:: JORDAN1J semantic presentation

REAL is V180() V181() V182() V186() set
NAT is non empty non trivial V6() V26() cardinal limit_cardinal V180() V181() V182() V183() V184() V185() V186() Element of bool REAL
bool REAL is set
NAT is non empty non trivial V6() V26() cardinal limit_cardinal V180() V181() V182() V183() V184() V185() V186() set
bool NAT is non empty non trivial V26() set
bool NAT is non empty non trivial V26() set
COMPLEX is V180() V186() set
1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
2 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
RAT is V180() V181() V182() V183() V186() set
INT is V180() V181() V182() V183() V184() V186() set
[:1,1:] is V26() set
bool [:1,1:] is V26() V30() set
[:[:1,1:],1:] is V26() set
bool [:[:1,1:],1:] is V26() V30() set
[:[:1,1:],REAL:] is set
bool [:[:1,1:],REAL:] is set
[:REAL,REAL:] is set
[:[:REAL,REAL:],REAL:] is set
bool [:[:REAL,REAL:],REAL:] is set
[:2,2:] is V26() set
[:[:2,2:],REAL:] is set
bool [:[:2,2:],REAL:] is set
bool [:REAL,REAL:] is set
TOP-REAL 2 is non empty non trivial TopSpace-like T_0 T_1 T_2 V107() V138() V139() V140() V141() V142() V143() V144() strict add-continuous Mult-continuous RLTopStruct
the U1 of (TOP-REAL 2) is non empty non trivial functional set
K233( the U1 of (TOP-REAL 2)) is non empty functional FinSequence-membered M11( the U1 of (TOP-REAL 2))
[: the U1 of (TOP-REAL 2),REAL:] is set
bool [: the U1 of (TOP-REAL 2),REAL:] is set
bool the U1 of (TOP-REAL 2) is set
{} is empty trivial V6() V10() V11() V12() Function-like functional V26() V30() cardinal {} -element FinSequence-membered ext-real non positive non negative V180() V181() V182() V183() V184() V185() V186() set
the empty trivial V6() V10() V11() V12() Function-like functional V26() V30() cardinal {} -element FinSequence-membered ext-real non positive non negative V180() V181() V182() V183() V184() V185() V186() set is empty trivial V6() V10() V11() V12() Function-like functional V26() V30() cardinal {} -element FinSequence-membered ext-real non positive non negative V180() V181() V182() V183() V184() V185() V186() set
3 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
4 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
0 is empty trivial V6() V10() V11() V12() Function-like functional V26() V30() cardinal {} -element FinSequence-membered V37() ext-real non positive non negative V179() V180() V181() V182() V183() V184() V185() V186() Element of NAT
Seg 1 is non empty trivial V26() 1 -element V180() V181() V182() V183() V184() V185() Element of bool NAT
{1} is non empty trivial V26() V30() 1 -element V180() V181() V182() V183() V184() V185() set
Seg 2 is non empty V26() 2 -element V180() V181() V182() V183() V184() V185() Element of bool NAT
{1,2} is non empty V26() V30() V180() V181() V182() V183() V184() V185() set
K74({}) is set
rng {} is set
X is V13() non empty-yielding V16( NAT ) V17(K233( 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 K233( the U1 of (TOP-REAL 2))
width X is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
len X is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
k is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
k is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
Y is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
j is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
X * (j,k) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(X * (j,k)) `1 is V11() V12() ext-real Element of REAL
X * (Y,k) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(X * (Y,k)) `1 is V11() V12() ext-real Element of REAL
X * (j,k) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(X * (j,k)) `1 is V11() V12() ext-real Element of REAL
X * (j,1) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(X * (j,1)) `1 is V11() V12() ext-real Element of REAL
X is V13() non empty-yielding V16( NAT ) V17(K233( 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 K233( the U1 of (TOP-REAL 2))
len X is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
width X is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
Y is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
j is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
k is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
