:: JORDAN1G semantic presentation

REAL is V200() V201() V202() V206() set
NAT is non empty non trivial V6() V26() cardinal limit_cardinal V200() V201() V202() V203() V204() V205() V206() Element of bool REAL
bool REAL is set
NAT is non empty non trivial V6() V26() cardinal limit_cardinal V200() V201() V202() V203() V204() V205() V206() set
bool NAT is non empty non trivial V26() set
bool NAT is non empty non trivial V26() set
COMPLEX is V200() V206() set
1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
2 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
K356() is TopStruct
the U1 of K356() is set
[:1,1:] is V13() V26() set
bool [:1,1:] is V26() V30() set
[:[:1,1:],1:] is V13() V26() set
bool [:[:1,1:],1:] is V26() V30() set
[:[:1,1:],REAL:] is V13() set
bool [:[:1,1:],REAL:] is set
[:REAL,REAL:] is V13() set
[:[:REAL,REAL:],REAL:] is V13() set
bool [:[:REAL,REAL:],REAL:] is set
[:2,2:] is V13() V26() set
[:[:2,2:],REAL:] is V13() set
bool [:[:2,2:],REAL:] is set
K384() is V171() L15()
K394() is TopSpace-like T_0 T_1 T_2 TopStruct
RAT is V200() V201() V202() V203() V206() set
INT is V200() V201() V202() V203() V204() V206() set
bool [:REAL,REAL:] is set
TOP-REAL 2 is non empty non trivial TopSpace-like V104() V135() V136() V137() V138() V139() V140() V141() strict RLTopStruct
the U1 of (TOP-REAL 2) is non empty non trivial set
[: the U1 of (TOP-REAL 2),REAL:] is V13() set
bool [: the U1 of (TOP-REAL 2),REAL:] is set
bool the U1 of (TOP-REAL 2) is set
K238( the U1 of (TOP-REAL 2)) is non empty functional FinSequence-membered M11( the U1 of (TOP-REAL 2))
{} is empty trivial V6() V10() V11() V12() V13() non-empty empty-yielding V16( NAT ) Function-like one-to-one constant functional V26() V27() V30() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative V200() V201() V202() V203() V204() V205() V206() set
the empty trivial V6() V10() V11() V12() V13() non-empty empty-yielding V16( NAT ) Function-like one-to-one constant functional V26() V27() V30() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative V200() V201() V202() V203() V204() V205() V206() set is empty trivial V6() V10() V11() V12() V13() non-empty empty-yielding V16( NAT ) Function-like one-to-one constant functional V26() V27() V30() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative V200() V201() V202() V203() V204() V205() V206() set
3 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
4 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
0 is empty trivial V6() V10() V11() V12() V13() non-empty empty-yielding V16( NAT ) Function-like one-to-one constant functional V26() V27() V30() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V37() ext-real non positive non negative V199() V200() V201() V202() V203() V204() V205() V206() Element of NAT
Seg 1 is non empty trivial V26() 1 -element V200() V201() V202() V203() V204() V205() Element of bool NAT
{1} is non empty trivial V26() V30() 1 -element V200() V201() V202() V203() V204() V205() set
Seg 2 is non empty V26() 2 -element V200() V201() V202() V203() V204() V205() Element of bool NAT
{1,2} is non empty V26() V30() V200() V201() V202() V203() V204() V205() set
K396() is TopSpace-like SubSpace of K394()
the U1 of K396() is set
C is trivial V13() V16( NAT ) Function-like constant V26() FinSequence-like FinSubsequence-like set
n is set
{n} is non empty trivial V26() 1 -element set
i is set
j is set
[i,j] is non empty set
{i,j} is non empty V26() set
{i} is non empty trivial V26() 1 -element set
{{i,j},{i}} is non empty V26() V30() set
dom C is trivial V26() V200() V201() V202() V203() V204() V205() Element of bool NAT
<*j*> is non empty trivial V13() V16( NAT ) Function-like constant V26() 1 -element FinSequence-like FinSubsequence-like set
C is non empty non trivial V13() V16( NAT ) Function-like V26() FinSequence-like FinSubsequence-like set
Rev C is non empty V13() V16( NAT ) Function-like V26() FinSequence-like FinSubsequence-like set
n is set
<*n*> is non empty trivial V13() V16( NAT ) Function-like constant V26() 1 -element FinSequence-like FinSubsequence-like set
n is set
<*n*> is non empty trivial V13() V16( NAT ) Function-like constant V26() 1 -element FinSequence-like FinSubsequence-like set
Rev <*n*> is non empty V13() V16( NAT ) Function-like V26() FinSequence-like FinSubsequence-like set
C is non empty set
K238(C) is non empty functional FinSequence-membered M11(C)
n is V13() V16( NAT ) V17(C) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of C
i is V13() V16( NAT ) V17(K238(C)) Function-like V26() FinSequence-like FinSubsequence-like tabular FinSequence of K238(C)
j is set
n -: j is V13() V16( NAT ) V17(C) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of C
j .. n is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
n | (j .. n) is V13() V16( NAT ) V17(C) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of C
C is non empty set
K238(C) is non empty functional FinSequence-membered M11(C)
n is V13() V16( NAT ) V17(C) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of C
rng n is V26() set
i is V13() V16( NAT ) V17(K238(C)) Function-like V26() FinSequence-like FinSubsequence-like tabular FinSequence of K238(C)
j is Element of C
n :- j is non empty V13() V16( NAT ) V17(C) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of C
j .. n is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
Emax is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
Emax + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
n /^ Emax is V13() V16( NAT ) V17(C) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of C
C is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
n is non empty connected compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
Upper_Seq (n,C) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
Gauge (n,C) is V13() non empty-yielding V16( NAT ) V17(K238( the U1 of (TOP-REAL 2))) Function-like V26() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K238( the U1 of (TOP-REAL 2))
Cage (n,C) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
L~ (Cage (n,C)) is non empty closed connected V222() compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
W-min (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
W-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (n,C))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | (L~ (Cage (n,C))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:]
the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:] is set
K506(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj1 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
W-most (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
SW-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
proj2 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | (L~ (Cage (n,C))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:]
K506(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj2 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (n,C)))),(S-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
NW-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj2 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (n,C)))),(N-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (n,C)))),(NW-corner (L~ (Cage (n,C))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Cage (n,C)))),(NW-corner (L~ (Cage (n,C)))))) /\ (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ (Cage (n,C)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Cage (n,C)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),REAL:]
the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))) is set
[: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),REAL:] is set
K506(((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),(proj2 | (W-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (n,C)))),K506(((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),(proj2 | (W-most (L~ (Cage (n,C))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C))))) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
E-max (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj1 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
E-most (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
SE-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
|[(E-bound (L~ (Cage (n,C)))),(S-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
NE-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
|[(E-bound (L~ (Cage (n,C)))),(N-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Cage (n,C)))),(NE-corner (L~ (Cage (n,C))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SE-corner (L~ (Cage (n,C)))),(NE-corner (L~ (Cage (n,C)))))) /\ (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ (Cage (n,C)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Cage (n,C)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),REAL:]
the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))) is set
[: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),REAL:] is set
K507(((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),(proj2 | (E-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (n,C)))),K507(((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),(proj2 | (E-most (L~ (Cage (n,C))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
(Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) -: (E-max (L~ (Cage (n,C)))) is V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like special unfolded FinSequence of the U1 of (TOP-REAL 2)
C is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
n is non empty connected compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
Lower_Seq (n,C) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
Gauge (n,C) is V13() non empty-yielding V16( NAT ) V17(K238( the U1 of (TOP-REAL 2))) Function-like V26() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K238( the U1 of (TOP-REAL 2))
Cage (n,C) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
L~ (Cage (n,C)) is non empty closed connected V222() compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
W-min (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
W-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (n,C))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | (L~ (Cage (n,C))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:]
the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:] is set
K506(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj1 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
W-most (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
SW-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
proj2 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | (L~ (Cage (n,C))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:]
K506(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj2 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (n,C)))),(S-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
NW-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj2 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (n,C)))),(N-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (n,C)))),(NW-corner (L~ (Cage (n,C))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Cage (n,C)))),(NW-corner (L~ (Cage (n,C)))))) /\ (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ (Cage (n,C)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Cage (n,C)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),REAL:]
the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))) is set
[: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),REAL:] is set
K506(((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),(proj2 | (W-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (n,C)))),K506(((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),(proj2 | (W-most (L~ (Cage (n,C))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C))))) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
E-max (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj1 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
E-most (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
SE-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
|[(E-bound (L~ (Cage (n,C)))),(S-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
NE-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
|[(E-bound (L~ (Cage (n,C)))),(N-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Cage (n,C)))),(NE-corner (L~ (Cage (n,C))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SE-corner (L~ (Cage (n,C)))),(NE-corner (L~ (Cage (n,C)))))) /\ (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ (Cage (n,C)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Cage (n,C)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),REAL:]
the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))) is set
[: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),REAL:] is set
K507(((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),(proj2 | (E-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (n,C)))),K507(((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),(proj2 | (E-most (L~ (Cage (n,C))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
rng (Cage (n,C)) is non empty non trivial V26() set
rng (Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) is non empty non trivial V26() set
(Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) :- (E-max (L~ (Cage (n,C)))) is non empty V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
C is non empty connected compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
n is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
Upper_Seq (C,n) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
Gauge (C,n) is V13() non empty-yielding V16( NAT ) V17(K238( the U1 of (TOP-REAL 2))) Function-like V26() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K238( the U1 of (TOP-REAL 2))
Lower_Seq (C,n) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
Gauge (C,n) is V13() non empty-yielding V16( NAT ) V17(K238( the U1 of (TOP-REAL 2))) Function-like V26() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K238( the U1 of (TOP-REAL 2))
C is V13() V16( NAT ) V17(K238( the U1 of (TOP-REAL 2))) Function-like V26() FinSequence-like FinSubsequence-like tabular Y_equal-in-column Y_increasing-in-line FinSequence of K238( the U1 of (TOP-REAL 2))
Indices C is set
n is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
j is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
[n,j] is non empty set
{n,j} is non empty V26() V30() V200() V201() V202() V203() V204() V205() set
{n} is non empty trivial V26() V30() 1 -element V200() V201() V202() V203() V204() V205() set
{{n,j},{n}} is non empty V26() V30() set
i is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
Emax is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
[i,Emax] is non empty set
{i,Emax} is non empty V26() V30() V200() V201() V202() V203() V204() V205() set
{i} is non empty trivial V26() V30() 1 -element V200() V201() V202() V203() V204() V205() set
{{i,Emax},{i}} is non empty V26() V30() set
C * (n,j) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(C * (n,j)) `2 is V11() V12() ext-real Element of REAL
C * (i,Emax) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(C * (i,Emax)) `2 is V11() V12() ext-real Element of REAL
width C is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
len C is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
C * (n,Emax) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(C * (n,Emax)) `2 is V11() V12() ext-real Element of REAL
C * (1,Emax) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(C * (1,Emax)) `2 is V11() V12() ext-real Element of REAL
C is V13() V16( NAT ) V17(K238( the U1 of (TOP-REAL 2))) Function-like V26() FinSequence-like FinSubsequence-like tabular X_equal-in-line X_increasing-in-column FinSequence of K238( the U1 of (TOP-REAL 2))
Indices C is set
n is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
j is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
[n,j] is non empty set
{n,j} is non empty V26() V30() V200() V201() V202() V203() V204() V205() set
{n} is non empty trivial V26() V30() 1 -element V200() V201() V202() V203() V204() V205() set
{{n,j},{n}} is non empty V26() V30() set
i is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
Emax is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
[i,Emax] is non empty set
{i,Emax} is non empty V26() V30() V200() V201() V202() V203() V204() V205() set
{i} is non empty trivial V26() V30() 1 -element V200() V201() V202() V203() V204() V205() set
{{i,Emax},{i}} is non empty V26() V30() set
C * (n,j) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(C * (n,j)) `1 is V11() V12() ext-real Element of REAL
C * (i,Emax) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(C * (i,Emax)) `1 is V11() V12() ext-real Element of REAL
len C is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
width C is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
C * (n,1) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(C * (n,1)) `1 is V11() V12() ext-real Element of REAL
C * (n,Emax) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(C * (n,Emax)) `1 is V11() V12() ext-real Element of REAL
C is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like special unfolded standard FinSequence of the U1 of (TOP-REAL 2)
C /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
L~ C is non empty closed compact Element of bool the U1 of (TOP-REAL 2)
N-min (L~ C) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
N-most (L~ C) is Element of bool the U1 of (TOP-REAL 2)
NW-corner (L~ C) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
W-bound (L~ C) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ C) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | (L~ C) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ C)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ C)),REAL:]
the U1 of ((TOP-REAL 2) | (L~ C)) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ C)),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (L~ C)),REAL:] is set
K506(((TOP-REAL 2) | (L~ C)),(proj1 | (L~ C))) is V11() V12() ext-real Element of REAL
N-bound (L~ C) is V11() V12() ext-real Element of REAL
proj2 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | (L~ C) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ C)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ C)),REAL:]
K507(((TOP-REAL 2) | (L~ C)),(proj2 | (L~ C))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ C)),(N-bound (L~ C))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
NE-corner (L~ C) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
E-bound (L~ C) is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | (L~ C)),(proj1 | (L~ C))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ C)),(N-bound (L~ C))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((NW-corner (L~ C)),(NE-corner (L~ C))) is closed closed connected compact compact horizontal Element of bool the U1 of (TOP-REAL 2)
(LSeg ((NW-corner (L~ C)),(NE-corner (L~ C)))) /\ (L~ C) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (N-most (L~ C)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most (L~ C)) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (N-most (L~ C))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (N-most (L~ C))),REAL:]
the U1 of ((TOP-REAL 2) | (N-most (L~ C))) is set
[: the U1 of ((TOP-REAL 2) | (N-most (L~ C))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (N-most (L~ C))),REAL:] is set
K506(((TOP-REAL 2) | (N-most (L~ C))),(proj1 | (N-most (L~ C)))) is V11() V12() ext-real Element of REAL
|[K506(((TOP-REAL 2) | (N-most (L~ C))),(proj1 | (N-most (L~ C)))),(N-bound (L~ C))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
len C is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
C /. (len C) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
N-max (L~ C) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
K507(((TOP-REAL 2) | (N-most (L~ C))),(proj1 | (N-most (L~ C)))) is V11() V12() ext-real Element of REAL
|[K507(((TOP-REAL 2) | (N-most (L~ C))),(proj1 | (N-most (L~ C)))),(N-bound (L~ C))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
(N-max (L~ C)) `1 is V11() V12() ext-real Element of REAL
(N-min (L~ C)) `1 is V11() V12() ext-real Element of REAL
(N-min (L~ C)) .. C is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(N-min (L~ C)) `2 is V11() V12() ext-real Element of REAL
rng C is non empty V26() set
dom C is non empty non trivial V26() V200() V201() V202() V203() V204() V205() Element of bool NAT
C . ((N-min (L~ C)) .. C) is set
C /. ((N-min (L~ C)) .. C) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(N-max (L~ C)) `2 is V11() V12() ext-real Element of REAL
(N-max (L~ C)) `2 is V11() V12() ext-real Element of REAL
((N-min (L~ C)) .. C) -' 1 is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(((N-min (L~ C)) .. C) -' 1) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
C /. (((N-min (L~ C)) .. C) -' 1) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg (C,(((N-min (L~ C)) .. C) -' 1)) is closed Element of bool the U1 of (TOP-REAL 2)
((N-min (L~ C)) .. C) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
C /. (((N-min (L~ C)) .. C) + 1) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg (C,((N-min (L~ C)) .. C)) is closed Element of bool the U1 of (TOP-REAL 2)
(C /. (((N-min (L~ C)) .. C) + 1)) `1 is V11() V12() ext-real Element of REAL
(C /. (((N-min (L~ C)) .. C) -' 1)) `1 is V11() V12() ext-real Element of REAL
(C /. (((N-min (L~ C)) .. C) + 1)) `2 is V11() V12() ext-real Element of REAL
(C /. (((N-min (L~ C)) .. C) -' 1)) `2 is V11() V12() ext-real Element of REAL
LSeg ((C /. ((N-min (L~ C)) .. C)),(C /. (((N-min (L~ C)) .. C) + 1))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
LSeg ((C /. ((N-min (L~ C)) .. C)),(C /. (((N-min (L~ C)) .. C) -' 1))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg (C,(((N-min (L~ C)) .. C) -' 1))) /\ (LSeg (C,((N-min (L~ C)) .. C))) is Element of bool the U1 of (TOP-REAL 2)
((((N-min (L~ C)) .. C) -' 1) + 1) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
1 + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(((N-min (L~ C)) .. C) -' 1) + (1 + 1) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
{(C /. ((N-min (L~ C)) .. C))} is non empty trivial V26() 1 -element set
(C /. (((N-min (L~ C)) .. C) -' 1)) `2 is V11() V12() ext-real Element of REAL
(C /. (((N-min (L~ C)) .. C) -' 1)) `1 is V11() V12() ext-real Element of REAL
(C /. (((N-min (L~ C)) .. C) + 1)) `2 is V11() V12() ext-real Element of REAL
(C /. (((N-min (L~ C)) .. C) + 1)) `1 is V11() V12() ext-real Element of REAL
C is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like special unfolded standard FinSequence of the U1 of (TOP-REAL 2)
C /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
L~ C is non empty closed compact Element of bool the U1 of (TOP-REAL 2)
N-min (L~ C) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
N-most (L~ C) is Element of bool the U1 of (TOP-REAL 2)
NW-corner (L~ C) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
W-bound (L~ C) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ C) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | (L~ C) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ C)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ C)),REAL:]
the U1 of ((TOP-REAL 2) | (L~ C)) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ C)),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (L~ C)),REAL:] is set
K506(((TOP-REAL 2) | (L~ C)),(proj1 | (L~ C))) is V11() V12() ext-real Element of REAL
N-bound (L~ C) is V11() V12() ext-real Element of REAL
proj2 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | (L~ C) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ C)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ C)),REAL:]
K507(((TOP-REAL 2) | (L~ C)),(proj2 | (L~ C))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ C)),(N-bound (L~ C))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
NE-corner (L~ C) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
E-bound (L~ C) is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | (L~ C)),(proj1 | (L~ C))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ C)),(N-bound (L~ C))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((NW-corner (L~ C)),(NE-corner (L~ C))) is closed closed connected compact compact horizontal Element of bool the U1 of (TOP-REAL 2)
(LSeg ((NW-corner (L~ C)),(NE-corner (L~ C)))) /\ (L~ C) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (N-most (L~ C)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most (L~ C)) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (N-most (L~ C))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (N-most (L~ C))),REAL:]
the U1 of ((TOP-REAL 2) | (N-most (L~ C))) is set
[: the U1 of ((TOP-REAL 2) | (N-most (L~ C))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (N-most (L~ C))),REAL:] is set
K506(((TOP-REAL 2) | (N-most (L~ C))),(proj1 | (N-most (L~ C)))) is V11() V12() ext-real Element of REAL
|[K506(((TOP-REAL 2) | (N-most (L~ C))),(proj1 | (N-most (L~ C)))),(N-bound (L~ C))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
len C is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
C /. (len C) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
N-max (L~ C) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
K507(((TOP-REAL 2) | (N-most (L~ C))),(proj1 | (N-most (L~ C)))) is V11() V12() ext-real Element of REAL
|[K507(((TOP-REAL 2) | (N-most (L~ C))),(proj1 | (N-most (L~ C)))),(N-bound (L~ C))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
(N-max (L~ C)) `1 is V11() V12() ext-real Element of REAL
(N-min (L~ C)) `1 is V11() V12() ext-real Element of REAL
C is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like special unfolded standard FinSequence of the U1 of (TOP-REAL 2)
C /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
L~ C is non empty closed compact Element of bool the U1 of (TOP-REAL 2)
S-min (L~ C) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
S-most (L~ C) is Element of bool the U1 of (TOP-REAL 2)
SW-corner (L~ C) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
W-bound (L~ C) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ C) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | (L~ C) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ C)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ C)),REAL:]
the U1 of ((TOP-REAL 2) | (L~ C)) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ C)),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (L~ C)),REAL:] is set
K506(((TOP-REAL 2) | (L~ C)),(proj1 | (L~ C))) is V11() V12() ext-real Element of REAL
S-bound (L~ C) is V11() V12() ext-real Element of REAL
proj2 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | (L~ C) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ C)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ C)),REAL:]
K506(((TOP-REAL 2) | (L~ C)),(proj2 | (L~ C))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ C)),(S-bound (L~ C))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
SE-corner (L~ C) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
E-bound (L~ C) is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | (L~ C)),(proj1 | (L~ C))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ C)),(S-bound (L~ C))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ C)),(SE-corner (L~ C))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ C)),(SE-corner (L~ C)))) /\ (L~ C) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (S-most (L~ C)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (S-most (L~ C)) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (S-most (L~ C))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (S-most (L~ C))),REAL:]
the U1 of ((TOP-REAL 2) | (S-most (L~ C))) is set
[: the U1 of ((TOP-REAL 2) | (S-most (L~ C))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (S-most (L~ C))),REAL:] is set
K506(((TOP-REAL 2) | (S-most (L~ C))),(proj1 | (S-most (L~ C)))) is V11() V12() ext-real Element of REAL
|[K506(((TOP-REAL 2) | (S-most (L~ C))),(proj1 | (S-most (L~ C)))),(S-bound (L~ C))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
len C is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
C /. (len C) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
S-max (L~ C) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
K507(((TOP-REAL 2) | (S-most (L~ C))),(proj1 | (S-most (L~ C)))) is V11() V12() ext-real Element of REAL
|[K507(((TOP-REAL 2) | (S-most (L~ C))),(proj1 | (S-most (L~ C)))),(S-bound (L~ C))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
(S-max (L~ C)) `1 is V11() V12() ext-real Element of REAL
(S-min (L~ C)) `1 is V11() V12() ext-real Element of REAL
(S-min (L~ C)) .. C is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(S-min (L~ C)) `2 is V11() V12() ext-real Element of REAL
rng C is non empty V26() set
dom C is non empty non trivial V26() V200() V201() V202() V203() V204() V205() Element of bool NAT
C . ((S-min (L~ C)) .. C) is set
C /. ((S-min (L~ C)) .. C) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(S-max (L~ C)) `2 is V11() V12() ext-real Element of REAL
(S-max (L~ C)) `2 is V11() V12() ext-real Element of REAL
((S-min (L~ C)) .. C) -' 1 is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(((S-min (L~ C)) .. C) -' 1) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
C /. (((S-min (L~ C)) .. C) -' 1) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg (C,(((S-min (L~ C)) .. C) -' 1)) is closed Element of bool the U1 of (TOP-REAL 2)
((S-min (L~ C)) .. C) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
C /. (((S-min (L~ C)) .. C) + 1) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg (C,((S-min (L~ C)) .. C)) is closed Element of bool the U1 of (TOP-REAL 2)
(C /. (((S-min (L~ C)) .. C) + 1)) `1 is V11() V12() ext-real Element of REAL
(C /. (((S-min (L~ C)) .. C) -' 1)) `1 is V11() V12() ext-real Element of REAL
(C /. (((S-min (L~ C)) .. C) + 1)) `2 is V11() V12() ext-real Element of REAL
(C /. (((S-min (L~ C)) .. C) -' 1)) `2 is V11() V12() ext-real Element of REAL
LSeg ((C /. ((S-min (L~ C)) .. C)),(C /. (((S-min (L~ C)) .. C) + 1))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
LSeg ((C /. ((S-min (L~ C)) .. C)),(C /. (((S-min (L~ C)) .. C) -' 1))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg (C,(((S-min (L~ C)) .. C) -' 1))) /\ (LSeg (C,((S-min (L~ C)) .. C))) is Element of bool the U1 of (TOP-REAL 2)
((((S-min (L~ C)) .. C) -' 1) + 1) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
1 + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(((S-min (L~ C)) .. C) -' 1) + (1 + 1) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
{(C /. ((S-min (L~ C)) .. C))} is non empty trivial V26() 1 -element set
(C /. (((S-min (L~ C)) .. C) -' 1)) `2 is V11() V12() ext-real Element of REAL
(C /. (((S-min (L~ C)) .. C) -' 1)) `1 is V11() V12() ext-real Element of REAL
(C /. (((S-min (L~ C)) .. C) + 1)) `2 is V11() V12() ext-real Element of REAL
(C /. (((S-min (L~ C)) .. C) + 1)) `1 is V11() V12() ext-real Element of REAL
C is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like special unfolded standard FinSequence of the U1 of (TOP-REAL 2)
C /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
L~ C is non empty closed compact Element of bool the U1 of (TOP-REAL 2)
S-min (L~ C) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
S-most (L~ C) is Element of bool the U1 of (TOP-REAL 2)
SW-corner (L~ C) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
W-bound (L~ C) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ C) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | (L~ C) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ C)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ C)),REAL:]
the U1 of ((TOP-REAL 2) | (L~ C)) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ C)),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (L~ C)),REAL:] is set
K506(((TOP-REAL 2) | (L~ C)),(proj1 | (L~ C))) is V11() V12() ext-real Element of REAL
S-bound (L~ C) is V11() V12() ext-real Element of REAL
proj2 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | (L~ C) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ C)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ C)),REAL:]
K506(((TOP-REAL 2) | (L~ C)),(proj2 | (L~ C))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ C)),(S-bound (L~ C))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
SE-corner (L~ C) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
E-bound (L~ C) is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | (L~ C)),(proj1 | (L~ C))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ C)),(S-bound (L~ C))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ C)),(SE-corner (L~ C))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ C)),(SE-corner (L~ C)))) /\ (L~ C) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (S-most (L~ C)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (S-most (L~ C)) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (S-most (L~ C))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (S-most (L~ C))),REAL:]
the U1 of ((TOP-REAL 2) | (S-most (L~ C))) is set
[: the U1 of ((TOP-REAL 2) | (S-most (L~ C))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (S-most (L~ C))),REAL:] is set
K506(((TOP-REAL 2) | (S-most (L~ C))),(proj1 | (S-most (L~ C)))) is V11() V12() ext-real Element of REAL
|[K506(((TOP-REAL 2) | (S-most (L~ C))),(proj1 | (S-most (L~ C)))),(S-bound (L~ C))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
len C is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
C /. (len C) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
S-max (L~ C) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
K507(((TOP-REAL 2) | (S-most (L~ C))),(proj1 | (S-most (L~ C)))) is V11() V12() ext-real Element of REAL
|[K507(((TOP-REAL 2) | (S-most (L~ C))),(proj1 | (S-most (L~ C)))),(S-bound (L~ C))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
(S-max (L~ C)) `1 is V11() V12() ext-real Element of REAL
(S-min (L~ C)) `1 is V11() V12() ext-real Element of REAL
C is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like special unfolded standard FinSequence of the U1 of (TOP-REAL 2)
C /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
L~ C is non empty closed compact Element of bool the U1 of (TOP-REAL 2)
W-min (L~ C) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
W-bound (L~ C) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ C) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | (L~ C) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ C)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ C)),REAL:]
the U1 of ((TOP-REAL 2) | (L~ C)) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ C)),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (L~ C)),REAL:] is set
K506(((TOP-REAL 2) | (L~ C)),(proj1 | (L~ C))) is V11() V12() ext-real Element of REAL
W-most (L~ C) is Element of bool the U1 of (TOP-REAL 2)
SW-corner (L~ C) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
S-bound (L~ C) is V11() V12() ext-real Element of REAL
proj2 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | (L~ C) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ C)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ C)),REAL:]
K506(((TOP-REAL 2) | (L~ C)),(proj2 | (L~ C))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ C)),(S-bound (L~ C))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
NW-corner (L~ C) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
N-bound (L~ C) is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | (L~ C)),(proj2 | (L~ C))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ C)),(N-bound (L~ C))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ C)),(NW-corner (L~ C))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ C)),(NW-corner (L~ C)))) /\ (L~ C) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ C)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ C)) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (W-most (L~ C))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ C))),REAL:]
the U1 of ((TOP-REAL 2) | (W-most (L~ C))) is set
[: the U1 of ((TOP-REAL 2) | (W-most (L~ C))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ C))),REAL:] is set
K506(((TOP-REAL 2) | (W-most (L~ C))),(proj2 | (W-most (L~ C)))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ C)),K506(((TOP-REAL 2) | (W-most (L~ C))),(proj2 | (W-most (L~ C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
len C is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
C /. (len C) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
W-max (L~ C) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
K507(((TOP-REAL 2) | (W-most (L~ C))),(proj2 | (W-most (L~ C)))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ C)),K507(((TOP-REAL 2) | (W-most (L~ C))),(proj2 | (W-most (L~ C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
(W-max (L~ C)) `2 is V11() V12() ext-real Element of REAL
(W-min (L~ C)) `2 is V11() V12() ext-real Element of REAL
(W-min (L~ C)) .. C is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(W-min (L~ C)) `1 is V11() V12() ext-real Element of REAL
rng C is non empty V26() set
dom C is non empty non trivial V26() V200() V201() V202() V203() V204() V205() Element of bool NAT
C . ((W-min (L~ C)) .. C) is set
C /. ((W-min (L~ C)) .. C) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(W-max (L~ C)) `1 is V11() V12() ext-real Element of REAL
(W-max (L~ C)) `1 is V11() V12() ext-real Element of REAL
((W-min (L~ C)) .. C) -' 1 is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(((W-min (L~ C)) .. C) -' 1) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
C /. (((W-min (L~ C)) .. C) -' 1) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg (C,(((W-min (L~ C)) .. C) -' 1)) is closed Element of bool the U1 of (TOP-REAL 2)
((W-min (L~ C)) .. C) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
C /. (((W-min (L~ C)) .. C) + 1) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg (C,((W-min (L~ C)) .. C)) is closed Element of bool the U1 of (TOP-REAL 2)
(C /. (((W-min (L~ C)) .. C) + 1)) `2 is V11() V12() ext-real Element of REAL
(C /. (((W-min (L~ C)) .. C) -' 1)) `2 is V11() V12() ext-real Element of REAL
(C /. (((W-min (L~ C)) .. C) + 1)) `1 is V11() V12() ext-real Element of REAL
(C /. (((W-min (L~ C)) .. C) -' 1)) `1 is V11() V12() ext-real Element of REAL
LSeg ((C /. ((W-min (L~ C)) .. C)),(C /. (((W-min (L~ C)) .. C) + 1))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
LSeg ((C /. ((W-min (L~ C)) .. C)),(C /. (((W-min (L~ C)) .. C) -' 1))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg (C,(((W-min (L~ C)) .. C) -' 1))) /\ (LSeg (C,((W-min (L~ C)) .. C))) is Element of bool the U1 of (TOP-REAL 2)
((((W-min (L~ C)) .. C) -' 1) + 1) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
1 + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(((W-min (L~ C)) .. C) -' 1) + (1 + 1) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
{(C /. ((W-min (L~ C)) .. C))} is non empty trivial V26() 1 -element set
(C /. (((W-min (L~ C)) .. C) -' 1)) `1 is V11() V12() ext-real Element of REAL
(C /. (((W-min (L~ C)) .. C) -' 1)) `2 is V11() V12() ext-real Element of REAL
(C /. (((W-min (L~ C)) .. C) + 1)) `1 is V11() V12() ext-real Element of REAL
(C /. (((W-min (L~ C)) .. C) + 1)) `2 is V11() V12() ext-real Element of REAL
C is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like special unfolded standard FinSequence of the U1 of (TOP-REAL 2)
C /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
L~ C is non empty closed compact Element of bool the U1 of (TOP-REAL 2)
W-min (L~ C) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
W-bound (L~ C) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ C) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | (L~ C) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ C)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ C)),REAL:]
the U1 of ((TOP-REAL 2) | (L~ C)) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ C)),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (L~ C)),REAL:] is set
K506(((TOP-REAL 2) | (L~ C)),(proj1 | (L~ C))) is V11() V12() ext-real Element of REAL
W-most (L~ C) is Element of bool the U1 of (TOP-REAL 2)
SW-corner (L~ C) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
S-bound (L~ C) is V11() V12() ext-real Element of REAL
proj2 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | (L~ C) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ C)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ C)),REAL:]
K506(((TOP-REAL 2) | (L~ C)),(proj2 | (L~ C))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ C)),(S-bound (L~ C))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
NW-corner (L~ C) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
N-bound (L~ C) is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | (L~ C)),(proj2 | (L~ C))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ C)),(N-bound (L~ C))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ C)),(NW-corner (L~ C))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ C)),(NW-corner (L~ C)))) /\ (L~ C) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ C)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ C)) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (W-most (L~ C))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ C))),REAL:]
the U1 of ((TOP-REAL 2) | (W-most (L~ C))) is set
[: the U1 of ((TOP-REAL 2) | (W-most (L~ C))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ C))),REAL:] is set
K506(((TOP-REAL 2) | (W-most (L~ C))),(proj2 | (W-most (L~ C)))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ C)),K506(((TOP-REAL 2) | (W-most (L~ C))),(proj2 | (W-most (L~ C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
len C is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
C /. (len C) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
W-max (L~ C) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
K507(((TOP-REAL 2) | (W-most (L~ C))),(proj2 | (W-most (L~ C)))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ C)),K507(((TOP-REAL 2) | (W-most (L~ C))),(proj2 | (W-most (L~ C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
(W-max (L~ C)) `2 is V11() V12() ext-real Element of REAL
(W-min (L~ C)) `2 is V11() V12() ext-real Element of REAL
C is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like special unfolded standard FinSequence of the U1 of (TOP-REAL 2)
C /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
L~ C is non empty closed compact Element of bool the U1 of (TOP-REAL 2)
E-min (L~ C) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
E-bound (L~ C) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ C) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | (L~ C) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ C)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ C)),REAL:]
the U1 of ((TOP-REAL 2) | (L~ C)) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ C)),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (L~ C)),REAL:] is set
K507(((TOP-REAL 2) | (L~ C)),(proj1 | (L~ C))) is V11() V12() ext-real Element of REAL
E-most (L~ C) is Element of bool the U1 of (TOP-REAL 2)
SE-corner (L~ C) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
S-bound (L~ C) is V11() V12() ext-real Element of REAL
proj2 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | (L~ C) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ C)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ C)),REAL:]
K506(((TOP-REAL 2) | (L~ C)),(proj2 | (L~ C))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ C)),(S-bound (L~ C))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
NE-corner (L~ C) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
N-bound (L~ C) is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | (L~ C)),(proj2 | (L~ C))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ C)),(N-bound (L~ C))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ C)),(NE-corner (L~ C))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SE-corner (L~ C)),(NE-corner (L~ C)))) /\ (L~ C) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ C)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ C)) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (E-most (L~ C))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ C))),REAL:]
the U1 of ((TOP-REAL 2) | (E-most (L~ C))) is set
[: the U1 of ((TOP-REAL 2) | (E-most (L~ C))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ C))),REAL:] is set
K506(((TOP-REAL 2) | (E-most (L~ C))),(proj2 | (E-most (L~ C)))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ C)),K506(((TOP-REAL 2) | (E-most (L~ C))),(proj2 | (E-most (L~ C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
len C is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
C /. (len C) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
E-max (L~ C) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
K507(((TOP-REAL 2) | (E-most (L~ C))),(proj2 | (E-most (L~ C)))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ C)),K507(((TOP-REAL 2) | (E-most (L~ C))),(proj2 | (E-most (L~ C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
(E-max (L~ C)) `2 is V11() V12() ext-real Element of REAL
(E-min (L~ C)) `2 is V11() V12() ext-real Element of REAL
(E-min (L~ C)) .. C is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(E-min (L~ C)) `1 is V11() V12() ext-real Element of REAL
rng C is non empty V26() set
dom C is non empty non trivial V26() V200() V201() V202() V203() V204() V205() Element of bool NAT
C . ((E-min (L~ C)) .. C) is set
C /. ((E-min (L~ C)) .. C) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(E-max (L~ C)) `1 is V11() V12() ext-real Element of REAL
(E-max (L~ C)) `1 is V11() V12() ext-real Element of REAL
((E-min (L~ C)) .. C) -' 1 is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(((E-min (L~ C)) .. C) -' 1) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
C /. (((E-min (L~ C)) .. C) -' 1) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg (C,(((E-min (L~ C)) .. C) -' 1)) is closed Element of bool the U1 of (TOP-REAL 2)
((E-min (L~ C)) .. C) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
C /. (((E-min (L~ C)) .. C) + 1) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg (C,((E-min (L~ C)) .. C)) is closed Element of bool the U1 of (TOP-REAL 2)
(C /. (((E-min (L~ C)) .. C) + 1)) `2 is V11() V12() ext-real Element of REAL
(C /. (((E-min (L~ C)) .. C) -' 1)) `2 is V11() V12() ext-real Element of REAL
(C /. (((E-min (L~ C)) .. C) + 1)) `1 is V11() V12() ext-real Element of REAL
(C /. (((E-min (L~ C)) .. C) -' 1)) `1 is V11() V12() ext-real Element of REAL
LSeg ((C /. ((E-min (L~ C)) .. C)),(C /. (((E-min (L~ C)) .. C) + 1))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
LSeg ((C /. ((E-min (L~ C)) .. C)),(C /. (((E-min (L~ C)) .. C) -' 1))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg (C,(((E-min (L~ C)) .. C) -' 1))) /\ (LSeg (C,((E-min (L~ C)) .. C))) is Element of bool the U1 of (TOP-REAL 2)
((((E-min (L~ C)) .. C) -' 1) + 1) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
1 + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(((E-min (L~ C)) .. C) -' 1) + (1 + 1) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
{(C /. ((E-min (L~ C)) .. C))} is non empty trivial V26() 1 -element set
(C /. (((E-min (L~ C)) .. C) -' 1)) `1 is V11() V12() ext-real Element of REAL
(C /. (((E-min (L~ C)) .. C) -' 1)) `2 is V11() V12() ext-real Element of REAL
(C /. (((E-min (L~ C)) .. C) + 1)) `1 is V11() V12() ext-real Element of REAL
(C /. (((E-min (L~ C)) .. C) + 1)) `2 is V11() V12() ext-real Element of REAL
C is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like special unfolded standard FinSequence of the U1 of (TOP-REAL 2)
C /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
L~ C is non empty closed compact Element of bool the U1 of (TOP-REAL 2)
E-min (L~ C) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
E-bound (L~ C) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ C) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | (L~ C) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ C)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ C)),REAL:]
