: the carrier of ((TOP-REAL 2) | p)) is V11() real ext-real Element of REAL
W-most p is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
SW-corner p is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
|[(W-bound p),(S-bound p)]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
NW-corner p is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
|[(W-bound p),(N-bound p)]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner p),(NW-corner p)) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner p),(NW-corner p))) /\ p is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (W-most p) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (W-most p) is V15() V18( the carrier of ((TOP-REAL 2) | (W-most p))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (W-most p)), REAL ) V212((TOP-REAL 2) | (W-most p)) Element of K6(K7( the carrier of ((TOP-REAL 2) | (W-most p)),REAL))
the carrier of ((TOP-REAL 2) | (W-most p)) is set
K7( the carrier of ((TOP-REAL 2) | (W-most p)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (W-most p)),REAL)) is non empty set
lower_bound (proj2 | (W-most p)) is V11() real ext-real Element of REAL
(proj2 | (W-most p)) .: the carrier of ((TOP-REAL 2) | (W-most p)) is Element of K6(REAL)
lower_bound ((proj2 | (W-most p)) .: the carrier of ((TOP-REAL 2) | (W-most p))) is V11() real ext-real Element of REAL
|[(W-bound p),(lower_bound (proj2 | (W-most p)))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
rng (Cage (p,C)) is non trivial functional Element of K6( the carrier of (TOP-REAL 2))
(Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))) /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
W-max (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
W-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V15() V18( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))), REAL ) V212((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),REAL))
the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is set
K7( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),REAL)) is non empty set
lower_bound (proj1 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is V11() real ext-real Element of REAL
(proj1 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) .: the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is Element of K6(REAL)
lower_bound ((proj1 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) .: the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is V11() real ext-real Element of REAL
W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
SW-corner (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
S-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V11() real ext-real Element of REAL
proj2 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V15() V18( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))), REAL ) V212((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),REAL))
lower_bound (proj2 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is V11() real ext-real Element of REAL
(proj2 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) .: the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is Element of K6(REAL)
lower_bound ((proj2 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) .: the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),(S-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
NW-corner (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
N-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) .: the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),(N-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),(NW-corner (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),(NW-corner (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))))) /\ (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is V15() V18( the carrier of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))), REAL ) V212((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))),REAL))
the carrier of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is set
K7( the carrier of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))),REAL)) is non empty set
upper_bound (proj2 | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is V11() real ext-real Element of REAL
(proj2 | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is Element of K6(REAL)
upper_bound ((proj2 | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),(upper_bound (proj2 | (W-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(W-max (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) .. (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
N-min (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
NE-corner (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
E-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is V11() real ext-real Element of REAL
upper_bound ((proj1 | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) .: the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),(N-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((NW-corner (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),(NE-corner (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((NW-corner (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))),(NE-corner (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))))) /\ (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is V15() V18( the carrier of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))), REAL ) V212((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))),REAL))
the carrier of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is set
K7( the carrier of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))),REAL)) is non empty set
lower_bound (proj1 | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is V11() real ext-real Element of REAL
(proj1 | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is Element of K6(REAL)
lower_bound ((proj1 | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))))),(N-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(N-min (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) .. (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
N-max (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
upper_bound (proj1 | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) is V11() real ext-real Element of REAL
upper_bound ((proj1 | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))))) is V11() real ext-real Element of REAL
|[(upper_bound (proj1 | (N-most (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))))),(N-bound (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C))))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(N-max (L~ (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) .. (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(E-max (L~ (Cage (p,C)))) .. (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
ii2 is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like non constant V28() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard FinSequence of the carrier of (TOP-REAL 2)
right_cell (ii2,1,(Gauge (p,C))) is functional Element of K6( the carrier of (TOP-REAL 2))
L~ ii2 is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
(right_cell (ii2,1,(Gauge (p,C)))) \ (L~ ii2) is functional Element of K6( the carrier of (TOP-REAL 2))
RightComp ii2 is non empty functional Element of K6( the carrier of (TOP-REAL 2))
(L~ (jj1 ^' d1)) \/ (L~ p2) is non empty functional Element of K6( the carrier of (TOP-REAL 2))
((L~ jj1) \/ (L~ d1)) \/ (L~ p2) is non empty functional Element of K6( the carrier of (TOP-REAL 2))
(L~ (Upper_Seq (p,C))) \/ (L~ (Lower_Seq (p,C))) is non empty functional Element of K6( the carrier of (TOP-REAL 2))
right_cell ((Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))),1) is functional Element of K6( the carrier of (TOP-REAL 2))
GoB (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))) is V15() non empty-yielding V18( NAT ) V19(K307( the carrier of (TOP-REAL 2))) Function-like V28() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K307( the carrier of (TOP-REAL 2))
right_cell ((Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))),1,(GoB (Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))))) is functional Element of K6( the carrier of (TOP-REAL 2))
GoB (Cage (p,C)) is V15() non empty-yielding V18( NAT ) V19(K307( the carrier of (TOP-REAL 2))) Function-like V28() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K307( the carrier of (TOP-REAL 2))
right_cell ((Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))),1,(GoB (Cage (p,C)))) is functional Element of K6( the carrier of (TOP-REAL 2))
right_cell ((Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))),1,(Gauge (p,C))) is functional Element of K6( the carrier of (TOP-REAL 2))
(Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))) -: (E-max (L~ (Cage (p,C)))) is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like special unfolded FinSequence of the carrier of (TOP-REAL 2)
right_cell (((Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))) -: (E-max (L~ (Cage (p,C))))),1,(Gauge (p,C))) is functional Element of K6( the carrier of (TOP-REAL 2))
right_cell ((Upper_Seq (p,C)),1,(Gauge (p,C))) is functional Element of K6( the carrier of (TOP-REAL 2))
right_cell ((R_Cut ((Upper_Seq (p,C)),((Gauge (p,C)) * (p9,r)))),1,(Gauge (p,C))) is functional Element of K6( the carrier of (TOP-REAL 2))
right_cell ((jj1 ^' d1),1,(Gauge (p,C))) is functional Element of K6( the carrier of (TOP-REAL 2))
ii2 /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
ii2 /. 2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(jj1 ^' d1) /. 2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(Upper_Seq (p,C)) ^' (Lower_Seq (p,C)) is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
((Upper_Seq (p,C)) ^' (Lower_Seq (p,C))) /. 2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(Rotate ((Cage (p,C)),(W-min (L~ (Cage (p,C)))))) /. 2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(L~ jj1) \/ (L~ p2) is non empty functional Element of K6( the carrier of (TOP-REAL 2))
W-min ((L~ jj1) \/ (L~ p2)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
W-bound ((L~ jj1) \/ (L~ p2)) is V11() real ext-real Element of REAL
(TOP-REAL 2) | ((L~ jj1) \/ (L~ p2)) is strict T_2 SubSpace of TOP-REAL 2
proj1 | ((L~ jj1) \/ (L~ p2)) is V15() V18( the carrier of ((TOP-REAL 2) | ((L~ jj1) \/ (L~ p2)))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | ((L~ jj1) \/ (L~ p2))), REAL ) V212((TOP-REAL 2) | ((L~ jj1) \/ (L~ p2))) Element of K6(K7( the carrier of ((TOP-REAL 2) | ((L~ jj1) \/ (L~ p2))),REAL))
the carrier of ((TOP-REAL 2) | ((L~ jj1) \/ (L~ p2))) is set
K7( the carrier of ((TOP-REAL 2) | ((L~ jj1) \/ (L~ p2))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | ((L~ jj1) \/ (L~ p2))),REAL)) is non empty set
lower_bound (proj1 | ((L~ jj1) \/ (L~ p2))) is V11() real ext-real Element of REAL
(proj1 | ((L~ jj1) \/ (L~ p2))) .: the carrier of ((TOP-REAL 2) | ((L~ jj1) \/ (L~ p2))) is Element of K6(REAL)
lower_bound ((proj1 | ((L~ jj1) \/ (L~ p2))) .: the carrier of ((TOP-REAL 2) | ((L~ jj1) \/ (L~ p2)))) is V11() real ext-real Element of REAL
W-most ((L~ jj1) \/ (L~ p2)) is functional Element of K6( the carrier of (TOP-REAL 2))
SW-corner ((L~ jj1) \/ (L~ p2)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
S-bound ((L~ jj1) \/ (L~ p2)) is V11() real ext-real Element of REAL
proj2 | ((L~ jj1) \/ (L~ p2)) is V15() V18( the carrier of ((TOP-REAL 2) | ((L~ jj1) \/ (L~ p2)))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | ((L~ jj1) \/ (L~ p2))), REAL ) V212((TOP-REAL 2) | ((L~ jj1) \/ (L~ p2))) Element of K6(K7( the carrier of ((TOP-REAL 2) | ((L~ jj1) \/ (L~ p2))),REAL))
lower_bound (proj2 | ((L~ jj1) \/ (L~ p2))) is V11() real ext-real Element of REAL
(proj2 | ((L~ jj1) \/ (L~ p2))) .: the carrier of ((TOP-REAL 2) | ((L~ jj1) \/ (L~ p2))) is Element of K6(REAL)
lower_bound ((proj2 | ((L~ jj1) \/ (L~ p2))) .: the carrier of ((TOP-REAL 2) | ((L~ jj1) \/ (L~ p2)))) is V11() real ext-real Element of REAL
|[(W-bound ((L~ jj1) \/ (L~ p2))),(S-bound ((L~ jj1) \/ (L~ p2)))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
NW-corner ((L~ jj1) \/ (L~ p2)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
N-bound ((L~ jj1) \/ (L~ p2)) is V11() real ext-real Element of REAL
upper_bound (proj2 | ((L~ jj1) \/ (L~ p2))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | ((L~ jj1) \/ (L~ p2))) .: the carrier of ((TOP-REAL 2) | ((L~ jj1) \/ (L~ p2)))) is V11() real ext-real Element of REAL
|[(W-bound ((L~ jj1) \/ (L~ p2))),(N-bound ((L~ jj1) \/ (L~ p2)))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner ((L~ jj1) \/ (L~ p2))),(NW-corner ((L~ jj1) \/ (L~ p2)))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner ((L~ jj1) \/ (L~ p2))),(NW-corner ((L~ jj1) \/ (L~ p2))))) /\ ((L~ jj1) \/ (L~ p2)) is functional Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (W-most ((L~ jj1) \/ (L~ p2))) is strict T_2 SubSpace of TOP-REAL 2
proj2 | (W-most ((L~ jj1) \/ (L~ p2))) is V15() V18( the carrier of ((TOP-REAL 2) | (W-most ((L~ jj1) \/ (L~ p2))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (W-most ((L~ jj1) \/ (L~ p2)))), REAL ) V212((TOP-REAL 2) | (W-most ((L~ jj1) \/ (L~ p2)))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (W-most ((L~ jj1) \/ (L~ p2)))),REAL))
the carrier of ((TOP-REAL 2) | (W-most ((L~ jj1) \/ (L~ p2)))) is set
K7( the carrier of ((TOP-REAL 2) | (W-most ((L~ jj1) \/ (L~ p2)))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (W-most ((L~ jj1) \/ (L~ p2)))),REAL)) is non empty set
lower_bound (proj2 | (W-most ((L~ jj1) \/ (L~ p2)))) is V11() real ext-real Element of REAL
(proj2 | (W-most ((L~ jj1) \/ (L~ p2)))) .: the carrier of ((TOP-REAL 2) | (W-most ((L~ jj1) \/ (L~ p2)))) is Element of K6(REAL)
lower_bound ((proj2 | (W-most ((L~ jj1) \/ (L~ p2)))) .: the carrier of ((TOP-REAL 2) | (W-most ((L~ jj1) \/ (L~ p2))))) is V11() real ext-real Element of REAL
|[(W-bound ((L~ jj1) \/ (L~ p2))),(lower_bound (proj2 | (W-most ((L~ jj1) \/ (L~ p2)))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(W-min ((L~ jj1) \/ (L~ p2))) `1 is V11() real ext-real Element of REAL
((L~ jj1) \/ (L~ p2)) \/ (L~ d1) is non empty functional Element of K6( the carrier of (TOP-REAL 2))
W-min (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
W-bound (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)) is strict T_2 SubSpace of TOP-REAL 2
proj1 | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)) is V15() V18( the carrier of ((TOP-REAL 2) | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))), REAL ) V212((TOP-REAL 2) | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))),REAL))
the carrier of ((TOP-REAL 2) | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))) is set
K7( the carrier of ((TOP-REAL 2) | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))),REAL)) is non empty set
lower_bound (proj1 | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))) is V11() real ext-real Element of REAL
(proj1 | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))) .: the carrier of ((TOP-REAL 2) | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))) is Element of K6(REAL)
lower_bound ((proj1 | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))) .: the carrier of ((TOP-REAL 2) | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))) is V11() real ext-real Element of REAL
W-most (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)) is functional Element of K6( the carrier of (TOP-REAL 2))
SW-corner (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
S-bound (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)) is V11() real ext-real Element of REAL
proj2 | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)) is V15() V18( the carrier of ((TOP-REAL 2) | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))), REAL ) V212((TOP-REAL 2) | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))),REAL))
lower_bound (proj2 | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))) is V11() real ext-real Element of REAL
(proj2 | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))) .: the carrier of ((TOP-REAL 2) | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))) is Element of K6(REAL)
lower_bound ((proj2 | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))) .: the carrier of ((TOP-REAL 2) | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))) is V11() real ext-real Element of REAL
|[(W-bound (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))),(S-bound (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
NW-corner (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
N-bound (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)) is V11() real ext-real Element of REAL
upper_bound (proj2 | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))) .: the carrier of ((TOP-REAL 2) | (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))) is V11() real ext-real Element of REAL
|[(W-bound (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))),(N-bound (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))),(NW-corner (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))),(NW-corner (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))))) /\ (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)) is functional Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (W-most (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))) is strict T_2 SubSpace of TOP-REAL 2
proj2 | (W-most (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))) is V15() V18( the carrier of ((TOP-REAL 2) | (W-most (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (W-most (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))), REAL ) V212((TOP-REAL 2) | (W-most (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (W-most (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))),REAL))
the carrier of ((TOP-REAL 2) | (W-most (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))) is set
K7( the carrier of ((TOP-REAL 2) | (W-most (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (W-most (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))),REAL)) is non empty set
lower_bound (proj2 | (W-most (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))) is V11() real ext-real Element of REAL
(proj2 | (W-most (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))) .: the carrier of ((TOP-REAL 2) | (W-most (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))) is Element of K6(REAL)
lower_bound ((proj2 | (W-most (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))) .: the carrier of ((TOP-REAL 2) | (W-most (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))))) is V11() real ext-real Element of REAL
|[(W-bound (((L~ jj1) \/ (L~ p2)) \/ (L~ d1))),(lower_bound (proj2 | (W-most (((L~ jj1) \/ (L~ p2)) \/ (L~ d1)))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
W-min (L~ ii2) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
W-bound (L~ ii2) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ ii2) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ ii2) is V15() V18( the carrier of ((TOP-REAL 2) | (L~ ii2))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ ii2)), REAL ) V212((TOP-REAL 2) | (L~ ii2)) Element of K6(K7( the carrier of ((TOP-REAL 2) | (L~ ii2)),REAL))
the carrier of ((TOP-REAL 2) | (L~ ii2)) is set
K7( the carrier of ((TOP-REAL 2) | (L~ ii2)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (L~ ii2)),REAL)) is non empty set
lower_bound (proj1 | (L~ ii2)) is V11() real ext-real Element of REAL