k is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
X * (j,k) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(X * (j,k)) `2 is V11() V12() ext-real Element of REAL
X * (Y,k) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(X * (Y,k)) `2 is V11() V12() ext-real Element of REAL
X * (Y,k) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(X * (Y,k)) `2 is V11() V12() ext-real Element of REAL
X * (1,k) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(X * (1,k)) `2 is V11() V12() ext-real Element of REAL
X is non empty V13() V16( NAT ) Function-like V26() FinSequence-like FinSubsequence-like set
Y is V13() V16( NAT ) Function-like V26() FinSequence-like FinSubsequence-like set
X ^' Y is V13() V16( NAT ) Function-like V26() FinSequence-like FinSubsequence-like set
len Y is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(2,(len Y)) -cut Y is V13() V16( NAT ) Function-like V26() FinSequence-like FinSubsequence-like set
X ^ ((2,(len Y)) -cut Y) is non empty V13() V16( NAT ) Function-like V26() FinSequence-like FinSubsequence-like set
X is non empty functional connected bounded compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
Y is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
Cage (X,Y) 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 (X,Y)) is non empty functional V71( TOP-REAL 2) connected bounded being_simple_closed_curve compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
E-max (L~ (Cage (X,Y))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Cage (X,Y))) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (X,Y))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | (L~ (Cage (X,Y))) is V13() V16( the U1 of ((TOP-REAL 2) | (L~ (Cage (X,Y))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (X,Y)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (X,Y)))),REAL:]
the U1 of ((TOP-REAL 2) | (L~ (Cage (X,Y)))) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ (Cage (X,Y)))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (X,Y)))),REAL:] is set
K446(((TOP-REAL 2) | (L~ (Cage (X,Y)))),(proj1 | (L~ (Cage (X,Y))))) is V11() V12() ext-real Element of REAL
E-most (L~ (Cage (X,Y))) is functional Element of bool the U1 of (TOP-REAL 2)
SE-corner (L~ (Cage (X,Y))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Cage (X,Y))) is V11() V12() ext-real Element of REAL
proj2 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | (L~ (Cage (X,Y))) is V13() V16( the U1 of ((TOP-REAL 2) | (L~ (Cage (X,Y))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (X,Y)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (X,Y)))),REAL:]
K445(((TOP-REAL 2) | (L~ (Cage (X,Y)))),(proj2 | (L~ (Cage (X,Y))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (X,Y)))),(S-bound (L~ (Cage (X,Y))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NE-corner (L~ (Cage (X,Y))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Cage (X,Y))) is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | (L~ (Cage (X,Y)))),(proj2 | (L~ (Cage (X,Y))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (X,Y)))),(N-bound (L~ (Cage (X,Y))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Cage (X,Y)))),(NE-corner (L~ (Cage (X,Y))))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SE-corner (L~ (Cage (X,Y)))),(NE-corner (L~ (Cage (X,Y)))))) /\ (L~ (Cage (X,Y))) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ (Cage (X,Y)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Cage (X,Y)))) is V13() V16( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (X,Y)))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (X,Y))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (X,Y))))),REAL:]
the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (X,Y))))) is set
[: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (X,Y))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (X,Y))))),REAL:] is set
K446(((TOP-REAL 2) | (E-most (L~ (Cage (X,Y))))),(proj2 | (E-most (L~ (Cage (X,Y)))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (X,Y)))),K446(((TOP-REAL 2) | (E-most (L~ (Cage (X,Y))))),(proj2 | (E-most (L~ (Cage (X,Y))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(Cage (X,Y)) -: (E-max (L~ (Cage (X,Y)))) 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 (X,Y)) -: (E-max (L~ (Cage (X,Y))))) is functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