the U1 of ((TOP-REAL 2) | (L~ C)) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ C)),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (L~ C)),REAL:] is set
K507(((TOP-REAL 2) | (L~ C)),(proj1 | (L~ C))) is V11() V12() ext-real Element of REAL
E-most (L~ C) is Element of bool the U1 of (TOP-REAL 2)
SE-corner (L~ C) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
S-bound (L~ C) is V11() V12() ext-real Element of REAL
proj2 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | (L~ C) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ C)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ C)),REAL:]
K506(((TOP-REAL 2) | (L~ C)),(proj2 | (L~ C))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ C)),(S-bound (L~ C))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
NE-corner (L~ C) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
N-bound (L~ C) is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | (L~ C)),(proj2 | (L~ C))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ C)),(N-bound (L~ C))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ C)),(NE-corner (L~ C))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SE-corner (L~ C)),(NE-corner (L~ C)))) /\ (L~ C) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ C)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ C)) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (E-most (L~ C))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ C))),REAL:]
the U1 of ((TOP-REAL 2) | (E-most (L~ C))) is set
[: the U1 of ((TOP-REAL 2) | (E-most (L~ C))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ C))),REAL:] is set
K506(((TOP-REAL 2) | (E-most (L~ C))),(proj2 | (E-most (L~ C)))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ C)),K506(((TOP-REAL 2) | (E-most (L~ C))),(proj2 | (E-most (L~ C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
len C is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
C /. (len C) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
E-max (L~ C) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
K507(((TOP-REAL 2) | (E-most (L~ C))),(proj2 | (E-most (L~ C)))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ C)),K507(((TOP-REAL 2) | (E-most (L~ C))),(proj2 | (E-most (L~ C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
(E-max (L~ C)) `2 is V11() V12() ext-real Element of REAL
(E-min (L~ C)) `2 is V11() V12() ext-real Element of REAL
C is non empty set
n is V13() V16( NAT ) V17(C) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of C
rng n is V26() set
i is Element of C
j is Element of C
j .. n is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
i .. n is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
n -: i is V13() V16( NAT ) V17(C) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of C
(n -: i) :- j is non empty V13() V16( NAT ) V17(C) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of C
n :- j is non empty V13() V16( NAT ) V17(C) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of C
(n :- j) -: i is V13() V16( NAT ) V17(C) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of C
n | (i .. n) is V13() V16( NAT ) V17(C) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of C
i .. (n :- j) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(n :- j) | (i .. (n :- j)) is V13() V16( NAT ) V17(C) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of C
Emax is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
Emax + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
n /^ Emax is V13() V16( NAT ) V17(C) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of C
i .. (n /^ Emax) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
Emax + (i .. (n /^ Emax)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(i .. n) - Emax is V11() V12() ext-real set
(i .. n) -' Emax is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
rng (n -: i) is V26() set
j .. (n -: i) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
Nbo is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
Nbo + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(n -: i) /^ Nbo is V13() V16( NAT ) V17(C) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of C
C is non empty connected compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
n is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
Cage (C,n) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
L~ (Cage (C,n)) is non empty closed connected V222() compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
W-min (L~ (Cage (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
W-bound (L~ (Cage (C,n))) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (C,n))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | (L~ (Cage (C,n))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL:]
the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL:] is set
K506(((TOP-REAL 2) | (L~ (Cage (C,n)))),(proj1 | (L~ (Cage (C,n))))) is V11() V12() ext-real Element of REAL
W-most (L~ (Cage (C,n))) is Element of bool the U1 of (TOP-REAL 2)
SW-corner (L~ (Cage (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Cage (C,n))) is V11() V12() ext-real Element of REAL
proj2 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | (L~ (Cage (C,n))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL:]
K506(((TOP-REAL 2) | (L~ (Cage (C,n)))),(proj2 | (L~ (Cage (C,n))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (C,n)))),(S-bound (L~ (Cage (C,n))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
NW-corner (L~ (Cage (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Cage (C,n))) is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | (L~ (Cage (C,n)))),(proj2 | (L~ (Cage (C,n))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (C,n)))),(N-bound (L~ (Cage (C,n))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (C,n)))),(NW-corner (L~ (Cage (C,n))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Cage (C,n)))),(NW-corner (L~ (Cage (C,n)))))) /\ (L~ (Cage (C,n))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ (Cage (C,n)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Cage (C,n)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),REAL:]
the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))) is set
[: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),REAL:] is set
K506(((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),(proj2 | (W-most (L~ (Cage (C,n)))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (C,n)))),K506(((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),(proj2 | (W-most (L~ (Cage (C,n))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
(Cage (C,n)) -: (W-min (L~ (Cage (C,n)))) is V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like special unfolded FinSequence of the U1 of (TOP-REAL 2)
L~ ((Cage (C,n)) -: (W-min (L~ (Cage (C,n))))) is closed compact Element of bool the U1 of (TOP-REAL 2)
(Cage (C,n)) :- (W-min (L~ (Cage (C,n)))) is non empty V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
L~ ((Cage (C,n)) :- (W-min (L~ (Cage (C,n))))) is closed compact Element of bool the U1 of (TOP-REAL 2)
(L~ ((Cage (C,n)) -: (W-min (L~ (Cage (C,n)))))) /\ (L~ ((Cage (C,n)) :- (W-min (L~ (Cage (C,n)))))) is Element of bool the U1 of (TOP-REAL 2)
N-min (L~ (Cage (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
N-most (L~ (Cage (C,n))) is Element of bool the U1 of (TOP-REAL 2)
NE-corner (L~ (Cage (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Cage (C,n))) is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | (L~ (Cage (C,n)))),(proj1 | (L~ (Cage (C,n))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (C,n)))),(N-bound (L~ (Cage (C,n))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((NW-corner (L~ (Cage (C,n)))),(NE-corner (L~ (Cage (C,n))))) is closed closed connected compact compact horizontal Element of bool the U1 of (TOP-REAL 2)
(LSeg ((NW-corner (L~ (Cage (C,n)))),(NE-corner (L~ (Cage (C,n)))))) /\ (L~ (Cage (C,n))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (N-most (L~ (Cage (C,n)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most (L~ (Cage (C,n)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (C,n))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (C,n))))),REAL:]
the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (C,n))))) is set
[: the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (C,n))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (C,n))))),REAL:] is set
K506(((TOP-REAL 2) | (N-most (L~ (Cage (C,n))))),(proj1 | (N-most (L~ (Cage (C,n)))))) is V11() V12() ext-real Element of REAL
|[K506(((TOP-REAL 2) | (N-most (L~ (Cage (C,n))))),(proj1 | (N-most (L~ (Cage (C,n)))))),(N-bound (L~ (Cage (C,n))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
{(N-min (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n))))} is non empty V26() set
N-max (L~ (Cage (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
K507(((TOP-REAL 2) | (N-most (L~ (Cage (C,n))))),(proj1 | (N-most (L~ (Cage (C,n)))))) is V11() V12() ext-real Element of REAL
|[K507(((TOP-REAL 2) | (N-most (L~ (Cage (C,n))))),(proj1 | (N-most (L~ (Cage (C,n)))))),(N-bound (L~ (Cage (C,n))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
S-max (L~ (Cage (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
S-most (L~ (Cage (C,n))) is Element of bool the U1 of (TOP-REAL 2)
SE-corner (L~ (Cage (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
|[(E-bound (L~ (Cage (C,n)))),(S-bound (L~ (Cage (C,n))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (C,n)))),(SE-corner (L~ (Cage (C,n))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Cage (C,n)))),(SE-corner (L~ (Cage (C,n)))))) /\ (L~ (Cage (C,n))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (S-most (L~ (Cage (C,n)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (S-most (L~ (Cage (C,n)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (C,n))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (C,n))))),REAL:]
the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (C,n))))) is set
[: the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (C,n))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (C,n))))),REAL:] is set
K507(((TOP-REAL 2) | (S-most (L~ (Cage (C,n))))),(proj1 | (S-most (L~ (Cage (C,n)))))) is V11() V12() ext-real Element of REAL
|[K507(((TOP-REAL 2) | (S-most (L~ (Cage (C,n))))),(proj1 | (S-most (L~ (Cage (C,n)))))),(S-bound (L~ (Cage (C,n))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
S-min (L~ (Cage (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
K506(((TOP-REAL 2) | (S-most (L~ (Cage (C,n))))),(proj1 | (S-most (L~ (Cage (C,n)))))) is V11() V12() ext-real Element of REAL
|[K506(((TOP-REAL 2) | (S-most (L~ (Cage (C,n))))),(proj1 | (S-most (L~ (Cage (C,n)))))),(S-bound (L~ (Cage (C,n))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
E-max (L~ (Cage (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
E-most (L~ (Cage (C,n))) is Element of bool the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Cage (C,n)))),(NE-corner (L~ (Cage (C,n))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SE-corner (L~ (Cage (C,n)))),(NE-corner (L~ (Cage (C,n)))))) /\ (L~ (Cage (C,n))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ (Cage (C,n)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Cage (C,n)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),REAL:]
the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))) is set
[: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),REAL:] is set
K507(((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),(proj2 | (E-most (L~ (Cage (C,n)))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (C,n)))),K507(((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),(proj2 | (E-most (L~ (Cage (C,n))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
E-min (L~ (Cage (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
K506(((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),(proj2 | (E-most (L~ (Cage (C,n)))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (C,n)))),K506(((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),(proj2 | (E-most (L~ (Cage (C,n))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
rng (Cage (C,n)) is non empty non trivial V26() set
len ((Cage (C,n)) -: (W-min (L~ (Cage (C,n))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(W-min (L~ (Cage (C,n)))) .. (Cage (C,n)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
((Cage (C,n)) -: (W-min (L~ (Cage (C,n))))) /. (len ((Cage (C,n)) -: (W-min (L~ (Cage (C,n)))))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
rng ((Cage (C,n)) -: (W-min (L~ (Cage (C,n))))) is V26() set
(Cage (C,n)) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(E-min (L~ (Cage (C,n)))) .. (Cage (C,n)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(E-max (L~ (Cage (C,n)))) .. (Cage (C,n)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(N-max (L~ (Cage (C,n)))) .. (Cage (C,n)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(S-max (L~ (Cage (C,n)))) .. (Cage (C,n)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(S-min (L~ (Cage (C,n)))) .. (Cage (C,n)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
((Cage (C,n)) -: (W-min (L~ (Cage (C,n))))) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
{(N-min (L~ (Cage (C,n)))),(N-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n))))} is V26() set
g is set
card {(N-min (L~ (Cage (C,n)))),(N-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n))))} is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
card (rng ((Cage (C,n)) -: (W-min (L~ (Cage (C,n)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
((Cage (C,n)) :- (W-min (L~ (Cage (C,n))))) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
rng ((Cage (C,n)) :- (W-min (L~ (Cage (C,n))))) is non empty V26() set
len ((Cage (C,n)) :- (W-min (L~ (Cage (C,n))))) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
((Cage (C,n)) :- (W-min (L~ (Cage (C,n))))) /. (len ((Cage (C,n)) :- (W-min (L~ (Cage (C,n)))))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
len (Cage (C,n)) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Cage (C,n)) /. (len (Cage (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
g is set
card {(N-min (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n))))} is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
card (rng ((Cage (C,n)) :- (W-min (L~ (Cage (C,n)))))) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
dom ((Cage (C,n)) :- (W-min (L~ (Cage (C,n))))) is non empty V26() V200() V201() V202() V203() V204() V205() Element of bool NAT
card (dom ((Cage (C,n)) :- (W-min (L~ (Cage (C,n)))))) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
W-max (L~ (Cage (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
K507(((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),(proj2 | (W-most (L~ (Cage (C,n)))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (C,n)))),K507(((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),(proj2 | (W-most (L~ (Cage (C,n))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
(N-min (L~ (Cage (C,n)))) `2 is V11() V12() ext-real Element of REAL
(W-max (L~ (Cage (C,n)))) `2 is V11() V12() ext-real Element of REAL
(N-max (L~ (Cage (C,n)))) `2 is V11() V12() ext-real Element of REAL
dom ((Cage (C,n)) -: (W-min (L~ (Cage (C,n))))) is V26() V200() V201() V202() V203() V204() V205() Element of bool NAT
card (dom ((Cage (C,n)) -: (W-min (L~ (Cage (C,n)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
g is set
h is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
GCw is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
GCw + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
LSeg (((Cage (C,n)) -: (W-min (L~ (Cage (C,n))))),GCw) is closed Element of bool the U1 of (TOP-REAL 2)
LSeg ((Cage (C,n)),GCw) is closed Element of bool the U1 of (TOP-REAL 2)
RevL is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
RevL + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
LSeg (((Cage (C,n)) :- (W-min (L~ (Cage (C,n))))),RevL) is closed Element of bool the U1 of (TOP-REAL 2)
RevL -' 1 is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(RevL -' 1) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
1 + ((W-min (L~ (Cage (C,n)))) .. (Cage (C,n))) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
((RevL -' 1) + 1) + ((W-min (L~ (Cage (C,n)))) .. (Cage (C,n))) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(len (Cage (C,n))) - ((W-min (L~ (Cage (C,n)))) .. (Cage (C,n))) is V11() V12() ext-real set
((len (Cage (C,n))) - ((W-min (L~ (Cage (C,n)))) .. (Cage (C,n)))) + 1 is V11() V12() ext-real set
RevL - 1 is V11() V12() ext-real set
(RevL - 1) + ((W-min (L~ (Cage (C,n)))) .. (Cage (C,n))) is V11() V12() ext-real set
1 - 1 is V11() V12() ext-real set
(RevL -' 1) + ((W-min (L~ (Cage (C,n)))) .. (Cage (C,n))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
LSeg ((Cage (C,n)),((RevL -' 1) + ((W-min (L~ (Cage (C,n)))) .. (Cage (C,n))))) is closed Element of bool the U1 of (TOP-REAL 2)
((W-min (L~ (Cage (C,n)))) .. (Cage (C,n))) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
((RevL -' 1) + ((W-min (L~ (Cage (C,n)))) .. (Cage (C,n)))) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
((W-min (L~ (Cage (C,n)))) .. (Cage (C,n))) -' 1 is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(((W-min (L~ (Cage (C,n)))) .. (Cage (C,n))) -' 1) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(LSeg ((Cage (C,n)),GCw)) /\ (LSeg ((Cage (C,n)),((RevL -' 1) + ((W-min (L~ (Cage (C,n)))) .. (Cage (C,n)))))) is Element of bool the U1 of (TOP-REAL 2)
0 + 3 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(LSeg ((Cage (C,n)),GCw)) /\ (LSeg ((Cage (C,n)),((RevL -' 1) + ((W-min (L~ (Cage (C,n)))) .. (Cage (C,n)))))) is Element of bool the U1 of (TOP-REAL 2)
(len (Cage (C,n))) - 1 is V11() V12() ext-real set
(len (Cage (C,n))) -' 1 is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(LSeg ((Cage (C,n)),GCw)) /\ (LSeg ((Cage (C,n)),((RevL -' 1) + ((W-min (L~ (Cage (C,n)))) .. (Cage (C,n)))))) is Element of bool the U1 of (TOP-REAL 2)
{((Cage (C,n)) /. 1)} is non empty trivial V26() 1 -element set
1 + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(((W-min (L~ (Cage (C,n)))) .. (Cage (C,n))) -' 1) + (1 + 1) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
0 + ((W-min (L~ (Cage (C,n)))) .. (Cage (C,n))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(LSeg ((Cage (C,n)),GCw)) /\ (LSeg ((Cage (C,n)),((RevL -' 1) + ((W-min (L~ (Cage (C,n)))) .. (Cage (C,n)))))) is Element of bool the U1 of (TOP-REAL 2)
(Cage (C,n)) /. ((W-min (L~ (Cage (C,n)))) .. (Cage (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
{((Cage (C,n)) /. ((W-min (L~ (Cage (C,n)))) .. (Cage (C,n))))} is non empty trivial V26() 1 -element set
g is set
C is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
n is non empty connected compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
Lower_Seq (n,C) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq standard FinSequence of the U1 of (TOP-REAL 2)
Cage (n,C) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
L~ (Cage (n,C)) is non empty closed connected V222() compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
E-max (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (n,C))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | (L~ (Cage (n,C))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:]
the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:] is set
K507(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj1 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
E-most (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
SE-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
proj2 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | (L~ (Cage (n,C))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:]
K506(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj2 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (n,C)))),(S-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
NE-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj2 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (n,C)))),(N-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Cage (n,C)))),(NE-corner (L~ (Cage (n,C))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SE-corner (L~ (Cage (n,C)))),(NE-corner (L~ (Cage (n,C)))))) /\ (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ (Cage (n,C)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Cage (n,C)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),REAL:]
the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))) is set
[: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),REAL:] is set
K507(((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),(proj2 | (E-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (n,C)))),K507(((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),(proj2 | (E-most (L~ (Cage (n,C))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
Rotate ((Cage (n,C)),(E-max (L~ (Cage (n,C))))) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
W-min (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
W-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
K506(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj1 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
W-most (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
SW-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
|[(W-bound (L~ (Cage (n,C)))),(S-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
NW-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
|[(W-bound (L~ (Cage (n,C)))),(N-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (n,C)))),(NW-corner (L~ (Cage (n,C))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Cage (n,C)))),(NW-corner (L~ (Cage (n,C)))))) /\ (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ (Cage (n,C)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Cage (n,C)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),REAL:]
the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))) is set
[: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),REAL:] is set
K506(((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),(proj2 | (W-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (n,C)))),K506(((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),(proj2 | (W-most (L~ (Cage (n,C))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
(Rotate ((Cage (n,C)),(E-max (L~ (Cage (n,C)))))) -: (W-min (L~ (Cage (n,C)))) is V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like special unfolded FinSequence of the U1 of (TOP-REAL 2)
N-min (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
N-most (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
LSeg ((NW-corner (L~ (Cage (n,C)))),(NE-corner (L~ (Cage (n,C))))) is closed closed connected compact compact horizontal Element of bool the U1 of (TOP-REAL 2)
(LSeg ((NW-corner (L~ (Cage (n,C)))),(NE-corner (L~ (Cage (n,C)))))) /\ (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (N-most (L~ (Cage (n,C)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most (L~ (Cage (n,C)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))),REAL:]
the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))) is set
[: the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))),REAL:] is set
K506(((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))),(proj1 | (N-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[K506(((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))),(proj1 | (N-most (L~ (Cage (n,C)))))),(N-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
N-max (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
K507(((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))),(proj1 | (N-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[K507(((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))),(proj1 | (N-most (L~ (Cage (n,C)))))),(N-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
W-max (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
K507(((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),(proj2 | (W-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (n,C)))),K507(((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),(proj2 | (W-most (L~ (Cage (n,C))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
E-min (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
K506(((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),(proj2 | (E-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (n,C)))),K506(((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),(proj2 | (E-most (L~ (Cage (n,C))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
S-max (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
S-most (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (n,C)))),(SE-corner (L~ (Cage (n,C))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Cage (n,C)))),(SE-corner (L~ (Cage (n,C)))))) /\ (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (S-most (L~ (Cage (n,C)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (S-most (L~ (Cage (n,C)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))),REAL:]
the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))) is set
[: the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))),REAL:] is set
K507(((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))),(proj1 | (S-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[K507(((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))),(proj1 | (S-most (L~ (Cage (n,C)))))),(S-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
S-min (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
K506(((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))),(proj1 | (S-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[K506(((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))),(proj1 | (S-most (L~ (Cage (n,C)))))),(S-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C))))) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
rng (Cage (n,C)) is non empty non trivial V26() set
(N-min (L~ (Cage (n,C)))) `2 is V11() V12() ext-real Element of REAL
(W-max (L~ (Cage (n,C)))) `2 is V11() V12() ext-real Element of REAL
{(N-min (L~ (Cage (n,C)))),(W-min (L~ (Cage (n,C))))} is non empty V26() set
card {(N-min (L~ (Cage (n,C)))),(W-min (L~ (Cage (n,C))))} is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Cage (n,C)) -: (W-min (L~ (Cage (n,C)))) is V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like special unfolded FinSequence of the U1 of (TOP-REAL 2)
len ((Cage (n,C)) -: (W-min (L~ (Cage (n,C))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(W-min (L~ (Cage (n,C)))) .. (Cage (n,C)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
((Cage (n,C)) -: (W-min (L~ (Cage (n,C))))) /. (len ((Cage (n,C)) -: (W-min (L~ (Cage (n,C)))))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
rng ((Cage (n,C)) -: (W-min (L~ (Cage (n,C))))) is V26() set
((Cage (n,C)) -: (W-min (L~ (Cage (n,C))))) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(Cage (n,C)) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
g is set
card (rng ((Cage (n,C)) -: (W-min (L~ (Cage (n,C)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
dom ((Cage (n,C)) -: (W-min (L~ (Cage (n,C))))) is V26() V200() V201() V202() V203() V204() V205() Element of bool NAT
card (dom ((Cage (n,C)) -: (W-min (L~ (Cage (n,C)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
L~ ((Cage (n,C)) -: (W-min (L~ (Cage (n,C))))) is closed compact Element of bool the U1 of (TOP-REAL 2)
(E-min (L~ (Cage (n,C)))) .. (Cage (n,C)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(S-max (L~ (Cage (n,C)))) .. (Cage (n,C)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(E-max (L~ (Cage (n,C)))) .. (Cage (n,C)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(S-min (L~ (Cage (n,C)))) .. (Cage (n,C)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(N-max (L~ (Cage (n,C)))) `1 is V11() V12() ext-real Element of REAL
(NE-corner (L~ (Cage (n,C)))) `1 is V11() V12() ext-real Element of REAL
(N-min (L~ (Cage (n,C)))) `1 is V11() V12() ext-real Element of REAL
(Cage (n,C)) :- (W-min (L~ (Cage (n,C)))) is non empty V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
rng ((Cage (n,C)) :- (W-min (L~ (Cage (n,C))))) is non empty V26() set
((Cage (n,C)) :- (W-min (L~ (Cage (n,C))))) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
len ((Cage (n,C)) :- (W-min (L~ (Cage (n,C))))) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
((Cage (n,C)) :- (W-min (L~ (Cage (n,C))))) /. (len ((Cage (n,C)) :- (W-min (L~ (Cage (n,C)))))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
len (Cage (n,C)) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Cage (n,C)) /. (len (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
g is set
card (rng ((Cage (n,C)) :- (W-min (L~ (Cage (n,C)))))) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
dom ((Cage (n,C)) :- (W-min (L~ (Cage (n,C))))) is non empty V26() V200() V201() V202() V203() V204() V205() Element of bool NAT
card (dom ((Cage (n,C)) :- (W-min (L~ (Cage (n,C)))))) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
L~ ((Cage (n,C)) :- (W-min (L~ (Cage (n,C))))) is closed compact Element of bool the U1 of (TOP-REAL 2)
(L~ ((Cage (n,C)) -: (W-min (L~ (Cage (n,C)))))) /\ (L~ ((Cage (n,C)) :- (W-min (L~ (Cage (n,C)))))) is Element of bool the U1 of (TOP-REAL 2)
(N-max (L~ (Cage (n,C)))) .. (Cage (n,C)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(N-min (L~ (Cage (n,C)))) .. (Cage (n,C)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(E-max (L~ (Cage (n,C)))) .. ((Cage (n,C)) -: (W-min (L~ (Cage (n,C))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(N-min (L~ (Cage (n,C)))) .. ((Cage (n,C)) -: (W-min (L~ (Cage (n,C))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
((Cage (n,C)) -: (W-min (L~ (Cage (n,C))))) /^ 1 is V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like special unfolded FinSequence of the U1 of (TOP-REAL 2)
rng (((Cage (n,C)) -: (W-min (L~ (Cage (n,C))))) /^ 1) is V26() set
(rng (((Cage (n,C)) -: (W-min (L~ (Cage (n,C))))) /^ 1)) \ (rng ((Cage (n,C)) :- (W-min (L~ (Cage (n,C)))))) is V26() Element of bool (rng (((Cage (n,C)) -: (W-min (L~ (Cage (n,C))))) /^ 1))
bool (rng (((Cage (n,C)) -: (W-min (L~ (Cage (n,C))))) /^ 1)) is V26() V30() set
(Cage (n,C)) :- (E-max (L~ (Cage (n,C)))) is non empty V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
rng ((Cage (n,C)) :- (E-max (L~ (Cage (n,C))))) is non empty V26() set
(Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) :- (E-max (L~ (Cage (n,C)))) is non empty V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
((Cage (n,C)) :- (W-min (L~ (Cage (n,C))))) ^ (((Cage (n,C)) -: (W-min (L~ (Cage (n,C))))) /^ 1) is non empty V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
(((Cage (n,C)) :- (W-min (L~ (Cage (n,C))))) ^ (((Cage (n,C)) -: (W-min (L~ (Cage (n,C))))) /^ 1)) :- (E-max (L~ (Cage (n,C)))) is non empty V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
(((Cage (n,C)) -: (W-min (L~ (Cage (n,C))))) /^ 1) :- (E-max (L~ (Cage (n,C)))) is non empty V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
((Cage (n,C)) -: (W-min (L~ (Cage (n,C))))) :- (E-max (L~ (Cage (n,C)))) is non empty V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
((Cage (n,C)) :- (E-max (L~ (Cage (n,C))))) -: (W-min (L~ (Cage (n,C)))) is V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
(Cage (n,C)) -: (E-max (L~ (Cage (n,C)))) is V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like special unfolded FinSequence of the U1 of (TOP-REAL 2)
((Cage (n,C)) -: (E-max (L~ (Cage (n,C))))) /^ 1 is V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like special unfolded FinSequence of the U1 of (TOP-REAL 2)
((Cage (n,C)) :- (E-max (L~ (Cage (n,C))))) ^ (((Cage (n,C)) -: (E-max (L~ (Cage (n,C))))) /^ 1) is non empty V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
(((Cage (n,C)) :- (E-max (L~ (Cage (n,C))))) ^ (((Cage (n,C)) -: (E-max (L~ (Cage (n,C))))) /^ 1)) -: (W-min (L~ (Cage (n,C)))) is V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
C is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
n is non empty compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
Upper_Seq (n,C) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
Cage (n,C) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
L~ (Cage (n,C)) is non empty closed connected V222() compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
W-min (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
W-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (n,C))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | (L~ (Cage (n,C))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:]
the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:] is set
K506(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj1 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
W-most (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
SW-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
proj2 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | (L~ (Cage (n,C))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:]
K506(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj2 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (n,C)))),(S-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
NW-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj2 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (n,C)))),(N-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (n,C)))),(NW-corner (L~ (Cage (n,C))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Cage (n,C)))),(NW-corner (L~ (Cage (n,C)))))) /\ (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ (Cage (n,C)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Cage (n,C)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),REAL:]
the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))) is set
[: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),REAL:] is set
K506(((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),(proj2 | (W-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (n,C)))),K506(((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),(proj2 | (W-most (L~ (Cage (n,C))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
(W-min (L~ (Cage (n,C)))) .. (Upper_Seq (n,C)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Upper_Seq (n,C)) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
C is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
n is non empty compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
Upper_Seq (n,C) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
Cage (n,C) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
L~ (Cage (n,C)) is non empty closed connected V222() compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
W-max (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
W-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (n,C))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | (L~ (Cage (n,C))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:]
the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:] is set
K506(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj1 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
W-most (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
SW-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
proj2 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | (L~ (Cage (n,C))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:]
K506(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj2 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (n,C)))),(S-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
NW-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj2 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (n,C)))),(N-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (n,C)))),(NW-corner (L~ (Cage (n,C))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Cage (n,C)))),(NW-corner (L~ (Cage (n,C)))))) /\ (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ (Cage (n,C)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Cage (n,C)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),REAL:]
the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))) is set
[: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),REAL:] is set
K507(((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),(proj2 | (W-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (n,C)))),K507(((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),(proj2 | (W-most (L~ (Cage (n,C))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
(W-max (L~ (Cage (n,C)))) .. (Upper_Seq (n,C)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
W-min (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
K506(((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),(proj2 | (W-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (n,C)))),K506(((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),(proj2 | (W-most (L~ (Cage (n,C))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
(W-min (L~ (Cage (n,C)))) .. (Upper_Seq (n,C)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
N-min (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
N-most (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
NE-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj1 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (n,C)))),(N-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((NW-corner (L~ (Cage (n,C)))),(NE-corner (L~ (Cage (n,C))))) is closed closed connected compact compact horizontal Element of bool the U1 of (TOP-REAL 2)
(LSeg ((NW-corner (L~ (Cage (n,C)))),(NE-corner (L~ (Cage (n,C)))))) /\ (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (N-most (L~ (Cage (n,C)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most (L~ (Cage (n,C)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))),REAL:]
the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))) is set
[: the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))),REAL:] is set
K506(((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))),(proj1 | (N-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[K506(((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))),(proj1 | (N-most (L~ (Cage (n,C)))))),(N-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
N-max (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
K507(((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))),(proj1 | (N-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[K507(((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))),(proj1 | (N-most (L~ (Cage (n,C)))))),(N-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
E-max (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
E-most (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
SE-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
|[(E-bound (L~ (Cage (n,C)))),(S-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Cage (n,C)))),(NE-corner (L~ (Cage (n,C))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SE-corner (L~ (Cage (n,C)))),(NE-corner (L~ (Cage (n,C)))))) /\ (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ (Cage (n,C)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Cage (n,C)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),REAL:]
the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))) is set
[: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),REAL:] is set
K507(((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),(proj2 | (E-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (n,C)))),K507(((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),(proj2 | (E-most (L~ (Cage (n,C))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C))))) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
L~ (Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) is non empty closed connected V222() compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
rng (Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) is non empty non trivial V26() set
rng (Cage (n,C)) is non empty non trivial V26() set
(Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(W-max (L~ (Cage (n,C)))) .. (Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(W-min (L~ (Cage (n,C)))) .. (Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) -: (E-max (L~ (Cage (n,C)))) is V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like special unfolded FinSequence of the U1 of (TOP-REAL 2)
(N-max (L~ (Cage (n,C)))) .. (Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(E-max (L~ (Cage (n,C)))) .. (Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(N-min (L~ (Cage (n,C)))) .. (Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(W-min (L~ (Cage (n,C)))) .. ((Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) -: (E-max (L~ (Cage (n,C))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
C is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
n is non empty compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
Upper_Seq (n,C) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
Cage (n,C) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
L~ (Cage (n,C)) is non empty closed connected V222() compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
W-max (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
W-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (n,C))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | (L~ (Cage (n,C))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:]
the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:] is set
K506(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj1 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
W-most (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
SW-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
proj2 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | (L~ (Cage (n,C))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:]
K506(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj2 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (n,C)))),(S-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
NW-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj2 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (n,C)))),(N-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (n,C)))),(NW-corner (L~ (Cage (n,C))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Cage (n,C)))),(NW-corner (L~ (Cage (n,C)))))) /\ (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ (Cage (n,C)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Cage (n,C)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),REAL:]
the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))) is set
[: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),REAL:] is set
K507(((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),(proj2 | (W-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (n,C)))),K507(((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),(proj2 | (W-most (L~ (Cage (n,C))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
(W-max (L~ (Cage (n,C)))) .. (Upper_Seq (n,C)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
N-min (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
N-most (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
NE-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj1 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (n,C)))),(N-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((NW-corner (L~ (Cage (n,C)))),(NE-corner (L~ (Cage (n,C))))) is closed closed connected compact compact horizontal Element of bool the U1 of (TOP-REAL 2)
(LSeg ((NW-corner (L~ (Cage (n,C)))),(NE-corner (L~ (Cage (n,C)))))) /\ (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (N-most (L~ (Cage (n,C)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most (L~ (Cage (n,C)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))),REAL:]
the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))) is set
[: the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))),REAL:] is set
K506(((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))),(proj1 | (N-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[K506(((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))),(proj1 | (N-most (L~ (Cage (n,C)))))),(N-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
(N-min (L~ (Cage (n,C)))) .. (Upper_Seq (n,C)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
W-min (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
K506(((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),(proj2 | (W-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (n,C)))),K506(((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),(proj2 | (W-most (L~ (Cage (n,C))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
N-max (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
K507(((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))),(proj1 | (N-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[K507(((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))),(proj1 | (N-most (L~ (Cage (n,C)))))),(N-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
E-max (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
E-most (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
SE-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
|[(E-bound (L~ (Cage (n,C)))),(S-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Cage (n,C)))),(NE-corner (L~ (Cage (n,C))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SE-corner (L~ (Cage (n,C)))),(NE-corner (L~ (Cage (n,C)))))) /\ (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ (Cage (n,C)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Cage (n,C)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),REAL:]
the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))) is set
[: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),REAL:] is set
K507(((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),(proj2 | (E-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (n,C)))),K507(((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),(proj2 | (E-most (L~ (Cage (n,C))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C))))) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
L~ (Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) is non empty closed connected V222() compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
rng (Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) is non empty non trivial V26() set
rng (Cage (n,C)) is non empty non trivial V26() set
(Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(W-max (L~ (Cage (n,C)))) .. (Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(N-min (L~ (Cage (n,C)))) .. (Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) -: (E-max (L~ (Cage (n,C)))) is V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like special unfolded FinSequence of the U1 of (TOP-REAL 2)
(N-max (L~ (Cage (n,C)))) .. (Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(E-max (L~ (Cage (n,C)))) .. (Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(W-max (L~ (Cage (n,C)))) .. ((Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) -: (E-max (L~ (Cage (n,C))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
C is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
n is non empty compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
Upper_Seq (n,C) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
Cage (n,C) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
L~ (Cage (n,C)) is non empty closed connected V222() compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
N-max (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
N-most (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
NW-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
W-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (n,C))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | (L~ (Cage (n,C))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:]
the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:] is set
K506(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj1 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
N-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
proj2 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | (L~ (Cage (n,C))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:]