(proj1 | (L~ ii2)) .: the carrier of ((TOP-REAL 2) | (L~ ii2)) is Element of K6(REAL)
lower_bound ((proj1 | (L~ ii2)) .: the carrier of ((TOP-REAL 2) | (L~ ii2))) is V11() real ext-real Element of REAL
W-most (L~ ii2) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
SW-corner (L~ ii2) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
S-bound (L~ ii2) is V11() real ext-real Element of REAL
proj2 | (L~ ii2) is V15() V18( the carrier of ((TOP-REAL 2) | (L~ ii2))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ ii2)), REAL ) V212((TOP-REAL 2) | (L~ ii2)) Element of K6(K7( the carrier of ((TOP-REAL 2) | (L~ ii2)),REAL))
lower_bound (proj2 | (L~ ii2)) is V11() real ext-real Element of REAL
(proj2 | (L~ ii2)) .: the carrier of ((TOP-REAL 2) | (L~ ii2)) is Element of K6(REAL)
lower_bound ((proj2 | (L~ ii2)) .: the carrier of ((TOP-REAL 2) | (L~ ii2))) is V11() real ext-real Element of REAL
|[(W-bound (L~ ii2)),(S-bound (L~ ii2))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
NW-corner (L~ ii2) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
N-bound (L~ ii2) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ ii2)) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (L~ ii2)) .: the carrier of ((TOP-REAL 2) | (L~ ii2))) is V11() real ext-real Element of REAL
|[(W-bound (L~ ii2)),(N-bound (L~ ii2))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner (L~ ii2)),(NW-corner (L~ ii2))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner (L~ ii2)),(NW-corner (L~ ii2)))) /\ (L~ ii2) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (W-most (L~ ii2)) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (W-most (L~ ii2)) is V15() V18( the carrier of ((TOP-REAL 2) | (W-most (L~ ii2)))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (W-most (L~ ii2))), REAL ) V212((TOP-REAL 2) | (W-most (L~ ii2))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (W-most (L~ ii2))),REAL))
the carrier of ((TOP-REAL 2) | (W-most (L~ ii2))) is set
K7( the carrier of ((TOP-REAL 2) | (W-most (L~ ii2))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (W-most (L~ ii2))),REAL)) is non empty set
lower_bound (proj2 | (W-most (L~ ii2))) is V11() real ext-real Element of REAL
(proj2 | (W-most (L~ ii2))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ ii2))) is Element of K6(REAL)
lower_bound ((proj2 | (W-most (L~ ii2))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ ii2)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ ii2)),(lower_bound (proj2 | (W-most (L~ ii2))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
rng ii2 is non trivial functional Element of K6( the carrier of (TOP-REAL 2))
dom ii2 is non trivial Element of K6(NAT)
(ii2 /. 2) `1 is V11() real ext-real Element of REAL
(W-min (L~ ii2)) `1 is V11() real ext-real Element of REAL
Rotate (ii2,(W-min (L~ ii2))) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like non constant V28() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard FinSequence of the carrier of (TOP-REAL 2)
(Rotate (ii2,(W-min (L~ ii2)))) /. 2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(Upper_Seq (p,C)) . (len (Upper_Seq (p,C))) is V15() Function-like set
(Upper_Seq (p,C)) /. (len (Upper_Seq (p,C))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
east_halfline (E-max p) is non empty functional connected V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
Gji is set
Gij9 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(east_halfline (E-max p)) /\ (L~ (Cage (p,C))) is functional Element of K6( the carrier of (TOP-REAL 2))
Gij9 `1 is V11() real ext-real Element of REAL
Gij is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like non constant V28() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the carrier of (TOP-REAL 2)
L~ Gij is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
Gji is set
Gij9 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
Gij9 `1 is V11() real ext-real Element of REAL
Gij9 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
Gij9 `1 is V11() real ext-real Element of REAL
Gij9 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
Gij9 `1 is V11() real ext-real Element of REAL
Gij9 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
Gij9 `1 is V11() real ext-real Element of REAL
p9 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
(len (Gauge (p,C))) - 1 is V11() real ext-real Element of REAL
(len (Gauge (p,C))) + (- 1) is V11() real ext-real set
(len (Gauge (p,C))) -' 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(Gauge (p,C)) * (((len (Gauge (p,C))) -' 1),1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * (((len (Gauge (p,C))) -' 1),1)) `1 is V11() real ext-real Element of REAL
(E-max p) `1 is V11() real ext-real Element of REAL
Gij9 `2 is V11() real ext-real Element of REAL
(E-max p) `2 is V11() real ext-real Element of REAL
Gji is set
Gij9 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(east_halfline (E-max p)) /\ (L~ (Cage (p,C))) is functional Element of K6( the carrier of (TOP-REAL 2))
Gij9 `1 is V11() real ext-real Element of REAL
(E-max p) `2 is V11() real ext-real Element of REAL
Gij9 `2 is V11() real ext-real Element of REAL
Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like non constant V28() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the carrier of (TOP-REAL 2)
right_cell ((Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))),1) is functional Element of K6( the carrier of (TOP-REAL 2))
(Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))) -: (W-min (L~ (Cage (p,C)))) is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like special unfolded FinSequence of the carrier of (TOP-REAL 2)
LSeg ((Lower_Seq (p,C)),1) is functional Element of K6( the carrier of (TOP-REAL 2))
LSeg ((Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))),1) is functional Element of K6( the carrier of (TOP-REAL 2))
L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
len (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
GoB (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))) is V15() non empty-yielding V18( NAT ) V19(K307( the carrier of (TOP-REAL 2))) Function-like V28() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K307( the carrier of (TOP-REAL 2))
(Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))) /. 1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
E-max (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
E-bound (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))) is V15() V18( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))), REAL ) V212((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))),REAL))
the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) is set
K7( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))),REAL)) is non empty set
upper_bound (proj1 | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) is V11() real ext-real Element of REAL
(proj1 | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) .: the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) is Element of K6(REAL)
upper_bound ((proj1 | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) .: the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) is V11() real ext-real Element of REAL
E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
SE-corner (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
S-bound (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))) is V11() real ext-real Element of REAL
proj2 | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))) is V15() V18( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))), REAL ) V212((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))),REAL))
lower_bound (proj2 | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) is V11() real ext-real Element of REAL
(proj2 | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) .: the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) is Element of K6(REAL)
lower_bound ((proj2 | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) .: the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))),(S-bound (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
NE-corner (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
N-bound (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) .: the carrier of ((TOP-REAL 2) | (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))),(N-bound (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))),(NE-corner (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SE-corner (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))),(NE-corner (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))))) /\ (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))) is V15() V18( the carrier of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))), REAL ) V212((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))),REAL))
the carrier of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) is set
K7( the carrier of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))),REAL)) is non empty set
upper_bound (proj2 | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) is V11() real ext-real Element of REAL
(proj2 | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) is Element of K6(REAL)
upper_bound ((proj2 | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))))),(upper_bound (proj2 | (E-most (L~ (Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C))))))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))) /. (1 + 1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
x is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
x9 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
x9 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
[x,(x9 + 1)] is set
{x,(x9 + 1)} is non empty set
{x} is non empty trivial V35(1) set
{{x,(x9 + 1)},{x}} is non empty set
[x,x9] is set
{x,x9} is non empty set
{{x,x9},{x}} is non empty set
(Gauge (p,C)) * (x,(x9 + 1)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(Gauge (p,C)) * (x,x9) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
jj2 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(Gauge (p,C)) * ((len (Gauge (p,C))),jj2) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
[(len (Gauge (p,C))),jj2] is set
{(len (Gauge (p,C))),jj2} is non empty set
{{(len (Gauge (p,C))),jj2},{(len (Gauge (p,C)))}} is non empty set
x + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
(x9 + 1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
x -' 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
cell ((Gauge (p,C)),(x -' 1),x9) is functional Element of K6( the carrier of (TOP-REAL 2))
(x -' 1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
4 - 1 is V11() real ext-real Element of REAL
4 + (- 1) is V11() real ext-real set
x - 1 is V11() real ext-real Element of REAL
x + (- 1) is V11() real ext-real set
(Gauge (p,C)) * ((x -' 1),x9) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * ((x -' 1),x9)) `2 is V11() real ext-real Element of REAL
(Gauge (p,C)) * ((x -' 1),(x9 + 1)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * ((x -' 1),(x9 + 1))) `2 is V11() real ext-real Element of REAL
(Gauge (p,C)) * (1,x9) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * (1,x9)) `2 is V11() real ext-real Element of REAL
((Gauge (p,C)) * (x,x9)) `2 is V11() real ext-real Element of REAL
(Gauge (p,C)) * (1,(x9 + 1)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * (1,(x9 + 1))) `2 is V11() real ext-real Element of REAL
((Gauge (p,C)) * (x,(x9 + 1))) `2 is V11() real ext-real Element of REAL
(Gauge (p,C)) * ((len (Gauge (p,C))),x9) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * ((len (Gauge (p,C))),x9)) `1 is V11() real ext-real Element of REAL
(Gauge (p,C)) * ((len (Gauge (p,C))),(x9 + 1)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * ((len (Gauge (p,C))),(x9 + 1))) `1 is V11() real ext-real Element of REAL
LSeg (((Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))) /. 1),((Rotate ((Cage (p,C)),(E-max (L~ (Cage (p,C)))))) /. (1 + 1))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
Index (Gij9,p2) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
LSeg (p2,(Index (Gij9,p2))) is functional Element of K6( the carrier of (TOP-REAL 2))
((Gauge (p,C)) * (s,rr)) .. (Lower_Seq (p,C)) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
mid ((Lower_Seq (p,C)),(((Gauge (p,C)) * (s,rr)) .. (Lower_Seq (p,C))),(len (Lower_Seq (p,C)))) is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V28() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
Index (((Gauge (p,C)) * (s,rr)),(Lower_Seq (p,C))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(Index (((Gauge (p,C)) * (s,rr)),(Lower_Seq (p,C)))) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
t is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative set
(Lower_Seq (p,C)) . t is V15() Function-like set
len (L_Cut ((Lower_Seq (p,C)),((Gauge (p,C)) * (s,rr)))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(len (Lower_Seq (p,C))) - (Index (((Gauge (p,C)) * (s,rr)),(Lower_Seq (p,C)))) is V11() real ext-real Element of REAL
- (Index (((Gauge (p,C)) * (s,rr)),(Lower_Seq (p,C)))) is V11() real ext-real non positive set
(len (Lower_Seq (p,C))) + (- (Index (((Gauge (p,C)) * (s,rr)),(Lower_Seq (p,C))))) is V11() real ext-real set
(Index (Gij9,p2)) + (((Gauge (p,C)) * (s,rr)) .. (Lower_Seq (p,C))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
((Index (Gij9,p2)) + (((Gauge (p,C)) * (s,rr)) .. (Lower_Seq (p,C)))) -' 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
0 + (Index (((Gauge (p,C)) * (s,rr)),(Lower_Seq (p,C)))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(len (Lower_Seq (p,C))) -' (Index (((Gauge (p,C)) * (s,rr)),(Lower_Seq (p,C)))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(Index (Gij9,p2)) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
((len (Lower_Seq (p,C))) -' (Index (((Gauge (p,C)) * (s,rr)),(Lower_Seq (p,C))))) - 1 is V11() real ext-real Element of REAL
((len (Lower_Seq (p,C))) -' (Index (((Gauge (p,C)) * (s,rr)),(Lower_Seq (p,C))))) + (- 1) is V11() real ext-real set
((len (Lower_Seq (p,C))) - (Index (((Gauge (p,C)) * (s,rr)),(Lower_Seq (p,C))))) - 1 is V11() real ext-real Element of REAL
((len (Lower_Seq (p,C))) - (Index (((Gauge (p,C)) * (s,rr)),(Lower_Seq (p,C))))) + (- 1) is V11() real ext-real set
(len (Lower_Seq (p,C))) - (((Gauge (p,C)) * (s,rr)) .. (Lower_Seq (p,C))) is V11() real ext-real Element of REAL
- (((Gauge (p,C)) * (s,rr)) .. (Lower_Seq (p,C))) is V11() real ext-real non positive set
(len (Lower_Seq (p,C))) + (- (((Gauge (p,C)) * (s,rr)) .. (Lower_Seq (p,C)))) is V11() real ext-real set
(len (Lower_Seq (p,C))) -' (((Gauge (p,C)) * (s,rr)) .. (Lower_Seq (p,C))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
((len (Lower_Seq (p,C))) -' (((Gauge (p,C)) * (s,rr)) .. (Lower_Seq (p,C)))) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
LSeg ((mid ((Lower_Seq (p,C)),(((Gauge (p,C)) * (s,rr)) .. (Lower_Seq (p,C))),(len (Lower_Seq (p,C))))),(Index (Gij9,p2))) is functional Element of K6( the carrier of (TOP-REAL 2))
LSeg ((Lower_Seq (p,C)),(((Index (Gij9,p2)) + (((Gauge (p,C)) * (s,rr)) .. (Lower_Seq (p,C)))) -' 1)) is functional Element of K6( the carrier of (TOP-REAL 2))
(1 + 1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
((1 + 1) + 1) - 1 is V11() real ext-real Element of REAL
((1 + 1) + 1) + (- 1) is V11() real ext-real set
((Index (Gij9,p2)) + (((Gauge (p,C)) * (s,rr)) .. (Lower_Seq (p,C)))) - 1 is V11() real ext-real Element of REAL
((Index (Gij9,p2)) + (((Gauge (p,C)) * (s,rr)) .. (Lower_Seq (p,C)))) + (- 1) is V11() real ext-real set
(LSeg ((Lower_Seq (p,C)),1)) /\ (LSeg ((Lower_Seq (p,C)),(((Index (Gij9,p2)) + (((Gauge (p,C)) * (s,rr)) .. (Lower_Seq (p,C)))) -' 1))) is functional Element of K6( the carrier of (TOP-REAL 2))
(Lower_Seq (p,C)) /. 2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
{((Lower_Seq (p,C)) /. 2)} is non empty trivial functional V35(1) set
Gij9 .. (Lower_Seq (p,C)) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(Gauge (p,C)) * ((len (Gauge (p,C))),r) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,C)) * ((len (Gauge (p,C))),r)) `1 is V11() real ext-real Element of REAL
(L~ Gij) ` is non empty functional Element of K6( the carrier of (TOP-REAL 2))
Gji is functional Element of K6( the carrier of (TOP-REAL 2))
UBD (L~ Gij) is non empty functional open connected Element of K6( the carrier of (TOP-REAL 2))
LeftComp Gij is non empty functional Element of K6( the carrier of (TOP-REAL 2))
{((Gauge (p,C)) * (p9,rr))} is non empty trivial functional V35(1) set
((Gauge (p,C)) * (p9,r)) `2 is V11() real ext-real Element of REAL
{((Gauge (p,C)) * (p9,rr))} is non empty trivial functional V35(1) set
((Gauge (p,C)) * (p9,r)) `2 is V11() real ext-real Element of REAL
C is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
C + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
p is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
Gauge (p,(C + 1)) is V15() non empty-yielding V18( NAT ) V19(K307( the carrier of (TOP-REAL 2))) Function-like V28() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K307( the carrier of (TOP-REAL 2))
len (Gauge (p,(C + 1))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
width (Gauge (p,(C + 1))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
Cage (p,(C + 1)) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like non constant V28() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the carrier of (TOP-REAL 2)
L~ (Cage (p,(C + 1))) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
Lower_Arc (L~ (Cage (p,(C + 1)))) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
Upper_Arc (L~ (Cage (p,(C + 1)))) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
Lower_Arc p is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
p9 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
s is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
r is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
rr is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(Gauge (p,(C + 1))) * (p9,rr) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(Gauge (p,(C + 1))) * (s,r) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(Gauge (p,(C + 1))) * (s,rr) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) \/ (LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) is non empty functional Element of K6( the carrier of (TOP-REAL 2))
Lower_Seq (p,(C + 1)) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V28() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
L~ (Lower_Seq (p,(C + 1))) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
Upper_Seq (p,(C + 1)) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V28() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
L~ (Upper_Seq (p,(C + 1))) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
[s,r] is set
{s,r} is non empty set
{s} is non empty trivial V35(1) set
{{s,r},{s}} is non empty set
Indices (Gauge (p,(C + 1))) is set
[s,rr] is set
{s,rr} is non empty set
{{s,rr},{s}} is non empty set
((Gauge (p,(C + 1))) * (s,r)) `1 is V11() real ext-real Element of REAL
(Gauge (p,(C + 1))) * (s,1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,(C + 1))) * (s,1)) `1 is V11() real ext-real Element of REAL
((Gauge (p,(C + 1))) * (s,rr)) `1 is V11() real ext-real Element of REAL
((Gauge (p,(C + 1))) * (s,rr)) `2 is V11() real ext-real Element of REAL
(Gauge (p,(C + 1))) * (1,rr) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,(C + 1))) * (1,rr)) `2 is V11() real ext-real Element of REAL
((Gauge (p,(C + 1))) * (p9,rr)) `2 is V11() real ext-real Element of REAL