(Cage (X,Y)) :- (E-max (L~ (Cage (X,Y)))) 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 (X,Y)) :- (E-max (L~ (Cage (X,Y))))) is functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
(L~ ((Cage (X,Y)) -: (E-max (L~ (Cage (X,Y)))))) /\ (L~ ((Cage (X,Y)) :- (E-max (L~ (Cage (X,Y)))))) is functional Element of bool the U1 of (TOP-REAL 2)
N-min (L~ (Cage (X,Y))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-most (L~ (Cage (X,Y))) is functional Element of bool the U1 of (TOP-REAL 2)
NW-corner (L~ (Cage (X,Y))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-bound (L~ (Cage (X,Y))) is V11() V12() ext-real Element of REAL
K445(((TOP-REAL 2) | (L~ (Cage (X,Y)))),(proj1 | (L~ (Cage (X,Y))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (X,Y)))),(N-bound (L~ (Cage (X,Y))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((NW-corner (L~ (Cage (X,Y)))),(NE-corner (L~ (Cage (X,Y))))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((NW-corner (L~ (Cage (X,Y)))),(NE-corner (L~ (Cage (X,Y)))))) /\ (L~ (Cage (X,Y))) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (N-most (L~ (Cage (X,Y)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most (L~ (Cage (X,Y)))) is V13() V16( the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (X,Y)))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (X,Y))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (X,Y))))),REAL:]
the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (X,Y))))) is set
[: the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (X,Y))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (X,Y))))),REAL:] is set
K445(((TOP-REAL 2) | (N-most (L~ (Cage (X,Y))))),(proj1 | (N-most (L~ (Cage (X,Y)))))) is V11() V12() ext-real Element of REAL
|[K445(((TOP-REAL 2) | (N-most (L~ (Cage (X,Y))))),(proj1 | (N-most (L~ (Cage (X,Y)))))),(N-bound (L~ (Cage (X,Y))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
{(N-min (L~ (Cage (X,Y)))),(E-max (L~ (Cage (X,Y))))} is non empty functional V26() V30() set
(E-max (L~ (Cage (X,Y)))) `1 is V11() V12() ext-real Element of REAL
rng (Cage (X,Y)) is non empty non trivial V26() set
((Cage (X,Y)) :- (E-max (L~ (Cage (X,Y))))) /. 1 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
rng ((Cage (X,Y)) :- (E-max (L~ (Cage (X,Y))))) is V26() set
len ((Cage (X,Y)) :- (E-max (L~ (Cage (X,Y))))) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
((Cage (X,Y)) :- (E-max (L~ (Cage (X,Y))))) /. (len ((Cage (X,Y)) :- (E-max (L~ (Cage (X,Y)))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
len (Cage (X,Y)) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(Cage (X,Y)) /. (len (Cage (X,Y))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(Cage (X,Y)) /. 1 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LS is set
card {(N-min (L~ (Cage (X,Y)))),(E-max (L~ (Cage (X,Y))))} is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
card (rng ((Cage (X,Y)) :- (E-max (L~ (Cage (X,Y)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
dom ((Cage (X,Y)) :- (E-max (L~ (Cage (X,Y))))) is V26() V180() V181() V182() V183() V184() V185() Element of bool NAT
card (dom ((Cage (X,Y)) :- (E-max (L~ (Cage (X,Y)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
N-max (L~ (Cage (X,Y))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
K446(((TOP-REAL 2) | (N-most (L~ (Cage (X,Y))))),(proj1 | (N-most (L~ (Cage (X,Y)))))) is V11() V12() ext-real Element of REAL
|[K446(((TOP-REAL 2) | (N-most (L~ (Cage (X,Y))))),(proj1 | (N-most (L~ (Cage (X,Y)))))),(N-bound (L~ (Cage (X,Y))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(N-max (L~ (Cage (X,Y)))) `1 is V11() V12() ext-real Element of REAL
len ((Cage (X,Y)) -: (E-max (L~ (Cage (X,Y))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(E-max (L~ (Cage (X,Y)))) .. (Cage (X,Y)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
((Cage (X,Y)) -: (E-max (L~ (Cage (X,Y))))) /. (len ((Cage (X,Y)) -: (E-max (L~ (Cage (X,Y)))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
rng ((Cage (X,Y)) -: (E-max (L~ (Cage (X,Y))))) is V26() set
((Cage (X,Y)) -: (E-max (L~ (Cage (X,Y))))) /. 1 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LS is set
card (rng ((Cage (X,Y)) -: (E-max (L~ (Cage (X,Y)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