K507(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj2 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (n,C)))),(N-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
NE-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj1 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (n,C)))),(N-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((NW-corner (L~ (Cage (n,C)))),(NE-corner (L~ (Cage (n,C))))) is closed closed connected compact compact horizontal Element of bool the U1 of (TOP-REAL 2)
(LSeg ((NW-corner (L~ (Cage (n,C)))),(NE-corner (L~ (Cage (n,C)))))) /\ (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (N-most (L~ (Cage (n,C)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most (L~ (Cage (n,C)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))),REAL:]
the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))) is set
[: the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))),REAL:] is set
K507(((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))),(proj1 | (N-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[K507(((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))),(proj1 | (N-most (L~ (Cage (n,C)))))),(N-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
(N-max (L~ (Cage (n,C)))) .. (Upper_Seq (n,C)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
N-min (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
K506(((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))),(proj1 | (N-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[K506(((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))),(proj1 | (N-most (L~ (Cage (n,C)))))),(N-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
(N-min (L~ (Cage (n,C)))) .. (Upper_Seq (n,C)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
W-min (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
W-most (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
SW-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
K506(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj2 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (n,C)))),(S-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (n,C)))),(NW-corner (L~ (Cage (n,C))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Cage (n,C)))),(NW-corner (L~ (Cage (n,C)))))) /\ (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ (Cage (n,C)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Cage (n,C)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),REAL:]
the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))) is set
[: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),REAL:] is set
K506(((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),(proj2 | (W-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (n,C)))),K506(((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),(proj2 | (W-most (L~ (Cage (n,C))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
E-max (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
E-most (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
SE-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
|[(E-bound (L~ (Cage (n,C)))),(S-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Cage (n,C)))),(NE-corner (L~ (Cage (n,C))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SE-corner (L~ (Cage (n,C)))),(NE-corner (L~ (Cage (n,C)))))) /\ (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ (Cage (n,C)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Cage (n,C)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),REAL:]
the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))) is set
[: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),REAL:] is set
K507(((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),(proj2 | (E-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (n,C)))),K507(((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),(proj2 | (E-most (L~ (Cage (n,C))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C))))) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
L~ (Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) is non empty closed connected V222() compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
rng (Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) is non empty non trivial V26() set
rng (Cage (n,C)) is non empty non trivial V26() set
(Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(N-max (L~ (Cage (n,C)))) .. (Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(N-min (L~ (Cage (n,C)))) .. (Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(E-max (L~ (Cage (n,C)))) .. (Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) -: (E-max (L~ (Cage (n,C)))) is V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like special unfolded FinSequence of the U1 of (TOP-REAL 2)
(N-min (L~ (Cage (n,C)))) .. ((Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) -: (E-max (L~ (Cage (n,C))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
C is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
n is non empty compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
Upper_Seq (n,C) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
Cage (n,C) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
L~ (Cage (n,C)) is non empty closed connected V222() compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
N-max (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
N-most (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
NW-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
W-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (n,C))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | (L~ (Cage (n,C))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:]
the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:] is set
K506(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj1 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
N-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
proj2 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | (L~ (Cage (n,C))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:]
K507(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj2 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (n,C)))),(N-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
NE-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj1 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (n,C)))),(N-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((NW-corner (L~ (Cage (n,C)))),(NE-corner (L~ (Cage (n,C))))) is closed closed connected compact compact horizontal Element of bool the U1 of (TOP-REAL 2)
(LSeg ((NW-corner (L~ (Cage (n,C)))),(NE-corner (L~ (Cage (n,C)))))) /\ (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (N-most (L~ (Cage (n,C)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most (L~ (Cage (n,C)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))),REAL:]
the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))) is set
[: the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))),REAL:] is set
K507(((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))),(proj1 | (N-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[K507(((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))),(proj1 | (N-most (L~ (Cage (n,C)))))),(N-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
(N-max (L~ (Cage (n,C)))) .. (Upper_Seq (n,C)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
E-max (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
E-most (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
SE-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
K506(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj2 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (n,C)))),(S-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Cage (n,C)))),(NE-corner (L~ (Cage (n,C))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SE-corner (L~ (Cage (n,C)))),(NE-corner (L~ (Cage (n,C)))))) /\ (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ (Cage (n,C)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Cage (n,C)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),REAL:]
the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))) is set
[: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),REAL:] is set
K507(((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),(proj2 | (E-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (n,C)))),K507(((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),(proj2 | (E-most (L~ (Cage (n,C))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
(E-max (L~ (Cage (n,C)))) .. (Upper_Seq (n,C)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
W-min (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
W-most (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
SW-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
|[(W-bound (L~ (Cage (n,C)))),(S-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (n,C)))),(NW-corner (L~ (Cage (n,C))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Cage (n,C)))),(NW-corner (L~ (Cage (n,C)))))) /\ (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ (Cage (n,C)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Cage (n,C)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),REAL:]
the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))) is set
[: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),REAL:] is set
K506(((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),(proj2 | (W-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (n,C)))),K506(((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),(proj2 | (W-most (L~ (Cage (n,C))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C))))) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
L~ (Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) is non empty closed connected V222() compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
rng (Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) is non empty non trivial V26() set
rng (Cage (n,C)) is non empty non trivial V26() set
(Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(N-max (L~ (Cage (n,C)))) .. (Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(E-max (L~ (Cage (n,C)))) .. (Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) -: (E-max (L~ (Cage (n,C)))) is V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like special unfolded FinSequence of the U1 of (TOP-REAL 2)
(N-max (L~ (Cage (n,C)))) .. ((Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) -: (E-max (L~ (Cage (n,C))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
C is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
n is non empty compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
Upper_Seq (n,C) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
Cage (n,C) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
L~ (Cage (n,C)) is non empty closed connected V222() compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
E-max (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (n,C))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | (L~ (Cage (n,C))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:]
the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:] is set
K507(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj1 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
E-most (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
SE-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
proj2 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | (L~ (Cage (n,C))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:]
K506(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj2 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (n,C)))),(S-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
NE-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj2 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (n,C)))),(N-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Cage (n,C)))),(NE-corner (L~ (Cage (n,C))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SE-corner (L~ (Cage (n,C)))),(NE-corner (L~ (Cage (n,C)))))) /\ (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ (Cage (n,C)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Cage (n,C)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),REAL:]
the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))) is set
[: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),REAL:] is set
K507(((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),(proj2 | (E-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (n,C)))),K507(((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),(proj2 | (E-most (L~ (Cage (n,C))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
(E-max (L~ (Cage (n,C)))) .. (Upper_Seq (n,C)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
len (Upper_Seq (n,C)) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
rng (Cage (n,C)) is non empty non trivial V26() set
W-min (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
W-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
K506(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj1 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
W-most (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
SW-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
|[(W-bound (L~ (Cage (n,C)))),(S-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
NW-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
|[(W-bound (L~ (Cage (n,C)))),(N-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (n,C)))),(NW-corner (L~ (Cage (n,C))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Cage (n,C)))),(NW-corner (L~ (Cage (n,C)))))) /\ (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ (Cage (n,C)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Cage (n,C)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),REAL:]
the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))) is set
[: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),REAL:] is set
K506(((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),(proj2 | (W-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (n,C)))),K506(((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),(proj2 | (W-most (L~ (Cage (n,C))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C))))) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
rng (Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) is non empty non trivial V26() set
(Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) -: (E-max (L~ (Cage (n,C)))) is V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like special unfolded FinSequence of the U1 of (TOP-REAL 2)
(E-max (L~ (Cage (n,C)))) .. (Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
rng (Upper_Seq (n,C)) is non empty V26() set
(Upper_Seq (n,C)) /. (len (Upper_Seq (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
C is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
n is non empty compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
Lower_Seq (n,C) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
Cage (n,C) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
L~ (Cage (n,C)) is non empty closed connected V222() compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
E-max (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (n,C))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | (L~ (Cage (n,C))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:]
the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:] is set
K507(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj1 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
E-most (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
SE-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
proj2 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | (L~ (Cage (n,C))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:]
K506(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj2 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (n,C)))),(S-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
NE-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj2 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (n,C)))),(N-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Cage (n,C)))),(NE-corner (L~ (Cage (n,C))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SE-corner (L~ (Cage (n,C)))),(NE-corner (L~ (Cage (n,C)))))) /\ (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ (Cage (n,C)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Cage (n,C)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),REAL:]
the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))) is set
[: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),REAL:] is set
K507(((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),(proj2 | (E-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (n,C)))),K507(((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),(proj2 | (E-most (L~ (Cage (n,C))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
(E-max (L~ (Cage (n,C)))) .. (Lower_Seq (n,C)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Lower_Seq (n,C)) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
C is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
n is non empty connected compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
Lower_Seq (n,C) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq standard FinSequence of the U1 of (TOP-REAL 2)
Cage (n,C) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
L~ (Cage (n,C)) is non empty closed connected V222() compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
E-min (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (n,C))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | (L~ (Cage (n,C))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:]
the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:] is set
K507(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj1 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
E-most (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
SE-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
proj2 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | (L~ (Cage (n,C))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:]
K506(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj2 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (n,C)))),(S-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
NE-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj2 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (n,C)))),(N-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Cage (n,C)))),(NE-corner (L~ (Cage (n,C))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SE-corner (L~ (Cage (n,C)))),(NE-corner (L~ (Cage (n,C)))))) /\ (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ (Cage (n,C)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Cage (n,C)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),REAL:]
the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))) is set
[: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),REAL:] is set
K506(((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),(proj2 | (E-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (n,C)))),K506(((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),(proj2 | (E-most (L~ (Cage (n,C))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
(E-min (L~ (Cage (n,C)))) .. (Lower_Seq (n,C)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
E-max (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
K507(((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),(proj2 | (E-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (n,C)))),K507(((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),(proj2 | (E-most (L~ (Cage (n,C))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
(E-max (L~ (Cage (n,C)))) .. (Lower_Seq (n,C)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
S-max (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
S-most (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
SW-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
W-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
K506(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj1 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (n,C)))),(S-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (n,C)))),(SE-corner (L~ (Cage (n,C))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Cage (n,C)))),(SE-corner (L~ (Cage (n,C)))))) /\ (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (S-most (L~ (Cage (n,C)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (S-most (L~ (Cage (n,C)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))),REAL:]
the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))) is set
[: the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))),REAL:] is set
K507(((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))),(proj1 | (S-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[K507(((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))),(proj1 | (S-most (L~ (Cage (n,C)))))),(S-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
S-min (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
K506(((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))),(proj1 | (S-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[K506(((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))),(proj1 | (S-most (L~ (Cage (n,C)))))),(S-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
W-min (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
W-most (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
NW-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
|[(W-bound (L~ (Cage (n,C)))),(N-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (n,C)))),(NW-corner (L~ (Cage (n,C))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Cage (n,C)))),(NW-corner (L~ (Cage (n,C)))))) /\ (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ (Cage (n,C)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Cage (n,C)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),REAL:]
the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))) is set
[: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),REAL:] is set
K506(((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),(proj2 | (W-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (n,C)))),K506(((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),(proj2 | (W-most (L~ (Cage (n,C))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
Rotate ((Cage (n,C)),(E-max (L~ (Cage (n,C))))) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
(Rotate ((Cage (n,C)),(E-max (L~ (Cage (n,C)))))) -: (W-min (L~ (Cage (n,C)))) is V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like special unfolded FinSequence of the U1 of (TOP-REAL 2)
L~ (Rotate ((Cage (n,C)),(E-max (L~ (Cage (n,C)))))) is non empty closed connected V222() compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
rng (Rotate ((Cage (n,C)),(E-max (L~ (Cage (n,C)))))) is non empty non trivial V26() set
rng (Cage (n,C)) is non empty non trivial V26() set
(Rotate ((Cage (n,C)),(E-max (L~ (Cage (n,C)))))) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(E-min (L~ (Cage (n,C)))) .. (Rotate ((Cage (n,C)),(E-max (L~ (Cage (n,C)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(E-max (L~ (Cage (n,C)))) .. (Rotate ((Cage (n,C)),(E-max (L~ (Cage (n,C)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(S-min (L~ (Cage (n,C)))) .. (Rotate ((Cage (n,C)),(E-max (L~ (Cage (n,C)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(W-min (L~ (Cage (n,C)))) .. (Rotate ((Cage (n,C)),(E-max (L~ (Cage (n,C)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(S-max (L~ (Cage (n,C)))) .. (Rotate ((Cage (n,C)),(E-max (L~ (Cage (n,C)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(E-max (L~ (Cage (n,C)))) .. ((Rotate ((Cage (n,C)),(E-max (L~ (Cage (n,C)))))) -: (W-min (L~ (Cage (n,C))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
C is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
n is non empty connected compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
Lower_Seq (n,C) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq standard FinSequence of the U1 of (TOP-REAL 2)
Cage (n,C) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
L~ (Cage (n,C)) is non empty closed connected V222() compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
E-min (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (n,C))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | (L~ (Cage (n,C))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:]
the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:] is set
K507(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj1 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
E-most (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
SE-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
proj2 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | (L~ (Cage (n,C))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:]
K506(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj2 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (n,C)))),(S-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
NE-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj2 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (n,C)))),(N-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Cage (n,C)))),(NE-corner (L~ (Cage (n,C))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SE-corner (L~ (Cage (n,C)))),(NE-corner (L~ (Cage (n,C)))))) /\ (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ (Cage (n,C)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Cage (n,C)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),REAL:]
the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))) is set
[: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),REAL:] is set
K506(((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),(proj2 | (E-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (n,C)))),K506(((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),(proj2 | (E-most (L~ (Cage (n,C))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
(E-min (L~ (Cage (n,C)))) .. (Lower_Seq (n,C)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
S-max (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
S-most (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
SW-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
W-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
K506(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj1 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (n,C)))),(S-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (n,C)))),(SE-corner (L~ (Cage (n,C))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Cage (n,C)))),(SE-corner (L~ (Cage (n,C)))))) /\ (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (S-most (L~ (Cage (n,C)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (S-most (L~ (Cage (n,C)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))),REAL:]
the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))) is set
[: the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))),REAL:] is set
K507(((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))),(proj1 | (S-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[K507(((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))),(proj1 | (S-most (L~ (Cage (n,C)))))),(S-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
(S-max (L~ (Cage (n,C)))) .. (Lower_Seq (n,C)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
E-max (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
K507(((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),(proj2 | (E-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (n,C)))),K507(((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),(proj2 | (E-most (L~ (Cage (n,C))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
S-min (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
K506(((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))),(proj1 | (S-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[K506(((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))),(proj1 | (S-most (L~ (Cage (n,C)))))),(S-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
W-min (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
W-most (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
NW-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
|[(W-bound (L~ (Cage (n,C)))),(N-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (n,C)))),(NW-corner (L~ (Cage (n,C))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Cage (n,C)))),(NW-corner (L~ (Cage (n,C)))))) /\ (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ (Cage (n,C)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Cage (n,C)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),REAL:]
the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))) is set
[: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),REAL:] is set
K506(((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),(proj2 | (W-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (n,C)))),K506(((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),(proj2 | (W-most (L~ (Cage (n,C))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
Rotate ((Cage (n,C)),(E-max (L~ (Cage (n,C))))) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
(Rotate ((Cage (n,C)),(E-max (L~ (Cage (n,C)))))) -: (W-min (L~ (Cage (n,C)))) is V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like special unfolded FinSequence of the U1 of (TOP-REAL 2)
L~ (Rotate ((Cage (n,C)),(E-max (L~ (Cage (n,C)))))) is non empty closed connected V222() compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
rng (Rotate ((Cage (n,C)),(E-max (L~ (Cage (n,C)))))) is non empty non trivial V26() set
rng (Cage (n,C)) is non empty non trivial V26() set
(Rotate ((Cage (n,C)),(E-max (L~ (Cage (n,C)))))) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(E-min (L~ (Cage (n,C)))) .. (Rotate ((Cage (n,C)),(E-max (L~ (Cage (n,C)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(S-max (L~ (Cage (n,C)))) .. (Rotate ((Cage (n,C)),(E-max (L~ (Cage (n,C)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(S-min (L~ (Cage (n,C)))) .. (Rotate ((Cage (n,C)),(E-max (L~ (Cage (n,C)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(W-min (L~ (Cage (n,C)))) .. (Rotate ((Cage (n,C)),(E-max (L~ (Cage (n,C)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(E-min (L~ (Cage (n,C)))) .. ((Rotate ((Cage (n,C)),(E-max (L~ (Cage (n,C)))))) -: (W-min (L~ (Cage (n,C))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
C is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
n is non empty connected compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
Lower_Seq (n,C) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq standard FinSequence of the U1 of (TOP-REAL 2)
Cage (n,C) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
L~ (Cage (n,C)) is non empty closed connected V222() compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
S-min (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
S-most (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
SW-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
W-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (n,C))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | (L~ (Cage (n,C))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:]
the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:] is set
K506(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj1 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
S-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
proj2 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | (L~ (Cage (n,C))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:]
K506(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj2 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (n,C)))),(S-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
SE-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj1 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (n,C)))),(S-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (n,C)))),(SE-corner (L~ (Cage (n,C))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Cage (n,C)))),(SE-corner (L~ (Cage (n,C)))))) /\ (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (S-most (L~ (Cage (n,C)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (S-most (L~ (Cage (n,C)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))),REAL:]
the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))) is set
[: the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))),REAL:] is set
K506(((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))),(proj1 | (S-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[K506(((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))),(proj1 | (S-most (L~ (Cage (n,C)))))),(S-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
(S-min (L~ (Cage (n,C)))) .. (Lower_Seq (n,C)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
S-max (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
K507(((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))),(proj1 | (S-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[K507(((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))),(proj1 | (S-most (L~ (Cage (n,C)))))),(S-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
(S-max (L~ (Cage (n,C)))) .. (Lower_Seq (n,C)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
E-max (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
E-most (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
NE-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj2 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (n,C)))),(N-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Cage (n,C)))),(NE-corner (L~ (Cage (n,C))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SE-corner (L~ (Cage (n,C)))),(NE-corner (L~ (Cage (n,C)))))) /\ (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ (Cage (n,C)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Cage (n,C)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),REAL:]
the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))) is set
[: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),REAL:] is set
K507(((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),(proj2 | (E-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (n,C)))),K507(((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),(proj2 | (E-most (L~ (Cage (n,C))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
W-min (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
W-most (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
NW-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
|[(W-bound (L~ (Cage (n,C)))),(N-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (n,C)))),(NW-corner (L~ (Cage (n,C))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Cage (n,C)))),(NW-corner (L~ (Cage (n,C)))))) /\ (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ (Cage (n,C)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Cage (n,C)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),REAL:]
the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))) is set
[: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),REAL:] is set
K506(((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),(proj2 | (W-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (n,C)))),K506(((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),(proj2 | (W-most (L~ (Cage (n,C))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
Rotate ((Cage (n,C)),(E-max (L~ (Cage (n,C))))) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
(Rotate ((Cage (n,C)),(E-max (L~ (Cage (n,C)))))) -: (W-min (L~ (Cage (n,C)))) is V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like special unfolded FinSequence of the U1 of (TOP-REAL 2)
L~ (Rotate ((Cage (n,C)),(E-max (L~ (Cage (n,C)))))) is non empty closed connected V222() compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
rng (Rotate ((Cage (n,C)),(E-max (L~ (Cage (n,C)))))) is non empty non trivial V26() set
rng (Cage (n,C)) is non empty non trivial V26() set
(Rotate ((Cage (n,C)),(E-max (L~ (Cage (n,C)))))) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(S-min (L~ (Cage (n,C)))) .. (Rotate ((Cage (n,C)),(E-max (L~ (Cage (n,C)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(S-max (L~ (Cage (n,C)))) .. (Rotate ((Cage (n,C)),(E-max (L~ (Cage (n,C)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(W-min (L~ (Cage (n,C)))) .. (Rotate ((Cage (n,C)),(E-max (L~ (Cage (n,C)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(S-max (L~ (Cage (n,C)))) .. ((Rotate ((Cage (n,C)),(E-max (L~ (Cage (n,C)))))) -: (W-min (L~ (Cage (n,C))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
C is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
n is non empty connected compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
Lower_Seq (n,C) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq standard FinSequence of the U1 of (TOP-REAL 2)
Cage (n,C) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
L~ (Cage (n,C)) is non empty closed connected V222() compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
S-min (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
S-most (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
SW-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
W-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (n,C))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | (L~ (Cage (n,C))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:]
the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:] is set
K506(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj1 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
S-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
proj2 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | (L~ (Cage (n,C))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:]
K506(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj2 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (n,C)))),(S-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
SE-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj1 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (n,C)))),(S-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (n,C)))),(SE-corner (L~ (Cage (n,C))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Cage (n,C)))),(SE-corner (L~ (Cage (n,C)))))) /\ (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (S-most (L~ (Cage (n,C)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (S-most (L~ (Cage (n,C)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))),REAL:]
the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))) is set
[: the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))),REAL:] is set
K506(((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))),(proj1 | (S-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[K506(((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))),(proj1 | (S-most (L~ (Cage (n,C)))))),(S-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
(S-min (L~ (Cage (n,C)))) .. (Lower_Seq (n,C)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
W-min (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
W-most (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
NW-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj2 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (n,C)))),(N-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (n,C)))),(NW-corner (L~ (Cage (n,C))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Cage (n,C)))),(NW-corner (L~ (Cage (n,C)))))) /\ (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ (Cage (n,C)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Cage (n,C)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),REAL:]
the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))) is set
[: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),REAL:] is set
K506(((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),(proj2 | (W-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (n,C)))),K506(((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),(proj2 | (W-most (L~ (Cage (n,C))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
(W-min (L~ (Cage (n,C)))) .. (Lower_Seq (n,C)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
E-max (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
E-most (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
NE-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
|[(E-bound (L~ (Cage (n,C)))),(N-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Cage (n,C)))),(NE-corner (L~ (Cage (n,C))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SE-corner (L~ (Cage (n,C)))),(NE-corner (L~ (Cage (n,C)))))) /\ (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ (Cage (n,C)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Cage (n,C)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),REAL:]
the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))) is set
[: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),REAL:] is set
K507(((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),(proj2 | (E-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (n,C)))),K507(((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),(proj2 | (E-most (L~ (Cage (n,C))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
Rotate ((Cage (n,C)),(E-max (L~ (Cage (n,C))))) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
(Rotate ((Cage (n,C)),(E-max (L~ (Cage (n,C)))))) -: (W-min (L~ (Cage (n,C)))) is V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like special unfolded FinSequence of the U1 of (TOP-REAL 2)
L~ (Rotate ((Cage (n,C)),(E-max (L~ (Cage (n,C)))))) is non empty closed connected V222() compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
rng (Rotate ((Cage (n,C)),(E-max (L~ (Cage (n,C)))))) is non empty non trivial V26() set
rng (Cage (n,C)) is non empty non trivial V26() set
(Rotate ((Cage (n,C)),(E-max (L~ (Cage (n,C)))))) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(S-min (L~ (Cage (n,C)))) .. (Rotate ((Cage (n,C)),(E-max (L~ (Cage (n,C)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(W-min (L~ (Cage (n,C)))) .. (Rotate ((Cage (n,C)),(E-max (L~ (Cage (n,C)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(S-min (L~ (Cage (n,C)))) .. ((Rotate ((Cage (n,C)),(E-max (L~ (Cage (n,C)))))) -: (W-min (L~ (Cage (n,C))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
C is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
n is non empty connected compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
Lower_Seq (n,C) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq standard FinSequence of the U1 of (TOP-REAL 2)
Cage (n,C) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
L~ (Cage (n,C)) is non empty closed connected V222() compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
W-min (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
W-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (n,C))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | (L~ (Cage (n,C))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:]
the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:] is set
K506(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj1 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
W-most (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
SW-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
proj2 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | (L~ (Cage (n,C))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:]
K506(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj2 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (n,C)))),(S-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
NW-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj2 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (n,C)))),(N-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (n,C)))),(NW-corner (L~ (Cage (n,C))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Cage (n,C)))),(NW-corner (L~ (Cage (n,C)))))) /\ (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ (Cage (n,C)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Cage (n,C)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),REAL:]
the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))) is set
[: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),REAL:] is set
K506(((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),(proj2 | (W-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (n,C)))),K506(((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),(proj2 | (W-most (L~ (Cage (n,C))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
(W-min (L~ (Cage (n,C)))) .. (Lower_Seq (n,C)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
len (Lower_Seq (n,C)) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
rng (Cage (n,C)) is non empty non trivial V26() set
E-max (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj1 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
E-most (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
SE-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
|[(E-bound (L~ (Cage (n,C)))),(S-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
NE-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
|[(E-bound (L~ (Cage (n,C)))),(N-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Cage (n,C)))),(NE-corner (L~ (Cage (n,C))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SE-corner (L~ (Cage (n,C)))),(NE-corner (L~ (Cage (n,C)))))) /\ (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ (Cage (n,C)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Cage (n,C)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),REAL:]
the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))) is set
[: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),REAL:] is set
K507(((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),(proj2 | (E-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (n,C)))),K507(((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),(proj2 | (E-most (L~ (Cage (n,C))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
Rotate ((Cage (n,C)),(E-max (L~ (Cage (n,C))))) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
rng (Rotate ((Cage (n,C)),(E-max (L~ (Cage (n,C)))))) is non empty non trivial V26() set
(Rotate ((Cage (n,C)),(E-max (L~ (Cage (n,C)))))) -: (W-min (L~ (Cage (n,C)))) is V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like special unfolded FinSequence of the U1 of (TOP-REAL 2)
(W-min (L~ (Cage (n,C)))) .. (Rotate ((Cage (n,C)),(E-max (L~ (Cage (n,C)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
rng (Lower_Seq (n,C)) is non empty V26() set
(Lower_Seq (n,C)) /. (len (Lower_Seq (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
C is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
n is non empty connected compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
Upper_Seq (n,C) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq standard FinSequence of the U1 of (TOP-REAL 2)
(Upper_Seq (n,C)) /. 2 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Upper_Seq (n,C)) /. 2) `1 is V11() V12() ext-real Element of REAL
Cage (n,C) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
L~ (Cage (n,C)) is non empty closed connected V222() compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
W-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (n,C))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | (L~ (Cage (n,C))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:]
the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:] is set
K506(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj1 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
W-min (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
W-most (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
SW-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
proj2 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | (L~ (Cage (n,C))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:]
K506(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj2 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (n,C)))),(S-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