[p9,rr] is set
{p9,rr} is non empty set
{p9} is non empty trivial V35(1) set
{{p9,rr},{p9}} is non empty set
(LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
proj2 .: ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1))))) is Element of K6(REAL)
lower_bound (proj2 .: ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))))) is V11() real ext-real Element of REAL
k1 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(Gauge (p,(C + 1))) * (s,k1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,(C + 1))) * (s,k1)) `2 is V11() real ext-real Element of REAL
((Gauge (p,(C + 1))) * (s,k1)) `1 is V11() real ext-real Element of REAL
|[(((Gauge (p,(C + 1))) * (s,1)) `1),(lower_bound (proj2 .: ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
|[(((Gauge (p,(C + 1))) * (s,1)) `1),(lower_bound (proj2 .: ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))))))]| `1 is V11() real ext-real Element of REAL
z9 is set
k is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
S-most k is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
SW-corner k is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
W-bound k is V11() real ext-real Element of REAL
(TOP-REAL 2) | k is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | k is V15() V18( the carrier of ((TOP-REAL 2) | k)) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | k), REAL ) V212((TOP-REAL 2) | k) Element of K6(K7( the carrier of ((TOP-REAL 2) | k),REAL))
the carrier of ((TOP-REAL 2) | k) is set
K7( the carrier of ((TOP-REAL 2) | k),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | k),REAL)) is non empty set
lower_bound (proj1 | k) is V11() real ext-real Element of REAL
(proj1 | k) .: the carrier of ((TOP-REAL 2) | k) is Element of K6(REAL)
lower_bound ((proj1 | k) .: the carrier of ((TOP-REAL 2) | k)) is V11() real ext-real Element of REAL
S-bound k is V11() real ext-real Element of REAL
proj2 | k is V15() V18( the carrier of ((TOP-REAL 2) | k)) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | k), REAL ) V212((TOP-REAL 2) | k) Element of K6(K7( the carrier of ((TOP-REAL 2) | k),REAL))
lower_bound (proj2 | k) is V11() real ext-real Element of REAL
(proj2 | k) .: the carrier of ((TOP-REAL 2) | k) is Element of K6(REAL)
lower_bound ((proj2 | k) .: the carrier of ((TOP-REAL 2) | k)) is V11() real ext-real Element of REAL
|[(W-bound k),(S-bound k)]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
SE-corner k is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
E-bound k is V11() real ext-real Element of REAL
upper_bound (proj1 | k) is V11() real ext-real Element of REAL
upper_bound ((proj1 | k) .: the carrier of ((TOP-REAL 2) | k)) is V11() real ext-real Element of REAL
|[(E-bound k),(S-bound k)]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner k),(SE-corner k)) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner k),(SE-corner k))) /\ k is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
z9 is set
z is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
z `1 is V11() real ext-real Element of REAL
|[(((Gauge (p,(C + 1))) * (s,1)) `1),(lower_bound (proj2 .: ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))))))]| `2 is V11() real ext-real Element of REAL
S-bound ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1))))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1))))) is strict T_2 SubSpace of TOP-REAL 2
proj2 | ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1))))) is V15() V18( the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1))))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))))), REAL ) V212((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))))),REAL))
the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))))) is set
K7( the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))))),REAL)) is non empty set
lower_bound (proj2 | ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))))) is V11() real ext-real Element of REAL
(proj2 | ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))))) .: the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))))) is Element of K6(REAL)
lower_bound ((proj2 | ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))))) .: the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1))))))) is V11() real ext-real Element of REAL
S-min ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
S-most ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1))))) is functional Element of K6( the carrier of (TOP-REAL 2))
SW-corner ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
W-bound ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1))))) is V11() real ext-real Element of REAL
proj1 | ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1))))) is V15() V18( the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1))))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))))), REAL ) V212((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))))),REAL))
lower_bound (proj1 | ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))))) is V11() real ext-real Element of REAL
(proj1 | ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))))) .: the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))))) is Element of K6(REAL)
lower_bound ((proj1 | ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))))) .: the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1))))))) is V11() real ext-real Element of REAL
|[(W-bound ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))))),(S-bound ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
SE-corner ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
E-bound ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1))))) is V11() real ext-real Element of REAL
upper_bound (proj1 | ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))))) is V11() real ext-real Element of REAL
upper_bound ((proj1 | ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))))) .: the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1))))))) is V11() real ext-real Element of REAL
|[(E-bound ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))))),(S-bound ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))))),(SE-corner ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1))))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))))),(SE-corner ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))))))) /\ ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1))))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (S-most ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))))) is strict T_2 SubSpace of TOP-REAL 2
proj1 | (S-most ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))))) is V15() V18( the carrier of ((TOP-REAL 2) | (S-most ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (S-most ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1))))))), REAL ) V212((TOP-REAL 2) | (S-most ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1))))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (S-most ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1))))))),REAL))
the carrier of ((TOP-REAL 2) | (S-most ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1))))))) is set
K7( the carrier of ((TOP-REAL 2) | (S-most ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1))))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (S-most ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1))))))),REAL)) is non empty set
lower_bound (proj1 | (S-most ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1))))))) is V11() real ext-real Element of REAL
(proj1 | (S-most ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1))))))) .: the carrier of ((TOP-REAL 2) | (S-most ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1))))))) is Element of K6(REAL)
lower_bound ((proj1 | (S-most ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1))))))) .: the carrier of ((TOP-REAL 2) | (S-most ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))))))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (S-most ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))))))),(S-bound ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(S-min ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))))) `2 is V11() real ext-real Element of REAL
z `2 is V11() real ext-real Element of REAL
LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,k1))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
proj1 .: ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))) is Element of K6(REAL)
upper_bound (proj1 .: ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))) is V11() real ext-real Element of REAL
k1 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(Gauge (p,(C + 1))) * (k1,rr) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,(C + 1))) * (k1,rr)) `1 is V11() real ext-real Element of REAL
((Gauge (p,(C + 1))) * (k1,rr)) `2 is V11() real ext-real Element of REAL
|[(upper_bound (proj1 .: ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))),(((Gauge (p,(C + 1))) * (1,rr)) `2)]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
|[(upper_bound (proj1 .: ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))),(((Gauge (p,(C + 1))) * (1,rr)) `2)]| `2 is V11() real ext-real Element of REAL
z9 is set
k is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
E-most k is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
SE-corner k is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
E-bound k is V11() real ext-real Element of REAL
(TOP-REAL 2) | k is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | k is V15() V18( the carrier of ((TOP-REAL 2) | k)) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | k), REAL ) V212((TOP-REAL 2) | k) Element of K6(K7( the carrier of ((TOP-REAL 2) | k),REAL))
the carrier of ((TOP-REAL 2) | k) is set
K7( the carrier of ((TOP-REAL 2) | k),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | k),REAL)) is non empty set
upper_bound (proj1 | k) is V11() real ext-real Element of REAL
(proj1 | k) .: the carrier of ((TOP-REAL 2) | k) is Element of K6(REAL)
upper_bound ((proj1 | k) .: the carrier of ((TOP-REAL 2) | k)) is V11() real ext-real Element of REAL
S-bound k is V11() real ext-real Element of REAL
proj2 | k is V15() V18( the carrier of ((TOP-REAL 2) | k)) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | k), REAL ) V212((TOP-REAL 2) | k) Element of K6(K7( the carrier of ((TOP-REAL 2) | k),REAL))
lower_bound (proj2 | k) is V11() real ext-real Element of REAL
(proj2 | k) .: the carrier of ((TOP-REAL 2) | k) is Element of K6(REAL)
lower_bound ((proj2 | k) .: the carrier of ((TOP-REAL 2) | k)) is V11() real ext-real Element of REAL
|[(E-bound k),(S-bound k)]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
NE-corner k is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
N-bound k is V11() real ext-real Element of REAL
upper_bound (proj2 | k) is V11() real ext-real Element of REAL
upper_bound ((proj2 | k) .: the carrier of ((TOP-REAL 2) | k)) is V11() real ext-real Element of REAL
|[(E-bound k),(N-bound k)]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner k),(NE-corner k)) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SE-corner k),(NE-corner k))) /\ k is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
z9 is set
z is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
z `2 is V11() real ext-real Element of REAL
|[(upper_bound (proj1 .: ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))),(((Gauge (p,(C + 1))) * (1,rr)) `2)]| `1 is V11() real ext-real Element of REAL
E-bound ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))) is strict T_2 SubSpace of TOP-REAL 2
proj1 | ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))) is V15() V18( the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))), REAL ) V212((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))),REAL))
the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))) is set
K7( the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))),REAL)) is non empty set
upper_bound (proj1 | ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))) is V11() real ext-real Element of REAL
(proj1 | ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))) .: the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))) is Element of K6(REAL)
upper_bound ((proj1 | ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))) .: the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))) is V11() real ext-real Element of REAL
E-min ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
E-most ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))) is functional Element of K6( the carrier of (TOP-REAL 2))
SE-corner ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
S-bound ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))) is V11() real ext-real Element of REAL
proj2 | ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))) is V15() V18( the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))), REAL ) V212((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))),REAL))
lower_bound (proj2 | ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))) is V11() real ext-real Element of REAL
(proj2 | ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))) .: the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))) is Element of K6(REAL)
lower_bound ((proj2 | ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))) .: the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))) is V11() real ext-real Element of REAL
|[(E-bound ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))),(S-bound ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
NE-corner ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
N-bound ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))) is V11() real ext-real Element of REAL
upper_bound (proj2 | ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))) .: the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))) is V11() real ext-real Element of REAL
|[(E-bound ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))),(N-bound ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))),(NE-corner ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SE-corner ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))),(NE-corner ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))))) /\ ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (E-most ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))) is strict T_2 SubSpace of TOP-REAL 2
proj2 | (E-most ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))) is V15() V18( the carrier of ((TOP-REAL 2) | (E-most ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (E-most ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))), REAL ) V212((TOP-REAL 2) | (E-most ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (E-most ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))),REAL))
the carrier of ((TOP-REAL 2) | (E-most ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))) is set
K7( the carrier of ((TOP-REAL 2) | (E-most ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (E-most ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))),REAL)) is non empty set
lower_bound (proj2 | (E-most ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))) is V11() real ext-real Element of REAL
(proj2 | (E-most ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))) .: the carrier of ((TOP-REAL 2) | (E-most ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))) is Element of K6(REAL)
lower_bound ((proj2 | (E-most ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))) .: the carrier of ((TOP-REAL 2) | (E-most ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))))) is V11() real ext-real Element of REAL
|[(E-bound ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))),(lower_bound (proj2 | (E-most ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(E-min ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))) `1 is V11() real ext-real Element of REAL
z `1 is V11() real ext-real Element of REAL
LSeg (((Gauge (p,(C + 1))) * (k1,rr)),((Gauge (p,(C + 1))) * (p9,rr))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
proj1 .: ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))) is Element of K6(REAL)
lower_bound (proj1 .: ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))) is V11() real ext-real Element of REAL
k1 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(Gauge (p,(C + 1))) * (k1,rr) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,(C + 1))) * (k1,rr)) `1 is V11() real ext-real Element of REAL
((Gauge (p,(C + 1))) * (k1,rr)) `2 is V11() real ext-real Element of REAL
|[(lower_bound (proj1 .: ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))),(((Gauge (p,(C + 1))) * (1,rr)) `2)]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
|[(lower_bound (proj1 .: ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))),(((Gauge (p,(C + 1))) * (1,rr)) `2)]| `2 is V11() real ext-real Element of REAL
z9 is set
k is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
W-most k is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
SW-corner k is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
W-bound k is V11() real ext-real Element of REAL
(TOP-REAL 2) | k is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | k is V15() V18( the carrier of ((TOP-REAL 2) | k)) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | k), REAL ) V212((TOP-REAL 2) | k) Element of K6(K7( the carrier of ((TOP-REAL 2) | k),REAL))
the carrier of ((TOP-REAL 2) | k) is set
K7( the carrier of ((TOP-REAL 2) | k),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | k),REAL)) is non empty set
lower_bound (proj1 | k) is V11() real ext-real Element of REAL
(proj1 | k) .: the carrier of ((TOP-REAL 2) | k) is Element of K6(REAL)
lower_bound ((proj1 | k) .: the carrier of ((TOP-REAL 2) | k)) is V11() real ext-real Element of REAL
S-bound k is V11() real ext-real Element of REAL
proj2 | k is V15() V18( the carrier of ((TOP-REAL 2) | k)) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | k), REAL ) V212((TOP-REAL 2) | k) Element of K6(K7( the carrier of ((TOP-REAL 2) | k),REAL))
lower_bound (proj2 | k) is V11() real ext-real Element of REAL
(proj2 | k) .: the carrier of ((TOP-REAL 2) | k) is Element of K6(REAL)
lower_bound ((proj2 | k) .: the carrier of ((TOP-REAL 2) | k)) is V11() real ext-real Element of REAL
|[(W-bound k),(S-bound k)]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
NW-corner k is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
N-bound k is V11() real ext-real Element of REAL
upper_bound (proj2 | k) is V11() real ext-real Element of REAL
upper_bound ((proj2 | k) .: the carrier of ((TOP-REAL 2) | k)) is V11() real ext-real Element of REAL
|[(W-bound k),(N-bound k)]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner k),(NW-corner k)) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner k),(NW-corner k))) /\ k is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
z9 is set
z is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
z `2 is V11() real ext-real Element of REAL
|[(lower_bound (proj1 .: ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))),(((Gauge (p,(C + 1))) * (1,rr)) `2)]| `1 is V11() real ext-real Element of REAL
W-bound ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))) is strict T_2 SubSpace of TOP-REAL 2
proj1 | ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))) is V15() V18( the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))), REAL ) V212((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))),REAL))
the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))) is set