dom ((Cage (X,Y)) -: (E-max (L~ (Cage (X,Y))))) is V26() V180() V181() V182() V183() V184() V185() Element of bool NAT
card (dom ((Cage (X,Y)) -: (E-max (L~ (Cage (X,Y)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
LS is set
UA is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
Wmin is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
Wmin + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
LSeg (((Cage (X,Y)) -: (E-max (L~ (Cage (X,Y))))),Wmin) is functional Element of bool the U1 of (TOP-REAL 2)
LSeg ((Cage (X,Y)),Wmin) is functional Element of bool the U1 of (TOP-REAL 2)
Emax is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
Emax + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
LSeg (((Cage (X,Y)) :- (E-max (L~ (Cage (X,Y))))),Emax) is functional Element of bool the U1 of (TOP-REAL 2)
Emax -' 1 is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(Emax -' 1) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
1 + ((E-max (L~ (Cage (X,Y)))) .. (Cage (X,Y))) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
((Emax -' 1) + 1) + ((E-max (L~ (Cage (X,Y)))) .. (Cage (X,Y))) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(len (Cage (X,Y))) - ((E-max (L~ (Cage (X,Y)))) .. (Cage (X,Y))) is V11() V12() ext-real set
((len (Cage (X,Y))) - ((E-max (L~ (Cage (X,Y)))) .. (Cage (X,Y)))) + 1 is V11() V12() ext-real set
Emax - 1 is V11() V12() ext-real set
(Emax - 1) + ((E-max (L~ (Cage (X,Y)))) .. (Cage (X,Y))) is V11() V12() ext-real set
1 - 1 is V11() V12() ext-real set
(Emax -' 1) + ((E-max (L~ (Cage (X,Y)))) .. (Cage (X,Y))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
LSeg ((Cage (X,Y)),((Emax -' 1) + ((E-max (L~ (Cage (X,Y)))) .. (Cage (X,Y))))) is functional Element of bool the U1 of (TOP-REAL 2)
((E-max (L~ (Cage (X,Y)))) .. (Cage (X,Y))) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
((Emax -' 1) + ((E-max (L~ (Cage (X,Y)))) .. (Cage (X,Y)))) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
((E-max (L~ (Cage (X,Y)))) .. (Cage (X,Y))) -' 1 is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(((E-max (L~ (Cage (X,Y)))) .. (Cage (X,Y))) -' 1) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(LSeg ((Cage (X,Y)),Wmin)) /\ (LSeg ((Cage (X,Y)),((Emax -' 1) + ((E-max (L~ (Cage (X,Y)))) .. (Cage (X,Y)))))) is functional Element of bool the U1 of (TOP-REAL 2)
0 + 2 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(LSeg ((Cage (X,Y)),Wmin)) /\ (LSeg ((Cage (X,Y)),((Emax -' 1) + ((E-max (L~ (Cage (X,Y)))) .. (Cage (X,Y)))))) is functional Element of bool the U1 of (TOP-REAL 2)
(len (Cage (X,Y))) - 1 is V11() V12() ext-real set
(len (Cage (X,Y))) -' 1 is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(LSeg ((Cage (X,Y)),Wmin)) /\ (LSeg ((Cage (X,Y)),((Emax -' 1) + ((E-max (L~ (Cage (X,Y)))) .. (Cage (X,Y)))))) is functional Element of bool the U1 of (TOP-REAL 2)
{((Cage (X,Y)) /. 1)} is non empty trivial functional V26() V30() 1 -element set
1 + 2 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
LSeg ((Cage (X,Y)),1) is functional 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 V179() V180() V181() V182() V183() V184() V185() Element of NAT
LSeg ((Cage (X,Y)),(1 + 1)) is functional Element of bool the U1 of (TOP-REAL 2)
(LSeg ((Cage (X,Y)),1)) /\ (LSeg ((Cage (X,Y)),(1 + 1))) is functional Element of bool the U1 of (TOP-REAL 2)
(Cage (X,Y)) /. (1 + 1) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
{((Cage (X,Y)) /. (1 + 1))} is non empty trivial functional V26() V30() 1 -element set
0 + ((E-max (L~ (Cage (X,Y)))) .. (Cage (X,Y))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
0 + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
1 + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(((E-max (L~ (Cage (X,Y)))) .. (Cage (X,Y))) -' 1) + (1 + 1) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
0 + ((E-max (L~ (Cage (X,Y)))) .. (Cage (X,Y))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(LSeg ((Cage (X,Y)),Wmin)) /\ (LSeg ((Cage (X,Y)),((Emax -' 1) + ((E-max (L~ (Cage (X,Y)))) .. (Cage (X,Y)))))) is functional Element of bool the U1 of (TOP-REAL 2)
(Cage (X,Y)) /. ((E-max (L~ (Cage (X,Y)))) .. (Cage (X,Y))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