NW-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj2 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (n,C)))),(N-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (n,C)))),(NW-corner (L~ (Cage (n,C))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Cage (n,C)))),(NW-corner (L~ (Cage (n,C)))))) /\ (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ (Cage (n,C)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Cage (n,C)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),REAL:]
the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))) is set
[: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),REAL:] is set
K506(((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),(proj2 | (W-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (n,C)))),K506(((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),(proj2 | (W-most (L~ (Cage (n,C))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
E-max (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj1 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
E-most (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
SE-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
|[(E-bound (L~ (Cage (n,C)))),(S-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
NE-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
|[(E-bound (L~ (Cage (n,C)))),(N-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Cage (n,C)))),(NE-corner (L~ (Cage (n,C))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SE-corner (L~ (Cage (n,C)))),(NE-corner (L~ (Cage (n,C)))))) /\ (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ (Cage (n,C)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Cage (n,C)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),REAL:]
the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))) is set
[: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),REAL:] is set
K507(((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),(proj2 | (E-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (n,C)))),K507(((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),(proj2 | (E-most (L~ (Cage (n,C))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
N-min (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
N-most (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
LSeg ((NW-corner (L~ (Cage (n,C)))),(NE-corner (L~ (Cage (n,C))))) is closed closed connected compact compact horizontal Element of bool the U1 of (TOP-REAL 2)
(LSeg ((NW-corner (L~ (Cage (n,C)))),(NE-corner (L~ (Cage (n,C)))))) /\ (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (N-most (L~ (Cage (n,C)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most (L~ (Cage (n,C)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))),REAL:]
the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))) is set
[: the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))),REAL:] is set
K506(((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))),(proj1 | (N-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[K506(((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))),(proj1 | (N-most (L~ (Cage (n,C)))))),(N-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
rng (Cage (n,C)) is non empty non trivial V26() set
Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C))))) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
rng (Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) is non empty non trivial V26() set
len (Upper_Seq (n,C)) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
Seg (len (Upper_Seq (n,C))) is non empty V26() len (Upper_Seq (n,C)) -element V200() V201() V202() V203() V204() V205() Element of bool NAT
(E-max (L~ (Cage (n,C)))) .. (Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
Seg ((E-max (L~ (Cage (n,C)))) .. (Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C))))))) is V26() (E-max (L~ (Cage (n,C)))) .. (Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) -element V200() V201() V202() V203() V204() V205() Element of bool NAT
(Cage (n,C)) :- (W-min (L~ (Cage (n,C)))) is non empty V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
((Cage (n,C)) :- (W-min (L~ (Cage (n,C))))) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
rng ((Cage (n,C)) :- (W-min (L~ (Cage (n,C))))) is non empty V26() set
(Cage (n,C)) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
len (Cage (n,C)) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(W-min (L~ (Cage (n,C)))) .. (Cage (n,C)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
((W-min (L~ (Cage (n,C)))) .. (Cage (n,C))) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
W-max (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
K507(((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),(proj2 | (W-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (n,C)))),K507(((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),(proj2 | (W-most (L~ (Cage (n,C))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
(N-min (L~ (Cage (n,C)))) `2 is V11() V12() ext-real Element of REAL
(W-max (L~ (Cage (n,C)))) `2 is V11() V12() ext-real Element of REAL
{(N-min (L~ (Cage (n,C)))),(W-min (L~ (Cage (n,C))))} is non empty V26() set
card {(N-min (L~ (Cage (n,C)))),(W-min (L~ (Cage (n,C))))} is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
len ((Cage (n,C)) :- (W-min (L~ (Cage (n,C))))) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
((Cage (n,C)) :- (W-min (L~ (Cage (n,C))))) /. (len ((Cage (n,C)) :- (W-min (L~ (Cage (n,C)))))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(Cage (n,C)) /. (len (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
Sbo is set
card (rng ((Cage (n,C)) :- (W-min (L~ (Cage (n,C)))))) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
dom ((Cage (n,C)) :- (W-min (L~ (Cage (n,C))))) is non empty V26() V200() V201() V202() V203() V204() V205() Element of bool NAT
card (dom ((Cage (n,C)) :- (W-min (L~ (Cage (n,C)))))) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Upper_Seq (n,C)) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) -: (E-max (L~ (Cage (n,C)))) is V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like special unfolded FinSequence of the U1 of (TOP-REAL 2)
((Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) -: (E-max (L~ (Cage (n,C))))) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
1 -' 1 is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(1 -' 1) + ((W-min (L~ (Cage (n,C)))) .. (Cage (n,C))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Cage (n,C)) /. ((1 -' 1) + ((W-min (L~ (Cage (n,C)))) .. (Cage (n,C)))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
0 + ((W-min (L~ (Cage (n,C)))) .. (Cage (n,C))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Cage (n,C)) /. (0 + ((W-min (L~ (Cage (n,C)))) .. (Cage (n,C)))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) -: (E-max (L~ (Cage (n,C))))) /. 2 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) /. 2 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
2 -' 1 is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(2 -' 1) + ((W-min (L~ (Cage (n,C)))) .. (Cage (n,C))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Cage (n,C)) /. ((2 -' 1) + ((W-min (L~ (Cage (n,C)))) .. (Cage (n,C)))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
2 - 1 is V11() V12() ext-real set
(2 - 1) + ((W-min (L~ (Cage (n,C)))) .. (Cage (n,C))) is V11() V12() ext-real set
(Cage (n,C)) /. ((2 - 1) + ((W-min (L~ (Cage (n,C)))) .. (Cage (n,C)))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
C is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
n is non empty connected compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
Lower_Seq (n,C) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq standard FinSequence of the U1 of (TOP-REAL 2)
(Lower_Seq (n,C)) /. 2 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Lower_Seq (n,C)) /. 2) `1 is V11() V12() ext-real Element of REAL
Cage (n,C) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
L~ (Cage (n,C)) is non empty closed connected V222() compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
E-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (n,C))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | (L~ (Cage (n,C))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:]
the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:] is set
K507(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj1 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
E-max (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
E-most (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
SE-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
proj2 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | (L~ (Cage (n,C))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:]
K506(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj2 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (n,C)))),(S-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
NE-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj2 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (n,C)))),(N-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Cage (n,C)))),(NE-corner (L~ (Cage (n,C))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SE-corner (L~ (Cage (n,C)))),(NE-corner (L~ (Cage (n,C)))))) /\ (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ (Cage (n,C)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Cage (n,C)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),REAL:]
the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))) is set
[: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),REAL:] is set
K507(((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),(proj2 | (E-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (n,C)))),K507(((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),(proj2 | (E-most (L~ (Cage (n,C))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
E-min (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
K506(((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),(proj2 | (E-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (n,C)))),K506(((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),(proj2 | (E-most (L~ (Cage (n,C))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
S-max (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
S-most (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
SW-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
W-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
K506(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj1 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (n,C)))),(S-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (n,C)))),(SE-corner (L~ (Cage (n,C))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Cage (n,C)))),(SE-corner (L~ (Cage (n,C)))))) /\ (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (S-most (L~ (Cage (n,C)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (S-most (L~ (Cage (n,C)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))),REAL:]
the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))) is set
[: the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))),REAL:] is set
K507(((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))),(proj1 | (S-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[K507(((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))),(proj1 | (S-most (L~ (Cage (n,C)))))),(S-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
S-min (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
K506(((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))),(proj1 | (S-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[K506(((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))),(proj1 | (S-most (L~ (Cage (n,C)))))),(S-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
W-min (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
W-most (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
NW-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
|[(W-bound (L~ (Cage (n,C)))),(N-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (n,C)))),(NW-corner (L~ (Cage (n,C))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Cage (n,C)))),(NW-corner (L~ (Cage (n,C)))))) /\ (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ (Cage (n,C)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Cage (n,C)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),REAL:]
the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))) is set
[: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),REAL:] is set
K506(((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),(proj2 | (W-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (n,C)))),K506(((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),(proj2 | (W-most (L~ (Cage (n,C))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
N-min (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
N-most (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
LSeg ((NW-corner (L~ (Cage (n,C)))),(NE-corner (L~ (Cage (n,C))))) is closed closed connected compact compact horizontal Element of bool the U1 of (TOP-REAL 2)
(LSeg ((NW-corner (L~ (Cage (n,C)))),(NE-corner (L~ (Cage (n,C)))))) /\ (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (N-most (L~ (Cage (n,C)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most (L~ (Cage (n,C)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))),REAL:]
the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))) is set
[: the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))),REAL:] is set
K506(((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))),(proj1 | (N-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[K506(((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))),(proj1 | (N-most (L~ (Cage (n,C)))))),(N-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
rng (Cage (n,C)) is non empty non trivial V26() set
Rotate ((Cage (n,C)),(E-max (L~ (Cage (n,C))))) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
rng (Rotate ((Cage (n,C)),(E-max (L~ (Cage (n,C)))))) is non empty non trivial V26() set
len (Lower_Seq (n,C)) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(W-min (L~ (Cage (n,C)))) .. (Lower_Seq (n,C)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Rotate ((Cage (n,C)),(E-max (L~ (Cage (n,C)))))) -: (W-min (L~ (Cage (n,C)))) is V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like special unfolded FinSequence of the U1 of (TOP-REAL 2)
(W-min (L~ (Cage (n,C)))) .. ((Rotate ((Cage (n,C)),(E-max (L~ (Cage (n,C)))))) -: (W-min (L~ (Cage (n,C))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(W-min (L~ (Cage (n,C)))) .. (Rotate ((Cage (n,C)),(E-max (L~ (Cage (n,C)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
Seg ((W-min (L~ (Cage (n,C)))) .. (Rotate ((Cage (n,C)),(E-max (L~ (Cage (n,C))))))) is V26() (W-min (L~ (Cage (n,C)))) .. (Rotate ((Cage (n,C)),(E-max (L~ (Cage (n,C)))))) -element V200() V201() V202() V203() V204() V205() Element of bool NAT
(Cage (n,C)) :- (E-max (L~ (Cage (n,C)))) is non empty V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
((Cage (n,C)) :- (E-max (L~ (Cage (n,C))))) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
rng ((Cage (n,C)) :- (E-max (L~ (Cage (n,C))))) is non empty V26() set
N-max (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
K507(((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))),(proj1 | (N-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[K507(((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))),(proj1 | (N-most (L~ (Cage (n,C)))))),(N-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
(E-max (L~ (Cage (n,C)))) `1 is V11() V12() ext-real Element of REAL
(N-max (L~ (Cage (n,C)))) `1 is V11() V12() ext-real Element of REAL
{(N-min (L~ (Cage (n,C)))),(E-max (L~ (Cage (n,C))))} is non empty V26() set
card {(N-min (L~ (Cage (n,C)))),(E-max (L~ (Cage (n,C))))} is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Cage (n,C)) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(E-min (L~ (Cage (n,C)))) .. (Cage (n,C)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(E-max (L~ (Cage (n,C)))) .. (Cage (n,C)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(S-max (L~ (Cage (n,C)))) .. (Cage (n,C)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(S-min (L~ (Cage (n,C)))) .. (Cage (n,C)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(W-min (L~ (Cage (n,C)))) .. (Cage (n,C)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
len (Cage (n,C)) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
((E-max (L~ (Cage (n,C)))) .. (Cage (n,C))) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
len ((Cage (n,C)) :- (E-max (L~ (Cage (n,C))))) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
((Cage (n,C)) :- (E-max (L~ (Cage (n,C))))) /. (len ((Cage (n,C)) :- (E-max (L~ (Cage (n,C)))))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(Cage (n,C)) /. (len (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
FiP is set
card (rng ((Cage (n,C)) :- (E-max (L~ (Cage (n,C)))))) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
dom ((Cage (n,C)) :- (E-max (L~ (Cage (n,C))))) is non empty V26() V200() V201() V202() V203() V204() V205() Element of bool NAT
card (dom ((Cage (n,C)) :- (E-max (L~ (Cage (n,C)))))) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Lower_Seq (n,C)) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Rotate ((Cage (n,C)),(E-max (L~ (Cage (n,C)))))) -: (W-min (L~ (Cage (n,C))))) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(Rotate ((Cage (n,C)),(E-max (L~ (Cage (n,C)))))) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
1 -' 1 is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(1 -' 1) + ((E-max (L~ (Cage (n,C)))) .. (Cage (n,C))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Cage (n,C)) /. ((1 -' 1) + ((E-max (L~ (Cage (n,C)))) .. (Cage (n,C)))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
0 + ((E-max (L~ (Cage (n,C)))) .. (Cage (n,C))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Cage (n,C)) /. (0 + ((E-max (L~ (Cage (n,C)))) .. (Cage (n,C)))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Rotate ((Cage (n,C)),(E-max (L~ (Cage (n,C)))))) -: (W-min (L~ (Cage (n,C))))) /. 2 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(Rotate ((Cage (n,C)),(E-max (L~ (Cage (n,C)))))) /. 2 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
2 -' 1 is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(2 -' 1) + ((E-max (L~ (Cage (n,C)))) .. (Cage (n,C))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Cage (n,C)) /. ((2 -' 1) + ((E-max (L~ (Cage (n,C)))) .. (Cage (n,C)))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
2 - 1 is V11() V12() ext-real set
(2 - 1) + ((E-max (L~ (Cage (n,C)))) .. (Cage (n,C))) is V11() V12() ext-real set
(Cage (n,C)) /. ((2 - 1) + ((E-max (L~ (Cage (n,C)))) .. (Cage (n,C)))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
C is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
n is non empty connected compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
Cage (n,C) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
L~ (Cage (n,C)) is non empty closed connected V222() compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
W-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (n,C))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | (L~ (Cage (n,C))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:]
the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:] is set
K506(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj1 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
E-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj1 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
(W-bound (L~ (Cage (n,C)))) + (E-bound (L~ (Cage (n,C)))) is V11() V12() ext-real set
W-bound n is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | n is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | n is V13() Function-like V40( the U1 of ((TOP-REAL 2) | n), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | n),REAL:]
the U1 of ((TOP-REAL 2) | n) is non empty set
[: the U1 of ((TOP-REAL 2) | n),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | n),REAL:] is set
K506(((TOP-REAL 2) | n),(proj1 | n)) is V11() V12() ext-real Element of REAL
E-bound n is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | n),(proj1 | n)) is V11() V12() ext-real Element of REAL
(W-bound n) + (E-bound n) is V11() V12() ext-real set
(E-bound n) - (W-bound n) is V11() V12() ext-real set
2 |^ C is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
((E-bound n) - (W-bound n)) / (2 |^ C) is V11() V12() ext-real set
(E-bound n) + (((E-bound n) - (W-bound n)) / (2 |^ C)) is V11() V12() ext-real set
(W-bound (L~ (Cage (n,C)))) + ((E-bound n) + (((E-bound n) - (W-bound n)) / (2 |^ C))) is V11() V12() ext-real set
(W-bound n) - (((E-bound n) - (W-bound n)) / (2 |^ C)) is V11() V12() ext-real set
((W-bound n) - (((E-bound n) - (W-bound n)) / (2 |^ C))) + ((E-bound n) + (((E-bound n) - (W-bound n)) / (2 |^ C))) is V11() V12() ext-real set
C is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
n is non empty connected compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
Cage (n,C) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
L~ (Cage (n,C)) is non empty closed connected V222() compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
S-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (n,C))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj2 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | (L~ (Cage (n,C))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:]
the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:] is set
K506(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj2 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
N-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj2 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
(S-bound (L~ (Cage (n,C)))) + (N-bound (L~ (Cage (n,C)))) is V11() V12() ext-real set
S-bound n is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | n is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | n is V13() Function-like V40( the U1 of ((TOP-REAL 2) | n), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | n),REAL:]
the U1 of ((TOP-REAL 2) | n) is non empty set
[: the U1 of ((TOP-REAL 2) | n),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | n),REAL:] is set
K506(((TOP-REAL 2) | n),(proj2 | n)) is V11() V12() ext-real Element of REAL
N-bound n is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | n),(proj2 | n)) is V11() V12() ext-real Element of REAL
(S-bound n) + (N-bound n) is V11() V12() ext-real set
(N-bound n) - (S-bound n) is V11() V12() ext-real set
2 |^ C is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
((N-bound n) - (S-bound n)) / (2 |^ C) is V11() V12() ext-real set
(N-bound n) + (((N-bound n) - (S-bound n)) / (2 |^ C)) is V11() V12() ext-real set
(S-bound (L~ (Cage (n,C)))) + ((N-bound n) + (((N-bound n) - (S-bound n)) / (2 |^ C))) is V11() V12() ext-real set
(S-bound n) - (((N-bound n) - (S-bound n)) / (2 |^ C)) is V11() V12() ext-real set
((S-bound n) - (((N-bound n) - (S-bound n)) / (2 |^ C))) + ((N-bound n) + (((N-bound n) - (S-bound n)) / (2 |^ C))) is V11() V12() ext-real set
C is non empty connected compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
W-bound C is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | C is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | C is V13() Function-like V40( the U1 of ((TOP-REAL 2) | C), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | C),REAL:]
the U1 of ((TOP-REAL 2) | C) is non empty set
[: the U1 of ((TOP-REAL 2) | C),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | C),REAL:] is set
K506(((TOP-REAL 2) | C),(proj1 | C)) is V11() V12() ext-real Element of REAL
E-bound C is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | C),(proj1 | C)) is V11() V12() ext-real Element of REAL
(W-bound C) + (E-bound C) is V11() V12() ext-real set
((W-bound C) + (E-bound C)) / 2 is V11() V12() ext-real set
n is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
Gauge (C,n) is V13() non empty-yielding V16( NAT ) V17(K238( the U1 of (TOP-REAL 2))) Function-like V26() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K238( the U1 of (TOP-REAL 2))
width (Gauge (C,n)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
Center (Gauge (C,n)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
i is V6() V10() V11() V12() V26() cardinal ext-real non negative set
(Gauge (C,n)) * ((Center (Gauge (C,n))),i) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * ((Center (Gauge (C,n))),i)) `1 is V11() V12() ext-real Element of REAL
len (Gauge (C,n)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
Gauge (C,1) is V13() non empty-yielding V16( NAT ) V17(K238( the U1 of (TOP-REAL 2))) Function-like V26() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K238( the U1 of (TOP-REAL 2))
len (Gauge (C,1)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
j is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Gauge (C,n)) * ((Center (Gauge (C,n))),j) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * ((Center (Gauge (C,n))),j)) `1 is V11() V12() ext-real Element of REAL
Center (Gauge (C,1)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Gauge (C,1)) * ((Center (Gauge (C,1))),1) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Gauge (C,1)) * ((Center (Gauge (C,1))),1)) `1 is V11() V12() ext-real Element of REAL
C is non empty connected compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
S-bound C is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | C is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj2 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | C is V13() Function-like V40( the U1 of ((TOP-REAL 2) | C), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | C),REAL:]
the U1 of ((TOP-REAL 2) | C) is non empty set
[: the U1 of ((TOP-REAL 2) | C),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | C),REAL:] is set
K506(((TOP-REAL 2) | C),(proj2 | C)) is V11() V12() ext-real Element of REAL
N-bound C is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | C),(proj2 | C)) is V11() V12() ext-real Element of REAL
(S-bound C) + (N-bound C) is V11() V12() ext-real set
((S-bound C) + (N-bound C)) / 2 is V11() V12() ext-real set
i is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
n is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
Gauge (C,n) is V13() non empty-yielding V16( NAT ) V17(K238( the U1 of (TOP-REAL 2))) Function-like V26() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K238( the U1 of (TOP-REAL 2))
len (Gauge (C,n)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
Center (Gauge (C,n)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Gauge (C,n)) * (i,(Center (Gauge (C,n)))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (i,(Center (Gauge (C,n))))) `2 is V11() V12() ext-real Element of REAL
Gauge (C,1) is V13() non empty-yielding V16( NAT ) V17(K238( the U1 of (TOP-REAL 2))) Function-like V26() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K238( the U1 of (TOP-REAL 2))
len (Gauge (C,1)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
Center (Gauge (C,1)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Gauge (C,1)) * (1,(Center (Gauge (C,1)))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Gauge (C,1)) * (1,(Center (Gauge (C,1))))) `2 is V11() V12() ext-real Element of REAL
C is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
len C is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
C /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
n is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
i is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
mid (C,n,i) is V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
L~ (mid (C,n,i)) is closed compact Element of bool the U1 of (TOP-REAL 2)
len (mid (C,n,i)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
j is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
j + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
LSeg ((mid (C,n,i)),j) is closed Element of bool the U1 of (TOP-REAL 2)
i -' n is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(i -' n) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
j + n is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(j + n) -' 1 is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
LSeg (C,((j + n) -' 1)) is closed Element of bool the U1 of (TOP-REAL 2)
1 + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(1 + 1) - 1 is V11() V12() ext-real set
(j + n) - 1 is V11() V12() ext-real set
n - 1 is V11() V12() ext-real set
j + (n - 1) is V11() V12() ext-real set
1 - j is V11() V12() ext-real set
n -' i is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(n -' i) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
n - i is V11() V12() ext-real set
j - 1 is V11() V12() ext-real set
(j - 1) + i is V11() V12() ext-real set
1 - i is V11() V12() ext-real set
- (1 - i) is V11() V12() ext-real set
j + (- (1 - i)) is V11() V12() ext-real set
n - j is V11() V12() ext-real set
i - 1 is V11() V12() ext-real set
n -' j is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
LSeg (C,(n -' j)) is closed Element of bool the U1 of (TOP-REAL 2)
1 + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
C /. n is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
<*(C /. n)*> is non empty trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like constant V26() 1 -element FinSequence-like FinSubsequence-like special FinSequence of the U1 of (TOP-REAL 2)
C is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
len C is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
C /. (len C) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
n is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
i is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
mid (C,n,i) is V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
L~ (mid (C,n,i)) is closed compact Element of bool the U1 of (TOP-REAL 2)
len (mid (C,n,i)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
j is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
j + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
LSeg ((mid (C,n,i)),j) is closed Element of bool the U1 of (TOP-REAL 2)
i -' n is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(i -' n) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
1 + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
j + n is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(1 + 1) - 1 is V11() V12() ext-real set
(j + n) - 1 is V11() V12() ext-real set
(j + n) -' 1 is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
i - n is V11() V12() ext-real set
j - 1 is V11() V12() ext-real set
(j - 1) + n is V11() V12() ext-real set
dom C is non empty non trivial V26() V200() V201() V202() V203() V204() V205() Element of bool NAT
((j + n) - 1) + 1 is V11() V12() ext-real set
Seg (len C) is non empty V26() len C -element V200() V201() V202() V203() V204() V205() Element of bool NAT
((j + n) -' 1) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
LSeg (C,((j + n) -' 1)) is closed Element of bool the U1 of (TOP-REAL 2)
i + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(i + 1) - n is V11() V12() ext-real set
n -' i is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(n -' i) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
n - i is V11() V12() ext-real set
j - 1 is V11() V12() ext-real set
(j - 1) + i is V11() V12() ext-real set
1 - i is V11() V12() ext-real set
- (1 - i) is V11() V12() ext-real set
j + (- (1 - i)) is V11() V12() ext-real set
n - j is V11() V12() ext-real set
i - 1 is V11() V12() ext-real set
(n - j) + 1 is V11() V12() ext-real set
0 + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
n -' j is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
n - 1 is V11() V12() ext-real set
(n - 1) + 1 is V11() V12() ext-real set
(n -' j) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
dom C is non empty non trivial V26() V200() V201() V202() V203() V204() V205() Element of bool NAT
LSeg (C,(n -' j)) is closed Element of bool the U1 of (TOP-REAL 2)
C /. n is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
<*(C /. n)*> is non empty trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like constant V26() 1 -element FinSequence-like FinSubsequence-like special FinSequence of the U1 of (TOP-REAL 2)
C is non empty compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
n is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
Upper_Seq (C,n) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
rng (Upper_Seq (C,n)) is non empty V26() set
Cage (C,n) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
rng (Cage (C,n)) is non empty non trivial V26() set
Lower_Seq (C,n) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
rng (Lower_Seq (C,n)) is non empty V26() set
L~ (Cage (C,n)) is non empty closed connected V222() compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
E-max (L~ (Cage (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Cage (C,n))) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (C,n))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | (L~ (Cage (C,n))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL:]
the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL:] is set
K507(((TOP-REAL 2) | (L~ (Cage (C,n)))),(proj1 | (L~ (Cage (C,n))))) is V11() V12() ext-real Element of REAL
E-most (L~ (Cage (C,n))) is Element of bool the U1 of (TOP-REAL 2)
SE-corner (L~ (Cage (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Cage (C,n))) is V11() V12() ext-real Element of REAL
proj2 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | (L~ (Cage (C,n))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL:]
K506(((TOP-REAL 2) | (L~ (Cage (C,n)))),(proj2 | (L~ (Cage (C,n))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (C,n)))),(S-bound (L~ (Cage (C,n))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
NE-corner (L~ (Cage (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Cage (C,n))) is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | (L~ (Cage (C,n)))),(proj2 | (L~ (Cage (C,n))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (C,n)))),(N-bound (L~ (Cage (C,n))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Cage (C,n)))),(NE-corner (L~ (Cage (C,n))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SE-corner (L~ (Cage (C,n)))),(NE-corner (L~ (Cage (C,n)))))) /\ (L~ (Cage (C,n))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ (Cage (C,n)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Cage (C,n)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),REAL:]
the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))) is set
[: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),REAL:] is set
K507(((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),(proj2 | (E-most (L~ (Cage (C,n)))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (C,n)))),K507(((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),(proj2 | (E-most (L~ (Cage (C,n))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
W-min (L~ (Cage (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
W-bound (L~ (Cage (C,n))) is V11() V12() ext-real Element of REAL
K506(((TOP-REAL 2) | (L~ (Cage (C,n)))),(proj1 | (L~ (Cage (C,n))))) is V11() V12() ext-real Element of REAL
W-most (L~ (Cage (C,n))) is Element of bool the U1 of (TOP-REAL 2)
SW-corner (L~ (Cage (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
|[(W-bound (L~ (Cage (C,n)))),(S-bound (L~ (Cage (C,n))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
NW-corner (L~ (Cage (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
|[(W-bound (L~ (Cage (C,n)))),(N-bound (L~ (Cage (C,n))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (C,n)))),(NW-corner (L~ (Cage (C,n))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Cage (C,n)))),(NW-corner (L~ (Cage (C,n)))))) /\ (L~ (Cage (C,n))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ (Cage (C,n)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Cage (C,n)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),REAL:]
the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))) is set
[: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),REAL:] is set
K506(((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),(proj2 | (W-most (L~ (Cage (C,n)))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (C,n)))),K506(((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),(proj2 | (W-most (L~ (Cage (C,n))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
rng (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) is non empty non trivial V26() set
(Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) -: (E-max (L~ (Cage (C,n)))) is V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like special unfolded FinSequence of the U1 of (TOP-REAL 2)
(Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) :- (E-max (L~ (Cage (C,n)))) is non empty V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
C is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
n is non empty compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
Cage (n,C) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
Upper_Seq (n,C) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
(Upper_Seq (n,C)) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Upper_Seq (n,C)) /. 1) `1 is V11() V12() ext-real Element of REAL
L~ (Cage (n,C)) is non empty closed connected V222() compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
W-min (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
W-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (n,C))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | (L~ (Cage (n,C))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:]
the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:] is set
K506(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj1 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
W-most (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
SW-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
proj2 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | (L~ (Cage (n,C))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:]
K506(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj2 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (n,C)))),(S-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
NW-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj2 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (n,C)))),(N-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (n,C)))),(NW-corner (L~ (Cage (n,C))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Cage (n,C)))),(NW-corner (L~ (Cage (n,C)))))) /\ (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ (Cage (n,C)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Cage (n,C)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),REAL:]
the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))) is set
[: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),REAL:] is set
K506(((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),(proj2 | (W-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (n,C)))),K506(((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),(proj2 | (W-most (L~ (Cage (n,C))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
(W-min (L~ (Cage (n,C)))) `1 is V11() V12() ext-real Element of REAL
len (Upper_Seq (n,C)) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Upper_Seq (n,C)) /. (len (Upper_Seq (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Upper_Seq (n,C)) /. (len (Upper_Seq (n,C)))) `1 is V11() V12() ext-real Element of REAL
E-max (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj1 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
E-most (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
SE-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
|[(E-bound (L~ (Cage (n,C)))),(S-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
NE-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
|[(E-bound (L~ (Cage (n,C)))),(N-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Cage (n,C)))),(NE-corner (L~ (Cage (n,C))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SE-corner (L~ (Cage (n,C)))),(NE-corner (L~ (Cage (n,C)))))) /\ (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ (Cage (n,C)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Cage (n,C)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),REAL:]
the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))) is set
[: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),REAL:] is set
K507(((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),(proj2 | (E-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (n,C)))),K507(((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),(proj2 | (E-most (L~ (Cage (n,C))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
(E-max (L~ (Cage (n,C)))) `1 is V11() V12() ext-real Element of REAL
C is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
n is non empty compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
Cage (n,C) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
Lower_Seq (n,C) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
Rev (Lower_Seq (n,C)) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
(Rev (Lower_Seq (n,C))) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Rev (Lower_Seq (n,C))) /. 1) `1 is V11() V12() ext-real Element of REAL
len (Lower_Seq (n,C)) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Lower_Seq (n,C)) /. (len (Lower_Seq (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Lower_Seq (n,C)) /. (len (Lower_Seq (n,C)))) `1 is V11() V12() ext-real Element of REAL
L~ (Cage (n,C)) is non empty closed connected V222() compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
W-min (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
W-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (n,C))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | (L~ (Cage (n,C))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:]
the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:] is set
K506(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj1 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
W-most (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
SW-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
proj2 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | (L~ (Cage (n,C))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:]
K506(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj2 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (n,C)))),(S-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
NW-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj2 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (n,C)))),(N-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (n,C)))),(NW-corner (L~ (Cage (n,C))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Cage (n,C)))),(NW-corner (L~ (Cage (n,C)))))) /\ (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ (Cage (n,C)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Cage (n,C)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),REAL:]
the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))) is set
[: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),REAL:] is set
K506(((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),(proj2 | (W-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (n,C)))),K506(((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),(proj2 | (W-most (L~ (Cage (n,C))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
(W-min (L~ (Cage (n,C)))) `1 is V11() V12() ext-real Element of REAL
len (Rev (Lower_Seq (n,C))) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Rev (Lower_Seq (n,C))) /. (len (Rev (Lower_Seq (n,C)))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Rev (Lower_Seq (n,C))) /. (len (Rev (Lower_Seq (n,C))))) `1 is V11() V12() ext-real Element of REAL
(Rev (Lower_Seq (n,C))) /. (len (Lower_Seq (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Rev (Lower_Seq (n,C))) /. (len (Lower_Seq (n,C)))) `1 is V11() V12() ext-real Element of REAL
(Lower_Seq (n,C)) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Lower_Seq (n,C)) /. 1) `1 is V11() V12() ext-real Element of REAL
E-max (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj1 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
E-most (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
SE-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
|[(E-bound (L~ (Cage (n,C)))),(S-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
NE-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
|[(E-bound (L~ (Cage (n,C)))),(N-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Cage (n,C)))),(NE-corner (L~ (Cage (n,C))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SE-corner (L~ (Cage (n,C)))),(NE-corner (L~ (Cage (n,C)))))) /\ (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ (Cage (n,C)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Cage (n,C)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),REAL:]
the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))) is set
[: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),REAL:] is set
K507(((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),(proj2 | (E-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (n,C)))),K507(((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),(proj2 | (E-most (L~ (Cage (n,C))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
(E-max (L~ (Cage (n,C)))) `1 is V11() V12() ext-real Element of REAL
C is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
n is non empty connected compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
Gauge (n,C) is V13() non empty-yielding V16( NAT ) V17(K238( the U1 of (TOP-REAL 2))) Function-like V26() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K238( the U1 of (TOP-REAL 2))
len (Gauge (n,C)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
Upper_Seq (n,C) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq standard FinSequence of the U1 of (TOP-REAL 2)
rng (Upper_Seq (n,C)) is non empty V26() set
i is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Gauge (n,C)) * (i,1) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
dom (Upper_Seq (n,C)) is non empty non trivial V26() V200() V201() V202() V203() V204() V205() Element of bool NAT
j is V6() V10() V11() V12() V26() cardinal ext-real non negative set
(Upper_Seq (n,C)) . j is set
Emax is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
len (Upper_Seq (n,C)) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
Cage (n,C) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
L~ (Cage (n,C)) is non empty closed connected V222() compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
W-min (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
W-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (n,C))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | (L~ (Cage (n,C))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:]
the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:] is set
K506(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj1 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
W-most (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
SW-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
proj2 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | (L~ (Cage (n,C))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:]
K506(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj2 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (n,C)))),(S-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
NW-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj2 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (n,C)))),(N-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (n,C)))),(NW-corner (L~ (Cage (n,C))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Cage (n,C)))),(NW-corner (L~ (Cage (n,C)))))) /\ (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ (Cage (n,C)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Cage (n,C)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),REAL:]
the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))) is set
[: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),REAL:] is set