K7( the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))),REAL)) is non empty set
lower_bound (proj1 | ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))) is V11() real ext-real Element of REAL
(proj1 | ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))) .: the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))) is Element of K6(REAL)
lower_bound ((proj1 | ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))) .: the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))) is V11() real ext-real Element of REAL
W-min ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
W-most ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))) is functional Element of K6( the carrier of (TOP-REAL 2))
SW-corner ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
S-bound ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))) is V11() real ext-real Element of REAL
proj2 | ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))) is V15() V18( the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))), REAL ) V212((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))),REAL))
lower_bound (proj2 | ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))) is V11() real ext-real Element of REAL
(proj2 | ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))) .: the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))) is Element of K6(REAL)
lower_bound ((proj2 | ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))) .: the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))) is V11() real ext-real Element of REAL
|[(W-bound ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))),(S-bound ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
NW-corner ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
N-bound ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))) is V11() real ext-real Element of REAL
upper_bound (proj2 | ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))) .: the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))) is V11() real ext-real Element of REAL
|[(W-bound ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))),(N-bound ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))),(NW-corner ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))),(NW-corner ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))))) /\ ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (W-most ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))) is strict T_2 SubSpace of TOP-REAL 2
proj2 | (W-most ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))) is V15() V18( the carrier of ((TOP-REAL 2) | (W-most ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (W-most ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))), REAL ) V212((TOP-REAL 2) | (W-most ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (W-most ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))),REAL))
the carrier of ((TOP-REAL 2) | (W-most ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))) is set
K7( the carrier of ((TOP-REAL 2) | (W-most ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (W-most ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))),REAL)) is non empty set
lower_bound (proj2 | (W-most ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))) is V11() real ext-real Element of REAL
(proj2 | (W-most ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))) .: the carrier of ((TOP-REAL 2) | (W-most ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))) is Element of K6(REAL)
lower_bound ((proj2 | (W-most ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))) .: the carrier of ((TOP-REAL 2) | (W-most ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))))) is V11() real ext-real Element of REAL
|[(W-bound ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))),(lower_bound (proj2 | (W-most ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(W-min ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))) `1 is V11() real ext-real Element of REAL
z `1 is V11() real ext-real Element of REAL
LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (k1,rr))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
k1 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(Gauge (p,(C + 1))) * (s,k1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg (((Gauge (p,(C + 1))) * (s,k1)),((Gauge (p,(C + 1))) * (s,rr))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg (((Gauge (p,(C + 1))) * (s,k1)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
{((Gauge (p,(C + 1))) * (s,k1))} is non empty trivial functional V35(1) set
k2 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(Gauge (p,(C + 1))) * (k2,rr) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (k2,rr))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (k2,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
{((Gauge (p,(C + 1))) * (k2,rr))} is non empty trivial functional V35(1) set
(LSeg (((Gauge (p,(C + 1))) * (s,k1)),((Gauge (p,(C + 1))) * (s,rr)))) \/ (LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (k2,rr)))) is non empty functional Element of K6( the carrier of (TOP-REAL 2))
((LSeg (((Gauge (p,(C + 1))) * (s,k1)),((Gauge (p,(C + 1))) * (s,rr)))) \/ (LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (k2,rr))))) /\ (L~ (Lower_Seq (p,(C + 1)))) is functional Element of K6( the carrier of (TOP-REAL 2))
k is set
k is set
((LSeg (((Gauge (p,(C + 1))) * (s,k1)),((Gauge (p,(C + 1))) * (s,rr)))) \/ (LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (k2,rr))))) /\ (L~ (Upper_Seq (p,(C + 1)))) is functional Element of K6( the carrier of (TOP-REAL 2))
k is set
k is set
k2 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(Gauge (p,(C + 1))) * (k2,rr) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg (((Gauge (p,(C + 1))) * (k2,rr)),((Gauge (p,(C + 1))) * (s,rr))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg (((Gauge (p,(C + 1))) * (k2,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
{((Gauge (p,(C + 1))) * (k2,rr))} is non empty trivial functional V35(1) set
LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (k2,rr))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (k2,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(LSeg (((Gauge (p,(C + 1))) * (s,k1)),((Gauge (p,(C + 1))) * (s,rr)))) \/ (LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (k2,rr)))) is non empty functional Element of K6( the carrier of (TOP-REAL 2))
((LSeg (((Gauge (p,(C + 1))) * (s,k1)),((Gauge (p,(C + 1))) * (s,rr)))) \/ (LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (k2,rr))))) /\ (L~ (Lower_Seq (p,(C + 1)))) is functional Element of K6( the carrier of (TOP-REAL 2))
k is set
k is set
((LSeg (((Gauge (p,(C + 1))) * (s,k1)),((Gauge (p,(C + 1))) * (s,rr)))) \/ (LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (k2,rr))))) /\ (L~ (Upper_Seq (p,(C + 1)))) is functional Element of K6( the carrier of (TOP-REAL 2))
k is set
k is set
C is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
C + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
p is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
Gauge (p,(C + 1)) is V15() non empty-yielding V18( NAT ) V19(K307( the carrier of (TOP-REAL 2))) Function-like V28() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K307( the carrier of (TOP-REAL 2))
len (Gauge (p,(C + 1))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
width (Gauge (p,(C + 1))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
Cage (p,(C + 1)) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like non constant V28() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the carrier of (TOP-REAL 2)
L~ (Cage (p,(C + 1))) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
Lower_Arc (L~ (Cage (p,(C + 1)))) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
Upper_Arc (L~ (Cage (p,(C + 1)))) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
Upper_Arc p is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
p9 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
s is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
r is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
rr is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(Gauge (p,(C + 1))) * (p9,rr) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(Gauge (p,(C + 1))) * (s,r) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(Gauge (p,(C + 1))) * (s,rr) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) \/ (LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) is non empty functional Element of K6( the carrier of (TOP-REAL 2))
Lower_Seq (p,(C + 1)) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V28() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
L~ (Lower_Seq (p,(C + 1))) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
Upper_Seq (p,(C + 1)) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V28() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
L~ (Upper_Seq (p,(C + 1))) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
[s,r] is set
{s,r} is non empty set
{s} is non empty trivial V35(1) set
{{s,r},{s}} is non empty set
Indices (Gauge (p,(C + 1))) is set
[s,rr] is set
{s,rr} is non empty set
{{s,rr},{s}} is non empty set
((Gauge (p,(C + 1))) * (s,r)) `1 is V11() real ext-real Element of REAL
(Gauge (p,(C + 1))) * (s,1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,(C + 1))) * (s,1)) `1 is V11() real ext-real Element of REAL
((Gauge (p,(C + 1))) * (s,rr)) `1 is V11() real ext-real Element of REAL
((Gauge (p,(C + 1))) * (s,rr)) `2 is V11() real ext-real Element of REAL
(Gauge (p,(C + 1))) * (1,rr) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,(C + 1))) * (1,rr)) `2 is V11() real ext-real Element of REAL
((Gauge (p,(C + 1))) * (p9,rr)) `2 is V11() real ext-real Element of REAL
[p9,rr] is set
{p9,rr} is non empty set
{p9} is non empty trivial V35(1) set
{{p9,rr},{p9}} is non empty set
(LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
proj2 .: ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1))))) is Element of K6(REAL)
lower_bound (proj2 .: ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))))) is V11() real ext-real Element of REAL
k1 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(Gauge (p,(C + 1))) * (s,k1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,(C + 1))) * (s,k1)) `2 is V11() real ext-real Element of REAL
((Gauge (p,(C + 1))) * (s,k1)) `1 is V11() real ext-real Element of REAL
|[(((Gauge (p,(C + 1))) * (s,1)) `1),(lower_bound (proj2 .: ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
|[(((Gauge (p,(C + 1))) * (s,1)) `1),(lower_bound (proj2 .: ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))))))]| `1 is V11() real ext-real Element of REAL
z9 is set
k is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
S-most k is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
SW-corner k is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
W-bound k is V11() real ext-real Element of REAL
(TOP-REAL 2) | k is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | k is V15() V18( the carrier of ((TOP-REAL 2) | k)) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | k), REAL ) V212((TOP-REAL 2) | k) Element of K6(K7( the carrier of ((TOP-REAL 2) | k),REAL))
the carrier of ((TOP-REAL 2) | k) is set
K7( the carrier of ((TOP-REAL 2) | k),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | k),REAL)) is non empty set
lower_bound (proj1 | k) is V11() real ext-real Element of REAL
(proj1 | k) .: the carrier of ((TOP-REAL 2) | k) is Element of K6(REAL)
lower_bound ((proj1 | k) .: the carrier of ((TOP-REAL 2) | k)) is V11() real ext-real Element of REAL
S-bound k is V11() real ext-real Element of REAL
proj2 | k is V15() V18( the carrier of ((TOP-REAL 2) | k)) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | k), REAL ) V212((TOP-REAL 2) | k) Element of K6(K7( the carrier of ((TOP-REAL 2) | k),REAL))
lower_bound (proj2 | k) is V11() real ext-real Element of REAL
(proj2 | k) .: the carrier of ((TOP-REAL 2) | k) is Element of K6(REAL)
lower_bound ((proj2 | k) .: the carrier of ((TOP-REAL 2) | k)) is V11() real ext-real Element of REAL
|[(W-bound k),(S-bound k)]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
SE-corner k is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
E-bound k is V11() real ext-real Element of REAL
upper_bound (proj1 | k) is V11() real ext-real Element of REAL
upper_bound ((proj1 | k) .: the carrier of ((TOP-REAL 2) | k)) is V11() real ext-real Element of REAL
|[(E-bound k),(S-bound k)]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner k),(SE-corner k)) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner k),(SE-corner k))) /\ k is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
z9 is set
z is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
z `1 is V11() real ext-real Element of REAL
|[(((Gauge (p,(C + 1))) * (s,1)) `1),(lower_bound (proj2 .: ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))))))]| `2 is V11() real ext-real Element of REAL
S-bound ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1))))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1))))) is strict T_2 SubSpace of TOP-REAL 2
proj2 | ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1))))) is V15() V18( the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1))))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))))), REAL ) V212((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))))),REAL))
the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))))) is set
K7( the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))))),REAL)) is non empty set
lower_bound (proj2 | ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))))) is V11() real ext-real Element of REAL
(proj2 | ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))))) .: the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))))) is Element of K6(REAL)
lower_bound ((proj2 | ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))))) .: the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1))))))) is V11() real ext-real Element of REAL
S-min ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
S-most ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1))))) is functional Element of K6( the carrier of (TOP-REAL 2))
SW-corner ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
W-bound ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1))))) is V11() real ext-real Element of REAL
proj1 | ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1))))) is V15() V18( the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1))))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))))), REAL ) V212((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))))),REAL))
lower_bound (proj1 | ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))))) is V11() real ext-real Element of REAL
(proj1 | ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))))) .: the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))))) is Element of K6(REAL)
lower_bound ((proj1 | ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))))) .: the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1))))))) is V11() real ext-real Element of REAL
|[(W-bound ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))))),(S-bound ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
SE-corner ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
E-bound ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1))))) is V11() real ext-real Element of REAL
upper_bound (proj1 | ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))))) is V11() real ext-real Element of REAL
upper_bound ((proj1 | ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))))) .: the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1))))))) is V11() real ext-real Element of REAL
|[(E-bound ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))))),(S-bound ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))))),(SE-corner ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1))))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))))),(SE-corner ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))))))) /\ ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1))))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (S-most ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))))) is strict T_2 SubSpace of TOP-REAL 2
proj1 | (S-most ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))))) is V15() V18( the carrier of ((TOP-REAL 2) | (S-most ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (S-most ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1))))))), REAL ) V212((TOP-REAL 2) | (S-most ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1))))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (S-most ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1))))))),REAL))
the carrier of ((TOP-REAL 2) | (S-most ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1))))))) is set
K7( the carrier of ((TOP-REAL 2) | (S-most ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1))))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (S-most ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1))))))),REAL)) is non empty set
lower_bound (proj1 | (S-most ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1))))))) is V11() real ext-real Element of REAL
(proj1 | (S-most ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1))))))) .: the carrier of ((TOP-REAL 2) | (S-most ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1))))))) is Element of K6(REAL)
lower_bound ((proj1 | (S-most ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1))))))) .: the carrier of ((TOP-REAL 2) | (S-most ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))))))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (S-most ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))))))),(S-bound ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(S-min ((LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))))) `2 is V11() real ext-real Element of REAL
z `2 is V11() real ext-real Element of REAL
LSeg (((Gauge (p,(C + 1))) * (s,r)),((Gauge (p,(C + 1))) * (s,k1))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
proj1 .: ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))) is Element of K6(REAL)
upper_bound (proj1 .: ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))) is V11() real ext-real Element of REAL
k1 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(Gauge (p,(C + 1))) * (k1,rr) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,(C + 1))) * (k1,rr)) `1 is V11() real ext-real Element of REAL
((Gauge (p,(C + 1))) * (k1,rr)) `2 is V11() real ext-real Element of REAL
|[(upper_bound (proj1 .: ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))),(((Gauge (p,(C + 1))) * (1,rr)) `2)]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
|[(upper_bound (proj1 .: ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))),(((Gauge (p,(C + 1))) * (1,rr)) `2)]| `2 is V11() real ext-real Element of REAL
z9 is set
k is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
E-most k is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
SE-corner k is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
E-bound k is V11() real ext-real Element of REAL
(TOP-REAL 2) | k is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | k is V15() V18( the carrier of ((TOP-REAL 2) | k)) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | k), REAL ) V212((TOP-REAL 2) | k) Element of K6(K7( the carrier of ((TOP-REAL 2) | k),REAL))
the carrier of ((TOP-REAL 2) | k) is set
K7( the carrier of ((TOP-REAL 2) | k),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | k),REAL)) is non empty set