{((Cage (X,Y)) /. ((E-max (L~ (Cage (X,Y)))) .. (Cage (X,Y))))} is non empty trivial functional V26() V30() 1 -element set
LS is set
X is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
Y is non empty functional connected bounded compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
Upper_Seq (Y,X) 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 (Y,X) 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 (Y,X)) is non empty functional V71( TOP-REAL 2) connected bounded being_simple_closed_curve compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
E-max (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Cage (Y,X))) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (Y,X))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | (L~ (Cage (Y,X))) is V13() V16( the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))),REAL:]
the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))),REAL:] is set
K446(((TOP-REAL 2) | (L~ (Cage (Y,X)))),(proj1 | (L~ (Cage (Y,X))))) is V11() V12() ext-real Element of REAL
E-most (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
SE-corner (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Cage (Y,X))) is V11() V12() ext-real Element of REAL
proj2 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | (L~ (Cage (Y,X))) is V13() V16( the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))),REAL:]
K445(((TOP-REAL 2) | (L~ (Cage (Y,X)))),(proj2 | (L~ (Cage (Y,X))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (Y,X)))),(S-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NE-corner (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Cage (Y,X))) is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | (L~ (Cage (Y,X)))),(proj2 | (L~ (Cage (Y,X))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (Y,X)))),(N-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Cage (Y,X)))),(NE-corner (L~ (Cage (Y,X))))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SE-corner (L~ (Cage (Y,X)))),(NE-corner (L~ (Cage (Y,X)))))) /\ (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ (Cage (Y,X)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Cage (Y,X)))) is V13() V16( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X)))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),REAL:]
the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))) is set
[: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),REAL:] is set
K446(((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),(proj2 | (E-most (L~ (Cage (Y,X)))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (Y,X)))),K446(((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),(proj2 | (E-most (L~ (Cage (Y,X))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))) 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 (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-bound (L~ (Cage (Y,X))) is V11() V12() ext-real Element of REAL
K445(((TOP-REAL 2) | (L~ (Cage (Y,X)))),(proj1 | (L~ (Cage (Y,X))))) is V11() V12() ext-real Element of REAL
W-most (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
SW-corner (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
|[(W-bound (L~ (Cage (Y,X)))),(S-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NW-corner (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
|[(W-bound (L~ (Cage (Y,X)))),(N-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (Y,X)))),(NW-corner (L~ (Cage (Y,X))))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Cage (Y,X)))),(NW-corner (L~ (Cage (Y,X)))))) /\ (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ (Cage (Y,X)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Cage (Y,X)))) is V13() V16( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X)))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),REAL:]
the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))) is set
[: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),REAL:] is set
K445(((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),(proj2 | (W-most (L~ (Cage (Y,X)))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (Y,X)))),K445(((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),(proj2 | (W-most (L~ (Cage (Y,X))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))) :- (W-min (L~ (Cage (Y,X)))) 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)