K506(((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),(proj2 | (W-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (n,C)))),K506(((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),(proj2 | (W-most (L~ (Cage (n,C))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C))))) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
N-min (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
N-most (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
NE-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj1 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (n,C)))),(N-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((NW-corner (L~ (Cage (n,C)))),(NE-corner (L~ (Cage (n,C))))) is closed closed connected compact compact horizontal Element of bool the U1 of (TOP-REAL 2)
(LSeg ((NW-corner (L~ (Cage (n,C)))),(NE-corner (L~ (Cage (n,C)))))) /\ (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (N-most (L~ (Cage (n,C)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most (L~ (Cage (n,C)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))),REAL:]
the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))) is set
[: the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))),REAL:] is set
K506(((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))),(proj1 | (N-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[K506(((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))),(proj1 | (N-most (L~ (Cage (n,C)))))),(N-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
(N-min (L~ (Cage (n,C)))) .. (Upper_Seq (n,C)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
E-max (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
E-most (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
SE-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
|[(E-bound (L~ (Cage (n,C)))),(S-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Cage (n,C)))),(NE-corner (L~ (Cage (n,C))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SE-corner (L~ (Cage (n,C)))),(NE-corner (L~ (Cage (n,C)))))) /\ (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ (Cage (n,C)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Cage (n,C)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),REAL:]
the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))) is set
[: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),REAL:] is set
K507(((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),(proj2 | (E-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (n,C)))),K507(((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),(proj2 | (E-most (L~ (Cage (n,C))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
rng (Cage (n,C)) is non empty non trivial V26() set
rng (Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) is non empty non trivial V26() set
(Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
L~ (Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) is non empty closed connected V222() compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
N-max (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
K507(((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))),(proj1 | (N-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[K507(((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))),(proj1 | (N-most (L~ (Cage (n,C)))))),(N-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
(N-max (L~ (Cage (n,C)))) .. (Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(N-min (L~ (Cage (n,C)))) .. (Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(E-max (L~ (Cage (n,C)))) .. (Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(E-max (L~ (Cage (n,C)))) .. (Upper_Seq (n,C)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(N-max (L~ (Cage (n,C)))) .. (Upper_Seq (n,C)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
Lower_Seq (n,C) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq standard FinSequence of the U1 of (TOP-REAL 2)
len (Lower_Seq (n,C)) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
width (Gauge (n,C)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(W-min (L~ (Cage (n,C)))) .. (Upper_Seq (n,C)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
W-max (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
K507(((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),(proj2 | (W-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (n,C)))),K507(((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),(proj2 | (W-most (L~ (Cage (n,C))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
(W-max (L~ (Cage (n,C)))) .. (Upper_Seq (n,C)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) -: (E-max (L~ (Cage (n,C)))) is V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like special unfolded FinSequence of the U1 of (TOP-REAL 2)
(Upper_Seq (n,C)) /. ((N-min (L~ (Cage (n,C)))) .. (Upper_Seq (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Gauge (n,C)) * (i,1)) `2 is V11() V12() ext-real Element of REAL
mid ((Upper_Seq (n,C)),((N-min (L~ (Cage (n,C)))) .. (Upper_Seq (n,C))),Emax) is V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
Sbo is V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special FinSequence of the U1 of (TOP-REAL 2)
Rev Sbo is V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
len Sbo is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
len (Rev Sbo) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Rev Sbo) /. (len (Rev Sbo)) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Rev Sbo) /. (len (Rev Sbo))) `2 is V11() V12() ext-real Element of REAL
Sbo /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(Sbo /. 1) `2 is V11() V12() ext-real Element of REAL
((Upper_Seq (n,C)) /. ((N-min (L~ (Cage (n,C)))) .. (Upper_Seq (n,C)))) `2 is V11() V12() ext-real Element of REAL
(N-min (L~ (Cage (n,C)))) `2 is V11() V12() ext-real Element of REAL
(Rev Sbo) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Rev Sbo) /. 1) `2 is V11() V12() ext-real Element of REAL
Sbo /. (len Sbo) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(Sbo /. (len Sbo)) `2 is V11() V12() ext-real Element of REAL
(Upper_Seq (n,C)) /. Emax is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Upper_Seq (n,C)) /. Emax) `2 is V11() V12() ext-real Element of REAL
((Gauge (n,C)) * (i,1)) `2 is V11() V12() ext-real Element of REAL
Rev (Lower_Seq (n,C)) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
1 + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
len (Rev (Lower_Seq (n,C))) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
L~ (Rev (Lower_Seq (n,C))) is non empty closed compact Element of bool the U1 of (TOP-REAL 2)
L~ (Lower_Seq (n,C)) is non empty closed compact Element of bool the U1 of (TOP-REAL 2)
L~ (Rev Sbo) is closed compact Element of bool the U1 of (TOP-REAL 2)
SW is set
L~ Sbo is closed compact Element of bool the U1 of (TOP-REAL 2)
L~ (mid ((Upper_Seq (n,C)),((N-min (L~ (Cage (n,C)))) .. (Upper_Seq (n,C))),Emax)) is closed compact Element of bool the U1 of (TOP-REAL 2)
L~ (Upper_Seq (n,C)) is non empty closed compact Element of bool the U1 of (TOP-REAL 2)
(L~ (Upper_Seq (n,C))) /\ (L~ (Lower_Seq (n,C))) is Element of bool the U1 of (TOP-REAL 2)
{(W-min (L~ (Cage (n,C)))),(E-max (L~ (Cage (n,C))))} is non empty V26() set
(Upper_Seq (n,C)) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Gauge (n,C)) * (i,1)) `1 is V11() V12() ext-real Element of REAL
(Gauge (n,C)) * (1,1) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Gauge (n,C)) * (1,1)) `1 is V11() V12() ext-real Element of REAL
(Upper_Seq (n,C)) /. (len (Upper_Seq (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(SE-corner (L~ (Cage (n,C)))) `2 is V11() V12() ext-real Element of REAL
E-min (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
K506(((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),(proj2 | (E-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (n,C)))),K506(((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),(proj2 | (E-most (L~ (Cage (n,C))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
(E-min (L~ (Cage (n,C)))) `2 is V11() V12() ext-real Element of REAL
(E-max (L~ (Cage (n,C)))) `2 is V11() V12() ext-real Element of REAL
C is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
n is non empty connected compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
Gauge (n,C) is V13() non empty-yielding V16( NAT ) V17(K238( the U1 of (TOP-REAL 2))) Function-like V26() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K238( the U1 of (TOP-REAL 2))
len (Gauge (n,C)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
width (Gauge (n,C)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
Lower_Seq (n,C) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq standard FinSequence of the U1 of (TOP-REAL 2)
rng (Lower_Seq (n,C)) is non empty V26() set
i is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Gauge (n,C)) * (i,(width (Gauge (n,C)))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
dom (Lower_Seq (n,C)) is non empty non trivial V26() V200() V201() V202() V203() V204() V205() Element of bool NAT
Emax is V6() V10() V11() V12() V26() cardinal ext-real non negative set
(Lower_Seq (n,C)) . Emax is set
Nbo is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
len (Lower_Seq (n,C)) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
Upper_Seq (n,C) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq standard FinSequence of the U1 of (TOP-REAL 2)
len (Upper_Seq (n,C)) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
Cage (n,C) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
L~ (Cage (n,C)) is non empty closed connected V222() compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
E-max (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (n,C))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | (L~ (Cage (n,C))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:]
the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:] is set
K507(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj1 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
E-most (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
SE-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
proj2 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | (L~ (Cage (n,C))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:]
K506(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj2 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (n,C)))),(S-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
NE-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj2 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (n,C)))),(N-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Cage (n,C)))),(NE-corner (L~ (Cage (n,C))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SE-corner (L~ (Cage (n,C)))),(NE-corner (L~ (Cage (n,C)))))) /\ (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ (Cage (n,C)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Cage (n,C)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),REAL:]
the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))) is set
[: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),REAL:] is set
K507(((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),(proj2 | (E-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (n,C)))),K507(((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),(proj2 | (E-most (L~ (Cage (n,C))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
Rotate ((Cage (n,C)),(E-max (L~ (Cage (n,C))))) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
S-max (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
S-most (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
SW-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
W-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
K506(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj1 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (n,C)))),(S-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (n,C)))),(SE-corner (L~ (Cage (n,C))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Cage (n,C)))),(SE-corner (L~ (Cage (n,C)))))) /\ (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (S-most (L~ (Cage (n,C)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (S-most (L~ (Cage (n,C)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))),REAL:]
the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))) is set
[: the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))),REAL:] is set
K507(((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))),(proj1 | (S-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[K507(((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))),(proj1 | (S-most (L~ (Cage (n,C)))))),(S-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
(S-max (L~ (Cage (n,C)))) .. (Lower_Seq (n,C)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
rng (Cage (n,C)) is non empty non trivial V26() set
(Rotate ((Cage (n,C)),(E-max (L~ (Cage (n,C)))))) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
L~ (Rotate ((Cage (n,C)),(E-max (L~ (Cage (n,C)))))) is non empty closed connected V222() compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
S-min (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
K506(((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))),(proj1 | (S-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[K506(((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))),(proj1 | (S-most (L~ (Cage (n,C)))))),(S-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
(S-min (L~ (Cage (n,C)))) .. (Rotate ((Cage (n,C)),(E-max (L~ (Cage (n,C)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(S-max (L~ (Cage (n,C)))) .. (Rotate ((Cage (n,C)),(E-max (L~ (Cage (n,C)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
W-min (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
W-most (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
NW-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
|[(W-bound (L~ (Cage (n,C)))),(N-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (n,C)))),(NW-corner (L~ (Cage (n,C))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Cage (n,C)))),(NW-corner (L~ (Cage (n,C)))))) /\ (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ (Cage (n,C)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Cage (n,C)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),REAL:]
the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))) is set
[: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),REAL:] is set
K506(((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),(proj2 | (W-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (n,C)))),K506(((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),(proj2 | (W-most (L~ (Cage (n,C))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
(W-min (L~ (Cage (n,C)))) .. (Rotate ((Cage (n,C)),(E-max (L~ (Cage (n,C)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
rng (Rotate ((Cage (n,C)),(E-max (L~ (Cage (n,C)))))) is non empty non trivial V26() set
(W-min (L~ (Cage (n,C)))) .. (Lower_Seq (n,C)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(S-min (L~ (Cage (n,C)))) .. (Lower_Seq (n,C)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(E-max (L~ (Cage (n,C)))) .. (Lower_Seq (n,C)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
E-min (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
K506(((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),(proj2 | (E-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (n,C)))),K506(((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),(proj2 | (E-most (L~ (Cage (n,C))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
(E-min (L~ (Cage (n,C)))) .. (Lower_Seq (n,C)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Rotate ((Cage (n,C)),(E-max (L~ (Cage (n,C)))))) -: (W-min (L~ (Cage (n,C)))) is V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like special unfolded FinSequence of the U1 of (TOP-REAL 2)
(Lower_Seq (n,C)) /. ((S-max (L~ (Cage (n,C)))) .. (Lower_Seq (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Gauge (n,C)) * (i,(width (Gauge (n,C))))) `2 is V11() V12() ext-real Element of REAL
mid ((Lower_Seq (n,C)),((S-max (L~ (Cage (n,C)))) .. (Lower_Seq (n,C))),Nbo) is V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
Wbo is V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special FinSequence of the U1 of (TOP-REAL 2)
Wbo /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(Wbo /. 1) `2 is V11() V12() ext-real Element of REAL
((Lower_Seq (n,C)) /. ((S-max (L~ (Cage (n,C)))) .. (Lower_Seq (n,C)))) `2 is V11() V12() ext-real Element of REAL
(S-max (L~ (Cage (n,C)))) `2 is V11() V12() ext-real Element of REAL
len Wbo is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
1 + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
Wbo /. (len Wbo) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(Wbo /. (len Wbo)) `2 is V11() V12() ext-real Element of REAL
(Lower_Seq (n,C)) /. Nbo is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Lower_Seq (n,C)) /. Nbo) `2 is V11() V12() ext-real Element of REAL
((Gauge (n,C)) * (i,(width (Gauge (n,C))))) `2 is V11() V12() ext-real Element of REAL
L~ (Upper_Seq (n,C)) is non empty closed compact Element of bool the U1 of (TOP-REAL 2)
L~ Wbo is closed compact Element of bool the U1 of (TOP-REAL 2)
SW is set
L~ (mid ((Lower_Seq (n,C)),((S-max (L~ (Cage (n,C)))) .. (Lower_Seq (n,C))),Nbo)) is closed compact Element of bool the U1 of (TOP-REAL 2)
L~ (Lower_Seq (n,C)) is non empty closed compact Element of bool the U1 of (TOP-REAL 2)
(L~ (Lower_Seq (n,C))) /\ (L~ (Upper_Seq (n,C))) is Element of bool the U1 of (TOP-REAL 2)
{(W-min (L~ (Cage (n,C)))),(E-max (L~ (Cage (n,C))))} is non empty V26() set
(Lower_Seq (n,C)) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Gauge (n,C)) * (i,(width (Gauge (n,C))))) `1 is V11() V12() ext-real Element of REAL
(Gauge (n,C)) * ((len (Gauge (n,C))),(width (Gauge (n,C)))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Gauge (n,C)) * ((len (Gauge (n,C))),(width (Gauge (n,C))))) `1 is V11() V12() ext-real Element of REAL
(Lower_Seq (n,C)) /. (len (Lower_Seq (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
W-max (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
K507(((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),(proj2 | (W-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (n,C)))),K507(((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),(proj2 | (W-most (L~ (Cage (n,C))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
(W-max (L~ (Cage (n,C)))) `2 is V11() V12() ext-real Element of REAL
(NW-corner (L~ (Cage (n,C)))) `2 is V11() V12() ext-real Element of REAL
(W-min (L~ (Cage (n,C)))) `2 is V11() V12() ext-real Element of REAL
C is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
n is non empty connected compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
Gauge (n,C) is V13() non empty-yielding V16( NAT ) V17(K238( the U1 of (TOP-REAL 2))) Function-like V26() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K238( the U1 of (TOP-REAL 2))
len (Gauge (n,C)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
Upper_Seq (n,C) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq standard FinSequence of the U1 of (TOP-REAL 2)
L~ (Upper_Seq (n,C)) is non empty closed compact Element of bool the U1 of (TOP-REAL 2)
i is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Gauge (n,C)) * (i,1) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
len (Upper_Seq (n,C)) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
Emax is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
Emax + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
LSeg ((Upper_Seq (n,C)),Emax) is closed Element of bool the U1 of (TOP-REAL 2)
(Upper_Seq (n,C)) /. Emax is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(Upper_Seq (n,C)) /. (Emax + 1) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg (((Upper_Seq (n,C)) /. Emax),((Upper_Seq (n,C)) /. (Emax + 1))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
dom (Upper_Seq (n,C)) is non empty non trivial V26() V200() V201() V202() V203() V204() V205() Element of bool NAT
width (Gauge (n,C)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
[i,1] is non empty set
{i,1} is non empty V26() V30() V200() V201() V202() V203() V204() V205() set
{i} is non empty trivial V26() V30() 1 -element V200() V201() V202() V203() V204() V205() set
{{i,1},{i}} is non empty V26() V30() set
Indices (Gauge (n,C)) is set
rng (Upper_Seq (n,C)) is non empty V26() set
Nbo is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
Ebo is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
[Nbo,Ebo] is non empty set
{Nbo,Ebo} is non empty V26() V30() V200() V201() V202() V203() V204() V205() set
{Nbo} is non empty trivial V26() V30() 1 -element V200() V201() V202() V203() V204() V205() set
{{Nbo,Ebo},{Nbo}} is non empty V26() V30() set
(Gauge (n,C)) * (Nbo,Ebo) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
Sbo is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
Wbo is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
[Sbo,Wbo] is non empty set
{Sbo,Wbo} is non empty V26() V30() V200() V201() V202() V203() V204() V205() set
{Sbo} is non empty trivial V26() V30() 1 -element V200() V201() V202() V203() V204() V205() set
{{Sbo,Wbo},{Sbo}} is non empty V26() V30() set
(Gauge (n,C)) * (Sbo,Wbo) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
Ebo + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
Nbo + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
Sbo + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
Wbo + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
((Gauge (n,C)) * (Nbo,Ebo)) `2 is V11() V12() ext-real Element of REAL
((Gauge (n,C)) * (Sbo,Wbo)) `2 is V11() V12() ext-real Element of REAL
((Gauge (n,C)) * (i,1)) `2 is V11() V12() ext-real Element of REAL
((Gauge (n,C)) * (Nbo,Ebo)) `1 is V11() V12() ext-real Element of REAL
(Gauge (n,C)) * (Sbo,1) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Gauge (n,C)) * (Sbo,1)) `1 is V11() V12() ext-real Element of REAL
((Gauge (n,C)) * (Sbo,Wbo)) `1 is V11() V12() ext-real Element of REAL
((Gauge (n,C)) * (i,1)) `1 is V11() V12() ext-real Element of REAL
((Gauge (n,C)) * (Nbo,Ebo)) `2 is V11() V12() ext-real Element of REAL
(Gauge (n,C)) * (1,Wbo) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Gauge (n,C)) * (1,Wbo)) `2 is V11() V12() ext-real Element of REAL
((Gauge (n,C)) * (Sbo,Wbo)) `2 is V11() V12() ext-real Element of REAL
((Gauge (n,C)) * (i,1)) `2 is V11() V12() ext-real Element of REAL
((Gauge (n,C)) * (Nbo,Ebo)) `2 is V11() V12() ext-real Element of REAL
(Gauge (n,C)) * (1,Wbo) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Gauge (n,C)) * (1,Wbo)) `2 is V11() V12() ext-real Element of REAL
((Gauge (n,C)) * (Sbo,Wbo)) `2 is V11() V12() ext-real Element of REAL
((Gauge (n,C)) * (i,1)) `2 is V11() V12() ext-real Element of REAL
((Gauge (n,C)) * (Sbo,Wbo)) `2 is V11() V12() ext-real Element of REAL
((Gauge (n,C)) * (Nbo,Ebo)) `2 is V11() V12() ext-real Element of REAL
((Gauge (n,C)) * (i,1)) `2 is V11() V12() ext-real Element of REAL
((Gauge (n,C)) * (Nbo,Ebo)) `1 is V11() V12() ext-real Element of REAL
(Gauge (n,C)) * (Sbo,1) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Gauge (n,C)) * (Sbo,1)) `1 is V11() V12() ext-real Element of REAL
((Gauge (n,C)) * (Sbo,Wbo)) `1 is V11() V12() ext-real Element of REAL
((Gauge (n,C)) * (i,1)) `1 is V11() V12() ext-real Element of REAL
C is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
n is non empty connected compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
Gauge (n,C) is V13() non empty-yielding V16( NAT ) V17(K238( the U1 of (TOP-REAL 2))) Function-like V26() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K238( the U1 of (TOP-REAL 2))
len (Gauge (n,C)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
width (Gauge (n,C)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
Lower_Seq (n,C) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq standard FinSequence of the U1 of (TOP-REAL 2)
L~ (Lower_Seq (n,C)) is non empty closed compact Element of bool the U1 of (TOP-REAL 2)
j is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Gauge (n,C)) * (j,(width (Gauge (n,C)))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
len (Lower_Seq (n,C)) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
Nbo is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
Nbo + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
LSeg ((Lower_Seq (n,C)),Nbo) is closed Element of bool the U1 of (TOP-REAL 2)
(Lower_Seq (n,C)) /. Nbo is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(Lower_Seq (n,C)) /. (Nbo + 1) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg (((Lower_Seq (n,C)) /. Nbo),((Lower_Seq (n,C)) /. (Nbo + 1))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
dom (Lower_Seq (n,C)) is non empty non trivial V26() V200() V201() V202() V203() V204() V205() Element of bool NAT
[j,(width (Gauge (n,C)))] is non empty set
{j,(width (Gauge (n,C)))} is non empty V26() V30() V200() V201() V202() V203() V204() V205() set
{j} is non empty trivial V26() V30() 1 -element V200() V201() V202() V203() V204() V205() set
{{j,(width (Gauge (n,C)))},{j}} is non empty V26() V30() set
Indices (Gauge (n,C)) is set
rng (Lower_Seq (n,C)) is non empty V26() set
Ebo is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
Sbo is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
[Ebo,Sbo] is non empty set
{Ebo,Sbo} is non empty V26() V30() V200() V201() V202() V203() V204() V205() set
{Ebo} is non empty trivial V26() V30() 1 -element V200() V201() V202() V203() V204() V205() set
{{Ebo,Sbo},{Ebo}} is non empty V26() V30() set
(Gauge (n,C)) * (Ebo,Sbo) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
Wbo is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
SW is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
[Wbo,SW] is non empty set
{Wbo,SW} is non empty V26() V30() V200() V201() V202() V203() V204() V205() set
{Wbo} is non empty trivial V26() V30() 1 -element V200() V201() V202() V203() V204() V205() set
{{Wbo,SW},{Wbo}} is non empty V26() V30() set
(Gauge (n,C)) * (Wbo,SW) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
Sbo + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
Ebo + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
Wbo + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
SW + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
((Gauge (n,C)) * (Wbo,SW)) `2 is V11() V12() ext-real Element of REAL
((Gauge (n,C)) * (Ebo,Sbo)) `2 is V11() V12() ext-real Element of REAL
((Gauge (n,C)) * (j,(width (Gauge (n,C))))) `2 is V11() V12() ext-real Element of REAL
((Gauge (n,C)) * (Ebo,Sbo)) `1 is V11() V12() ext-real Element of REAL
(Gauge (n,C)) * (Wbo,1) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Gauge (n,C)) * (Wbo,1)) `1 is V11() V12() ext-real Element of REAL
((Gauge (n,C)) * (Wbo,SW)) `1 is V11() V12() ext-real Element of REAL
((Gauge (n,C)) * (j,(width (Gauge (n,C))))) `1 is V11() V12() ext-real Element of REAL
((Gauge (n,C)) * (Ebo,Sbo)) `2 is V11() V12() ext-real Element of REAL
(Gauge (n,C)) * (1,SW) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Gauge (n,C)) * (1,SW)) `2 is V11() V12() ext-real Element of REAL
((Gauge (n,C)) * (Wbo,SW)) `2 is V11() V12() ext-real Element of REAL
((Gauge (n,C)) * (j,(width (Gauge (n,C))))) `2 is V11() V12() ext-real Element of REAL
((Gauge (n,C)) * (Ebo,Sbo)) `2 is V11() V12() ext-real Element of REAL
(Gauge (n,C)) * (1,SW) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Gauge (n,C)) * (1,SW)) `2 is V11() V12() ext-real Element of REAL
((Gauge (n,C)) * (Wbo,SW)) `2 is V11() V12() ext-real Element of REAL
((Gauge (n,C)) * (j,(width (Gauge (n,C))))) `2 is V11() V12() ext-real Element of REAL
((Gauge (n,C)) * (Ebo,Sbo)) `2 is V11() V12() ext-real Element of REAL
((Gauge (n,C)) * (Wbo,SW)) `2 is V11() V12() ext-real Element of REAL
((Gauge (n,C)) * (j,(width (Gauge (n,C))))) `2 is V11() V12() ext-real Element of REAL
((Gauge (n,C)) * (Ebo,Sbo)) `1 is V11() V12() ext-real Element of REAL
(Gauge (n,C)) * (Wbo,1) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Gauge (n,C)) * (Wbo,1)) `1 is V11() V12() ext-real Element of REAL
((Gauge (n,C)) * (Wbo,SW)) `1 is V11() V12() ext-real Element of REAL
((Gauge (n,C)) * (j,(width (Gauge (n,C))))) `1 is V11() V12() ext-real Element of REAL
C is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
n is non empty connected compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
Gauge (n,C) is V13() non empty-yielding V16( NAT ) V17(K238( the U1 of (TOP-REAL 2))) Function-like V26() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K238( the U1 of (TOP-REAL 2))
len (Gauge (n,C)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
width (Gauge (n,C)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
Cage (n,C) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
L~ (Cage (n,C)) is non empty closed connected V222() compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
Lower_Seq (n,C) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq standard FinSequence of the U1 of (TOP-REAL 2)
L~ (Lower_Seq (n,C)) is non empty closed compact Element of bool the U1 of (TOP-REAL 2)
i is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
j is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Gauge (n,C)) * (i,j) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(Gauge (n,C)) * (i,1) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (n,C)) * (i,1)),((Gauge (n,C)) * (i,j))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
W-min (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
W-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (n,C))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | (L~ (Cage (n,C))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:]
the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:] is set
K506(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj1 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
W-most (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
SW-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
proj2 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | (L~ (Cage (n,C))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (n,C)))),REAL:]
K506(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj2 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (n,C)))),(S-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
NW-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj2 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (n,C)))),(N-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (n,C)))),(NW-corner (L~ (Cage (n,C))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Cage (n,C)))),(NW-corner (L~ (Cage (n,C)))))) /\ (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ (Cage (n,C)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Cage (n,C)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),REAL:]
the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))) is set
[: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),REAL:] is set
K506(((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),(proj2 | (W-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (n,C)))),K506(((TOP-REAL 2) | (W-most (L~ (Cage (n,C))))),(proj2 | (W-most (L~ (Cage (n,C))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C))))) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
E-max (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Cage (n,C))) is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | (L~ (Cage (n,C)))),(proj1 | (L~ (Cage (n,C))))) is V11() V12() ext-real Element of REAL
E-most (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
SE-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
|[(E-bound (L~ (Cage (n,C)))),(S-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
NE-corner (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
|[(E-bound (L~ (Cage (n,C)))),(N-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Cage (n,C)))),(NE-corner (L~ (Cage (n,C))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SE-corner (L~ (Cage (n,C)))),(NE-corner (L~ (Cage (n,C)))))) /\ (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ (Cage (n,C)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Cage (n,C)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),REAL:]
the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))) is set
[: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),REAL:] is set
K507(((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),(proj2 | (E-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (n,C)))),K507(((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),(proj2 | (E-most (L~ (Cage (n,C))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
(Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) :- (E-max (L~ (Cage (n,C)))) is non empty V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
len (Lower_Seq (n,C)) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
mid ((Lower_Seq (n,C)),2,(len (Lower_Seq (n,C)))) is V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
Upper_Seq (n,C) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq standard FinSequence of the U1 of (TOP-REAL 2)
L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j))) is V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
<*((Gauge (n,C)) * (i,1))*> is non empty trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like constant V26() 1 -element FinSequence-like FinSubsequence-like special FinSequence of the U1 of (TOP-REAL 2)
<*((Gauge (n,C)) * (i,1))*> ^ (L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j)))) is non empty V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
<*(NE-corner (L~ (Cage (n,C))))*> is non empty trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like constant V26() 1 -element FinSequence-like FinSubsequence-like special FinSequence of the U1 of (TOP-REAL 2)
(<*((Gauge (n,C)) * (i,1))*> ^ (L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j))))) ^ <*(NE-corner (L~ (Cage (n,C))))*> is non empty V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
L~ (Upper_Seq (n,C)) is non empty closed compact Element of bool the U1 of (TOP-REAL 2)
(L~ (Upper_Seq (n,C))) \/ (L~ (Lower_Seq (n,C))) is non empty Element of bool the U1 of (TOP-REAL 2)
(Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) -: (E-max (L~ (Cage (n,C)))) is V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like special unfolded FinSequence of the U1 of (TOP-REAL 2)
len (Upper_Seq (n,C)) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
((Gauge (n,C)) * (i,1)) `2 is V11() V12() ext-real Element of REAL
(Gauge (n,C)) * (1,1) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Gauge (n,C)) * (1,1)) `2 is V11() V12() ext-real Element of REAL
(W-min (L~ (Cage (n,C)))) `1 is V11() V12() ext-real Element of REAL
(W-min (L~ (Cage (n,C)))) `2 is V11() V12() ext-real Element of REAL
rng (Lower_Seq (n,C)) is non empty V26() set
((Gauge (n,C)) * (i,j)) `1 is V11() V12() ext-real Element of REAL
((Gauge (n,C)) * (i,j)) `2 is V11() V12() ext-real Element of REAL
(Lower_Seq (n,C)) /. (len (Lower_Seq (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Gauge (n,C)) * (1,1)) `1 is V11() V12() ext-real Element of REAL
(Gauge (n,C)) * (1,j) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (n,C)) * (1,1)),((Gauge (n,C)) * (1,j))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(Upper_Seq (n,C)) . (len (Upper_Seq (n,C))) is set
len (Cage (n,C)) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
rng (Cage (n,C)) is non empty non trivial V26() set
(NE-corner (L~ (Cage (n,C)))) `2 is V11() V12() ext-real Element of REAL
(NE-corner (L~ (Cage (n,C)))) `1 is V11() V12() ext-real Element of REAL
{ b₁ where b₁ is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2) : ( b₁ `1 = E-bound (L~ (Cage (n,C))) & b<sub>1</sub> `2 <= N-bound (L~ (Cage (n,C))) & S-bound (L~ (Cage (n,C))) <= b₁ `2 ) } is set
(E-max (L~ (Cage (n,C)))) `2 is V11() V12() ext-real Element of REAL
(E-max (L~ (Cage (n,C)))) `1 is V11() V12() ext-real Element of REAL
Index (((Gauge (n,C)) * (i,j)),(Upper_Seq (n,C))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Index (((Gauge (n,C)) * (i,j)),(Upper_Seq (n,C)))) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Upper_Seq (n,C)) . ((Index (((Gauge (n,C)) * (i,j)),(Upper_Seq (n,C)))) + 1) is set
<*((Gauge (n,C)) * (i,j))*> is non empty trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like constant V26() 1 -element FinSequence-like FinSubsequence-like special FinSequence of the U1 of (TOP-REAL 2)
mid ((Upper_Seq (n,C)),((Index (((Gauge (n,C)) * (i,j)),(Upper_Seq (n,C)))) + 1),(len (Upper_Seq (n,C)))) is V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
<*((Gauge (n,C)) * (i,j))*> ^ (mid ((Upper_Seq (n,C)),((Index (((Gauge (n,C)) * (i,j)),(Upper_Seq (n,C)))) + 1),(len (Upper_Seq (n,C))))) is non empty V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
rng (L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j)))) is V26() set
rng <*((Gauge (n,C)) * (i,j))*> is non empty trivial V26() 1 -element set
rng (mid ((Upper_Seq (n,C)),((Index (((Gauge (n,C)) * (i,j)),(Upper_Seq (n,C)))) + 1),(len (Upper_Seq (n,C))))) is V26() set
(rng <*((Gauge (n,C)) * (i,j))*>) \/ (rng (mid ((Upper_Seq (n,C)),((Index (((Gauge (n,C)) * (i,j)),(Upper_Seq (n,C)))) + 1),(len (Upper_Seq (n,C)))))) is non empty V26() set
{((Gauge (n,C)) * (i,j))} is non empty trivial V26() 1 -element set
{((Gauge (n,C)) * (i,j))} \/ (rng (mid ((Upper_Seq (n,C)),((Index (((Gauge (n,C)) * (i,j)),(Upper_Seq (n,C)))) + 1),(len (Upper_Seq (n,C)))))) is non empty V26() set
LaP is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
LaP + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Cage (n,C)) /. LaP is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(Cage (n,C)) /. (LaP + 1) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg (((Cage (n,C)) /. LaP),((Cage (n,C)) /. (LaP + 1))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
((Cage (n,C)) /. LaP) `1 is V11() V12() ext-real Element of REAL
((Cage (n,C)) /. (LaP + 1)) `1 is V11() V12() ext-real Element of REAL
((Cage (n,C)) /. LaP) `2 is V11() V12() ext-real Element of REAL
((Cage (n,C)) /. (LaP + 1)) `2 is V11() V12() ext-real Element of REAL
(NE-corner (L~ (Cage (n,C)))) `2 is V11() V12() ext-real Element of REAL
(NE-corner (L~ (Cage (n,C)))) `1 is V11() V12() ext-real Element of REAL
dom (Cage (n,C)) is non empty non trivial V26() V200() V201() V202() V203() V204() V205() Element of bool NAT
((Cage (n,C)) /. LaP) `2 is V11() V12() ext-real Element of REAL
((Cage (n,C)) /. (LaP + 1)) `2 is V11() V12() ext-real Element of REAL
((Cage (n,C)) /. LaP) `1 is V11() V12() ext-real Element of REAL
((Cage (n,C)) /. (LaP + 1)) `1 is V11() V12() ext-real Element of REAL
(NE-corner (L~ (Cage (n,C)))) `1 is V11() V12() ext-real Element of REAL
(NE-corner (L~ (Cage (n,C)))) `2 is V11() V12() ext-real Element of REAL
dom (Cage (n,C)) is non empty non trivial V26() V200() V201() V202() V203() V204() V205() Element of bool NAT
((Cage (n,C)) /. LaP) `1 is V11() V12() ext-real Element of REAL
((Cage (n,C)) /. (LaP + 1)) `1 is V11() V12() ext-real Element of REAL
((Cage (n,C)) /. LaP) `2 is V11() V12() ext-real Element of REAL
((Cage (n,C)) /. (LaP + 1)) `2 is V11() V12() ext-real Element of REAL
rng (Upper_Seq (n,C)) is non empty V26() set
Index (((Gauge (n,C)) * (i,j)),(Upper_Seq (n,C))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Index (((Gauge (n,C)) * (i,j)),(Upper_Seq (n,C)))) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Upper_Seq (n,C)) . ((Index (((Gauge (n,C)) * (i,j)),(Upper_Seq (n,C)))) + 1) is set
mid ((Upper_Seq (n,C)),((Index (((Gauge (n,C)) * (i,j)),(Upper_Seq (n,C)))) + 1),(len (Upper_Seq (n,C)))) is V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
rng (L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j)))) is V26() set
rng (Upper_Seq (n,C)) is non empty V26() set
Index (((Gauge (n,C)) * (i,j)),(Upper_Seq (n,C))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Index (((Gauge (n,C)) * (i,j)),(Upper_Seq (n,C)))) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Upper_Seq (n,C)) . ((Index (((Gauge (n,C)) * (i,j)),(Upper_Seq (n,C)))) + 1) is set
rng (L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j)))) is V26() set
rng (L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j)))) is V26() set
{((Gauge (n,C)) * (i,1))} is non empty trivial V26() 1 -element set
rng <*((Gauge (n,C)) * (i,1))*> is non empty trivial V26() 1 -element set
(rng <*((Gauge (n,C)) * (i,1))*>) \/ (rng (L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j))))) is non empty V26() set
rng (<*((Gauge (n,C)) * (i,1))*> ^ (L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j))))) is non empty V26() set
{(NE-corner (L~ (Cage (n,C))))} is non empty trivial V26() 1 -element set
rng <*(NE-corner (L~ (Cage (n,C))))*> is non empty trivial V26() 1 -element set
len ((<*((Gauge (n,C)) * (i,1))*> ^ (L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j))))) ^ <*(NE-corner (L~ (Cage (n,C))))*>) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
len (<*((Gauge (n,C)) * (i,1))*> ^ (L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j))))) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(len (<*((Gauge (n,C)) * (i,1))*> ^ (L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j)))))) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
len (L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j)))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
1 + (len (L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j))))) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(1 + (len (L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j)))))) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
0 + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
dom (L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j)))) is V26() V200() V201() V202() V203() V204() V205() Element of bool NAT
(L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j)))) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j)))) . 1 is set
(L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j)))) ^ <*(NE-corner (L~ (Cage (n,C))))*> is non empty V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
((L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j)))) ^ <*(NE-corner (L~ (Cage (n,C))))*>) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
1 + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
<*((Gauge (n,C)) * (i,1))*> ^ ((L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j)))) ^ <*(NE-corner (L~ (Cage (n,C))))*>) is non empty V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
((<*((Gauge (n,C)) * (i,1))*> ^ (L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j))))) ^ <*(NE-corner (L~ (Cage (n,C))))*>) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(((<*((Gauge (n,C)) * (i,1))*> ^ (L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j))))) ^ <*(NE-corner (L~ (Cage (n,C))))*>) /. 1) `2 is V11() V12() ext-real Element of REAL
((<*((Gauge (n,C)) * (i,1))*> ^ (L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j))))) ^ <*(NE-corner (L~ (Cage (n,C))))*>) /. (len ((<*((Gauge (n,C)) * (i,1))*> ^ (L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j))))) ^ <*(NE-corner (L~ (Cage (n,C))))*>)) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(((<*((Gauge (n,C)) * (i,1))*> ^ (L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j))))) ^ <*(NE-corner (L~ (Cage (n,C))))*>) /. (len ((<*((Gauge (n,C)) * (i,1))*> ^ (L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j))))) ^ <*(NE-corner (L~ (Cage (n,C))))*>))) `2 is V11() V12() ext-real Element of REAL
(Cage (n,C)) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
N-min (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
N-most (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
LSeg ((NW-corner (L~ (Cage (n,C)))),(NE-corner (L~ (Cage (n,C))))) is closed closed connected compact compact horizontal Element of bool the U1 of (TOP-REAL 2)
(LSeg ((NW-corner (L~ (Cage (n,C)))),(NE-corner (L~ (Cage (n,C)))))) /\ (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (N-most (L~ (Cage (n,C)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most (L~ (Cage (n,C)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))),REAL:]
the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))) is set
[: the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))),REAL:] is set
K506(((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))),(proj1 | (N-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[K506(((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))),(proj1 | (N-most (L~ (Cage (n,C)))))),(N-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
N-max (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
K507(((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))),(proj1 | (N-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[K507(((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))),(proj1 | (N-most (L~ (Cage (n,C)))))),(N-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
(N-max (L~ (Cage (n,C)))) .. (Cage (n,C)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(E-max (L~ (Cage (n,C)))) .. (Cage (n,C)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
E-min (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
K506(((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),(proj2 | (E-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (n,C)))),K506(((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),(proj2 | (E-most (L~ (Cage (n,C))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
(E-min (L~ (Cage (n,C)))) .. (Cage (n,C)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
S-max (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
S-most (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (n,C)))),(SE-corner (L~ (Cage (n,C))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Cage (n,C)))),(SE-corner (L~ (Cage (n,C)))))) /\ (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (S-most (L~ (Cage (n,C)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (S-most (L~ (Cage (n,C)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))),REAL:]
the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))) is set
[: the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))),REAL:] is set
K507(((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))),(proj1 | (S-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[K507(((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))),(proj1 | (S-most (L~ (Cage (n,C)))))),(S-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
(S-max (L~ (Cage (n,C)))) .. (Cage (n,C)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
S-min (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
K506(((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))),(proj1 | (S-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[K506(((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))),(proj1 | (S-most (L~ (Cage (n,C)))))),(S-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
(S-min (L~ (Cage (n,C)))) .. (Cage (n,C)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(W-min (L~ (Cage (n,C)))) .. (Cage (n,C)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
((E-max (L~ (Cage (n,C)))) .. (Cage (n,C))) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Cage (n,C)) /. ((E-max (L~ (Cage (n,C)))) .. (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(Cage (n,C)) /. (((E-max (L~ (Cage (n,C)))) .. (Cage (n,C))) + 1) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Cage (n,C)) /. (((E-max (L~ (Cage (n,C)))) .. (Cage (n,C))) + 1)) `1 is V11() V12() ext-real Element of REAL
(E-max (L~ (Cage (n,C)))) .. (Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(len (Cage (n,C))) + ((E-max (L~ (Cage (n,C)))) .. (Cage (n,C))) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
((len (Cage (n,C))) + ((E-max (L~ (Cage (n,C)))) .. (Cage (n,C)))) - ((W-min (L~ (Cage (n,C)))) .. (Cage (n,C))) is V11() V12() ext-real set
LaP is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
dom <*((Gauge (n,C)) * (i,1))*> is non empty trivial V26() 1 -element V200() V201() V202() V203() V204() V205() Element of bool NAT
<*((Gauge (n,C)) * (i,1))*> . LaP is set