upper_bound (proj1 | k) is V11() real ext-real Element of REAL
(proj1 | k) .: the carrier of ((TOP-REAL 2) | k) is Element of K6(REAL)
upper_bound ((proj1 | k) .: the carrier of ((TOP-REAL 2) | k)) is V11() real ext-real Element of REAL
S-bound k is V11() real ext-real Element of REAL
proj2 | k is V15() V18( the carrier of ((TOP-REAL 2) | k)) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | k), REAL ) V212((TOP-REAL 2) | k) Element of K6(K7( the carrier of ((TOP-REAL 2) | k),REAL))
lower_bound (proj2 | k) is V11() real ext-real Element of REAL
(proj2 | k) .: the carrier of ((TOP-REAL 2) | k) is Element of K6(REAL)
lower_bound ((proj2 | k) .: the carrier of ((TOP-REAL 2) | k)) is V11() real ext-real Element of REAL
|[(E-bound k),(S-bound k)]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
NE-corner k is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
N-bound k is V11() real ext-real Element of REAL
upper_bound (proj2 | k) is V11() real ext-real Element of REAL
upper_bound ((proj2 | k) .: the carrier of ((TOP-REAL 2) | k)) is V11() real ext-real Element of REAL
|[(E-bound k),(N-bound k)]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner k),(NE-corner k)) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SE-corner k),(NE-corner k))) /\ k is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
z9 is set
z is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
z `2 is V11() real ext-real Element of REAL
|[(upper_bound (proj1 .: ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))),(((Gauge (p,(C + 1))) * (1,rr)) `2)]| `1 is V11() real ext-real Element of REAL
E-bound ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))) is strict T_2 SubSpace of TOP-REAL 2
proj1 | ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))) is V15() V18( the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))), REAL ) V212((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))),REAL))
the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))) is set
K7( the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))),REAL)) is non empty set
upper_bound (proj1 | ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))) is V11() real ext-real Element of REAL
(proj1 | ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))) .: the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))) is Element of K6(REAL)
upper_bound ((proj1 | ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))) .: the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))) is V11() real ext-real Element of REAL
E-min ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
E-most ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))) is functional Element of K6( the carrier of (TOP-REAL 2))
SE-corner ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
S-bound ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))) is V11() real ext-real Element of REAL
proj2 | ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))) is V15() V18( the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))), REAL ) V212((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))),REAL))
lower_bound (proj2 | ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))) is V11() real ext-real Element of REAL
(proj2 | ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))) .: the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))) is Element of K6(REAL)
lower_bound ((proj2 | ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))) .: the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))) is V11() real ext-real Element of REAL
|[(E-bound ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))),(S-bound ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
NE-corner ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
N-bound ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))) is V11() real ext-real Element of REAL
upper_bound (proj2 | ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))) .: the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))) is V11() real ext-real Element of REAL
|[(E-bound ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))),(N-bound ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))),(NE-corner ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SE-corner ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))),(NE-corner ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))))) /\ ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (E-most ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))) is strict T_2 SubSpace of TOP-REAL 2
proj2 | (E-most ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))) is V15() V18( the carrier of ((TOP-REAL 2) | (E-most ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (E-most ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))), REAL ) V212((TOP-REAL 2) | (E-most ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (E-most ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))),REAL))
the carrier of ((TOP-REAL 2) | (E-most ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))) is set
K7( the carrier of ((TOP-REAL 2) | (E-most ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (E-most ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))),REAL)) is non empty set
lower_bound (proj2 | (E-most ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))) is V11() real ext-real Element of REAL
(proj2 | (E-most ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))) .: the carrier of ((TOP-REAL 2) | (E-most ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))) is Element of K6(REAL)
lower_bound ((proj2 | (E-most ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))) .: the carrier of ((TOP-REAL 2) | (E-most ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))))) is V11() real ext-real Element of REAL
|[(E-bound ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))),(lower_bound (proj2 | (E-most ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(E-min ((LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (p9,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))) `1 is V11() real ext-real Element of REAL
z `1 is V11() real ext-real Element of REAL
LSeg (((Gauge (p,(C + 1))) * (k1,rr)),((Gauge (p,(C + 1))) * (p9,rr))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
proj1 .: ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))) is Element of K6(REAL)
lower_bound (proj1 .: ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))) is V11() real ext-real Element of REAL
k1 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(Gauge (p,(C + 1))) * (k1,rr) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (p,(C + 1))) * (k1,rr)) `1 is V11() real ext-real Element of REAL
((Gauge (p,(C + 1))) * (k1,rr)) `2 is V11() real ext-real Element of REAL
|[(lower_bound (proj1 .: ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))),(((Gauge (p,(C + 1))) * (1,rr)) `2)]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
|[(lower_bound (proj1 .: ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))),(((Gauge (p,(C + 1))) * (1,rr)) `2)]| `2 is V11() real ext-real Element of REAL
z9 is set
k is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
W-most k is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
SW-corner k is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
W-bound k is V11() real ext-real Element of REAL
(TOP-REAL 2) | k is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | k is V15() V18( the carrier of ((TOP-REAL 2) | k)) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | k), REAL ) V212((TOP-REAL 2) | k) Element of K6(K7( the carrier of ((TOP-REAL 2) | k),REAL))
the carrier of ((TOP-REAL 2) | k) is set
K7( the carrier of ((TOP-REAL 2) | k),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | k),REAL)) is non empty set
lower_bound (proj1 | k) is V11() real ext-real Element of REAL
(proj1 | k) .: the carrier of ((TOP-REAL 2) | k) is Element of K6(REAL)
lower_bound ((proj1 | k) .: the carrier of ((TOP-REAL 2) | k)) is V11() real ext-real Element of REAL
S-bound k is V11() real ext-real Element of REAL
proj2 | k is V15() V18( the carrier of ((TOP-REAL 2) | k)) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | k), REAL ) V212((TOP-REAL 2) | k) Element of K6(K7( the carrier of ((TOP-REAL 2) | k),REAL))
lower_bound (proj2 | k) is V11() real ext-real Element of REAL
(proj2 | k) .: the carrier of ((TOP-REAL 2) | k) is Element of K6(REAL)
lower_bound ((proj2 | k) .: the carrier of ((TOP-REAL 2) | k)) is V11() real ext-real Element of REAL
|[(W-bound k),(S-bound k)]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
NW-corner k is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
N-bound k is V11() real ext-real Element of REAL
upper_bound (proj2 | k) is V11() real ext-real Element of REAL
upper_bound ((proj2 | k) .: the carrier of ((TOP-REAL 2) | k)) is V11() real ext-real Element of REAL
|[(W-bound k),(N-bound k)]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner k),(NW-corner k)) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner k),(NW-corner k))) /\ k is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
z9 is set
z is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
z `2 is V11() real ext-real Element of REAL
|[(lower_bound (proj1 .: ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))),(((Gauge (p,(C + 1))) * (1,rr)) `2)]| `1 is V11() real ext-real Element of REAL
W-bound ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))) is strict T_2 SubSpace of TOP-REAL 2
proj1 | ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))) is V15() V18( the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))), REAL ) V212((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))),REAL))
the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))) is set
K7( the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))),REAL)) is non empty set
lower_bound (proj1 | ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))) is V11() real ext-real Element of REAL
(proj1 | ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))) .: the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))) is Element of K6(REAL)
lower_bound ((proj1 | ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))) .: the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))) is V11() real ext-real Element of REAL
W-min ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
W-most ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))) is functional Element of K6( the carrier of (TOP-REAL 2))
SW-corner ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
S-bound ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))) is V11() real ext-real Element of REAL
proj2 | ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))) is V15() V18( the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))), REAL ) V212((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))),REAL))
lower_bound (proj2 | ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))) is V11() real ext-real Element of REAL
(proj2 | ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))) .: the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))) is Element of K6(REAL)
lower_bound ((proj2 | ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))) .: the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))) is V11() real ext-real Element of REAL
|[(W-bound ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))),(S-bound ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
NW-corner ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
N-bound ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))) is V11() real ext-real Element of REAL
upper_bound (proj2 | ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))) .: the carrier of ((TOP-REAL 2) | ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))) is V11() real ext-real Element of REAL
|[(W-bound ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))),(N-bound ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))),(NW-corner ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))),(NW-corner ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))))) /\ ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (W-most ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))) is strict T_2 SubSpace of TOP-REAL 2
proj2 | (W-most ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))) is V15() V18( the carrier of ((TOP-REAL 2) | (W-most ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (W-most ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))), REAL ) V212((TOP-REAL 2) | (W-most ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (W-most ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))),REAL))
the carrier of ((TOP-REAL 2) | (W-most ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))) is set
K7( the carrier of ((TOP-REAL 2) | (W-most ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (W-most ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))),REAL)) is non empty set
lower_bound (proj2 | (W-most ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))) is V11() real ext-real Element of REAL
(proj2 | (W-most ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))) .: the carrier of ((TOP-REAL 2) | (W-most ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))) is Element of K6(REAL)
lower_bound ((proj2 | (W-most ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))) .: the carrier of ((TOP-REAL 2) | (W-most ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))))) is V11() real ext-real Element of REAL
|[(W-bound ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))),(lower_bound (proj2 | (W-most ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1))))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(W-min ((LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))))) `1 is V11() real ext-real Element of REAL
z `1 is V11() real ext-real Element of REAL
LSeg (((Gauge (p,(C + 1))) * (p9,rr)),((Gauge (p,(C + 1))) * (k1,rr))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
k1 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(Gauge (p,(C + 1))) * (s,k1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg (((Gauge (p,(C + 1))) * (s,k1)),((Gauge (p,(C + 1))) * (s,rr))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg (((Gauge (p,(C + 1))) * (s,k1)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Upper_Seq (p,(C + 1)))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
{((Gauge (p,(C + 1))) * (s,k1))} is non empty trivial functional V35(1) set
k2 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(Gauge (p,(C + 1))) * (k2,rr) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (k2,rr))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (k2,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
{((Gauge (p,(C + 1))) * (k2,rr))} is non empty trivial functional V35(1) set
(LSeg (((Gauge (p,(C + 1))) * (s,k1)),((Gauge (p,(C + 1))) * (s,rr)))) \/ (LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (k2,rr)))) is non empty functional Element of K6( the carrier of (TOP-REAL 2))
((LSeg (((Gauge (p,(C + 1))) * (s,k1)),((Gauge (p,(C + 1))) * (s,rr)))) \/ (LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (k2,rr))))) /\ (L~ (Lower_Seq (p,(C + 1)))) is functional Element of K6( the carrier of (TOP-REAL 2))
k is set
k is set
((LSeg (((Gauge (p,(C + 1))) * (s,k1)),((Gauge (p,(C + 1))) * (s,rr)))) \/ (LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (k2,rr))))) /\ (L~ (Upper_Seq (p,(C + 1)))) is functional Element of K6( the carrier of (TOP-REAL 2))
k is set
k is set
k2 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(Gauge (p,(C + 1))) * (k2,rr) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg (((Gauge (p,(C + 1))) * (k2,rr)),((Gauge (p,(C + 1))) * (s,rr))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg (((Gauge (p,(C + 1))) * (k2,rr)),((Gauge (p,(C + 1))) * (s,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
{((Gauge (p,(C + 1))) * (k2,rr))} is non empty trivial functional V35(1) set
LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (k2,rr))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (k2,rr)))) /\ (L~ (Lower_Seq (p,(C + 1)))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(LSeg (((Gauge (p,(C + 1))) * (s,k1)),((Gauge (p,(C + 1))) * (s,rr)))) \/ (LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (k2,rr)))) is non empty functional Element of K6( the carrier of (TOP-REAL 2))
((LSeg (((Gauge (p,(C + 1))) * (s,k1)),((Gauge (p,(C + 1))) * (s,rr)))) \/ (LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (k2,rr))))) /\ (L~ (Lower_Seq (p,(C + 1)))) is functional Element of K6( the carrier of (TOP-REAL 2))
k is set
k is set
((LSeg (((Gauge (p,(C + 1))) * (s,k1)),((Gauge (p,(C + 1))) * (s,rr)))) \/ (LSeg (((Gauge (p,(C + 1))) * (s,rr)),((Gauge (p,(C + 1))) * (k2,rr))))) /\ (L~ (Upper_Seq (p,(C + 1)))) is functional Element of K6( the carrier of (TOP-REAL 2))
k is set
k is set
C is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
W-bound C is V11() real ext-real Element of REAL
(TOP-REAL 2) | C is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | C is V15() V18( the carrier of ((TOP-REAL 2) | C)) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | C), REAL ) V212((TOP-REAL 2) | C) Element of K6(K7( the carrier of ((TOP-REAL 2) | C),REAL))
the carrier of ((TOP-REAL 2) | C) is set
K7( the carrier of ((TOP-REAL 2) | C),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | C),REAL)) is non empty set
lower_bound (proj1 | C) is V11() real ext-real Element of REAL
(proj1 | C) .: the carrier of ((TOP-REAL 2) | C) is Element of K6(REAL)
lower_bound ((proj1 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
E-bound C is V11() real ext-real Element of REAL
upper_bound (proj1 | C) is V11() real ext-real Element of REAL
upper_bound ((proj1 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
(C) is functional Element of K6( the carrier of (TOP-REAL 2))
(C) is V15() V18( NAT ) V19(K291( the carrier of (TOP-REAL 2))) Function-like V40( NAT ,K291( the carrier of (TOP-REAL 2))) Element of K6(K7(NAT,K291( the carrier of (TOP-REAL 2))))
Lim_inf (C) is functional Element of K6( the carrier of (TOP-REAL 2))
(C) is functional Element of K6( the carrier of (TOP-REAL 2))
(C) is V15() V18( NAT ) V19(K291( the carrier of (TOP-REAL 2))) Function-like V40( NAT ,K291( the carrier of (TOP-REAL 2))) Element of K6(K7(NAT,K291( the carrier of (TOP-REAL 2))))
Lim_inf (C) is functional Element of K6( the carrier of (TOP-REAL 2))
p is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
p `1 is V11() real ext-real Element of REAL
Euclid 2 is non empty strict Reflexive discerning symmetric triangle Discerning MetrStruct
REAL 2 is non empty functional FinSequence-membered M16( REAL )
K308(2,REAL) is functional FinSequence-membered M16( REAL )
Pitag_dist 2 is V15() V18(K7((REAL 2),(REAL 2))) V19( REAL ) Function-like V40(K7((REAL 2),(REAL 2)), REAL ) Element of K6(K7(K7((REAL 2),(REAL 2)),REAL))
K7((REAL 2),(REAL 2)) is non empty set
K7(K7((REAL 2),(REAL 2)),REAL) is set
K6(K7(K7((REAL 2),(REAL 2)),REAL)) is non empty set
MetrStruct(# (REAL 2),(Pitag_dist 2) #) is strict MetrStruct
the carrier of (Euclid 2) is non empty set
(p `1) - (W-bound C) is V11() real ext-real Element of REAL
- (W-bound C) is V11() real ext-real set
(p `1) + (- (W-bound C)) is V11() real ext-real set
(E-bound C) - (p `1) is V11() real ext-real Element of REAL
- (p `1) is V11() real ext-real set
(E-bound C) + (- (p `1)) is V11() real ext-real set
min (((p `1) - (W-bound C)),((E-bound C) - (p `1))) is V11() real ext-real set
(W-bound C) + 0 is V11() real ext-real Element of REAL
(p `1) + 0 is V11() real ext-real Element of REAL
r is V11() real ext-real set
8 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
r / 8 is V11() real ext-real Element of REAL
8 " is non empty V11() real ext-real positive non negative set
r * (8 ") is V11() real ext-real set
p9 is Element of the carrier of (Euclid 2)
Ball (p9,(r / 8)) is Element of K6( the carrier of (Euclid 2))
K6( the carrier of (Euclid 2)) is non empty set
G is functional a_neighborhood of p
k1 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
k2 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
max (k1,k2) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
N-bound C is V11() real ext-real Element of REAL
proj2 | C is V15() V18( the carrier of ((TOP-REAL 2) | C)) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | C), REAL ) V212((TOP-REAL 2) | C) Element of K6(K7( the carrier of ((TOP-REAL 2) | C),REAL))
upper_bound (proj2 | C) is V11() real ext-real Element of REAL
(proj2 | C) .: the carrier of ((TOP-REAL 2) | C) is Element of K6(REAL)
upper_bound ((proj2 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
S-bound C is V11() real ext-real Element of REAL
lower_bound (proj2 | C) is V11() real ext-real Element of REAL
lower_bound ((proj2 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
(N-bound C) - (S-bound C) is V11() real ext-real Element of REAL
- (S-bound C) is V11() real ext-real set
(N-bound C) + (- (S-bound C)) is V11() real ext-real set
(E-bound C) - (W-bound C) is V11() real ext-real Element of REAL
(E-bound C) + (- (W-bound C)) is V11() real ext-real set
max (((N-bound C) - (S-bound C)),((E-bound C) - (W-bound C))) is V11() real ext-real set
max ((max (((N-bound C) - (S-bound C)),((E-bound C) - (W-bound C)))),(r / 8)) is V11() real ext-real set
(max ((max (((N-bound C) - (S-bound C)),((E-bound C) - (W-bound C)))),(r / 8))) / (r / 8) is V11() real ext-real Element of REAL
(r / 8) " is V11() real ext-real set
(max ((max (((N-bound C) - (S-bound C)),((E-bound C) - (W-bound C)))),(r / 8))) * ((r / 8) ") is V11() real ext-real set
log (2,1) is V11() real ext-real Element of REAL
log (2,((max ((max (((N-bound C) - (S-bound C)),((E-bound C) - (W-bound C)))),(r / 8))) / (r / 8))) is V11() real ext-real Element of REAL
[\(log (2,((max ((max (((N-bound C) - (S-bound C)),((E-bound C) - (W-bound C)))),(r / 8))) / (r / 8))))/] is integer set
m9 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
m9 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
2 to_power (m9 + 1) is V11() real ext-real Element of REAL
(m9 + 1) * 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
log (2,2) is V11() real ext-real Element of REAL
(m9 + 1) * (log (2,2)) is V11() real ext-real Element of REAL
log (2,(2 to_power (m9 + 1))) is V11() real ext-real Element of REAL
(2 to_power (m9 + 1)) * (r / 8) is V11() real ext-real Element of REAL
((max ((max (((N-bound C) - (S-bound C)),((E-bound C) - (W-bound C)))),(r / 8))) / (r / 8)) * (r / 8) is V11() real ext-real Element of REAL
((2 to_power (m9 + 1)) * (r / 8)) / (2 to_power (m9 + 1)) is V11() real ext-real Element of REAL
(2 to_power (m9 + 1)) " is V11() real ext-real set
((2 to_power (m9 + 1)) * (r / 8)) * ((2 to_power (m9 + 1)) ") is V11() real ext-real set
(max ((max (((N-bound C) - (S-bound C)),((E-bound C) - (W-bound C)))),(r / 8))) / (2 to_power (m9 + 1)) is V11() real ext-real Element of REAL
(max ((max (((N-bound C) - (S-bound C)),((E-bound C) - (W-bound C)))),(r / 8))) * ((2 to_power (m9 + 1)) ") is V11() real ext-real set
(r / 8) / (2 to_power (m9 + 1)) is V11() real ext-real Element of REAL
(r / 8) * ((2 to_power (m9 + 1)) ") is V11() real ext-real set
((r / 8) / (2 to_power (m9 + 1))) * (2 to_power (m9 + 1)) is V11() real ext-real Element of REAL
(max (((N-bound C) - (S-bound C)),((E-bound C) - (W-bound C)))) / (2 to_power (m9 + 1)) is V11() real ext-real Element of REAL
(max (((N-bound C) - (S-bound C)),((E-bound C) - (W-bound C)))) * ((2 to_power (m9 + 1)) ") is V11() real ext-real set
max ((max (k1,k2)),m9) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(max ((max (k1,k2)),m9)) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
Gauge (C,((max ((max (k1,k2)),m9)) + 1)) is V15() non empty-yielding V18( NAT ) V19(K307( the carrier of (TOP-REAL 2))) Function-like V28() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K307( the carrier of (TOP-REAL 2))
len (Gauge (C,((max ((max (k1,k2)),m9)) + 1))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
width (Gauge (C,((max ((max (k1,k2)),m9)) + 1))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(C) . ((max ((max (k1,k2)),m9)) + 1) is set
Cage (C,((max ((max (k1,k2)),m9)) + 1)) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like non constant V28() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the carrier of (TOP-REAL 2)
L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
Upper_Arc (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
p1 is set
p1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1)) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V28() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
L~ (Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
len (Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
i1 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
i1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
(Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. (i1 + 1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg (((Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i1),((Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. (i1 + 1))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
Seg (len (Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1)))) is non empty V28() V35( len (Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1)))) Element of K6(NAT)
dom (Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) is non trivial Element of K6(NAT)
Indices (Gauge (C,((max ((max (k1,k2)),m9)) + 1))) is set
ii1 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
jj1 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
[ii1,jj1] is set
{ii1,jj1} is non empty set
{ii1} is non empty trivial V35(1) set
{{ii1,jj1},{ii1}} is non empty set
(Gauge (C,((max ((max (k1,k2)),m9)) + 1))) * (ii1,jj1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(S-bound C) + 0 is V11() real ext-real Element of REAL
2 |^ (m9 + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
2 |^ ((max ((max (k1,k2)),m9)) + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
((N-bound C) - (S-bound C)) / (2 |^ ((max ((max (k1,k2)),m9)) + 1)) is V11() real ext-real Element of REAL
(2 |^ ((max ((max (k1,k2)),m9)) + 1)) " is V11() real ext-real non negative set
((N-bound C) - (S-bound C)) * ((2 |^ ((max ((max (k1,k2)),m9)) + 1)) ") is V11() real ext-real set
((N-bound C) - (S-bound C)) / (2 |^ (m9 + 1)) is V11() real ext-real Element of REAL
(2 |^ (m9 + 1)) " is V11() real ext-real non negative set
((N-bound C) - (S-bound C)) * ((2 |^ (m9 + 1)) ") is V11() real ext-real set
((E-bound C) - (W-bound C)) / (2 |^ ((max ((max (k1,k2)),m9)) + 1)) is V11() real ext-real Element of REAL
((E-bound C) - (W-bound C)) * ((2 |^ ((max ((max (k1,k2)),m9)) + 1)) ") is V11() real ext-real set
((E-bound C) - (W-bound C)) / (2 |^ (m9 + 1)) is V11() real ext-real Element of REAL
((E-bound C) - (W-bound C)) * ((2 |^ (m9 + 1)) ") is V11() real ext-real set
((N-bound C) - (S-bound C)) / (2 to_power (m9 + 1)) is V11() real ext-real Element of REAL
((N-bound C) - (S-bound C)) * ((2 to_power (m9 + 1)) ") is V11() real ext-real set
((E-bound C) - (W-bound C)) / (2 to_power (m9 + 1)) is V11() real ext-real Element of REAL
((E-bound C) - (W-bound C)) * ((2 to_power (m9 + 1)) ") is V11() real ext-real set
dist (((Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i1),((Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. (i1 + 1))) is V11() real ext-real Element of REAL
c1 is Element of the carrier of (Euclid 2)
c2 is Element of the carrier of (Euclid 2)
dist (c1,c2) is V11() real ext-real Element of REAL
((Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i1) - ((Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. (i1 + 1)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
|.(((Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i1) - ((Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. (i1 + 1))).| is V11() real ext-real non negative Element of REAL
p1 - ((Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
|.(p1 - ((Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i1)).| is V11() real ext-real non negative Element of REAL
p19 is Element of the carrier of (Euclid 2)
dist (p19,p9) is V11() real ext-real Element of REAL
p - p1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
|.(p - p1).| is V11() real ext-real non negative Element of REAL
2 * 4 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
r / (2 * 4) is V11() real ext-real Element of REAL
(2 * 4) " is V11() real ext-real non negative set
r * ((2 * 4) ") is V11() real ext-real set
(r / (2 * 4)) + (r / (2 * 4)) is V11() real ext-real Element of REAL
|.(p - p1).| + |.(p1 - ((Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i1)).| is V11() real ext-real non negative Element of REAL
p - ((Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
|.(p - ((Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i1)).| is V11() real ext-real non negative Element of REAL
r / 4 is V11() real ext-real Element of REAL
4 " is non empty V11() real ext-real positive non negative set
r * (4 ") is V11() real ext-real set
dist (p9,c1) is V11() real ext-real Element of REAL
Ball (p9,(r / 4)) is Element of K6( the carrier of (Euclid 2))
(C) . ((max ((max (k1,k2)),m9)) + 1) is set
Lower_Arc (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
p2 is set
p2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1)) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V28() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
L~ (Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
len (Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
i2 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
i2 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
(Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. (i2 + 1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg (((Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i2),((Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. (i2 + 1))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
Seg (len (Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1)))) is non empty V28() V35( len (Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1)))) Element of K6(NAT)
dom (Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) is non trivial Element of K6(NAT)
ii2 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
jj2 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
[ii2,jj2] is set
{ii2,jj2} is non empty set
{ii2} is non empty trivial V35(1) set
{{ii2,jj2},{ii2}} is non empty set
(Gauge (C,((max ((max (k1,k2)),m9)) + 1))) * (ii2,jj2) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
dist (((Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i2),((Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. (i2 + 1))) is V11() real ext-real Element of REAL
d1 is Element of the carrier of (Euclid 2)
d2 is Element of the carrier of (Euclid 2)
dist (d1,d2) is V11() real ext-real Element of REAL
((Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i2) - ((Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. (i2 + 1)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
|.(((Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i2) - ((Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. (i2 + 1))).| is V11() real ext-real non negative Element of REAL
p2 - ((Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i2) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
|.(p2 - ((Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i2)).| is V11() real ext-real non negative Element of REAL
p29 is Element of the carrier of (Euclid 2)
dist (p29,p9) is V11() real ext-real Element of REAL
p - p2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
|.(p - p2).| is V11() real ext-real non negative Element of REAL
|.(p - p2).| + |.(p2 - ((Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i2)).| is V11() real ext-real non negative Element of REAL
p - ((Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i2) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
|.(p - ((Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i2)).| is V11() real ext-real non negative Element of REAL
dist (p9,d1) is V11() real ext-real Element of REAL
(Gauge (C,((max ((max (k1,k2)),m9)) + 1))) * (ii2,jj1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(Gauge (C,((max ((max (k1,k2)),m9)) + 1))) * (ii1,jj2) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
r / 2 is V11() real ext-real Element of REAL
2 " is non empty V11() real ext-real positive non negative set
r * (2 ") is V11() real ext-real set
((Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i1) `1 is V11() real ext-real Element of REAL
(p `1) - (((Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i1) `1) is V11() real ext-real Element of REAL
- (((Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i1) `1) is V11() real ext-real set
(p `1) + (- (((Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i1) `1)) is V11() real ext-real set
abs ((p `1) - (((Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i1) `1)) is V11() real ext-real Element of REAL
W-bound (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))) is V15() V18( the carrier of ((TOP-REAL 2) | (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))), REAL ) V212((TOP-REAL 2) | (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))),REAL))
the carrier of ((TOP-REAL 2) | (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))) is set
K7( the carrier of ((TOP-REAL 2) | (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))),REAL)) is non empty set
lower_bound (proj1 | (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))) is V11() real ext-real Element of REAL
(proj1 | (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))) .: the carrier of ((TOP-REAL 2) | (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))) is Element of K6(REAL)
lower_bound ((proj1 | (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))) .: the carrier of ((TOP-REAL 2) | (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))))) is V11() real ext-real Element of REAL
(p `1) - (W-bound (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))) is V11() real ext-real Element of REAL
- (W-bound (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))) is V11() real ext-real set
(p `1) + (- (W-bound (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))))) is V11() real ext-real set
(Gauge (C,((max ((max (k1,k2)),m9)) + 1))) * ((len (Gauge (C,((max ((max (k1,k2)),m9)) + 1)))),jj1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (C,((max ((max (k1,k2)),m9)) + 1))) * ((len (Gauge (C,((max ((max (k1,k2)),m9)) + 1)))),jj1)) `1 is V11() real ext-real Element of REAL
E-bound (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))) is V11() real ext-real Element of REAL
upper_bound ((proj1 | (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))) .: the carrier of ((TOP-REAL 2) | (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))))) is V11() real ext-real Element of REAL
E-max (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
E-most (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
SE-corner (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
S-bound (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))) is V11() real ext-real Element of REAL
proj2 | (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))) is V15() V18( the carrier of ((TOP-REAL 2) | (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))), REAL ) V212((TOP-REAL 2) | (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))),REAL))
lower_bound (proj2 | (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))) is V11() real ext-real Element of REAL
(proj2 | (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))) .: the carrier of ((TOP-REAL 2) | (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))) is Element of K6(REAL)
lower_bound ((proj2 | (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))) .: the carrier of ((TOP-REAL 2) | (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))),(S-bound (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
NE-corner (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
N-bound (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))) .: the carrier of ((TOP-REAL 2) | (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))),(N-bound (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))),(NE-corner (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SE-corner (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))),(NE-corner (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))))) /\ (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (E-most (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))) is V15() V18( the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))))), REAL ) V212((TOP-REAL 2) | (E-most (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))))),REAL))
the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))))) is set
K7( the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))))),REAL)) is non empty set
upper_bound (proj2 | (E-most (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))))) is V11() real ext-real Element of REAL
(proj2 | (E-most (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))))) is Element of K6(REAL)
upper_bound ((proj2 | (E-most (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))),(upper_bound (proj2 | (E-most (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. (len (Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1)))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(Gauge (C,((max ((max (k1,k2)),m9)) + 1))) * (1,jj2) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (C,((max ((max (k1,k2)),m9)) + 1))) * (1,jj2)) `1 is V11() real ext-real Element of REAL
W-min (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
W-most (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
SW-corner (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
|[(W-bound (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))),(S-bound (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
NW-corner (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
|[(W-bound (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))),(N-bound (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))),(NW-corner (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))),(NW-corner (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))))) /\ (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (W-most (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))) is V15() V18( the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))))), REAL ) V212((TOP-REAL 2) | (W-most (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))))),REAL))
the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))))) is set
K7( the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))))),REAL)) is non empty set
lower_bound (proj2 | (W-most (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))))) is V11() real ext-real Element of REAL
(proj2 | (W-most (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))))) is Element of K6(REAL)