<*((Gauge (n,C)) * (i,1))*> /. LaP is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(Gauge (n,C)) * (1,1) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Gauge (n,C)) * (1,1)) `1 is V11() V12() ext-real Element of REAL
((Gauge (n,C)) * (i,1)) `1 is V11() V12() ext-real Element of REAL
(<*((Gauge (n,C)) * (i,1))*> /. LaP) `1 is V11() V12() ext-real Element of REAL
(Gauge (n,C)) * ((len (Gauge (n,C))),1) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Gauge (n,C)) * ((len (Gauge (n,C))),1)) `1 is V11() V12() ext-real Element of REAL
(<*((Gauge (n,C)) * (i,1))*> /. LaP) `2 is V11() V12() ext-real Element of REAL
dom (Lower_Seq (n,C)) is non empty non trivial V26() V200() V201() V202() V203() V204() V205() Element of bool NAT
<*((Gauge (n,C)) * (i,j))*> is non empty trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like constant V26() 1 -element FinSequence-like FinSubsequence-like special FinSequence of the U1 of (TOP-REAL 2)
1 + (((len (Cage (n,C))) + ((E-max (L~ (Cage (n,C)))) .. (Cage (n,C)))) - ((W-min (L~ (Cage (n,C)))) .. (Cage (n,C)))) is V11() V12() ext-real set
(1 + (((len (Cage (n,C))) + ((E-max (L~ (Cage (n,C)))) .. (Cage (n,C)))) - ((W-min (L~ (Cage (n,C)))) .. (Cage (n,C))))) + ((W-min (L~ (Cage (n,C)))) .. (Cage (n,C))) is V11() V12() ext-real set
((1 + (((len (Cage (n,C))) + ((E-max (L~ (Cage (n,C)))) .. (Cage (n,C)))) - ((W-min (L~ (Cage (n,C)))) .. (Cage (n,C))))) + ((W-min (L~ (Cage (n,C)))) .. (Cage (n,C)))) - (len (Cage (n,C))) is V11() V12() ext-real set
1 + ((E-max (L~ (Cage (n,C)))) .. (Cage (n,C))) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
Rev (mid ((Lower_Seq (n,C)),2,(len (Lower_Seq (n,C))))) is V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
0 + ((W-min (L~ (Cage (n,C)))) .. (Cage (n,C))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(1 + ((E-max (L~ (Cage (n,C)))) .. (Cage (n,C)))) - ((W-min (L~ (Cage (n,C)))) .. (Cage (n,C))) is V11() V12() ext-real set
(len (Cage (n,C))) + ((1 + ((E-max (L~ (Cage (n,C)))) .. (Cage (n,C)))) - ((W-min (L~ (Cage (n,C)))) .. (Cage (n,C)))) is V11() V12() ext-real set
(len (Cage (n,C))) + 0 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
2 + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(len (Cage (n,C))) - ((W-min (L~ (Cage (n,C)))) .. (Cage (n,C))) is V11() V12() ext-real set
((len (Cage (n,C))) - ((W-min (L~ (Cage (n,C)))) .. (Cage (n,C)))) + 1 is V11() V12() ext-real set
1 + ((E-max (L~ (Cage (n,C)))) .. (Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C))))))) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Cage (n,C)) :- (W-min (L~ (Cage (n,C)))) is non empty V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
len ((Cage (n,C)) :- (W-min (L~ (Cage (n,C))))) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
rng (Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) is non empty non trivial V26() set
L~ (L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j)))) is closed compact Element of bool the U1 of (TOP-REAL 2)
(Lower_Seq (n,C)) /. (1 + 1) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) /. (1 + ((E-max (L~ (Cage (n,C)))) .. (Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(1 + ((E-max (L~ (Cage (n,C)))) .. (Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))))) + ((W-min (L~ (Cage (n,C)))) .. (Cage (n,C))) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
((1 + ((E-max (L~ (Cage (n,C)))) .. (Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))))) + ((W-min (L~ (Cage (n,C)))) .. (Cage (n,C)))) -' (len (Cage (n,C))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Cage (n,C)) /. (((1 + ((E-max (L~ (Cage (n,C)))) .. (Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))))) + ((W-min (L~ (Cage (n,C)))) .. (Cage (n,C)))) -' (len (Cage (n,C)))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(mid ((Lower_Seq (n,C)),2,(len (Lower_Seq (n,C))))) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((mid ((Lower_Seq (n,C)),2,(len (Lower_Seq (n,C))))) /. 1) `1 is V11() V12() ext-real Element of REAL
len (mid ((Lower_Seq (n,C)),2,(len (Lower_Seq (n,C))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Rev (mid ((Lower_Seq (n,C)),2,(len (Lower_Seq (n,C)))))) /. (len (mid ((Lower_Seq (n,C)),2,(len (Lower_Seq (n,C)))))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Rev (mid ((Lower_Seq (n,C)),2,(len (Lower_Seq (n,C)))))) /. (len (mid ((Lower_Seq (n,C)),2,(len (Lower_Seq (n,C))))))) `1 is V11() V12() ext-real Element of REAL
len (Rev (mid ((Lower_Seq (n,C)),2,(len (Lower_Seq (n,C)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Rev (mid ((Lower_Seq (n,C)),2,(len (Lower_Seq (n,C)))))) /. (len (Rev (mid ((Lower_Seq (n,C)),2,(len (Lower_Seq (n,C))))))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Rev (mid ((Lower_Seq (n,C)),2,(len (Lower_Seq (n,C)))))) /. (len (Rev (mid ((Lower_Seq (n,C)),2,(len (Lower_Seq (n,C)))))))) `1 is V11() V12() ext-real Element of REAL
(Lower_Seq (n,C)) /. (len (Lower_Seq (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
len (Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) /. (len (Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C))))))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Lower_Seq (n,C)) /. (len (Lower_Seq (n,C)))) `1 is V11() V12() ext-real Element of REAL
(mid ((Lower_Seq (n,C)),2,(len (Lower_Seq (n,C))))) /. (len (mid ((Lower_Seq (n,C)),2,(len (Lower_Seq (n,C)))))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((mid ((Lower_Seq (n,C)),2,(len (Lower_Seq (n,C))))) /. (len (mid ((Lower_Seq (n,C)),2,(len (Lower_Seq (n,C))))))) `1 is V11() V12() ext-real Element of REAL
(Rev (mid ((Lower_Seq (n,C)),2,(len (Lower_Seq (n,C)))))) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Rev (mid ((Lower_Seq (n,C)),2,(len (Lower_Seq (n,C)))))) /. 1) `1 is V11() V12() ext-real Element of REAL
dom (Upper_Seq (n,C)) is non empty non trivial V26() V200() V201() V202() V203() V204() V205() Element of bool NAT
Index (((Gauge (n,C)) * (i,j)),(Upper_Seq (n,C))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Index (((Gauge (n,C)) * (i,j)),(Upper_Seq (n,C)))) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
mid ((Upper_Seq (n,C)),((Index (((Gauge (n,C)) * (i,j)),(Upper_Seq (n,C)))) + 1),(len (Upper_Seq (n,C)))) is V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
rng (Upper_Seq (n,C)) is non empty V26() set
{((Gauge (n,C)) * (i,j))} is non empty trivial V26() 1 -element set
rng <*((Gauge (n,C)) * (i,j))*> is non empty trivial V26() 1 -element set
(Upper_Seq (n,C)) . ((Index (((Gauge (n,C)) * (i,j)),(Upper_Seq (n,C)))) + 1) is set
rng (mid ((Upper_Seq (n,C)),((Index (((Gauge (n,C)) * (i,j)),(Upper_Seq (n,C)))) + 1),(len (Upper_Seq (n,C))))) is V26() set
(rng <*((Gauge (n,C)) * (i,j))*>) \/ (rng (mid ((Upper_Seq (n,C)),((Index (((Gauge (n,C)) * (i,j)),(Upper_Seq (n,C)))) + 1),(len (Upper_Seq (n,C)))))) is non empty V26() set
<*((Gauge (n,C)) * (i,j))*> ^ (mid ((Upper_Seq (n,C)),((Index (((Gauge (n,C)) * (i,j)),(Upper_Seq (n,C)))) + 1),(len (Upper_Seq (n,C))))) is non empty V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
rng (<*((Gauge (n,C)) * (i,j))*> ^ (mid ((Upper_Seq (n,C)),((Index (((Gauge (n,C)) * (i,j)),(Upper_Seq (n,C)))) + 1),(len (Upper_Seq (n,C)))))) is non empty V26() set
(Upper_Seq (n,C)) . ((Index (((Gauge (n,C)) * (i,j)),(Upper_Seq (n,C)))) + 1) is set
(Upper_Seq (n,C)) . ((Index (((Gauge (n,C)) * (i,j)),(Upper_Seq (n,C)))) + 1) is set
(Lower_Seq (n,C)) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) :- (E-max (L~ (Cage (n,C))))) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
L~ (mid ((Lower_Seq (n,C)),2,(len (Lower_Seq (n,C))))) is closed compact Element of bool the U1 of (TOP-REAL 2)
len <*((Gauge (n,C)) * (i,1))*> is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
<*((Gauge (n,C)) * (i,1))*> /. (len <*((Gauge (n,C)) * (i,1))*>) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(<*((Gauge (n,C)) * (i,1))*> /. (len <*((Gauge (n,C)) * (i,1))*>)) `1 is V11() V12() ext-real Element of REAL
<*((Gauge (n,C)) * (i,1))*> /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(<*((Gauge (n,C)) * (i,1))*> /. 1) `1 is V11() V12() ext-real Element of REAL
((L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j)))) /. 1) `1 is V11() V12() ext-real Element of REAL
(L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j)))) /. (len (L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j))))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j)))) . (len (L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j))))) is set
(Upper_Seq (n,C)) /. (len (Upper_Seq (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) -: (E-max (L~ (Cage (n,C))))) /. ((E-max (L~ (Cage (n,C)))) .. (Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C))))))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(<*((Gauge (n,C)) * (i,1))*> ^ (L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j))))) /. (len (<*((Gauge (n,C)) * (i,1))*> ^ (L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j)))))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((<*((Gauge (n,C)) * (i,1))*> ^ (L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j))))) /. (len (<*((Gauge (n,C)) * (i,1))*> ^ (L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j))))))) `1 is V11() V12() ext-real Element of REAL
(NE-corner (L~ (Cage (n,C)))) `1 is V11() V12() ext-real Element of REAL
<*(NE-corner (L~ (Cage (n,C))))*> /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(<*(NE-corner (L~ (Cage (n,C))))*> /. 1) `1 is V11() V12() ext-real Element of REAL
L~ (Rev (mid ((Lower_Seq (n,C)),2,(len (Lower_Seq (n,C)))))) is closed compact Element of bool the U1 of (TOP-REAL 2)
L~ ((<*((Gauge (n,C)) * (i,1))*> ^ (L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j))))) ^ <*(NE-corner (L~ (Cage (n,C))))*>) is closed compact Element of bool the U1 of (TOP-REAL 2)
g is set
L~ (<*((Gauge (n,C)) * (i,1))*> ^ ((L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j)))) ^ <*(NE-corner (L~ (Cage (n,C))))*>)) is closed compact Element of bool the U1 of (TOP-REAL 2)
LSeg (((Gauge (n,C)) * (i,1)),(((L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j)))) ^ <*(NE-corner (L~ (Cage (n,C))))*>) /. 1)) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
L~ ((L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j)))) ^ <*(NE-corner (L~ (Cage (n,C))))*>) is closed compact Element of bool the U1 of (TOP-REAL 2)
(LSeg (((Gauge (n,C)) * (i,1)),(((L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j)))) ^ <*(NE-corner (L~ (Cage (n,C))))*>) /. 1))) \/ (L~ ((L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j)))) ^ <*(NE-corner (L~ (Cage (n,C))))*>)) is Element of bool the U1 of (TOP-REAL 2)
LSeg (((L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j)))) /. (len (L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j)))))),(NE-corner (L~ (Cage (n,C))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(L~ (L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j))))) \/ (LSeg (((L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j)))) /. (len (L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j)))))),(NE-corner (L~ (Cage (n,C)))))) is Element of bool the U1 of (TOP-REAL 2)
(LSeg (((Gauge (n,C)) * (i,1)),(((L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j)))) ^ <*(NE-corner (L~ (Cage (n,C))))*>) /. 1))) \/ ((L~ (L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j))))) \/ (LSeg (((L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j)))) /. (len (L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j)))))),(NE-corner (L~ (Cage (n,C))))))) is Element of bool the U1 of (TOP-REAL 2)
<*((Gauge (n,C)) * (i,1)),((Gauge (n,C)) * (i,j))*> is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() 2 -element FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
L~ <*((Gauge (n,C)) * (i,1)),((Gauge (n,C)) * (i,j))*> is non empty closed compact Element of bool the U1 of (TOP-REAL 2)
(L~ (Upper_Seq (n,C))) /\ (L~ (Lower_Seq (n,C))) is Element of bool the U1 of (TOP-REAL 2)
{(W-min (L~ (Cage (n,C)))),(E-max (L~ (Cage (n,C))))} is non empty V26() set
(Upper_Seq (n,C)) . 1 is set
(Upper_Seq (n,C)) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
<*((Gauge (n,C)) * (i,1)),((Gauge (n,C)) * (i,j))*> is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() 2 -element FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
L~ <*((Gauge (n,C)) * (i,1)),((Gauge (n,C)) * (i,j))*> is non empty closed compact Element of bool the U1 of (TOP-REAL 2)
LSeg ((E-max (L~ (Cage (n,C)))),(NE-corner (L~ (Cage (n,C))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((E-max (L~ (Cage (n,C)))),(NE-corner (L~ (Cage (n,C)))))) /\ (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
{(E-max (L~ (Cage (n,C))))} is non empty trivial V26() 1 -element set
<*((Gauge (n,C)) * (i,1)),((Gauge (n,C)) * (i,j))*> is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() 2 -element FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
L~ <*((Gauge (n,C)) * (i,1)),((Gauge (n,C)) * (i,j))*> is non empty closed compact Element of bool the U1 of (TOP-REAL 2)
<*((Gauge (n,C)) * (i,1)),((Gauge (n,C)) * (i,j))*> is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() 2 -element FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
L~ <*((Gauge (n,C)) * (i,1)),((Gauge (n,C)) * (i,j))*> is non empty closed compact Element of bool the U1 of (TOP-REAL 2)
<*((Gauge (n,C)) * (i,1)),((Gauge (n,C)) * (i,j))*> is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() 2 -element FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
L~ <*((Gauge (n,C)) * (i,1)),((Gauge (n,C)) * (i,j))*> is non empty closed compact Element of bool the U1 of (TOP-REAL 2)
(Upper_Seq (n,C)) . (len (Upper_Seq (n,C))) is set
LaP is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
dom <*((Gauge (n,C)) * (i,1))*> is non empty trivial V26() 1 -element V200() V201() V202() V203() V204() V205() Element of bool NAT
<*((Gauge (n,C)) * (i,1))*> . LaP is set
<*((Gauge (n,C)) * (i,1))*> /. LaP is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(Gauge (n,C)) * (1,1) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Gauge (n,C)) * (1,1)) `1 is V11() V12() ext-real Element of REAL
((Gauge (n,C)) * (i,1)) `1 is V11() V12() ext-real Element of REAL
(<*((Gauge (n,C)) * (i,1))*> /. LaP) `1 is V11() V12() ext-real Element of REAL
(Gauge (n,C)) * ((len (Gauge (n,C))),1) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Gauge (n,C)) * ((len (Gauge (n,C))),1)) `1 is V11() V12() ext-real Element of REAL
(<*((Gauge (n,C)) * (i,1))*> /. LaP) `2 is V11() V12() ext-real Element of REAL
<*((Gauge (n,C)) * (i,j))*> is non empty trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like constant V26() 1 -element FinSequence-like FinSubsequence-like special FinSequence of the U1 of (TOP-REAL 2)
dom (Upper_Seq (n,C)) is non empty non trivial V26() V200() V201() V202() V203() V204() V205() Element of bool NAT
rng (Cage (n,C)) is non empty non trivial V26() set
rng (Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) is non empty non trivial V26() set
0 + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
len (L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j)))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
dom (L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j)))) is V26() V200() V201() V202() V203() V204() V205() Element of bool NAT
(L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j)))) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j)))) . 1 is set
(L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j)))) /. (len (L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j))))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j)))) . (len (L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j))))) is set
(Upper_Seq (n,C)) /. (len (Upper_Seq (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(E-max (L~ (Cage (n,C)))) .. (Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
((Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) -: (E-max (L~ (Cage (n,C))))) /. ((E-max (L~ (Cage (n,C)))) .. (Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C))))))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
len (<*((Gauge (n,C)) * (i,1))*> ^ (L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j))))) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(<*((Gauge (n,C)) * (i,1))*> ^ (L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j))))) /. (len (<*((Gauge (n,C)) * (i,1))*> ^ (L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j)))))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((<*((Gauge (n,C)) * (i,1))*> ^ (L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j))))) /. (len (<*((Gauge (n,C)) * (i,1))*> ^ (L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j))))))) `2 is V11() V12() ext-real Element of REAL
(<*((Gauge (n,C)) * (i,1))*> ^ (L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j))))) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((<*((Gauge (n,C)) * (i,1))*> ^ (L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j))))) /. 1) `2 is V11() V12() ext-real Element of REAL
(Cage (n,C)) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
N-min (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
N-most (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
LSeg ((NW-corner (L~ (Cage (n,C)))),(NE-corner (L~ (Cage (n,C))))) is closed closed connected compact compact horizontal Element of bool the U1 of (TOP-REAL 2)
(LSeg ((NW-corner (L~ (Cage (n,C)))),(NE-corner (L~ (Cage (n,C)))))) /\ (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (N-most (L~ (Cage (n,C)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most (L~ (Cage (n,C)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))),REAL:]
the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))) is set
[: the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))),REAL:] is set
K506(((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))),(proj1 | (N-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[K506(((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))),(proj1 | (N-most (L~ (Cage (n,C)))))),(N-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
N-max (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
K507(((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))),(proj1 | (N-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[K507(((TOP-REAL 2) | (N-most (L~ (Cage (n,C))))),(proj1 | (N-most (L~ (Cage (n,C)))))),(N-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
(N-max (L~ (Cage (n,C)))) .. (Cage (n,C)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(E-max (L~ (Cage (n,C)))) .. (Cage (n,C)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
E-min (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
K506(((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),(proj2 | (E-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (n,C)))),K506(((TOP-REAL 2) | (E-most (L~ (Cage (n,C))))),(proj2 | (E-most (L~ (Cage (n,C))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
(E-min (L~ (Cage (n,C)))) .. (Cage (n,C)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
S-max (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
S-most (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (n,C)))),(SE-corner (L~ (Cage (n,C))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Cage (n,C)))),(SE-corner (L~ (Cage (n,C)))))) /\ (L~ (Cage (n,C))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (S-most (L~ (Cage (n,C)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (S-most (L~ (Cage (n,C)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))),REAL:]
the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))) is set
[: the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))),REAL:] is set
K507(((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))),(proj1 | (S-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[K507(((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))),(proj1 | (S-most (L~ (Cage (n,C)))))),(S-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
(S-max (L~ (Cage (n,C)))) .. (Cage (n,C)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
S-min (L~ (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
K506(((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))),(proj1 | (S-most (L~ (Cage (n,C)))))) is V11() V12() ext-real Element of REAL
|[K506(((TOP-REAL 2) | (S-most (L~ (Cage (n,C))))),(proj1 | (S-most (L~ (Cage (n,C)))))),(S-bound (L~ (Cage (n,C))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
(S-min (L~ (Cage (n,C)))) .. (Cage (n,C)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(W-min (L~ (Cage (n,C)))) .. (Cage (n,C)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
len (Cage (n,C)) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
((E-max (L~ (Cage (n,C)))) .. (Cage (n,C))) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Cage (n,C)) /. ((E-max (L~ (Cage (n,C)))) .. (Cage (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(Cage (n,C)) /. (((E-max (L~ (Cage (n,C)))) .. (Cage (n,C))) + 1) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Cage (n,C)) /. (((E-max (L~ (Cage (n,C)))) .. (Cage (n,C))) + 1)) `1 is V11() V12() ext-real Element of REAL
1 + ((E-max (L~ (Cage (n,C)))) .. (Cage (n,C))) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
0 + ((W-min (L~ (Cage (n,C)))) .. (Cage (n,C))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(1 + ((E-max (L~ (Cage (n,C)))) .. (Cage (n,C)))) - ((W-min (L~ (Cage (n,C)))) .. (Cage (n,C))) is V11() V12() ext-real set
(len (Cage (n,C))) + ((1 + ((E-max (L~ (Cage (n,C)))) .. (Cage (n,C)))) - ((W-min (L~ (Cage (n,C)))) .. (Cage (n,C)))) is V11() V12() ext-real set
(len (Cage (n,C))) + 0 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
2 + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
Index (((Gauge (n,C)) * (i,j)),(Upper_Seq (n,C))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Index (((Gauge (n,C)) * (i,j)),(Upper_Seq (n,C)))) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
mid ((Upper_Seq (n,C)),((Index (((Gauge (n,C)) * (i,j)),(Upper_Seq (n,C)))) + 1),(len (Upper_Seq (n,C)))) is V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
rng (Upper_Seq (n,C)) is non empty V26() set
{((Gauge (n,C)) * (i,j))} is non empty trivial V26() 1 -element set
rng <*((Gauge (n,C)) * (i,j))*> is non empty trivial V26() 1 -element set
(Upper_Seq (n,C)) . ((Index (((Gauge (n,C)) * (i,j)),(Upper_Seq (n,C)))) + 1) is set
rng (mid ((Upper_Seq (n,C)),((Index (((Gauge (n,C)) * (i,j)),(Upper_Seq (n,C)))) + 1),(len (Upper_Seq (n,C))))) is V26() set
(rng <*((Gauge (n,C)) * (i,j))*>) \/ (rng (mid ((Upper_Seq (n,C)),((Index (((Gauge (n,C)) * (i,j)),(Upper_Seq (n,C)))) + 1),(len (Upper_Seq (n,C)))))) is non empty V26() set
<*((Gauge (n,C)) * (i,j))*> ^ (mid ((Upper_Seq (n,C)),((Index (((Gauge (n,C)) * (i,j)),(Upper_Seq (n,C)))) + 1),(len (Upper_Seq (n,C))))) is non empty V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
rng (<*((Gauge (n,C)) * (i,j))*> ^ (mid ((Upper_Seq (n,C)),((Index (((Gauge (n,C)) * (i,j)),(Upper_Seq (n,C)))) + 1),(len (Upper_Seq (n,C)))))) is non empty V26() set
rng (L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j)))) is V26() set
(Upper_Seq (n,C)) . ((Index (((Gauge (n,C)) * (i,j)),(Upper_Seq (n,C)))) + 1) is set
rng (L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j)))) is V26() set
(Upper_Seq (n,C)) . ((Index (((Gauge (n,C)) * (i,j)),(Upper_Seq (n,C)))) + 1) is set
rng (L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j)))) is V26() set
rng (L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j)))) is V26() set
{((Gauge (n,C)) * (i,1))} is non empty trivial V26() 1 -element set
rng <*((Gauge (n,C)) * (i,1))*> is non empty trivial V26() 1 -element set
(len (Cage (n,C))) + ((E-max (L~ (Cage (n,C)))) .. (Cage (n,C))) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
((len (Cage (n,C))) + ((E-max (L~ (Cage (n,C)))) .. (Cage (n,C)))) - ((W-min (L~ (Cage (n,C)))) .. (Cage (n,C))) is V11() V12() ext-real set
1 + (((len (Cage (n,C))) + ((E-max (L~ (Cage (n,C)))) .. (Cage (n,C)))) - ((W-min (L~ (Cage (n,C)))) .. (Cage (n,C)))) is V11() V12() ext-real set
(1 + (((len (Cage (n,C))) + ((E-max (L~ (Cage (n,C)))) .. (Cage (n,C)))) - ((W-min (L~ (Cage (n,C)))) .. (Cage (n,C))))) + ((W-min (L~ (Cage (n,C)))) .. (Cage (n,C))) is V11() V12() ext-real set
((1 + (((len (Cage (n,C))) + ((E-max (L~ (Cage (n,C)))) .. (Cage (n,C)))) - ((W-min (L~ (Cage (n,C)))) .. (Cage (n,C))))) + ((W-min (L~ (Cage (n,C)))) .. (Cage (n,C)))) - (len (Cage (n,C))) is V11() V12() ext-real set
1 + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
1 + (len (L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j))))) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
dom (Lower_Seq (n,C)) is non empty non trivial V26() V200() V201() V202() V203() V204() V205() Element of bool NAT
(Lower_Seq (n,C)) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) :- (E-max (L~ (Cage (n,C))))) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
L~ (mid ((Lower_Seq (n,C)),2,(len (Lower_Seq (n,C))))) is closed compact Element of bool the U1 of (TOP-REAL 2)
len <*((Gauge (n,C)) * (i,1))*> is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
<*((Gauge (n,C)) * (i,1))*> /. (len <*((Gauge (n,C)) * (i,1))*>) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(<*((Gauge (n,C)) * (i,1))*> /. (len <*((Gauge (n,C)) * (i,1))*>)) `1 is V11() V12() ext-real Element of REAL
<*((Gauge (n,C)) * (i,1))*> /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(<*((Gauge (n,C)) * (i,1))*> /. 1) `1 is V11() V12() ext-real Element of REAL
((L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j)))) /. 1) `1 is V11() V12() ext-real Element of REAL
L~ (<*((Gauge (n,C)) * (i,1))*> ^ (L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j))))) is closed compact Element of bool the U1 of (TOP-REAL 2)
LSeg (((Gauge (n,C)) * (i,1)),((L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j)))) /. 1)) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
L~ (L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j)))) is closed compact Element of bool the U1 of (TOP-REAL 2)
(LSeg (((Gauge (n,C)) * (i,1)),((L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j)))) /. 1))) \/ (L~ (L_Cut ((Upper_Seq (n,C)),((Gauge (n,C)) * (i,j))))) is Element of bool the U1 of (TOP-REAL 2)
(len (Cage (n,C))) - ((W-min (L~ (Cage (n,C)))) .. (Cage (n,C))) is V11() V12() ext-real set
((len (Cage (n,C))) - ((W-min (L~ (Cage (n,C)))) .. (Cage (n,C)))) + 1 is V11() V12() ext-real set
1 + ((E-max (L~ (Cage (n,C)))) .. (Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C))))))) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Cage (n,C)) :- (W-min (L~ (Cage (n,C)))) is non empty V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
len ((Cage (n,C)) :- (W-min (L~ (Cage (n,C))))) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
Rev (mid ((Lower_Seq (n,C)),2,(len (Lower_Seq (n,C))))) is V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
(Lower_Seq (n,C)) /. (1 + 1) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) /. (1 + ((E-max (L~ (Cage (n,C)))) .. (Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(1 + ((E-max (L~ (Cage (n,C)))) .. (Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))))) + ((W-min (L~ (Cage (n,C)))) .. (Cage (n,C))) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
((1 + ((E-max (L~ (Cage (n,C)))) .. (Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))))) + ((W-min (L~ (Cage (n,C)))) .. (Cage (n,C)))) -' (len (Cage (n,C))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Cage (n,C)) /. (((1 + ((E-max (L~ (Cage (n,C)))) .. (Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))))) + ((W-min (L~ (Cage (n,C)))) .. (Cage (n,C)))) -' (len (Cage (n,C)))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(mid ((Lower_Seq (n,C)),2,(len (Lower_Seq (n,C))))) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((mid ((Lower_Seq (n,C)),2,(len (Lower_Seq (n,C))))) /. 1) `1 is V11() V12() ext-real Element of REAL
len (mid ((Lower_Seq (n,C)),2,(len (Lower_Seq (n,C))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Rev (mid ((Lower_Seq (n,C)),2,(len (Lower_Seq (n,C)))))) /. (len (mid ((Lower_Seq (n,C)),2,(len (Lower_Seq (n,C)))))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Rev (mid ((Lower_Seq (n,C)),2,(len (Lower_Seq (n,C)))))) /. (len (mid ((Lower_Seq (n,C)),2,(len (Lower_Seq (n,C))))))) `1 is V11() V12() ext-real Element of REAL
len (Rev (mid ((Lower_Seq (n,C)),2,(len (Lower_Seq (n,C)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Rev (mid ((Lower_Seq (n,C)),2,(len (Lower_Seq (n,C)))))) /. (len (Rev (mid ((Lower_Seq (n,C)),2,(len (Lower_Seq (n,C))))))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Rev (mid ((Lower_Seq (n,C)),2,(len (Lower_Seq (n,C)))))) /. (len (Rev (mid ((Lower_Seq (n,C)),2,(len (Lower_Seq (n,C)))))))) `1 is V11() V12() ext-real Element of REAL
(Lower_Seq (n,C)) /. (len (Lower_Seq (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
len (Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) /. (len (Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C))))))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Lower_Seq (n,C)) /. (len (Lower_Seq (n,C)))) `1 is V11() V12() ext-real Element of REAL
(mid ((Lower_Seq (n,C)),2,(len (Lower_Seq (n,C))))) /. (len (mid ((Lower_Seq (n,C)),2,(len (Lower_Seq (n,C)))))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((mid ((Lower_Seq (n,C)),2,(len (Lower_Seq (n,C))))) /. (len (mid ((Lower_Seq (n,C)),2,(len (Lower_Seq (n,C))))))) `1 is V11() V12() ext-real Element of REAL
(Rev (mid ((Lower_Seq (n,C)),2,(len (Lower_Seq (n,C)))))) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Rev (mid ((Lower_Seq (n,C)),2,(len (Lower_Seq (n,C)))))) /. 1) `1 is V11() V12() ext-real Element of REAL
L~ (Rev (mid ((Lower_Seq (n,C)),2,(len (Lower_Seq (n,C)))))) is closed compact Element of bool the U1 of (TOP-REAL 2)
g is set
<*((Gauge (n,C)) * (i,1)),((Gauge (n,C)) * (i,j))*> is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() 2 -element FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
L~ <*((Gauge (n,C)) * (i,1)),((Gauge (n,C)) * (i,j))*> is non empty closed compact Element of bool the U1 of (TOP-REAL 2)
(L~ (Upper_Seq (n,C))) /\ (L~ (Lower_Seq (n,C))) is Element of bool the U1 of (TOP-REAL 2)
{(W-min (L~ (Cage (n,C)))),(E-max (L~ (Cage (n,C))))} is non empty V26() set
(Upper_Seq (n,C)) . 1 is set
(Upper_Seq (n,C)) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
<*((Gauge (n,C)) * (i,1)),((Gauge (n,C)) * (i,j))*> is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() 2 -element FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
L~ <*((Gauge (n,C)) * (i,1)),((Gauge (n,C)) * (i,j))*> is non empty closed compact Element of bool the U1 of (TOP-REAL 2)
<*((Gauge (n,C)) * (i,1)),((Gauge (n,C)) * (i,j))*> is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() 2 -element FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
L~ <*((Gauge (n,C)) * (i,1)),((Gauge (n,C)) * (i,j))*> is non empty closed compact Element of bool the U1 of (TOP-REAL 2)
<*((Gauge (n,C)) * (i,1)),((Gauge (n,C)) * (i,j))*> is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() 2 -element FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
L~ <*((Gauge (n,C)) * (i,1)),((Gauge (n,C)) * (i,j))*> is non empty closed compact Element of bool the U1 of (TOP-REAL 2)
(Upper_Seq (n,C)) . (len (Upper_Seq (n,C))) is set
rng (Lower_Seq (n,C)) is non empty V26() set
rng (Cage (n,C)) is non empty non trivial V26() set
rng (Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) is non empty non trivial V26() set
dom (Upper_Seq (n,C)) is non empty non trivial V26() V200() V201() V202() V203() V204() V205() Element of bool NAT
(Upper_Seq (n,C)) /. (len (Upper_Seq (n,C))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(E-max (L~ (Cage (n,C)))) .. (Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
((Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C)))))) -: (E-max (L~ (Cage (n,C))))) /. ((E-max (L~ (Cage (n,C)))) .. (Rotate ((Cage (n,C)),(W-min (L~ (Cage (n,C))))))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(Upper_Seq (n,C)) . (len (Upper_Seq (n,C))) is set
C is non empty connected compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
n is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
Upper_Seq (C,n) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq standard FinSequence of the U1 of (TOP-REAL 2)
L~ (Upper_Seq (C,n)) is non empty closed compact Element of bool the U1 of (TOP-REAL 2)
Cage (C,n) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
L~ (Cage (C,n)) is non empty closed connected V222() compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
W-bound (L~ (Cage (C,n))) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (C,n))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | (L~ (Cage (C,n))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL:]
the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL:] is set
K506(((TOP-REAL 2) | (L~ (Cage (C,n)))),(proj1 | (L~ (Cage (C,n))))) is V11() V12() ext-real Element of REAL
E-bound (L~ (Cage (C,n))) is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | (L~ (Cage (C,n)))),(proj1 | (L~ (Cage (C,n))))) is V11() V12() ext-real Element of REAL
(W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n)))) is V11() V12() ext-real set
((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2 is V11() V12() ext-real set
Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2) is Element of bool the U1 of (TOP-REAL 2)
W-min (L~ (Cage (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
W-most (L~ (Cage (C,n))) is Element of bool the U1 of (TOP-REAL 2)
SW-corner (L~ (Cage (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Cage (C,n))) is V11() V12() ext-real Element of REAL
proj2 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | (L~ (Cage (C,n))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL:]
K506(((TOP-REAL 2) | (L~ (Cage (C,n)))),(proj2 | (L~ (Cage (C,n))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (C,n)))),(S-bound (L~ (Cage (C,n))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
NW-corner (L~ (Cage (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Cage (C,n))) is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | (L~ (Cage (C,n)))),(proj2 | (L~ (Cage (C,n))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (C,n)))),(N-bound (L~ (Cage (C,n))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (C,n)))),(NW-corner (L~ (Cage (C,n))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Cage (C,n)))),(NW-corner (L~ (Cage (C,n)))))) /\ (L~ (Cage (C,n))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ (Cage (C,n)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Cage (C,n)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),REAL:]
the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))) is set
[: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),REAL:] is set
K506(((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),(proj2 | (W-most (L~ (Cage (C,n)))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (C,n)))),K506(((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),(proj2 | (W-most (L~ (Cage (C,n))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
E-max (L~ (Cage (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
E-most (L~ (Cage (C,n))) is Element of bool the U1 of (TOP-REAL 2)
SE-corner (L~ (Cage (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
|[(E-bound (L~ (Cage (C,n)))),(S-bound (L~ (Cage (C,n))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
NE-corner (L~ (Cage (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
|[(E-bound (L~ (Cage (C,n)))),(N-bound (L~ (Cage (C,n))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Cage (C,n)))),(NE-corner (L~ (Cage (C,n))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SE-corner (L~ (Cage (C,n)))),(NE-corner (L~ (Cage (C,n)))))) /\ (L~ (Cage (C,n))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ (Cage (C,n)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Cage (C,n)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),REAL:]
the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))) is set
[: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),REAL:] is set
K507(((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),(proj2 | (E-most (L~ (Cage (C,n)))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (C,n)))),K507(((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),(proj2 | (E-most (L~ (Cage (C,n))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
rng (Upper_Seq (C,n)) is non empty V26() set
Gauge (C,n) is V13() non empty-yielding V16( NAT ) V17(K238( the U1 of (TOP-REAL 2))) Function-like V26() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K238( the U1 of (TOP-REAL 2))
Center (Gauge (C,n)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Upper_Seq (C,n)) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
len (Upper_Seq (C,n)) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Upper_Seq (C,n)) /. (len (Upper_Seq (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(W-min (L~ (Cage (C,n)))) `1 is V11() V12() ext-real Element of REAL
len (Gauge (C,n)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(E-max (L~ (Cage (C,n)))) `1 is V11() V12() ext-real Element of REAL
(L~ (Upper_Seq (C,n))) /\ (Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)) is Element of bool the U1 of (TOP-REAL 2)
Wbo is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
Wbo + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
LSeg ((Upper_Seq (C,n)),Wbo) is closed Element of bool the U1 of (TOP-REAL 2)
(Upper_Seq (C,n)) /. Wbo is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(Upper_Seq (C,n)) /. (Wbo + 1) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg (((Upper_Seq (C,n)) /. Wbo),((Upper_Seq (C,n)) /. (Wbo + 1))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
dom (Upper_Seq (C,n)) is non empty non trivial V26() V200() V201() V202() V203() V204() V205() Element of bool NAT
(First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) `1 is V11() V12() ext-real Element of REAL
First_Point ((LSeg ((Upper_Seq (C,n)),Wbo)),((Upper_Seq (C,n)) /. Wbo),((Upper_Seq (C,n)) /. (Wbo + 1)),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Upper_Seq (C,n)) /. (Wbo + 1)) `1 is V11() V12() ext-real Element of REAL
{ b₁ where b₁ is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2) : b₁ `1 = ((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2 } is set
((Upper_Seq (C,n)) /. Wbo) `1 is V11() V12() ext-real Element of REAL
((Upper_Seq (C,n)) /. Wbo) `2 is V11() V12() ext-real Element of REAL
((Upper_Seq (C,n)) /. (Wbo + 1)) `2 is V11() V12() ext-real Element of REAL
(First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) `2 is V11() V12() ext-real Element of REAL
Indices (Gauge (C,n)) is set
SW is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
FiP is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
[SW,FiP] is non empty set
{SW,FiP} is non empty V26() V30() V200() V201() V202() V203() V204() V205() set
{SW} is non empty trivial V26() V30() 1 -element V200() V201() V202() V203() V204() V205() set
{{SW,FiP},{SW}} is non empty V26() V30() set
(Gauge (C,n)) * (SW,FiP) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
LaP is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
g is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
[LaP,g] is non empty set
{LaP,g} is non empty V26() V30() V200() V201() V202() V203() V204() V205() set
{LaP} is non empty trivial V26() V30() 1 -element V200() V201() V202() V203() V204() V205() set
{{LaP,g},{LaP}} is non empty V26() V30() set
(Gauge (C,n)) * (LaP,g) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
FiP + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
SW + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
LaP + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
g + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
width (Gauge (C,n)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Gauge (C,n)) * ((Center (Gauge (C,n))),FiP) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * ((Center (Gauge (C,n))),FiP)) `1 is V11() V12() ext-real Element of REAL
W-bound C is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | C is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | C is V13() Function-like V40( the U1 of ((TOP-REAL 2) | C), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | C),REAL:]
the U1 of ((TOP-REAL 2) | C) is non empty set
[: the U1 of ((TOP-REAL 2) | C),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | C),REAL:] is set
K506(((TOP-REAL 2) | C),(proj1 | C)) is V11() V12() ext-real Element of REAL
E-bound C is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | C),(proj1 | C)) is V11() V12() ext-real Element of REAL
(W-bound C) + (E-bound C) is V11() V12() ext-real set
((W-bound C) + (E-bound C)) / 2 is V11() V12() ext-real set
((Gauge (C,n)) * ((Center (Gauge (C,n))),FiP)) `2 is V11() V12() ext-real Element of REAL
(Gauge (C,n)) * (1,FiP) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (1,FiP)) `2 is V11() V12() ext-real Element of REAL
((Gauge (C,n)) * (SW,FiP)) `1 is V11() V12() ext-real Element of REAL
(Gauge (C,n)) * ((SW + 1),FiP) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * ((SW + 1),FiP)) `1 is V11() V12() ext-real Element of REAL
(Gauge (C,n)) * (LaP,FiP) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (LaP,FiP)) `1 is V11() V12() ext-real Element of REAL
(Gauge (C,n)) * ((LaP + 1),FiP) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * ((LaP + 1),FiP)) `1 is V11() V12() ext-real Element of REAL
C is non empty connected compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
n is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
Lower_Seq (C,n) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq standard FinSequence of the U1 of (TOP-REAL 2)
L~ (Lower_Seq (C,n)) is non empty closed compact Element of bool the U1 of (TOP-REAL 2)
Cage (C,n) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
L~ (Cage (C,n)) is non empty closed connected V222() compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
W-bound (L~ (Cage (C,n))) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (C,n))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | (L~ (Cage (C,n))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL:]
the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL:] is set
K506(((TOP-REAL 2) | (L~ (Cage (C,n)))),(proj1 | (L~ (Cage (C,n))))) is V11() V12() ext-real Element of REAL
E-bound (L~ (Cage (C,n))) is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | (L~ (Cage (C,n)))),(proj1 | (L~ (Cage (C,n))))) is V11() V12() ext-real Element of REAL
(W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n)))) is V11() V12() ext-real set
((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2 is V11() V12() ext-real set
Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2) is Element of bool the U1 of (TOP-REAL 2)
E-max (L~ (Cage (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
E-most (L~ (Cage (C,n))) is Element of bool the U1 of (TOP-REAL 2)
SE-corner (L~ (Cage (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Cage (C,n))) is V11() V12() ext-real Element of REAL
proj2 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | (L~ (Cage (C,n))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL:]
K506(((TOP-REAL 2) | (L~ (Cage (C,n)))),(proj2 | (L~ (Cage (C,n))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (C,n)))),(S-bound (L~ (Cage (C,n))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
NE-corner (L~ (Cage (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Cage (C,n))) is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | (L~ (Cage (C,n)))),(proj2 | (L~ (Cage (C,n))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (C,n)))),(N-bound (L~ (Cage (C,n))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Cage (C,n)))),(NE-corner (L~ (Cage (C,n))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SE-corner (L~ (Cage (C,n)))),(NE-corner (L~ (Cage (C,n)))))) /\ (L~ (Cage (C,n))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ (Cage (C,n)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Cage (C,n)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),REAL:]
the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))) is set
[: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),REAL:] is set
K507(((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),(proj2 | (E-most (L~ (Cage (C,n)))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (C,n)))),K507(((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),(proj2 | (E-most (L~ (Cage (C,n))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
W-min (L~ (Cage (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
W-most (L~ (Cage (C,n))) is Element of bool the U1 of (TOP-REAL 2)
SW-corner (L~ (Cage (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
|[(W-bound (L~ (Cage (C,n)))),(S-bound (L~ (Cage (C,n))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
NW-corner (L~ (Cage (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
|[(W-bound (L~ (Cage (C,n)))),(N-bound (L~ (Cage (C,n))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (C,n)))),(NW-corner (L~ (Cage (C,n))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Cage (C,n)))),(NW-corner (L~ (Cage (C,n)))))) /\ (L~ (Cage (C,n))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ (Cage (C,n)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Cage (C,n)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),REAL:]
the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))) is set
[: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),REAL:] is set
K506(((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),(proj2 | (W-most (L~ (Cage (C,n)))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (C,n)))),K506(((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),(proj2 | (W-most (L~ (Cage (C,n))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
rng (Lower_Seq (C,n)) is non empty V26() set
(Lower_Seq (C,n)) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
len (Lower_Seq (C,n)) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Lower_Seq (C,n)) /. (len (Lower_Seq (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(W-min (L~ (Cage (C,n)))) `1 is V11() V12() ext-real Element of REAL
(E-max (L~ (Cage (C,n)))) `1 is V11() V12() ext-real Element of REAL
(L~ (Lower_Seq (C,n))) /\ (Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)) is Element of bool the U1 of (TOP-REAL 2)
Wbo is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
Wbo + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
LSeg ((Lower_Seq (C,n)),Wbo) is closed Element of bool the U1 of (TOP-REAL 2)
(Lower_Seq (C,n)) /. Wbo is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(Lower_Seq (C,n)) /. (Wbo + 1) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg (((Lower_Seq (C,n)) /. Wbo),((Lower_Seq (C,n)) /. (Wbo + 1))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
dom (Lower_Seq (C,n)) is non empty non trivial V26() V200() V201() V202() V203() V204() V205() Element of bool NAT
(Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) `1 is V11() V12() ext-real Element of REAL
Last_Point ((LSeg ((Lower_Seq (C,n)),Wbo)),((Lower_Seq (C,n)) /. Wbo),((Lower_Seq (C,n)) /. (Wbo + 1)),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Lower_Seq (C,n)) /. (Wbo + 1)) `1 is V11() V12() ext-real Element of REAL
{ b₁ where b₁ is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2) : b₁ `1 = ((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2 } is set
((Lower_Seq (C,n)) /. Wbo) `1 is V11() V12() ext-real Element of REAL
((Lower_Seq (C,n)) /. Wbo) `2 is V11() V12() ext-real Element of REAL
((Lower_Seq (C,n)) /. (Wbo + 1)) `2 is V11() V12() ext-real Element of REAL
(Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) `2 is V11() V12() ext-real Element of REAL
Gauge (C,n) is V13() non empty-yielding V16( NAT ) V17(K238( the U1 of (TOP-REAL 2))) Function-like V26() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K238( the U1 of (TOP-REAL 2))
Indices (Gauge (C,n)) is set
SW is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
FiP is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
[SW,FiP] is non empty set