lower_bound ((proj2 | (W-most (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))),(lower_bound (proj2 | (W-most (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. (len (Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1)))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i2) `1 is V11() real ext-real Element of REAL
(((Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i2) `1) - (p `1) is V11() real ext-real Element of REAL
(((Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i2) `1) + (- (p `1)) is V11() real ext-real set
abs ((((Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i2) `1) - (p `1)) is V11() real ext-real Element of REAL
((Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i2) - p is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
|.(((Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i2) - p).| is V11() real ext-real non negative Element of REAL
(E-bound (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))) - (p `1) is V11() real ext-real Element of REAL
(E-bound (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))) + (- (p `1)) is V11() real ext-real set
rr is V11() real ext-real Element of REAL
rr / 4 is V11() real ext-real Element of REAL
rr * (4 ") is V11() real ext-real set
Ball (p9,(rr / 4)) is Element of K6( the carrier of (Euclid 2))
Ball (p9,rr) is Element of K6( the carrier of (Euclid 2))
((Gauge (C,((max ((max (k1,k2)),m9)) + 1))) * (ii2,jj1)) `1 is V11() real ext-real Element of REAL
(Gauge (C,((max ((max (k1,k2)),m9)) + 1))) * (ii2,1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (C,((max ((max (k1,k2)),m9)) + 1))) * (ii2,1)) `1 is V11() real ext-real Element of REAL
((Gauge (C,((max ((max (k1,k2)),m9)) + 1))) * (ii2,jj1)) `2 is V11() real ext-real Element of REAL
(Gauge (C,((max ((max (k1,k2)),m9)) + 1))) * (1,jj1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (C,((max ((max (k1,k2)),m9)) + 1))) * (1,jj1)) `2 is V11() real ext-real Element of REAL
((Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i1) `2 is V11() real ext-real Element of REAL
((Gauge (C,((max ((max (k1,k2)),m9)) + 1))) * (ii1,jj2)) `1 is V11() real ext-real Element of REAL
(Gauge (C,((max ((max (k1,k2)),m9)) + 1))) * (ii1,1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (C,((max ((max (k1,k2)),m9)) + 1))) * (ii1,1)) `1 is V11() real ext-real Element of REAL
((Gauge (C,((max ((max (k1,k2)),m9)) + 1))) * (ii1,jj2)) `2 is V11() real ext-real Element of REAL
((Gauge (C,((max ((max (k1,k2)),m9)) + 1))) * (1,jj2)) `2 is V11() real ext-real Element of REAL
((Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i2) `2 is V11() real ext-real Element of REAL
p `2 is V11() real ext-real Element of REAL
(((Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i1) `2) - (p `2) is V11() real ext-real Element of REAL
- (p `2) is V11() real ext-real set
(((Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i1) `2) + (- (p `2)) is V11() real ext-real set
abs ((((Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i1) `2) - (p `2)) is V11() real ext-real Element of REAL
((Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i1) - p is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
|.(((Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i1) - p).| is V11() real ext-real non negative Element of REAL
(abs ((((Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i2) `1) - (p `1))) + (abs ((((Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i1) `2) - (p `2))) is V11() real ext-real Element of REAL
2 * 2 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
r / (2 * 2) is V11() real ext-real Element of REAL
(2 * 2) " is V11() real ext-real non negative set
r * ((2 * 2) ") is V11() real ext-real set
(r / (2 * 2)) + (r / (2 * 2)) is V11() real ext-real Element of REAL
(((Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i1) `1) - (p `1) is V11() real ext-real Element of REAL
(((Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i1) `1) + (- (p `1)) is V11() real ext-real set
abs ((((Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i1) `1) - (p `1)) is V11() real ext-real Element of REAL
(((Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i2) `2) - (p `2) is V11() real ext-real Element of REAL
(((Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i2) `2) + (- (p `2)) is V11() real ext-real set
abs ((((Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i2) `2) - (p `2)) is V11() real ext-real Element of REAL
(abs ((((Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i1) `1) - (p `1))) + (abs ((((Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i2) `2) - (p `2))) is V11() real ext-real Element of REAL
((Gauge (C,((max ((max (k1,k2)),m9)) + 1))) * (ii2,jj1)) - p is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
|.(((Gauge (C,((max ((max (k1,k2)),m9)) + 1))) * (ii2,jj1)) - p).| is V11() real ext-real non negative Element of REAL
Gij9 is Element of the carrier of (Euclid 2)
dist (Gij9,p9) is V11() real ext-real Element of REAL
Ball (p9,r) is Element of K6( the carrier of (Euclid 2))
((Gauge (C,((max ((max (k1,k2)),m9)) + 1))) * (ii1,jj2)) - p is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
|.(((Gauge (C,((max ((max (k1,k2)),m9)) + 1))) * (ii1,jj2)) - p).| is V11() real ext-real non negative Element of REAL
Gji9 is Element of the carrier of (Euclid 2)
dist (Gji9,p9) is V11() real ext-real Element of REAL
LSeg (((Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i2),((Gauge (C,((max ((max (k1,k2)),m9)) + 1))) * (ii2,jj1))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
LSeg (((Gauge (C,((max ((max (k1,k2)),m9)) + 1))) * (ii2,jj1)),((Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i1)) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
LSeg (((Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i2),((Gauge (C,((max ((max (k1,k2)),m9)) + 1))) * (ii1,jj2))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
LSeg (((Gauge (C,((max ((max (k1,k2)),m9)) + 1))) * (ii1,jj2)),((Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i1)) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg (((Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i2),((Gauge (C,((max ((max (k1,k2)),m9)) + 1))) * (ii2,jj1)))) \/ (LSeg (((Gauge (C,((max ((max (k1,k2)),m9)) + 1))) * (ii2,jj1)),((Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i1))) is non empty functional Element of K6( the carrier of (TOP-REAL 2))
x is set
x9 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
x9 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
x9 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
x9 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
Upper_Arc C is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
LSeg (((Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i1),((Gauge (C,((max ((max (k1,k2)),m9)) + 1))) * (ii1,jj2))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
LSeg (((Gauge (C,((max ((max (k1,k2)),m9)) + 1))) * (ii1,jj2)),((Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i2)) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg (((Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i1),((Gauge (C,((max ((max (k1,k2)),m9)) + 1))) * (ii1,jj2)))) \/ (LSeg (((Gauge (C,((max ((max (k1,k2)),m9)) + 1))) * (ii1,jj2)),((Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i2))) is non empty functional Element of K6( the carrier of (TOP-REAL 2))
x is set
x9 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
x9 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
x9 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
x9 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
Upper_Arc C is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
Upper_Arc C is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
Upper_Arc C is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
Cl (Upper_Arc C) is functional bounded Element of K6( the carrier of (TOP-REAL 2))
r is V11() real ext-real set
r / 8 is V11() real ext-real Element of REAL
r * (8 ") is V11() real ext-real set
Ball (p9,(r / 8)) is Element of K6( the carrier of (Euclid 2))
G is functional a_neighborhood of p
k1 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
k2 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
max (k1,k2) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
max ((max (((N-bound C) - (S-bound C)),((E-bound C) - (W-bound C)))),(r / 8)) is V11() real ext-real set
(max ((max (((N-bound C) - (S-bound C)),((E-bound C) - (W-bound C)))),(r / 8))) / (r / 8) is V11() real ext-real Element of REAL
(r / 8) " is V11() real ext-real set
(max ((max (((N-bound C) - (S-bound C)),((E-bound C) - (W-bound C)))),(r / 8))) * ((r / 8) ") is V11() real ext-real set
log (2,((max ((max (((N-bound C) - (S-bound C)),((E-bound C) - (W-bound C)))),(r / 8))) / (r / 8))) is V11() real ext-real Element of REAL
[\(log (2,((max ((max (((N-bound C) - (S-bound C)),((E-bound C) - (W-bound C)))),(r / 8))) / (r / 8))))/] is integer set
m9 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
m9 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
2 to_power (m9 + 1) is V11() real ext-real Element of REAL
(m9 + 1) * 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(m9 + 1) * (log (2,2)) is V11() real ext-real Element of REAL
log (2,(2 to_power (m9 + 1))) is V11() real ext-real Element of REAL
(2 to_power (m9 + 1)) * (r / 8) is V11() real ext-real Element of REAL
((max ((max (((N-bound C) - (S-bound C)),((E-bound C) - (W-bound C)))),(r / 8))) / (r / 8)) * (r / 8) is V11() real ext-real Element of REAL
((2 to_power (m9 + 1)) * (r / 8)) / (2 to_power (m9 + 1)) is V11() real ext-real Element of REAL
(2 to_power (m9 + 1)) " is V11() real ext-real set
((2 to_power (m9 + 1)) * (r / 8)) * ((2 to_power (m9 + 1)) ") is V11() real ext-real set
(max ((max (((N-bound C) - (S-bound C)),((E-bound C) - (W-bound C)))),(r / 8))) / (2 to_power (m9 + 1)) is V11() real ext-real Element of REAL
(max ((max (((N-bound C) - (S-bound C)),((E-bound C) - (W-bound C)))),(r / 8))) * ((2 to_power (m9 + 1)) ") is V11() real ext-real set
(r / 8) / (2 to_power (m9 + 1)) is V11() real ext-real Element of REAL
(r / 8) * ((2 to_power (m9 + 1)) ") is V11() real ext-real set
((r / 8) / (2 to_power (m9 + 1))) * (2 to_power (m9 + 1)) is V11() real ext-real Element of REAL
(max (((N-bound C) - (S-bound C)),((E-bound C) - (W-bound C)))) / (2 to_power (m9 + 1)) is V11() real ext-real Element of REAL
(max (((N-bound C) - (S-bound C)),((E-bound C) - (W-bound C)))) * ((2 to_power (m9 + 1)) ") is V11() real ext-real set
max ((max (k1,k2)),m9) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(max ((max (k1,k2)),m9)) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
Gauge (C,((max ((max (k1,k2)),m9)) + 1)) is V15() non empty-yielding V18( NAT ) V19(K307( the carrier of (TOP-REAL 2))) Function-like V28() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K307( the carrier of (TOP-REAL 2))
len (Gauge (C,((max ((max (k1,k2)),m9)) + 1))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
width (Gauge (C,((max ((max (k1,k2)),m9)) + 1))) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
(C) . ((max ((max (k1,k2)),m9)) + 1) is set
Cage (C,((max ((max (k1,k2)),m9)) + 1)) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like non constant V28() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the carrier of (TOP-REAL 2)
L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
Upper_Arc (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
p1 is set
p1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1)) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V28() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
L~ (Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
len (Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
i1 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
i1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
(Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. (i1 + 1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg (((Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i1),((Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. (i1 + 1))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
Seg (len (Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1)))) is non empty V28() V35( len (Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1)))) Element of K6(NAT)
dom (Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) is non trivial Element of K6(NAT)
Indices (Gauge (C,((max ((max (k1,k2)),m9)) + 1))) is set
ii1 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
jj1 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
[ii1,jj1] is set
{ii1,jj1} is non empty set
{ii1} is non empty trivial V35(1) set
{{ii1,jj1},{ii1}} is non empty set
(Gauge (C,((max ((max (k1,k2)),m9)) + 1))) * (ii1,jj1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
2 |^ (m9 + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
2 |^ ((max ((max (k1,k2)),m9)) + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
((N-bound C) - (S-bound C)) / (2 |^ ((max ((max (k1,k2)),m9)) + 1)) is V11() real ext-real Element of REAL
(2 |^ ((max ((max (k1,k2)),m9)) + 1)) " is V11() real ext-real non negative set
((N-bound C) - (S-bound C)) * ((2 |^ ((max ((max (k1,k2)),m9)) + 1)) ") is V11() real ext-real set
((N-bound C) - (S-bound C)) / (2 |^ (m9 + 1)) is V11() real ext-real Element of REAL
(2 |^ (m9 + 1)) " is V11() real ext-real non negative set
((N-bound C) - (S-bound C)) * ((2 |^ (m9 + 1)) ") is V11() real ext-real set
((E-bound C) - (W-bound C)) / (2 |^ ((max ((max (k1,k2)),m9)) + 1)) is V11() real ext-real Element of REAL
((E-bound C) - (W-bound C)) * ((2 |^ ((max ((max (k1,k2)),m9)) + 1)) ") is V11() real ext-real set
((E-bound C) - (W-bound C)) / (2 |^ (m9 + 1)) is V11() real ext-real Element of REAL
((E-bound C) - (W-bound C)) * ((2 |^ (m9 + 1)) ") is V11() real ext-real set
((N-bound C) - (S-bound C)) / (2 to_power (m9 + 1)) is V11() real ext-real Element of REAL
((N-bound C) - (S-bound C)) * ((2 to_power (m9 + 1)) ") is V11() real ext-real set
((E-bound C) - (W-bound C)) / (2 to_power (m9 + 1)) is V11() real ext-real Element of REAL
((E-bound C) - (W-bound C)) * ((2 to_power (m9 + 1)) ") is V11() real ext-real set
dist (((Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i1),((Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. (i1 + 1))) is V11() real ext-real Element of REAL
c1 is Element of the carrier of (Euclid 2)
c2 is Element of the carrier of (Euclid 2)
dist (c1,c2) is V11() real ext-real Element of REAL
((Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i1) - ((Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. (i1 + 1)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
|.(((Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i1) - ((Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. (i1 + 1))).| is V11() real ext-real non negative Element of REAL
p1 - ((Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
|.(p1 - ((Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i1)).| is V11() real ext-real non negative Element of REAL
p19 is Element of the carrier of (Euclid 2)
dist (p19,p9) is V11() real ext-real Element of REAL
p - p1 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
|.(p - p1).| is V11() real ext-real non negative Element of REAL
r / (2 * 4) is V11() real ext-real Element of REAL
r * ((2 * 4) ") is V11() real ext-real set
(r / (2 * 4)) + (r / (2 * 4)) is V11() real ext-real Element of REAL
|.(p - p1).| + |.(p1 - ((Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i1)).| is V11() real ext-real non negative Element of REAL
p - ((Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
|.(p - ((Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i1)).| is V11() real ext-real non negative Element of REAL
r / 4 is V11() real ext-real Element of REAL
r * (4 ") is V11() real ext-real set
dist (p9,c1) is V11() real ext-real Element of REAL
Ball (p9,(r / 4)) is Element of K6( the carrier of (Euclid 2))
(C) . ((max ((max (k1,k2)),m9)) + 1) is set
Lower_Arc (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
p2 is set
p2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1)) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V28() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
L~ (Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
len (Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
i2 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
i2 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real positive non negative Element of NAT
(Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. (i2 + 1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg (((Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i2),((Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. (i2 + 1))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
Seg (len (Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1)))) is non empty V28() V35( len (Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1)))) Element of K6(NAT)
dom (Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) is non trivial Element of K6(NAT)
ii2 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
jj2 is epsilon-transitive epsilon-connected ordinal natural V11() real V28() V33() ext-real non negative Element of NAT
[ii2,jj2] is set
{ii2,jj2} is non empty set
{ii2} is non empty trivial V35(1) set
{{ii2,jj2},{ii2}} is non empty set
(Gauge (C,((max ((max (k1,k2)),m9)) + 1))) * (ii2,jj2) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
dist (((Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i2),((Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. (i2 + 1))) is V11() real ext-real Element of REAL
d1 is Element of the carrier of (Euclid 2)
d2 is Element of the carrier of (Euclid 2)
dist (d1,d2) is V11() real ext-real Element of REAL
((Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i2) - ((Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. (i2 + 1)) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
|.(((Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i2) - ((Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. (i2 + 1))).| is V11() real ext-real non negative Element of REAL
p2 - ((Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i2) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
|.(p2 - ((Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i2)).| is V11() real ext-real non negative Element of REAL
p29 is Element of the carrier of (Euclid 2)
dist (p29,p9) is V11() real ext-real Element of REAL
p - p2 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
|.(p - p2).| is V11() real ext-real non negative Element of REAL
|.(p - p2).| + |.(p2 - ((Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i2)).| is V11() real ext-real non negative Element of REAL
p - ((Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i2) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
|.(p - ((Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i2)).| is V11() real ext-real non negative Element of REAL
dist (p9,d1) is V11() real ext-real Element of REAL
(Gauge (C,((max ((max (k1,k2)),m9)) + 1))) * (ii2,jj1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(Gauge (C,((max ((max (k1,k2)),m9)) + 1))) * (ii1,jj2) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
r / 2 is V11() real ext-real Element of REAL
r * (2 ") is V11() real ext-real set
((Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i1) `1 is V11() real ext-real Element of REAL
(p `1) - (((Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i1) `1) is V11() real ext-real Element of REAL
- (((Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i1) `1) is V11() real ext-real set
(p `1) + (- (((Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i1) `1)) is V11() real ext-real set
abs ((p `1) - (((Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i1) `1)) is V11() real ext-real Element of REAL
W-bound (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))) is V15() V18( the carrier of ((TOP-REAL 2) | (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))), REAL ) V212((TOP-REAL 2) | (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))),REAL))
the carrier of ((TOP-REAL 2) | (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))) is set
K7( the carrier of ((TOP-REAL 2) | (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))),REAL)) is non empty set
lower_bound (proj1 | (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))) is V11() real ext-real Element of REAL
(proj1 | (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))) .: the carrier of ((TOP-REAL 2) | (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))) is Element of K6(REAL)
lower_bound ((proj1 | (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))) .: the carrier of ((TOP-REAL 2) | (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))))) is V11() real ext-real Element of REAL
(p `1) - (W-bound (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))) is V11() real ext-real Element of REAL
- (W-bound (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))) is V11() real ext-real set
(p `1) + (- (W-bound (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))))) is V11() real ext-real set
(Gauge (C,((max ((max (k1,k2)),m9)) + 1))) * ((len (Gauge (C,((max ((max (k1,k2)),m9)) + 1)))),jj1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (C,((max ((max (k1,k2)),m9)) + 1))) * ((len (Gauge (C,((max ((max (k1,k2)),m9)) + 1)))),jj1)) `1 is V11() real ext-real Element of REAL
E-bound (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))) is V11() real ext-real Element of REAL
upper_bound ((proj1 | (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))) .: the carrier of ((TOP-REAL 2) | (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))))) is V11() real ext-real Element of REAL
E-max (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
E-most (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
SE-corner (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
S-bound (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))) is V11() real ext-real Element of REAL
proj2 | (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))) is V15() V18( the carrier of ((TOP-REAL 2) | (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))), REAL ) V212((TOP-REAL 2) | (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))),REAL))
lower_bound (proj2 | (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))) is V11() real ext-real Element of REAL
(proj2 | (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))) .: the carrier of ((TOP-REAL 2) | (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))) is Element of K6(REAL)
lower_bound ((proj2 | (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))) .: the carrier of ((TOP-REAL 2) | (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))),(S-bound (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
NE-corner (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
N-bound (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))) .: the carrier of ((TOP-REAL 2) | (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))),(N-bound (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))),(NE-corner (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SE-corner (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))),(NE-corner (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))))) /\ (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (E-most (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))) is V15() V18( the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))))), REAL ) V212((TOP-REAL 2) | (E-most (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))))),REAL))
the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))))) is set
K7( the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))))),REAL)) is non empty set
upper_bound (proj2 | (E-most (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))))) is V11() real ext-real Element of REAL
(proj2 | (E-most (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))))) is Element of K6(REAL)
upper_bound ((proj2 | (E-most (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))),(upper_bound (proj2 | (E-most (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. (len (Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1)))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(Gauge (C,((max ((max (k1,k2)),m9)) + 1))) * (1,jj2) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (C,((max ((max (k1,k2)),m9)) + 1))) * (1,jj2)) `1 is V11() real ext-real Element of REAL
W-min (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
W-most (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))) is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
SW-corner (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
|[(W-bound (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))),(S-bound (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
NW-corner (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
|[(W-bound (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))),(N-bound (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))),(NW-corner (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))),(NW-corner (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))))) /\ (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (W-most (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))) is V15() V18( the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))))), REAL ) V212((TOP-REAL 2) | (W-most (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))))) Element of K6(K7( the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))))),REAL))
the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))))) is set
K7( the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))))),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))))),REAL)) is non empty set
lower_bound (proj2 | (W-most (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))))) is V11() real ext-real Element of REAL
(proj2 | (W-most (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))))) is Element of K6(REAL)
lower_bound ((proj2 | (W-most (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))),(lower_bound (proj2 | (W-most (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1)))))))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
(Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. (len (Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1)))) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i2) `1 is V11() real ext-real Element of REAL
(((Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i2) `1) - (p `1) is V11() real ext-real Element of REAL
(((Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i2) `1) + (- (p `1)) is V11() real ext-real set
abs ((((Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i2) `1) - (p `1)) is V11() real ext-real Element of REAL
((Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i2) - p is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
|.(((Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i2) - p).| is V11() real ext-real non negative Element of REAL
(E-bound (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))) - (p `1) is V11() real ext-real Element of REAL
(E-bound (L~ (Cage (C,((max ((max (k1,k2)),m9)) + 1))))) + (- (p `1)) is V11() real ext-real set
rr is V11() real ext-real Element of REAL
rr / 4 is V11() real ext-real Element of REAL
rr * (4 ") is V11() real ext-real set
Ball (p9,(rr / 4)) is Element of K6( the carrier of (Euclid 2))
Ball (p9,rr) is Element of K6( the carrier of (Euclid 2))
((Gauge (C,((max ((max (k1,k2)),m9)) + 1))) * (ii2,jj1)) `1 is V11() real ext-real Element of REAL
(Gauge (C,((max ((max (k1,k2)),m9)) + 1))) * (ii2,1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (C,((max ((max (k1,k2)),m9)) + 1))) * (ii2,1)) `1 is V11() real ext-real Element of REAL
((Gauge (C,((max ((max (k1,k2)),m9)) + 1))) * (ii2,jj1)) `2 is V11() real ext-real Element of REAL
(Gauge (C,((max ((max (k1,k2)),m9)) + 1))) * (1,jj1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (C,((max ((max (k1,k2)),m9)) + 1))) * (1,jj1)) `2 is V11() real ext-real Element of REAL
((Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i1) `2 is V11() real ext-real Element of REAL
((Gauge (C,((max ((max (k1,k2)),m9)) + 1))) * (ii1,jj2)) `1 is V11() real ext-real Element of REAL
(Gauge (C,((max ((max (k1,k2)),m9)) + 1))) * (ii1,1) is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
((Gauge (C,((max ((max (k1,k2)),m9)) + 1))) * (ii1,1)) `1 is V11() real ext-real Element of REAL
((Gauge (C,((max ((max (k1,k2)),m9)) + 1))) * (ii1,jj2)) `2 is V11() real ext-real Element of REAL
((Gauge (C,((max ((max (k1,k2)),m9)) + 1))) * (1,jj2)) `2 is V11() real ext-real Element of REAL
((Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i2) `2 is V11() real ext-real Element of REAL
(((Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i1) `2) - (p `2) is V11() real ext-real Element of REAL
(((Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i1) `2) + (- (p `2)) is V11() real ext-real set
abs ((((Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i1) `2) - (p `2)) is V11() real ext-real Element of REAL
((Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i1) - p is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
|.(((Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i1) - p).| is V11() real ext-real non negative Element of REAL
(abs ((((Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i2) `1) - (p `1))) + (abs ((((Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i1) `2) - (p `2))) is V11() real ext-real Element of REAL
r / (2 * 2) is V11() real ext-real Element of REAL
r * ((2 * 2) ") is V11() real ext-real set
(r / (2 * 2)) + (r / (2 * 2)) is V11() real ext-real Element of REAL
(((Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i1) `1) - (p `1) is V11() real ext-real Element of REAL
(((Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i1) `1) + (- (p `1)) is V11() real ext-real set
abs ((((Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i1) `1) - (p `1)) is V11() real ext-real Element of REAL
(((Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i2) `2) - (p `2) is V11() real ext-real Element of REAL
(((Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i2) `2) + (- (p `2)) is V11() real ext-real set
abs ((((Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i2) `2) - (p `2)) is V11() real ext-real Element of REAL
(abs ((((Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i1) `1) - (p `1))) + (abs ((((Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i2) `2) - (p `2))) is V11() real ext-real Element of REAL
((Gauge (C,((max ((max (k1,k2)),m9)) + 1))) * (ii2,jj1)) - p is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
|.(((Gauge (C,((max ((max (k1,k2)),m9)) + 1))) * (ii2,jj1)) - p).| is V11() real ext-real non negative Element of REAL
Gij9 is Element of the carrier of (Euclid 2)
dist (Gij9,p9) is V11() real ext-real Element of REAL
Ball (p9,r) is Element of K6( the carrier of (Euclid 2))
((Gauge (C,((max ((max (k1,k2)),m9)) + 1))) * (ii1,jj2)) - p is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
|.(((Gauge (C,((max ((max (k1,k2)),m9)) + 1))) * (ii1,jj2)) - p).| is V11() real ext-real non negative Element of REAL
Gji9 is Element of the carrier of (Euclid 2)
dist (Gji9,p9) is V11() real ext-real Element of REAL
LSeg (((Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i2),((Gauge (C,((max ((max (k1,k2)),m9)) + 1))) * (ii2,jj1))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
LSeg (((Gauge (C,((max ((max (k1,k2)),m9)) + 1))) * (ii2,jj1)),((Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i1)) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
LSeg (((Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i2),((Gauge (C,((max ((max (k1,k2)),m9)) + 1))) * (ii1,jj2))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
LSeg (((Gauge (C,((max ((max (k1,k2)),m9)) + 1))) * (ii1,jj2)),((Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i1)) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg (((Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i2),((Gauge (C,((max ((max (k1,k2)),m9)) + 1))) * (ii2,jj1)))) \/ (LSeg (((Gauge (C,((max ((max (k1,k2)),m9)) + 1))) * (ii2,jj1)),((Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i1))) is non empty functional Element of K6( the carrier of (TOP-REAL 2))
x is set
x9 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
x9 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
x9 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
x9 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
Lower_Arc C is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
LSeg (((Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i1),((Gauge (C,((max ((max (k1,k2)),m9)) + 1))) * (ii1,jj2))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
LSeg (((Gauge (C,((max ((max (k1,k2)),m9)) + 1))) * (ii1,jj2)),((Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i2)) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg (((Upper_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i1),((Gauge (C,((max ((max (k1,k2)),m9)) + 1))) * (ii1,jj2)))) \/ (LSeg (((Gauge (C,((max ((max (k1,k2)),m9)) + 1))) * (ii1,jj2)),((Lower_Seq (C,((max ((max (k1,k2)),m9)) + 1))) /. i2))) is non empty functional Element of K6( the carrier of (TOP-REAL 2))
x is set
x9 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
x9 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
x9 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
x9 is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
Lower_Arc C is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
Lower_Arc C is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
Lower_Arc C is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
Cl (Lower_Arc C) is functional bounded Element of K6( the carrier of (TOP-REAL 2))
(Upper_Arc C) /\ (Lower_Arc C) is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
W-min C is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
W-most C is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
SW-corner C is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
|[(W-bound C),(S-bound C)]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
NW-corner C is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
|[(W-bound C),(N-bound C)]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner C),(NW-corner C)) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SW-corner C),(NW-corner C))) /\ C is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (W-most C) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (W-most C) is V15() V18( the carrier of ((TOP-REAL 2) | (W-most C))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (W-most C)), REAL ) V212((TOP-REAL 2) | (W-most C)) Element of K6(K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL))
the carrier of ((TOP-REAL 2) | (W-most C)) is set
K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (W-most C)),REAL)) is non empty set
lower_bound (proj2 | (W-most C)) is V11() real ext-real Element of REAL
(proj2 | (W-most C)) .: the carrier of ((TOP-REAL 2) | (W-most C)) is Element of K6(REAL)
lower_bound ((proj2 | (W-most C)) .: the carrier of ((TOP-REAL 2) | (W-most C))) is V11() real ext-real Element of REAL
|[(W-bound C),(lower_bound (proj2 | (W-most C)))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
E-max C is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
E-most C is non empty functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
SE-corner C is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
|[(E-bound C),(S-bound C)]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
NE-corner C is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
|[(E-bound C),(N-bound C)]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner C),(NE-corner C)) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the carrier of (TOP-REAL 2))
(LSeg ((SE-corner C),(NE-corner C))) /\ C is functional closed bounded compact Element of K6( the carrier of (TOP-REAL 2))
(TOP-REAL 2) | (E-most C) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (E-most C) is V15() V18( the carrier of ((TOP-REAL 2) | (E-most C))) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | (E-most C)), REAL ) V212((TOP-REAL 2) | (E-most C)) Element of K6(K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL))
the carrier of ((TOP-REAL 2) | (E-most C)) is set
K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | (E-most C)),REAL)) is non empty set
upper_bound (proj2 | (E-most C)) is V11() real ext-real Element of REAL
(proj2 | (E-most C)) .: the carrier of ((TOP-REAL 2) | (E-most C)) is Element of K6(REAL)
upper_bound ((proj2 | (E-most C)) .: the carrier of ((TOP-REAL 2) | (E-most C))) is V11() real ext-real Element of REAL
|[(E-bound C),(upper_bound (proj2 | (E-most C)))]| is non empty non trivial V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
{(W-min C),(E-max C)} is non empty functional set
C is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the carrier of (TOP-REAL 2))
W-bound C is V11() real ext-real Element of REAL
(TOP-REAL 2) | C is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | C is V15() V18( the carrier of ((TOP-REAL 2) | C)) V19( REAL ) Function-like V40( the carrier of ((TOP-REAL 2) | C), REAL ) V212((TOP-REAL 2) | C) Element of K6(K7( the carrier of ((TOP-REAL 2) | C),REAL))
the carrier of ((TOP-REAL 2) | C) is set
K7( the carrier of ((TOP-REAL 2) | C),REAL) is set
K6(K7( the carrier of ((TOP-REAL 2) | C),REAL)) is non empty set
lower_bound (proj1 | C) is V11() real ext-real Element of REAL
(proj1 | C) .: the carrier of ((TOP-REAL 2) | C) is Element of K6(REAL)
lower_bound ((proj1 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
E-bound C is V11() real ext-real Element of REAL
upper_bound (proj1 | C) is V11() real ext-real Element of REAL
upper_bound ((proj1 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
(W-bound C) + (E-bound C) is V11() real ext-real Element of REAL
((W-bound C) + (E-bound C)) / 2 is V11() real ext-real Element of REAL
2 " is non empty V11() real ext-real positive non negative set
((W-bound C) + (E-bound C)) * (2 ") is V11() real ext-real set
(C) is functional Element of K6( the carrier of (TOP-REAL 2))
(C) is V15() V18( NAT ) V19(K291( the carrier of (TOP-REAL 2))) Function-like V40( NAT ,K291( the carrier of (TOP-REAL 2))) Element of K6(K7(NAT,K291( the carrier of (TOP-REAL 2))))
Lim_inf (C) is functional Element of K6( the carrier of (TOP-REAL 2))
(C) is functional Element of K6( the carrier of (TOP-REAL 2))
(C) is V15() V18( NAT ) V19(K291( the carrier of (TOP-REAL 2))) Function-like V40( NAT ,K291( the carrier of (TOP-REAL 2))) Element of K6(K7(NAT,K291( the carrier of (TOP-REAL 2))))
Lim_inf (C) is functional Element of K6( the carrier of (TOP-REAL 2))
p is V15() V18( NAT ) Function-like V28() V35(2) FinSequence-like FinSubsequence-like V168() Element of the carrier of (TOP-REAL 2)
p `1 is V11() real ext-real Element of REAL