{SW,FiP} is non empty V26() V30() V200() V201() V202() V203() V204() V205() set
{SW} is non empty trivial V26() V30() 1 -element V200() V201() V202() V203() V204() V205() set
{{SW,FiP},{SW}} is non empty V26() V30() set
(Gauge (C,n)) * (SW,FiP) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
LaP is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
g is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
[LaP,g] is non empty set
{LaP,g} is non empty V26() V30() V200() V201() V202() V203() V204() V205() set
{LaP} is non empty trivial V26() V30() 1 -element V200() V201() V202() V203() V204() V205() set
{{LaP,g},{LaP}} is non empty V26() V30() set
(Gauge (C,n)) * (LaP,g) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
FiP + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
SW + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
LaP + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
g + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
len (Gauge (C,n)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
Center (Gauge (C,n)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
width (Gauge (C,n)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Gauge (C,n)) * ((Center (Gauge (C,n))),FiP) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * ((Center (Gauge (C,n))),FiP)) `1 is V11() V12() ext-real Element of REAL
W-bound C is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | C is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | C is V13() Function-like V40( the U1 of ((TOP-REAL 2) | C), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | C),REAL:]
the U1 of ((TOP-REAL 2) | C) is non empty set
[: the U1 of ((TOP-REAL 2) | C),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | C),REAL:] is set
K506(((TOP-REAL 2) | C),(proj1 | C)) is V11() V12() ext-real Element of REAL
E-bound C is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | C),(proj1 | C)) is V11() V12() ext-real Element of REAL
(W-bound C) + (E-bound C) is V11() V12() ext-real set
((W-bound C) + (E-bound C)) / 2 is V11() V12() ext-real set
((Gauge (C,n)) * ((Center (Gauge (C,n))),FiP)) `2 is V11() V12() ext-real Element of REAL
(Gauge (C,n)) * (1,FiP) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (1,FiP)) `2 is V11() V12() ext-real Element of REAL
((Gauge (C,n)) * (SW,FiP)) `1 is V11() V12() ext-real Element of REAL
(Gauge (C,n)) * ((SW + 1),FiP) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * ((SW + 1),FiP)) `1 is V11() V12() ext-real Element of REAL
(Gauge (C,n)) * (LaP,FiP) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (LaP,FiP)) `1 is V11() V12() ext-real Element of REAL
(Gauge (C,n)) * ((LaP + 1),FiP) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * ((LaP + 1),FiP)) `1 is V11() V12() ext-real Element of REAL
C is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
rng C is non empty V26() set
n is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
R_Cut (C,n) is V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
n .. C is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
mid (C,1,(n .. C)) is V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
dom C is non empty non trivial V26() V200() V201() V202() V203() V204() V205() Element of bool NAT
i is V6() V10() V11() V12() V26() cardinal ext-real non negative set
C . i is set
j is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
len C is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
L~ C is non empty closed compact Element of bool the U1 of (TOP-REAL 2)
Index (n,C) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
0 + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
j - 1 is V11() V12() ext-real set
C . 1 is set
mid (C,1,(Index (n,C))) is V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
<*n*> is non empty trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like constant V26() 1 -element FinSequence-like FinSubsequence-like special FinSequence of the U1 of (TOP-REAL 2)
(mid (C,1,(Index (n,C)))) ^ <*n*> is non empty V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
(Index (n,C)) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
len (mid (C,1,(Index (n,C)))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Index (n,C)) -' 1 is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
((Index (n,C)) -' 1) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
j -' 1 is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
mid (C,1,j) is V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
len (mid (C,1,j)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(j -' 1) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
dom (mid (C,1,j)) is V26() V200() V201() V202() V203() V204() V205() Element of bool NAT
Seg j is V26() j -element V200() V201() V202() V203() V204() V205() Element of bool NAT
Emax is V6() V10() V11() V12() V26() cardinal ext-real non negative set
dom (mid (C,1,(Index (n,C)))) is V26() V200() V201() V202() V203() V204() V205() Element of bool NAT
(mid (C,1,j)) . Emax is set
Nbo is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
C . Nbo is set
(mid (C,1,(Index (n,C)))) . Nbo is set
((mid (C,1,(Index (n,C)))) ^ <*n*>) . Emax is set
(mid (C,1,j)) . Emax is set
Nbo is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
C . Nbo is set
((mid (C,1,(Index (n,C)))) ^ <*n*>) . Emax is set
(mid (C,1,j)) . Emax is set
((mid (C,1,(Index (n,C)))) ^ <*n*>) . Emax is set
(mid (C,1,j)) . Emax is set
((mid (C,1,(Index (n,C)))) ^ <*n*>) . Emax is set
len ((mid (C,1,(Index (n,C)))) ^ <*n*>) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
<*n*> is non empty trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like constant V26() 1 -element FinSequence-like FinSubsequence-like special FinSequence of the U1 of (TOP-REAL 2)
C /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
C is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
L~ C is non empty closed compact Element of bool the U1 of (TOP-REAL 2)
C /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
len C is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
C /. (len C) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
rng C is non empty V26() set
n is closed Element of bool the U1 of (TOP-REAL 2)
First_Point ((L~ C),(C /. 1),(C /. (len C)),n) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(First_Point ((L~ C),(C /. 1),(C /. (len C)),n)) .. C is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
mid (C,1,((First_Point ((L~ C),(C /. 1),(C /. (len C)),n)) .. C)) is V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
L~ (mid (C,1,((First_Point ((L~ C),(C /. 1),(C /. (len C)),n)) .. C))) is closed compact Element of bool the U1 of (TOP-REAL 2)
(L~ (mid (C,1,((First_Point ((L~ C),(C /. 1),(C /. (len C)),n)) .. C)))) /\ n is Element of bool the U1 of (TOP-REAL 2)
{(First_Point ((L~ C),(C /. 1),(C /. (len C)),n))} is non empty trivial V26() 1 -element set
R_Cut (C,(First_Point ((L~ C),(C /. 1),(C /. (len C)),n))) is V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
L~ (R_Cut (C,(First_Point ((L~ C),(C /. 1),(C /. (len C)),n)))) is closed compact Element of bool the U1 of (TOP-REAL 2)
(L~ (R_Cut (C,(First_Point ((L~ C),(C /. 1),(C /. (len C)),n))))) /\ n is Element of bool the U1 of (TOP-REAL 2)
C is non empty connected compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
n is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
Upper_Seq (C,n) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq standard FinSequence of the U1 of (TOP-REAL 2)
L~ (Upper_Seq (C,n)) is non empty closed compact Element of bool the U1 of (TOP-REAL 2)
Cage (C,n) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
L~ (Cage (C,n)) is non empty closed connected V222() compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
W-bound (L~ (Cage (C,n))) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (C,n))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | (L~ (Cage (C,n))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL:]
the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL:] is set
K506(((TOP-REAL 2) | (L~ (Cage (C,n)))),(proj1 | (L~ (Cage (C,n))))) is V11() V12() ext-real Element of REAL
E-bound (L~ (Cage (C,n))) is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | (L~ (Cage (C,n)))),(proj1 | (L~ (Cage (C,n))))) is V11() V12() ext-real Element of REAL
(W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n)))) is V11() V12() ext-real set
((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2 is V11() V12() ext-real set
Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2) is Element of bool the U1 of (TOP-REAL 2)
W-min (L~ (Cage (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
W-most (L~ (Cage (C,n))) is Element of bool the U1 of (TOP-REAL 2)
SW-corner (L~ (Cage (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Cage (C,n))) is V11() V12() ext-real Element of REAL
proj2 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | (L~ (Cage (C,n))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL:]
K506(((TOP-REAL 2) | (L~ (Cage (C,n)))),(proj2 | (L~ (Cage (C,n))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (C,n)))),(S-bound (L~ (Cage (C,n))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
NW-corner (L~ (Cage (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Cage (C,n))) is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | (L~ (Cage (C,n)))),(proj2 | (L~ (Cage (C,n))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (C,n)))),(N-bound (L~ (Cage (C,n))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (C,n)))),(NW-corner (L~ (Cage (C,n))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Cage (C,n)))),(NW-corner (L~ (Cage (C,n)))))) /\ (L~ (Cage (C,n))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ (Cage (C,n)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Cage (C,n)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),REAL:]
the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))) is set
[: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),REAL:] is set
K506(((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),(proj2 | (W-most (L~ (Cage (C,n)))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (C,n)))),K506(((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),(proj2 | (W-most (L~ (Cage (C,n))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
E-max (L~ (Cage (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
E-most (L~ (Cage (C,n))) is Element of bool the U1 of (TOP-REAL 2)
SE-corner (L~ (Cage (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
|[(E-bound (L~ (Cage (C,n)))),(S-bound (L~ (Cage (C,n))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
NE-corner (L~ (Cage (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
|[(E-bound (L~ (Cage (C,n)))),(N-bound (L~ (Cage (C,n))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Cage (C,n)))),(NE-corner (L~ (Cage (C,n))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SE-corner (L~ (Cage (C,n)))),(NE-corner (L~ (Cage (C,n)))))) /\ (L~ (Cage (C,n))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ (Cage (C,n)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Cage (C,n)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),REAL:]
the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))) is set
[: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),REAL:] is set
K507(((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),(proj2 | (E-most (L~ (Cage (C,n)))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (C,n)))),K507(((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),(proj2 | (E-most (L~ (Cage (C,n))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
Gauge (C,n) is V13() non empty-yielding V16( NAT ) V17(K238( the U1 of (TOP-REAL 2))) Function-like V26() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K238( the U1 of (TOP-REAL 2))
Center (Gauge (C,n)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Gauge (C,n)) * ((Center (Gauge (C,n))),1) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
FiP is non empty V6() V10() V11() V12() V26() cardinal ext-real positive non negative set
(Upper_Seq (C,n)) /. FiP is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Upper_Seq (C,n)) /. FiP) `1 is V11() V12() ext-real Element of REAL
FiP + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Upper_Seq (C,n)) /. (FiP + 1) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Upper_Seq (C,n)) /. (FiP + 1)) `1 is V11() V12() ext-real Element of REAL
len (Gauge (C,n)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
width (Gauge (C,n)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
((Gauge (C,n)) * ((Center (Gauge (C,n))),1)) `1 is V11() V12() ext-real Element of REAL
W-bound C is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | C is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | C is V13() Function-like V40( the U1 of ((TOP-REAL 2) | C), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | C),REAL:]
the U1 of ((TOP-REAL 2) | C) is non empty set
[: the U1 of ((TOP-REAL 2) | C),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | C),REAL:] is set
K506(((TOP-REAL 2) | C),(proj1 | C)) is V11() V12() ext-real Element of REAL
E-bound C is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | C),(proj1 | C)) is V11() V12() ext-real Element of REAL
(W-bound C) + (E-bound C) is V11() V12() ext-real set
((W-bound C) + (E-bound C)) / 2 is V11() V12() ext-real set
len (Upper_Seq (C,n)) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Upper_Seq (C,n)) /. (len (Upper_Seq (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
rng (Upper_Seq (C,n)) is non empty V26() set
dom (Upper_Seq (C,n)) is non empty non trivial V26() V200() V201() V202() V203() V204() V205() Element of bool NAT
(Upper_Seq (C,n)) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
Indices (Gauge (C,n)) is set
LaP is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Upper_Seq (C,n)) /. LaP is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
LaP + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Upper_Seq (C,n)) /. (LaP + 1) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
g is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
h is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
[g,h] is non empty set
{g,h} is non empty V26() V30() V200() V201() V202() V203() V204() V205() set
{g} is non empty trivial V26() V30() 1 -element V200() V201() V202() V203() V204() V205() set
{{g,h},{g}} is non empty V26() V30() set
(Gauge (C,n)) * (g,h) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
GCw is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
RevL is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
[GCw,RevL] is non empty set
{GCw,RevL} is non empty V26() V30() V200() V201() V202() V203() V204() V205() set
{GCw} is non empty trivial V26() V30() 1 -element V200() V201() V202() V203() V204() V205() set
{{GCw,RevL},{GCw}} is non empty V26() V30() set
(Gauge (C,n)) * (GCw,RevL) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
h + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
g + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
GCw + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
RevL + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Gauge (C,n)) * (GCw,1) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (GCw,1)) `1 is V11() V12() ext-real Element of REAL
1 + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
mid ((Upper_Seq (C,n)),1,((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n)))) is V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
len (mid ((Upper_Seq (C,n)),1,((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n))) -' 1 is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n))) -' 1) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
rng (mid ((Upper_Seq (C,n)),1,((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n))))) is V26() set
L~ (mid ((Upper_Seq (C,n)),1,((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n))))) is closed compact Element of bool the U1 of (TOP-REAL 2)
(Upper_Seq (C,n)) /. ((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(W-min (L~ (Cage (C,n)))) `1 is V11() V12() ext-real Element of REAL
(E-max (L~ (Cage (C,n)))) `1 is V11() V12() ext-real Element of REAL
First_Point ((L~ (Upper_Seq (C,n))),((Upper_Seq (C,n)) /. 1),((Upper_Seq (C,n)) /. (len (Upper_Seq (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(L~ (mid ((Upper_Seq (C,n)),1,((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n)))))) /\ (Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)) is Element of bool the U1 of (TOP-REAL 2)
{(First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))))} is non empty trivial V26() 1 -element set
(Upper_Seq (C,n)) | ((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n))) is V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. FinSequence of the U1 of (TOP-REAL 2)
Seg ((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n))) is V26() (First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n)) -element V200() V201() V202() V203() V204() V205() Element of bool NAT
(Upper_Seq (C,n)) | (Seg ((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n)))) is V13() V16( NAT ) V16( Seg ((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n)))) V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like Element of bool [:NAT, the U1 of (TOP-REAL 2):]
[:NAT, the U1 of (TOP-REAL 2):] is non empty non trivial V13() V26() set
bool [:NAT, the U1 of (TOP-REAL 2):] is non empty non trivial V26() set
{ b₁ where b₁ is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2) : b₁ `1 = ((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2 } is set
(Gauge (C,n)) * (GCw,1) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (GCw,1)) `1 is V11() V12() ext-real Element of REAL
(Upper_Seq (C,n)) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Upper_Seq (C,n)) /. 1) `1 is V11() V12() ext-real Element of REAL
SW is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Upper_Seq (C,n)) /. SW is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Upper_Seq (C,n)) /. SW) `1 is V11() V12() ext-real Element of REAL
C is non empty connected compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
n is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
Lower_Seq (C,n) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq standard FinSequence of the U1 of (TOP-REAL 2)
Rev (Lower_Seq (C,n)) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
L~ (Rev (Lower_Seq (C,n))) is non empty closed compact Element of bool the U1 of (TOP-REAL 2)
Cage (C,n) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
L~ (Cage (C,n)) is non empty closed connected V222() compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
W-bound (L~ (Cage (C,n))) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (C,n))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | (L~ (Cage (C,n))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL:]
the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL:] is set
K506(((TOP-REAL 2) | (L~ (Cage (C,n)))),(proj1 | (L~ (Cage (C,n))))) is V11() V12() ext-real Element of REAL
E-bound (L~ (Cage (C,n))) is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | (L~ (Cage (C,n)))),(proj1 | (L~ (Cage (C,n))))) is V11() V12() ext-real Element of REAL
(W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n)))) is V11() V12() ext-real set
((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2 is V11() V12() ext-real set
Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2) is Element of bool the U1 of (TOP-REAL 2)
W-min (L~ (Cage (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
W-most (L~ (Cage (C,n))) is Element of bool the U1 of (TOP-REAL 2)
SW-corner (L~ (Cage (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Cage (C,n))) is V11() V12() ext-real Element of REAL
proj2 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | (L~ (Cage (C,n))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL:]
K506(((TOP-REAL 2) | (L~ (Cage (C,n)))),(proj2 | (L~ (Cage (C,n))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (C,n)))),(S-bound (L~ (Cage (C,n))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
NW-corner (L~ (Cage (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Cage (C,n))) is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | (L~ (Cage (C,n)))),(proj2 | (L~ (Cage (C,n))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (C,n)))),(N-bound (L~ (Cage (C,n))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (C,n)))),(NW-corner (L~ (Cage (C,n))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Cage (C,n)))),(NW-corner (L~ (Cage (C,n)))))) /\ (L~ (Cage (C,n))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ (Cage (C,n)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Cage (C,n)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),REAL:]
the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))) is set
[: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),REAL:] is set
K506(((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),(proj2 | (W-most (L~ (Cage (C,n)))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (C,n)))),K506(((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),(proj2 | (W-most (L~ (Cage (C,n))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
E-max (L~ (Cage (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
E-most (L~ (Cage (C,n))) is Element of bool the U1 of (TOP-REAL 2)
SE-corner (L~ (Cage (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
|[(E-bound (L~ (Cage (C,n)))),(S-bound (L~ (Cage (C,n))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
NE-corner (L~ (Cage (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
|[(E-bound (L~ (Cage (C,n)))),(N-bound (L~ (Cage (C,n))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Cage (C,n)))),(NE-corner (L~ (Cage (C,n))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SE-corner (L~ (Cage (C,n)))),(NE-corner (L~ (Cage (C,n)))))) /\ (L~ (Cage (C,n))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ (Cage (C,n)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Cage (C,n)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),REAL:]
the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))) is set
[: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),REAL:] is set
K507(((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),(proj2 | (E-most (L~ (Cage (C,n)))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (C,n)))),K507(((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),(proj2 | (E-most (L~ (Cage (C,n))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
First_Point ((L~ (Rev (Lower_Seq (C,n)))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(First_Point ((L~ (Rev (Lower_Seq (C,n)))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Rev (Lower_Seq (C,n))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
L~ (Lower_Seq (C,n)) is non empty closed compact Element of bool the U1 of (TOP-REAL 2)
Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
len (Rev (Lower_Seq (C,n))) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
len (Lower_Seq (C,n)) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
rng (Rev (Lower_Seq (C,n))) is non empty V26() set
rng (Lower_Seq (C,n)) is non empty V26() set
(W-min (L~ (Cage (C,n)))) `1 is V11() V12() ext-real Element of REAL
(E-max (L~ (Cage (C,n)))) `1 is V11() V12() ext-real Element of REAL
(Rev (Lower_Seq (C,n))) /. (len (Rev (Lower_Seq (C,n)))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(Lower_Seq (C,n)) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
Gauge (C,n) is V13() non empty-yielding V16( NAT ) V17(K238( the U1 of (TOP-REAL 2))) Function-like V26() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K238( the U1 of (TOP-REAL 2))
Center (Gauge (C,n)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Gauge (C,n)) * ((Center (Gauge (C,n))),1) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
g is non empty V6() V10() V11() V12() V26() cardinal ext-real positive non negative set
(Rev (Lower_Seq (C,n))) /. g is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Rev (Lower_Seq (C,n))) /. g) `1 is V11() V12() ext-real Element of REAL
g + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Rev (Lower_Seq (C,n))) /. (g + 1) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Rev (Lower_Seq (C,n))) /. (g + 1)) `1 is V11() V12() ext-real Element of REAL
len (Gauge (C,n)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
width (Gauge (C,n)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
((Gauge (C,n)) * ((Center (Gauge (C,n))),1)) `1 is V11() V12() ext-real Element of REAL
W-bound C is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | C is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | C is V13() Function-like V40( the U1 of ((TOP-REAL 2) | C), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | C),REAL:]
the U1 of ((TOP-REAL 2) | C) is non empty set
[: the U1 of ((TOP-REAL 2) | C),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | C),REAL:] is set
K506(((TOP-REAL 2) | C),(proj1 | C)) is V11() V12() ext-real Element of REAL
E-bound C is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | C),(proj1 | C)) is V11() V12() ext-real Element of REAL
(W-bound C) + (E-bound C) is V11() V12() ext-real set
((W-bound C) + (E-bound C)) / 2 is V11() V12() ext-real set
(Lower_Seq (C,n)) /. (len (Lower_Seq (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(Rev (Lower_Seq (C,n))) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(L~ (Lower_Seq (C,n))) /\ (Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)) is Element of bool the U1 of (TOP-REAL 2)
dom (Rev (Lower_Seq (C,n))) is non empty non trivial V26() V200() V201() V202() V203() V204() V205() Element of bool NAT
Indices (Gauge (C,n)) is set
h is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Rev (Lower_Seq (C,n))) /. h is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
h + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Rev (Lower_Seq (C,n))) /. (h + 1) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
GCw is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
RevL is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
[GCw,RevL] is non empty set
{GCw,RevL} is non empty V26() V30() V200() V201() V202() V203() V204() V205() set
{GCw} is non empty trivial V26() V30() 1 -element V200() V201() V202() V203() V204() V205() set
{{GCw,RevL},{GCw}} is non empty V26() V30() set
(Gauge (C,n)) * (GCw,RevL) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
g is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
RevLS is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
[g,RevLS] is non empty set
{g,RevLS} is non empty V26() V30() V200() V201() V202() V203() V204() V205() set
{g} is non empty trivial V26() V30() 1 -element V200() V201() V202() V203() V204() V205() set
{{g,RevLS},{g}} is non empty V26() V30() set
(Gauge (C,n)) * (g,RevLS) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
RevL + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
GCw + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
g + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
RevLS + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Gauge (C,n)) * (g,1) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (g,1)) `1 is V11() V12() ext-real Element of REAL
{ b₁ where b₁ is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2) : b₁ `1 = ((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2 } is set
(Rev (Lower_Seq (C,n))) /. ((First_Point ((L~ (Rev (Lower_Seq (C,n)))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Rev (Lower_Seq (C,n)))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
1 + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
mid ((Rev (Lower_Seq (C,n))),1,((First_Point ((L~ (Rev (Lower_Seq (C,n)))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Rev (Lower_Seq (C,n))))) is V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
len (mid ((Rev (Lower_Seq (C,n))),1,((First_Point ((L~ (Rev (Lower_Seq (C,n)))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Rev (Lower_Seq (C,n)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
((First_Point ((L~ (Rev (Lower_Seq (C,n)))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Rev (Lower_Seq (C,n)))) -' 1 is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(((First_Point ((L~ (Rev (Lower_Seq (C,n)))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Rev (Lower_Seq (C,n)))) -' 1) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
rng (mid ((Rev (Lower_Seq (C,n))),1,((First_Point ((L~ (Rev (Lower_Seq (C,n)))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Rev (Lower_Seq (C,n)))))) is V26() set
L~ (mid ((Rev (Lower_Seq (C,n))),1,((First_Point ((L~ (Rev (Lower_Seq (C,n)))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Rev (Lower_Seq (C,n)))))) is closed compact Element of bool the U1 of (TOP-REAL 2)
(L~ (mid ((Rev (Lower_Seq (C,n))),1,((First_Point ((L~ (Rev (Lower_Seq (C,n)))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Rev (Lower_Seq (C,n))))))) /\ (Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)) is Element of bool the U1 of (TOP-REAL 2)
{(First_Point ((L~ (Rev (Lower_Seq (C,n)))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))))} is non empty trivial V26() 1 -element set
(Rev (Lower_Seq (C,n))) | ((First_Point ((L~ (Rev (Lower_Seq (C,n)))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Rev (Lower_Seq (C,n)))) is V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. FinSequence of the U1 of (TOP-REAL 2)
Seg ((First_Point ((L~ (Rev (Lower_Seq (C,n)))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Rev (Lower_Seq (C,n)))) is V26() (First_Point ((L~ (Rev (Lower_Seq (C,n)))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Rev (Lower_Seq (C,n))) -element V200() V201() V202() V203() V204() V205() Element of bool NAT
(Rev (Lower_Seq (C,n))) | (Seg ((First_Point ((L~ (Rev (Lower_Seq (C,n)))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Rev (Lower_Seq (C,n))))) is V13() V16( NAT ) V16( Seg ((First_Point ((L~ (Rev (Lower_Seq (C,n)))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Rev (Lower_Seq (C,n))))) V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like Element of bool [:NAT, the U1 of (TOP-REAL 2):]
[:NAT, the U1 of (TOP-REAL 2):] is non empty non trivial V13() V26() set
bool [:NAT, the U1 of (TOP-REAL 2):] is non empty non trivial V26() set
(Gauge (C,n)) * (g,1) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (g,1)) `1 is V11() V12() ext-real Element of REAL
(Rev (Lower_Seq (C,n))) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Rev (Lower_Seq (C,n))) /. 1) `1 is V11() V12() ext-real Element of REAL
(Lower_Seq (C,n)) /. (len (Lower_Seq (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
LaP is V6() V10() V11() V12() V26() cardinal ext-real non negative set
(Rev (Lower_Seq (C,n))) /. LaP is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Rev (Lower_Seq (C,n))) /. LaP) `1 is V11() V12() ext-real Element of REAL
C is non empty connected compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
n is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
Upper_Seq (C,n) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq standard FinSequence of the U1 of (TOP-REAL 2)
L~ (Upper_Seq (C,n)) is non empty closed compact Element of bool the U1 of (TOP-REAL 2)
Cage (C,n) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
L~ (Cage (C,n)) is non empty closed connected V222() compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
W-bound (L~ (Cage (C,n))) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (C,n))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | (L~ (Cage (C,n))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL:]
the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL:] is set
K506(((TOP-REAL 2) | (L~ (Cage (C,n)))),(proj1 | (L~ (Cage (C,n))))) is V11() V12() ext-real Element of REAL
E-bound (L~ (Cage (C,n))) is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | (L~ (Cage (C,n)))),(proj1 | (L~ (Cage (C,n))))) is V11() V12() ext-real Element of REAL
(W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n)))) is V11() V12() ext-real set
((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2 is V11() V12() ext-real set
Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2) is Element of bool the U1 of (TOP-REAL 2)
W-min (L~ (Cage (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
W-most (L~ (Cage (C,n))) is Element of bool the U1 of (TOP-REAL 2)
SW-corner (L~ (Cage (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Cage (C,n))) is V11() V12() ext-real Element of REAL
proj2 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | (L~ (Cage (C,n))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL:]
K506(((TOP-REAL 2) | (L~ (Cage (C,n)))),(proj2 | (L~ (Cage (C,n))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (C,n)))),(S-bound (L~ (Cage (C,n))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
NW-corner (L~ (Cage (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Cage (C,n))) is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | (L~ (Cage (C,n)))),(proj2 | (L~ (Cage (C,n))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (C,n)))),(N-bound (L~ (Cage (C,n))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (C,n)))),(NW-corner (L~ (Cage (C,n))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Cage (C,n)))),(NW-corner (L~ (Cage (C,n)))))) /\ (L~ (Cage (C,n))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ (Cage (C,n)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Cage (C,n)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),REAL:]
the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))) is set
[: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),REAL:] is set
K506(((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),(proj2 | (W-most (L~ (Cage (C,n)))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (C,n)))),K506(((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),(proj2 | (W-most (L~ (Cage (C,n))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
E-max (L~ (Cage (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
E-most (L~ (Cage (C,n))) is Element of bool the U1 of (TOP-REAL 2)
SE-corner (L~ (Cage (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
|[(E-bound (L~ (Cage (C,n)))),(S-bound (L~ (Cage (C,n))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
NE-corner (L~ (Cage (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
|[(E-bound (L~ (Cage (C,n)))),(N-bound (L~ (Cage (C,n))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Cage (C,n)))),(NE-corner (L~ (Cage (C,n))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SE-corner (L~ (Cage (C,n)))),(NE-corner (L~ (Cage (C,n)))))) /\ (L~ (Cage (C,n))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ (Cage (C,n)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Cage (C,n)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),REAL:]
the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))) is set
[: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),REAL:] is set
K507(((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),(proj2 | (E-most (L~ (Cage (C,n)))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (C,n)))),K507(((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),(proj2 | (E-most (L~ (Cage (C,n))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
mid ((Upper_Seq (C,n)),2,((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n)))) is V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
rng (mid ((Upper_Seq (C,n)),2,((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n))))) is V26() set
(Upper_Seq (C,n)) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
len (Upper_Seq (C,n)) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Upper_Seq (C,n)) /. (len (Upper_Seq (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
rng (Upper_Seq (C,n)) is non empty V26() set
dom (Upper_Seq (C,n)) is non empty non trivial V26() V200() V201() V202() V203() V204() V205() Element of bool NAT
(E-max (L~ (Cage (C,n)))) `1 is V11() V12() ext-real Element of REAL
(W-min (L~ (Cage (C,n)))) `1 is V11() V12() ext-real Element of REAL
(L~ (Upper_Seq (C,n))) /\ (Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)) is Element of bool the U1 of (TOP-REAL 2)
(First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) `1 is V11() V12() ext-real Element of REAL
((Upper_Seq (C,n)) /. 1) .. (Upper_Seq (C,n)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(W-min (L~ (Cage (C,n)))) .. (Upper_Seq (C,n)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
1 + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(1 + 1) + 0 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n))) - 2 is V11() V12() ext-real set
((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n))) -' 2 is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
len (mid ((Upper_Seq (C,n)),2,((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n))) - 2) + 1 is V11() V12() ext-real set
SW is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
SW `1 is V11() V12() ext-real Element of REAL
dom (mid ((Upper_Seq (C,n)),2,((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n))))) is V26() V200() V201() V202() V203() V204() V205() Element of bool NAT
FiP is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(mid ((Upper_Seq (C,n)),2,((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n))))) /. FiP is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
FiP + 2 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(1 + 1) - 1 is V11() V12() ext-real set
(FiP + 2) - 1 is V11() V12() ext-real set
(FiP + 2) -' 1 is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Upper_Seq (C,n)) /. ((FiP + 2) -' 1) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
2 - 1 is V11() V12() ext-real set
FiP + (2 - 1) is V11() V12() ext-real set
(Upper_Seq (C,n)) /. (FiP + (2 - 1)) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n))) - 2) + 1) + 1 is V11() V12() ext-real set
FiP + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
C is non empty connected compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
n is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
Upper_Seq (C,n) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq standard FinSequence of the U1 of (TOP-REAL 2)
L~ (Upper_Seq (C,n)) is non empty closed compact Element of bool the U1 of (TOP-REAL 2)
Cage (C,n) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
L~ (Cage (C,n)) is non empty closed connected V222() compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
W-bound (L~ (Cage (C,n))) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (C,n))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | (L~ (Cage (C,n))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL:]
the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL:] is set
K506(((TOP-REAL 2) | (L~ (Cage (C,n)))),(proj1 | (L~ (Cage (C,n))))) is V11() V12() ext-real Element of REAL
E-bound (L~ (Cage (C,n))) is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | (L~ (Cage (C,n)))),(proj1 | (L~ (Cage (C,n))))) is V11() V12() ext-real Element of REAL
(W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n)))) is V11() V12() ext-real set
((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2 is V11() V12() ext-real set
Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2) is Element of bool the U1 of (TOP-REAL 2)
W-min (L~ (Cage (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
W-most (L~ (Cage (C,n))) is Element of bool the U1 of (TOP-REAL 2)
SW-corner (L~ (Cage (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Cage (C,n))) is V11() V12() ext-real Element of REAL
proj2 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | (L~ (Cage (C,n))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL:]
K506(((TOP-REAL 2) | (L~ (Cage (C,n)))),(proj2 | (L~ (Cage (C,n))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (C,n)))),(S-bound (L~ (Cage (C,n))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
NW-corner (L~ (Cage (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Cage (C,n))) is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | (L~ (Cage (C,n)))),(proj2 | (L~ (Cage (C,n))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (C,n)))),(N-bound (L~ (Cage (C,n))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (C,n)))),(NW-corner (L~ (Cage (C,n))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Cage (C,n)))),(NW-corner (L~ (Cage (C,n)))))) /\ (L~ (Cage (C,n))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ (Cage (C,n)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Cage (C,n)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),REAL:]
the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))) is set
[: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),REAL:] is set
K506(((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),(proj2 | (W-most (L~ (Cage (C,n)))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (C,n)))),K506(((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),(proj2 | (W-most (L~ (Cage (C,n))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
E-max (L~ (Cage (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
E-most (L~ (Cage (C,n))) is Element of bool the U1 of (TOP-REAL 2)
SE-corner (L~ (Cage (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
|[(E-bound (L~ (Cage (C,n)))),(S-bound (L~ (Cage (C,n))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
NE-corner (L~ (Cage (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
|[(E-bound (L~ (Cage (C,n)))),(N-bound (L~ (Cage (C,n))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Cage (C,n)))),(NE-corner (L~ (Cage (C,n))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SE-corner (L~ (Cage (C,n)))),(NE-corner (L~ (Cage (C,n)))))) /\ (L~ (Cage (C,n))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ (Cage (C,n)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Cage (C,n)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),REAL:]
the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))) is set
[: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),REAL:] is set
K507(((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),(proj2 | (E-most (L~ (Cage (C,n)))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (C,n)))),K507(((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),(proj2 | (E-most (L~ (Cage (C,n))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) `2 is V11() V12() ext-real Element of REAL
Lower_Seq (C,n) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq standard FinSequence of the U1 of (TOP-REAL 2)
L~ (Lower_Seq (C,n)) is non empty closed compact Element of bool the U1 of (TOP-REAL 2)
Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) `2 is V11() V12() ext-real Element of REAL
(First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
mid ((Upper_Seq (C,n)),2,((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n)))) is V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
|[(E-bound (L~ (Cage (C,n)))),((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) `2)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
<*|[(E-bound (L~ (Cage (C,n)))),((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) `2)]|*> is non empty trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like constant V26() 1 -element FinSequence-like FinSubsequence-like special FinSequence of the U1 of (TOP-REAL 2)
(mid ((Upper_Seq (C,n)),2,((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n))))) ^ <*|[(E-bound (L~ (Cage (C,n)))),((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) `2)]|*> is non empty V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
<*(SW-corner (L~ (Cage (C,n))))*> is non empty trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like constant V26() 1 -element FinSequence-like FinSubsequence-like special FinSequence of the U1 of (TOP-REAL 2)
Rev (Lower_Seq (C,n)) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
(Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) is V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. FinSequence of the U1 of (TOP-REAL 2)
<*(SW-corner (L~ (Cage (C,n))))*> ^ ((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))))) is non empty V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
|[(((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2),(N-bound (L~ (Cage (C,n))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
<*|[(((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2),(N-bound (L~ (Cage (C,n))))]|*> is non empty trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like constant V26() 1 -element FinSequence-like FinSubsequence-like special FinSequence of the U1 of (TOP-REAL 2)
(<*(SW-corner (L~ (Cage (C,n))))*> ^ ((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))))) ^ <*|[(((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2),(N-bound (L~ (Cage (C,n))))]|*> is non empty V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
(Upper_Seq (C,n)) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(W-min (L~ (Cage (C,n)))) `1 is V11() V12() ext-real Element of REAL
(E-max (L~ (Cage (C,n)))) `1 is V11() V12() ext-real Element of REAL
Gauge (C,n) is V13() non empty-yielding V16( NAT ) V17(K238( the U1 of (TOP-REAL 2))) Function-like V26() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K238( the U1 of (TOP-REAL 2))
Center (Gauge (C,n)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
width (Gauge (C,n)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Gauge (C,n)) * ((Center (Gauge (C,n))),(width (Gauge (C,n)))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
len (Gauge (C,n)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
((Gauge (C,n)) * ((Center (Gauge (C,n))),(width (Gauge (C,n))))) `2 is V11() V12() ext-real Element of REAL
(SW-corner (L~ (Cage (C,n)))) `2 is V11() V12() ext-real Element of REAL
(W-min (L~ (Cage (C,n)))) `2 is V11() V12() ext-real Element of REAL
|[(((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2),(N-bound (L~ (Cage (C,n))))]| `2 is V11() V12() ext-real Element of REAL
rng ((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))))) is V26() set
rng (Rev (Lower_Seq (C,n))) is non empty V26() set
(Lower_Seq (C,n)) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
len (Lower_Seq (C,n)) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Lower_Seq (C,n)) /. (len (Lower_Seq (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(L~ (Lower_Seq (C,n))) /\ (Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)) is Element of bool the U1 of (TOP-REAL 2)
(L~ (Upper_Seq (C,n))) \/ (L~ (Lower_Seq (C,n))) is non empty Element of bool the U1 of (TOP-REAL 2)
rng (Upper_Seq (C,n)) is non empty V26() set
dom (Upper_Seq (C,n)) is non empty non trivial V26() V200() V201() V202() V203() V204() V205() Element of bool NAT
((Gauge (C,n)) * ((Center (Gauge (C,n))),(width (Gauge (C,n))))) `1 is V11() V12() ext-real Element of REAL
W-bound C is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | C is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | C is V13() Function-like V40( the U1 of ((TOP-REAL 2) | C), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | C),REAL:]
the U1 of ((TOP-REAL 2) | C) is non empty set
[: the U1 of ((TOP-REAL 2) | C),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | C),REAL:] is set
K506(((TOP-REAL 2) | C),(proj1 | C)) is V11() V12() ext-real Element of REAL
E-bound C is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | C),(proj1 | C)) is V11() V12() ext-real Element of REAL
(W-bound C) + (E-bound C) is V11() V12() ext-real set
((W-bound C) + (E-bound C)) / 2 is V11() V12() ext-real set
rng (Lower_Seq (C,n)) is non empty V26() set
{(SW-corner (L~ (Cage (C,n))))} is non empty trivial V26() 1 -element set
rng <*(SW-corner (L~ (Cage (C,n))))*> is non empty trivial V26() 1 -element set
(rng <*(SW-corner (L~ (Cage (C,n))))*>) \/ (rng ((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))))) is non empty V26() set
rng (<*(SW-corner (L~ (Cage (C,n))))*> ^ ((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))))) is non empty V26() set
{|[(((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2),(N-bound (L~ (Cage (C,n))))]|} is non empty trivial functional V26() V30() 1 -element set
(rng (<*(SW-corner (L~ (Cage (C,n))))*> ^ ((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))))))) /\ {|[(((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2),(N-bound (L~ (Cage (C,n))))]|} is V26() set
rng <*|[(((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2),(N-bound (L~ (Cage (C,n))))]|*> is non empty trivial V26() 1 -element set
(rng (<*(SW-corner (L~ (Cage (C,n))))*> ^ ((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))))))) /\ (rng <*|[(((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2),(N-bound (L~ (Cage (C,n))))]|*>) is V26() set
len ((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Rev (Lower_Seq (C,n))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
len (Upper_Seq (C,n)) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Upper_Seq (C,n)) /. (len (Upper_Seq (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(L~ (Upper_Seq (C,n))) /\ (Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)) is Element of bool the U1 of (TOP-REAL 2)
g is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
dom <*|[(E-bound (L~ (Cage (C,n)))),((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) `2)]|*> is non empty trivial V26() 1 -element V200() V201() V202() V203() V204() V205() Element of bool NAT
<*|[(E-bound (L~ (Cage (C,n)))),((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) `2)]|*> /. g is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(<*|[(E-bound (L~ (Cage (C,n)))),((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) `2)]|*> /. g) `1 is V11() V12() ext-real Element of REAL
(<*|[(E-bound (L~ (Cage (C,n)))),((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) `2)]|*> /. g) `2 is V11() V12() ext-real Element of REAL
(First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) `1 is V11() V12() ext-real Element of REAL
rng (mid ((Upper_Seq (C,n)),2,((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n))))) is V26() set
{|[(E-bound (L~ (Cage (C,n)))),((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) `2)]|} is non empty trivial functional V26() V30() 1 -element set
(rng (mid ((Upper_Seq (C,n)),2,((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n)))))) /\ {|[(E-bound (L~ (Cage (C,n)))),((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) `2)]|} is V26() set
g is set
|[(E-bound (L~ (Cage (C,n)))),((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) `2)]| `1 is V11() V12() ext-real Element of REAL
rng <*|[(E-bound (L~ (Cage (C,n)))),((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) `2)]|*> is non empty trivial V26() 1 -element set
(Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) `1 is V11() V12() ext-real Element of REAL
(L~ (Upper_Seq (C,n))) /\ (L~ (Lower_Seq (C,n))) is Element of bool the U1 of (TOP-REAL 2)
{(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n))))} is non empty V26() set
len (mid ((Upper_Seq (C,n)),2,((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(mid ((Upper_Seq (C,n)),2,((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n))))) /. (len (mid ((Upper_Seq (C,n)),2,((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n)))))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((mid ((Upper_Seq (C,n)),2,((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n))))) /. (len (mid ((Upper_Seq (C,n)),2,((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n))))))) `2 is V11() V12() ext-real Element of REAL
(Upper_Seq (C,n)) /. ((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Upper_Seq (C,n)) /. ((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n)))) `2 is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (C,n)))),((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) `2)]| `2 is V11() V12() ext-real Element of REAL
<*|[(E-bound (L~ (Cage (C,n)))),((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) `2)]|*> /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(<*|[(E-bound (L~ (Cage (C,n)))),((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) `2)]|*> /. 1) `2 is V11() V12() ext-real Element of REAL
(Upper_Seq (C,n)) /. 2 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
g is V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special FinSequence of the U1 of (TOP-REAL 2)
len g is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
g /. (len g) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(g /. (len g)) `1 is V11() V12() ext-real Element of REAL
len <*|[(E-bound (L~ (Cage (C,n)))),((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) `2)]|*> is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
<*|[(E-bound (L~ (Cage (C,n)))),((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) `2)]|*> /. (len <*|[(E-bound (L~ (Cage (C,n)))),((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) `2)]|*>) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(<*|[(E-bound (L~ (Cage (C,n)))),((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) `2)]|*> /. (len <*|[(E-bound (L~ (Cage (C,n)))),((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) `2)]|*>)) `1 is V11() V12() ext-real Element of REAL
(<*|[(E-bound (L~ (Cage (C,n)))),((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) `2)]|*> /. 1) `1 is V11() V12() ext-real Element of REAL
dom (mid ((Upper_Seq (C,n)),2,((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n))))) is V26() V200() V201() V202() V203() V204() V205() Element of bool NAT
g /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(g /. 1) `1 is V11() V12() ext-real Element of REAL
(mid ((Upper_Seq (C,n)),2,((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n))))) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((mid ((Upper_Seq (C,n)),2,((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n))))) /. 1) `1 is V11() V12() ext-real Element of REAL
(Upper_Seq (C,n)) /. 2 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Upper_Seq (C,n)) /. 2) `1 is V11() V12() ext-real Element of REAL
rng (Cage (C,n)) is non empty non trivial V26() set
(SW-corner (L~ (Cage (C,n)))) `1 is V11() V12() ext-real Element of REAL
len (Cage (C,n)) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
{(SW-corner (L~ (Cage (C,n))))} /\ (rng ((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))))) is V26() set
(rng <*(SW-corner (L~ (Cage (C,n))))*>) /\ (rng ((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))))) is V26() set
First_Point ((L~ (Lower_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
len <*(SW-corner (L~ (Cage (C,n))))*> is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
<*(SW-corner (L~ (Cage (C,n))))*> /. (len <*(SW-corner (L~ (Cage (C,n))))*>) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(<*(SW-corner (L~ (Cage (C,n))))*> /. (len <*(SW-corner (L~ (Cage (C,n))))*>)) `1 is V11() V12() ext-real Element of REAL
<*(SW-corner (L~ (Cage (C,n))))*> /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(<*(SW-corner (L~ (Cage (C,n))))*> /. 1) `1 is V11() V12() ext-real Element of REAL
(SW-corner (L~ (Cage (C,n)))) `1 is V11() V12() ext-real Element of REAL
((Lower_Seq (C,n)) /. (len (Lower_Seq (C,n)))) `1 is V11() V12() ext-real Element of REAL
(Rev (Lower_Seq (C,n))) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Rev (Lower_Seq (C,n))) /. 1) `1 is V11() V12() ext-real Element of REAL
((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))))) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))))) /. 1) `1 is V11() V12() ext-real Element of REAL
h is V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like special FinSequence of the U1 of (TOP-REAL 2)
h -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) is V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like special FinSequence of the U1 of (TOP-REAL 2)
<*(SW-corner (L~ (Cage (C,n))))*> ^ (h -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))))) is non empty V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
len (<*(SW-corner (L~ (Cage (C,n))))*> ^ ((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))))) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(<*(SW-corner (L~ (Cage (C,n))))*> ^ ((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))))) /. (len (<*(SW-corner (L~ (Cage (C,n))))*> ^ ((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))))))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((<*(SW-corner (L~ (Cage (C,n))))*> ^ ((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))))) /. (len (<*(SW-corner (L~ (Cage (C,n))))*> ^ ((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))))))) `1 is V11() V12() ext-real Element of REAL
((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))))) /. (len ((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))))) /. (len ((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))))))) `1 is V11() V12() ext-real Element of REAL
((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))))) /. ((Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Rev (Lower_Seq (C,n)))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))))) /. ((Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Rev (Lower_Seq (C,n))))) `1 is V11() V12() ext-real Element of REAL
|[(((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2),(N-bound (L~ (Cage (C,n))))]| `1 is V11() V12() ext-real Element of REAL
<*|[(((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2),(N-bound (L~ (Cage (C,n))))]|*> /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(<*|[(((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2),(N-bound (L~ (Cage (C,n))))]|*> /. 1) `1 is V11() V12() ext-real Element of REAL
midU is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
dom <*(SW-corner (L~ (Cage (C,n))))*> is non empty trivial V26() 1 -element V200() V201() V202() V203() V204() V205() Element of bool NAT
<*(SW-corner (L~ (Cage (C,n))))*> /. midU is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(<*(SW-corner (L~ (Cage (C,n))))*> /. midU) `1 is V11() V12() ext-real Element of REAL
(<*(SW-corner (L~ (Cage (C,n))))*> /. midU) `2 is V11() V12() ext-real Element of REAL
midU is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
dom <*|[(((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2),(N-bound (L~ (Cage (C,n))))]|*> is non empty trivial V26() 1 -element V200() V201() V202() V203() V204() V205() Element of bool NAT
<*|[(((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2),(N-bound (L~ (Cage (C,n))))]|*> /. midU is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(<*|[(((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2),(N-bound (L~ (Cage (C,n))))]|*> /. midU) `1 is V11() V12() ext-real Element of REAL
(<*|[(((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2),(N-bound (L~ (Cage (C,n))))]|*> /. midU) `2 is V11() V12() ext-real Element of REAL
L~ (Rev (Lower_Seq (C,n))) is non empty closed compact Element of bool the U1 of (TOP-REAL 2)
FiP2 is V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special FinSequence of the U1 of (TOP-REAL 2)
1 + (len ((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))))) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
dom FiP2 is V26() V200() V201() V202() V203() V204() V205() Element of bool NAT
FiP2 /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
FiP2 . 1 is set
(FiP2 /. 1) `2 is V11() V12() ext-real Element of REAL
(<*(SW-corner (L~ (Cage (C,n))))*> ^ ((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))))) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((<*(SW-corner (L~ (Cage (C,n))))*> ^ ((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))))) /. 1) `2 is V11() V12() ext-real Element of REAL
len FiP2 is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(len (<*(SW-corner (L~ (Cage (C,n))))*> ^ ((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))))))) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
1 + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
((Upper_Seq (C,n)) /. 1) .. (Upper_Seq (C,n)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(W-min (L~ (Cage (C,n)))) .. (Upper_Seq (C,n)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(1 + 1) + 0 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n))) - 2 is V11() V12() ext-real set
((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n))) -' 2 is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n))) - 2) + 1 is V11() V12() ext-real set
2 - 1 is V11() V12() ext-real set
((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n))) - (2 - 1) is V11() V12() ext-real set
dom ((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))))) is V26() V200() V201() V202() V203() V204() V205() Element of bool NAT
((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))))) ^ <*|[(((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2),(N-bound (L~ (Cage (C,n))))]|*> is non empty V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
(((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))))) ^ <*|[(((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2),(N-bound (L~ (Cage (C,n))))]|*>) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(len (mid ((Upper_Seq (C,n)),2,((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n)))))) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
L~ g is closed compact Element of bool the U1 of (TOP-REAL 2)
L~ (mid ((Upper_Seq (C,n)),2,((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n))))) is closed compact Element of bool the U1 of (TOP-REAL 2)
LSeg (((mid ((Upper_Seq (C,n)),2,((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n))))) /. (len (mid ((Upper_Seq (C,n)),2,((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n))))))),|[(E-bound (L~ (Cage (C,n)))),((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) `2)]|) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(L~ (mid ((Upper_Seq (C,n)),2,((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n)))))) \/ (LSeg (((mid ((Upper_Seq (C,n)),2,((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n))))) /. (len (mid ((Upper_Seq (C,n)),2,((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n))))))),|[(E-bound (L~ (Cage (C,n)))),((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) `2)]|)) is Element of bool the U1 of (TOP-REAL 2)
L~ ((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))))) is closed compact Element of bool the U1 of (TOP-REAL 2)
(Rev (Lower_Seq (C,n))) :- (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) is non empty V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
L~ ((Rev (Lower_Seq (C,n))) :- (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))))) is closed compact Element of bool the U1 of (TOP-REAL 2)
(L~ ((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))))) \/ (L~ ((Rev (Lower_Seq (C,n))) :- (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))))) is Element of bool the U1 of (TOP-REAL 2)
LSeg ((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))),|[(E-bound (L~ (Cage (C,n)))),((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) `2)]|) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
LSeg ((Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))),|[(((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2),(N-bound (L~ (Cage (C,n))))]|) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
FiP2 /. (len FiP2) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(FiP2 /. (len FiP2)) `2 is V11() V12() ext-real Element of REAL
L~ FiP2 is closed compact Element of bool the U1 of (TOP-REAL 2)
midU is set
<*(SW-corner (L~ (Cage (C,n))))*> ^ (((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))))) ^ <*|[(((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2),(N-bound (L~ (Cage (C,n))))]|*>) is non empty V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
L~ (<*(SW-corner (L~ (Cage (C,n))))*> ^ (((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))))) ^ <*|[(((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2),(N-bound (L~ (Cage (C,n))))]|*>)) is closed compact Element of bool the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (C,n)))),((((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))))) ^ <*|[(((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2),(N-bound (L~ (Cage (C,n))))]|*>) /. 1)) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
L~ (((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))))) ^ <*|[(((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2),(N-bound (L~ (Cage (C,n))))]|*>) is closed compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Cage (C,n)))),((((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))))) ^ <*|[(((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2),(N-bound (L~ (Cage (C,n))))]|*>) /. 1))) \/ (L~ (((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))))) ^ <*|[(((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2),(N-bound (L~ (Cage (C,n))))]|*>)) is Element of bool the U1 of (TOP-REAL 2)
LSeg ((((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))))) /. (len ((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))))))),|[(((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2),(N-bound (L~ (Cage (C,n))))]|) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(L~ ((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))))) \/ (LSeg ((((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))))) /. (len ((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))))))),|[(((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2),(N-bound (L~ (Cage (C,n))))]|)) is Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Cage (C,n)))),((((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))))) ^ <*|[(((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2),(N-bound (L~ (Cage (C,n))))]|*>) /. 1))) \/ ((L~ ((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))))) \/ (LSeg ((((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))))) /. (len ((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))))))),|[(((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2),(N-bound (L~ (Cage (C,n))))]|))) is Element of bool the U1 of (TOP-REAL 2)
x is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
x `2 is V11() V12() ext-real Element of REAL
x `1 is V11() V12() ext-real Element of REAL
x `2 is V11() V12() ext-real Element of REAL
x is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
x + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))))) /. x is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))))) /. (x + 1) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))))) /. x),(((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))))) /. (x + 1))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(Rev (Lower_Seq (C,n))) /. x is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Rev (Lower_Seq (C,n))) /. x) `1 is V11() V12() ext-real Element of REAL
Seg ((Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Rev (Lower_Seq (C,n)))) is V26() (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Rev (Lower_Seq (C,n))) -element V200() V201() V202() V203() V204() V205() Element of bool NAT
(Rev (Lower_Seq (C,n))) /. (x + 1) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
x `1 is V11() V12() ext-real Element of REAL
(((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))))) /. x) `1 is V11() V12() ext-real Element of REAL
(((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))))) /. (x + 1)) `1 is V11() V12() ext-real Element of REAL
((Rev (Lower_Seq (C,n))) /. (x + 1)) `1 is V11() V12() ext-real Element of REAL
len (Rev (Lower_Seq (C,n))) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
LSeg (((Rev (Lower_Seq (C,n))) /. x),((Rev (Lower_Seq (C,n))) /. (x + 1))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
LSeg ((Rev (Lower_Seq (C,n))),x) is closed Element of bool the U1 of (TOP-REAL 2)
x `2 is V11() V12() ext-real Element of REAL
x `1 is V11() V12() ext-real Element of REAL
x is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
x + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(mid ((Upper_Seq (C,n)),2,((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n))))) /. x is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(mid ((Upper_Seq (C,n)),2,((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n))))) /. (x + 1) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg (((mid ((Upper_Seq (C,n)),2,((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n))))) /. x),((mid ((Upper_Seq (C,n)),2,((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n))))) /. (x + 1))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
x + 2 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(1 + 1) - 1 is V11() V12() ext-real set
(x + 2) - 1 is V11() V12() ext-real set
(x + 2) -' 1 is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Upper_Seq (C,n)) /. ((x + 2) -' 1) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
x + (2 - 1) is V11() V12() ext-real set
(Upper_Seq (C,n)) /. (x + (2 - 1)) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(x + 1) + 2 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
((x + 1) + 2) - 1 is V11() V12() ext-real set
((x + 1) + 2) -' 1 is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Upper_Seq (C,n)) /. (((x + 1) + 2) -' 1) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(x + 1) + (2 - 1) is V11() V12() ext-real set
(Upper_Seq (C,n)) /. ((x + 1) + (2 - 1)) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(x + 1) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n))) - 1 is V11() V12() ext-real set
(((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n))) - 1) + 1 is V11() V12() ext-real set
((mid ((Upper_Seq (C,n)),2,((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n))))) /. x) `1 is V11() V12() ext-real Element of REAL
LSeg ((Upper_Seq (C,n)),(x + 1)) is closed Element of bool the U1 of (TOP-REAL 2)
((x + 1) + 1) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
((mid ((Upper_Seq (C,n)),2,((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n))))) /. (x + 1)) `1 is V11() V12() ext-real Element of REAL
((mid ((Upper_Seq (C,n)),2,((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n))))) /. x) `2 is V11() V12() ext-real Element of REAL
((mid ((Upper_Seq (C,n)),2,((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n))))) /. (x + 1)) `2 is V11() V12() ext-real Element of REAL
((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))))) ^ <*|[(((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2),(N-bound (L~ (Cage (C,n))))]|*> is non empty V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
RevLS is V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like special FinSequence of the U1 of (TOP-REAL 2)
RevLS -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) is V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like special FinSequence of the U1 of (TOP-REAL 2)
(rng ((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))))) /\ {|[(((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2),(N-bound (L~ (Cage (C,n))))]|} is V26() set
(rng ((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))))) /\ (rng <*|[(((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2),(N-bound (L~ (Cage (C,n))))]|*>) is V26() set
((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))))) /. (len ((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))))) /. (len ((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))))))) `1 is V11() V12() ext-real Element of REAL
((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))))) /. ((Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Rev (Lower_Seq (C,n)))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))))) /. ((Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Rev (Lower_Seq (C,n))))) `1 is V11() V12() ext-real Element of REAL
|[(((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2),(N-bound (L~ (Cage (C,n))))]| `1 is V11() V12() ext-real Element of REAL
<*|[(((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2),(N-bound (L~ (Cage (C,n))))]|*> /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(<*|[(((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2),(N-bound (L~ (Cage (C,n))))]|*> /. 1) `1 is V11() V12() ext-real Element of REAL
FiP2 is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
dom <*|[(((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2),(N-bound (L~ (Cage (C,n))))]|*> is non empty trivial V26() 1 -element V200() V201() V202() V203() V204() V205() Element of bool NAT
<*|[(((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2),(N-bound (L~ (Cage (C,n))))]|*> /. FiP2 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(<*|[(((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2),(N-bound (L~ (Cage (C,n))))]|*> /. FiP2) `1 is V11() V12() ext-real Element of REAL
(<*|[(((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2),(N-bound (L~ (Cage (C,n))))]|*> /. FiP2) `2 is V11() V12() ext-real Element of REAL
h is V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special FinSequence of the U1 of (TOP-REAL 2)
len h is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(len ((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))))) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
h /. (len h) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(h /. (len h)) `2 is V11() V12() ext-real Element of REAL
L~ (Rev (Lower_Seq (C,n))) is non empty closed compact Element of bool the U1 of (TOP-REAL 2)
L~ ((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))))) is closed compact Element of bool the U1 of (TOP-REAL 2)
(Rev (Lower_Seq (C,n))) :- (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) is non empty V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
L~ ((Rev (Lower_Seq (C,n))) :- (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))))) is closed compact Element of bool the U1 of (TOP-REAL 2)
(L~ ((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))))) \/ (L~ ((Rev (Lower_Seq (C,n))) :- (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))))) is Element of bool the U1 of (TOP-REAL 2)
0 + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
dom h is V26() V200() V201() V202() V203() V204() V205() Element of bool NAT
h /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
h . 1 is set
(h /. 1) `2 is V11() V12() ext-real Element of REAL
((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))))) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))))) /. 1) `2 is V11() V12() ext-real Element of REAL
(Rev (Lower_Seq (C,n))) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Rev (Lower_Seq (C,n))) /. 1) `2 is V11() V12() ext-real Element of REAL
((Lower_Seq (C,n)) /. (len (Lower_Seq (C,n)))) `2 is V11() V12() ext-real Element of REAL
First_Point ((L~ (Lower_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
L~ g is closed compact Element of bool the U1 of (TOP-REAL 2)
L~ (mid ((Upper_Seq (C,n)),2,((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n))))) is closed compact Element of bool the U1 of (TOP-REAL 2)
LSeg (((mid ((Upper_Seq (C,n)),2,((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n))))) /. (len (mid ((Upper_Seq (C,n)),2,((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n))))))),|[(E-bound (L~ (Cage (C,n)))),((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) `2)]|) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(L~ (mid ((Upper_Seq (C,n)),2,((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n)))))) \/ (LSeg (((mid ((Upper_Seq (C,n)),2,((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n))))) /. (len (mid ((Upper_Seq (C,n)),2,((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n))))))),|[(E-bound (L~ (Cage (C,n)))),((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) `2)]|)) is Element of bool the U1 of (TOP-REAL 2)
((Upper_Seq (C,n)) /. 1) .. (Upper_Seq (C,n)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(W-min (L~ (Cage (C,n)))) .. (Upper_Seq (C,n)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
1 + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(1 + 1) + 0 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n))) - 2 is V11() V12() ext-real set
((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n))) -' 2 is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n))) - 2) + 1 is V11() V12() ext-real set
2 - 1 is V11() V12() ext-real set
((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n))) - (2 - 1) is V11() V12() ext-real set
LSeg ((Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))),|[(((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2),(N-bound (L~ (Cage (C,n))))]|) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(len (mid ((Upper_Seq (C,n)),2,((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n)))))) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
L~ h is closed compact Element of bool the U1 of (TOP-REAL 2)
x is set
LSeg ((((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))))) /. (len ((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))))))),|[(((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2),(N-bound (L~ (Cage (C,n))))]|) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(L~ ((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))))) \/ (LSeg ((((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))))) /. (len ((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))))))),|[(((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2),(N-bound (L~ (Cage (C,n))))]|)) is Element of bool the U1 of (TOP-REAL 2)
LSeg ((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))),|[(E-bound (L~ (Cage (C,n)))),((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) `2)]|) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
x is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
x `2 is V11() V12() ext-real Element of REAL
i is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
i + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))))) /. i is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))))) /. (i + 1) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))))) /. i),(((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))))) /. (i + 1))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(Rev (Lower_Seq (C,n))) /. i is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
((Rev (Lower_Seq (C,n))) /. i) `1 is V11() V12() ext-real Element of REAL
Seg ((Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Rev (Lower_Seq (C,n)))) is V26() (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Rev (Lower_Seq (C,n))) -element V200() V201() V202() V203() V204() V205() Element of bool NAT
(Rev (Lower_Seq (C,n))) /. (i + 1) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
x `1 is V11() V12() ext-real Element of REAL
(((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))))) /. i) `1 is V11() V12() ext-real Element of REAL
(((Rev (Lower_Seq (C,n))) -: (Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))))) /. (i + 1)) `1 is V11() V12() ext-real Element of REAL
((Rev (Lower_Seq (C,n))) /. (i + 1)) `1 is V11() V12() ext-real Element of REAL
len (Rev (Lower_Seq (C,n))) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
LSeg (((Rev (Lower_Seq (C,n))) /. i),((Rev (Lower_Seq (C,n))) /. (i + 1))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
LSeg ((Rev (Lower_Seq (C,n))),i) is closed Element of bool the U1 of (TOP-REAL 2)
x is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
x `2 is V11() V12() ext-real Element of REAL
x `1 is V11() V12() ext-real Element of REAL
i is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
i + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(mid ((Upper_Seq (C,n)),2,((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n))))) /. i is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(mid ((Upper_Seq (C,n)),2,((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n))))) /. (i + 1) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg (((mid ((Upper_Seq (C,n)),2,((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n))))) /. i),((mid ((Upper_Seq (C,n)),2,((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n))))) /. (i + 1))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
i + 2 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(1 + 1) - 1 is V11() V12() ext-real set
(i + 2) - 1 is V11() V12() ext-real set
(i + 2) -' 1 is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Upper_Seq (C,n)) /. ((i + 2) -' 1) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
i + (2 - 1) is V11() V12() ext-real set
(Upper_Seq (C,n)) /. (i + (2 - 1)) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(i + 1) + 2 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
((i + 1) + 2) - 1 is V11() V12() ext-real set
((i + 1) + 2) -' 1 is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Upper_Seq (C,n)) /. (((i + 1) + 2) -' 1) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(i + 1) + (2 - 1) is V11() V12() ext-real set
(Upper_Seq (C,n)) /. ((i + 1) + (2 - 1)) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(i + 1) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n))) - 1 is V11() V12() ext-real set
(((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n))) - 1) + 1 is V11() V12() ext-real set
((mid ((Upper_Seq (C,n)),2,((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n))))) /. i) `1 is V11() V12() ext-real Element of REAL
LSeg ((Upper_Seq (C,n)),(i + 1)) is closed Element of bool the U1 of (TOP-REAL 2)
((i + 1) + 1) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
((mid ((Upper_Seq (C,n)),2,((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n))))) /. (i + 1)) `1 is V11() V12() ext-real Element of REAL
((mid ((Upper_Seq (C,n)),2,((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n))))) /. i) `2 is V11() V12() ext-real Element of REAL
((mid ((Upper_Seq (C,n)),2,((First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) .. (Upper_Seq (C,n))))) /. (i + 1)) `2 is V11() V12() ext-real Element of REAL
x is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
C is non empty connected compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
n is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
Upper_Seq (C,n) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq standard FinSequence of the U1 of (TOP-REAL 2)
L~ (Upper_Seq (C,n)) is non empty closed compact Element of bool the U1 of (TOP-REAL 2)
Cage (C,n) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
L~ (Cage (C,n)) is non empty closed connected V222() compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
Upper_Arc (L~ (Cage (C,n))) is non empty Element of bool the U1 of (TOP-REAL 2)
W-min (L~ (Cage (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
W-bound (L~ (Cage (C,n))) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (C,n))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | (L~ (Cage (C,n))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL:]
the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL:] is set
K506(((TOP-REAL 2) | (L~ (Cage (C,n)))),(proj1 | (L~ (Cage (C,n))))) is V11() V12() ext-real Element of REAL
W-most (L~ (Cage (C,n))) is Element of bool the U1 of (TOP-REAL 2)
SW-corner (L~ (Cage (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Cage (C,n))) is V11() V12() ext-real Element of REAL
proj2 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | (L~ (Cage (C,n))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL:]
K506(((TOP-REAL 2) | (L~ (Cage (C,n)))),(proj2 | (L~ (Cage (C,n))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (C,n)))),(S-bound (L~ (Cage (C,n))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
NW-corner (L~ (Cage (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Cage (C,n))) is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | (L~ (Cage (C,n)))),(proj2 | (L~ (Cage (C,n))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (C,n)))),(N-bound (L~ (Cage (C,n))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (C,n)))),(NW-corner (L~ (Cage (C,n))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Cage (C,n)))),(NW-corner (L~ (Cage (C,n)))))) /\ (L~ (Cage (C,n))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ (Cage (C,n)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Cage (C,n)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),REAL:]
the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))) is set
[: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),REAL:] is set
K506(((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),(proj2 | (W-most (L~ (Cage (C,n)))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (C,n)))),K506(((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),(proj2 | (W-most (L~ (Cage (C,n))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
rng (Cage (C,n)) is non empty non trivial V26() set
E-max (L~ (Cage (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Cage (C,n))) is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | (L~ (Cage (C,n)))),(proj1 | (L~ (Cage (C,n))))) is V11() V12() ext-real Element of REAL
E-most (L~ (Cage (C,n))) is Element of bool the U1 of (TOP-REAL 2)
SE-corner (L~ (Cage (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
|[(E-bound (L~ (Cage (C,n)))),(S-bound (L~ (Cage (C,n))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
NE-corner (L~ (Cage (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
|[(E-bound (L~ (Cage (C,n)))),(N-bound (L~ (Cage (C,n))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Cage (C,n)))),(NE-corner (L~ (Cage (C,n))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SE-corner (L~ (Cage (C,n)))),(NE-corner (L~ (Cage (C,n)))))) /\ (L~ (Cage (C,n))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ (Cage (C,n)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Cage (C,n)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),REAL:]
the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))) is set
[: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),REAL:] is set
K507(((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),(proj2 | (E-most (L~ (Cage (C,n)))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (C,n)))),K507(((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),(proj2 | (E-most (L~ (Cage (C,n))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
rng (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) is non empty non trivial V26() set
(Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) -: (E-max (L~ (Cage (C,n)))) is V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like special unfolded FinSequence of the U1 of (TOP-REAL 2)
(Upper_Seq (C,n)) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
len (Upper_Seq (C,n)) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Upper_Seq (C,n)) /. (len (Upper_Seq (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(E-max (L~ (Cage (C,n)))) .. (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
((Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) -: (E-max (L~ (Cage (C,n))))) /. ((E-max (L~ (Cage (C,n)))) .. (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n)))) is V11() V12() ext-real set
((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2 is V11() V12() ext-real set
Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2) is Element of bool the U1 of (TOP-REAL 2)
First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) `2 is V11() V12() ext-real Element of REAL
Lower_Seq (C,n) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq standard FinSequence of the U1 of (TOP-REAL 2)
L~ (Lower_Seq (C,n)) is non empty closed compact Element of bool the U1 of (TOP-REAL 2)
Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) `2 is V11() V12() ext-real Element of REAL
(Lower_Seq (C,n)) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) :- (E-max (L~ (Cage (C,n)))) is non empty V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
((Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) :- (E-max (L~ (Cage (C,n))))) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
len (Lower_Seq (C,n)) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Lower_Seq (C,n)) /. (len (Lower_Seq (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
len (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) /. (len (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(L~ (Upper_Seq (C,n))) /\ (L~ (Lower_Seq (C,n))) is Element of bool the U1 of (TOP-REAL 2)
{(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n))))} is non empty V26() set
(L~ (Upper_Seq (C,n))) \/ (L~ (Lower_Seq (C,n))) is non empty Element of bool the U1 of (TOP-REAL 2)
C is non empty connected compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
n is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
Lower_Seq (C,n) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq standard FinSequence of the U1 of (TOP-REAL 2)
L~ (Lower_Seq (C,n)) is non empty closed compact Element of bool the U1 of (TOP-REAL 2)
Cage (C,n) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
L~ (Cage (C,n)) is non empty closed connected V222() compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
Lower_Arc (L~ (Cage (C,n))) is non empty Element of bool the U1 of (TOP-REAL 2)
W-min (L~ (Cage (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
W-bound (L~ (Cage (C,n))) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (C,n))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | (L~ (Cage (C,n))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL:]
the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL:] is set
K506(((TOP-REAL 2) | (L~ (Cage (C,n)))),(proj1 | (L~ (Cage (C,n))))) is V11() V12() ext-real Element of REAL
W-most (L~ (Cage (C,n))) is Element of bool the U1 of (TOP-REAL 2)
SW-corner (L~ (Cage (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Cage (C,n))) is V11() V12() ext-real Element of REAL
proj2 is V13() Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | (L~ (Cage (C,n))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL:]
K506(((TOP-REAL 2) | (L~ (Cage (C,n)))),(proj2 | (L~ (Cage (C,n))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (C,n)))),(S-bound (L~ (Cage (C,n))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
NW-corner (L~ (Cage (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Cage (C,n))) is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | (L~ (Cage (C,n)))),(proj2 | (L~ (Cage (C,n))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (C,n)))),(N-bound (L~ (Cage (C,n))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (C,n)))),(NW-corner (L~ (Cage (C,n))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Cage (C,n)))),(NW-corner (L~ (Cage (C,n)))))) /\ (L~ (Cage (C,n))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ (Cage (C,n)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Cage (C,n)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),REAL:]
the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))) is set
[: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),REAL:] is set
K506(((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),(proj2 | (W-most (L~ (Cage (C,n)))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (C,n)))),K506(((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),(proj2 | (W-most (L~ (Cage (C,n))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
rng (Cage (C,n)) is non empty non trivial V26() set
(Lower_Seq (C,n)) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
E-max (L~ (Cage (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Cage (C,n))) is V11() V12() ext-real Element of REAL
K507(((TOP-REAL 2) | (L~ (Cage (C,n)))),(proj1 | (L~ (Cage (C,n))))) is V11() V12() ext-real Element of REAL
E-most (L~ (Cage (C,n))) is Element of bool the U1 of (TOP-REAL 2)
SE-corner (L~ (Cage (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
|[(E-bound (L~ (Cage (C,n)))),(S-bound (L~ (Cage (C,n))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
NE-corner (L~ (Cage (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
|[(E-bound (L~ (Cage (C,n)))),(N-bound (L~ (Cage (C,n))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Cage (C,n)))),(NE-corner (L~ (Cage (C,n))))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SE-corner (L~ (Cage (C,n)))),(NE-corner (L~ (Cage (C,n)))))) /\ (L~ (Cage (C,n))) is Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ (Cage (C,n)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Cage (C,n)))) is V13() Function-like V40( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),REAL:]
the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))) is set
[: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),REAL:] is V13() set
bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),REAL:] is set
K507(((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),(proj2 | (E-most (L~ (Cage (C,n)))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (C,n)))),K507(((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),(proj2 | (E-most (L~ (Cage (C,n))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V191() Element of the U1 of (TOP-REAL 2)
(Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) :- (E-max (L~ (Cage (C,n)))) is non empty V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
((Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) :- (E-max (L~ (Cage (C,n))))) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
rng (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) is non empty non trivial V26() set
len (Lower_Seq (C,n)) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Lower_Seq (C,n)) /. (len (Lower_Seq (C,n))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
len (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) /. (len (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) /. 1 is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
Upper_Seq (C,n) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq standard FinSequence of the U1 of (TOP-REAL 2)
L~ (Upper_Seq (C,n)) is non empty closed compact Element of bool the U1 of (TOP-REAL 2)
Upper_Arc (L~ (Cage (C,n))) is non empty Element of bool the U1 of (TOP-REAL 2)
(W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n)))) is V11() V12() ext-real set
((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2 is V11() V12() ext-real set
Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2) is Element of bool the U1 of (TOP-REAL 2)
First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(First_Point ((L~ (Upper_Seq (C,n))),(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) `2 is V11() V12() ext-real Element of REAL
Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2))) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(Last_Point ((L~ (Lower_Seq (C,n))),(E-max (L~ (Cage (C,n)))),(W-min (L~ (Cage (C,n)))),(Vertical_Line (((W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n))))) / 2)))) `2 is V11() V12() ext-real Element of REAL
(L~ (Upper_Seq (C,n))) /\ (L~ (Lower_Seq (C,n))) is Element of bool the U1 of (TOP-REAL 2)
{(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n))))} is non empty V26() set
(L~ (Upper_Seq (C,n))) \/ (L~ (Lower_Seq (C,n))) is non empty Element of bool the U1 of (TOP-REAL 2)
C is non empty connected compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
n is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
Gauge (C,n) is V13() non empty-yielding V16( NAT ) V17(K238( the U1 of (TOP-REAL 2))) Function-like V26() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K238( the U1 of (TOP-REAL 2))
len (Gauge (C,n)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
width (Gauge (C,n)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
Cage (C,n) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like non constant V26() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
L~ (Cage (C,n)) is non empty closed connected V222() compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
Lower_Arc (L~ (Cage (C,n))) is non empty Element of bool the U1 of (TOP-REAL 2)
Lower_Seq (C,n) is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like one-to-one V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq standard FinSequence of the U1 of (TOP-REAL 2)
L~ (Lower_Seq (C,n)) is non empty closed compact Element of bool the U1 of (TOP-REAL 2)
i is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
j is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V199() V200() V201() V202() V203() V204() V205() Element of NAT
(Gauge (C,n)) * (i,j) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
(Gauge (C,n)) * (i,1) is 2 -element FinSequence-like V191() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (C,n)) * (i,1)),((Gauge (C,n)) * (i,j))) is closed closed connected compact compact Element of bool the U1 of (TOP-REAL 2)