N-min (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-most (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
LSeg ((NW-corner (L~ (Cage (Y,X)))),(NE-corner (L~ (Cage (Y,X))))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((NW-corner (L~ (Cage (Y,X)))),(NE-corner (L~ (Cage (Y,X)))))) /\ (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (N-most (L~ (Cage (Y,X)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most (L~ (Cage (Y,X)))) is V13() V16( the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (Y,X)))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (Y,X))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (Y,X))))),REAL:]
the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (Y,X))))) is set
[: the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (Y,X))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (Y,X))))),REAL:] is set
K445(((TOP-REAL 2) | (N-most (L~ (Cage (Y,X))))),(proj1 | (N-most (L~ (Cage (Y,X)))))) is V11() V12() ext-real Element of REAL
|[K445(((TOP-REAL 2) | (N-most (L~ (Cage (Y,X))))),(proj1 | (N-most (L~ (Cage (Y,X)))))),(N-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-max (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
K446(((TOP-REAL 2) | (N-most (L~ (Cage (Y,X))))),(proj1 | (N-most (L~ (Cage (Y,X)))))) is V11() V12() ext-real Element of REAL
|[K446(((TOP-REAL 2) | (N-most (L~ (Cage (Y,X))))),(proj1 | (N-most (L~ (Cage (Y,X)))))),(N-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-max (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
K446(((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),(proj2 | (W-most (L~ (Cage (Y,X)))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (Y,X)))),K446(((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),(proj2 | (W-most (L~ (Cage (Y,X))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-min (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
K445(((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),(proj2 | (E-most (L~ (Cage (Y,X)))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (Y,X)))),K445(((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),(proj2 | (E-most (L~ (Cage (Y,X))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-max (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-most (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (Y,X)))),(SE-corner (L~ (Cage (Y,X))))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Cage (Y,X)))),(SE-corner (L~ (Cage (Y,X)))))) /\ (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (S-most (L~ (Cage (Y,X)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (S-most (L~ (Cage (Y,X)))) is V13() V16( the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (Y,X)))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (Y,X))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (Y,X))))),REAL:]
the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (Y,X))))) is set
[: the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (Y,X))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (Y,X))))),REAL:] is set
K446(((TOP-REAL 2) | (S-most (L~ (Cage (Y,X))))),(proj1 | (S-most (L~ (Cage (Y,X)))))) is V11() V12() ext-real Element of REAL
|[K446(((TOP-REAL 2) | (S-most (L~ (Cage (Y,X))))),(proj1 | (S-most (L~ (Cage (Y,X)))))),(S-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-min (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
K445(((TOP-REAL 2) | (S-most (L~ (Cage (Y,X))))),(proj1 | (S-most (L~ (Cage (Y,X)))))) is V11() V12() ext-real Element of REAL
|[K445(((TOP-REAL 2) | (S-most (L~ (Cage (Y,X))))),(proj1 | (S-most (L~ (Cage (Y,X)))))),(S-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))) 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 (Y,X)) is non empty non trivial V26() set
(Cage (Y,X)) /. 1 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(E-min (L~ (Cage (Y,X)))) .. (Cage (Y,X)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(S-max (L~ (Cage (Y,X)))) .. (Cage (Y,X)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(E-max (L~ (Cage (Y,X)))) .. (Cage (Y,X)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(S-min (L~ (Cage (Y,X)))) .. (Cage (Y,X)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(W-min (L~ (Cage (Y,X)))) .. (Cage (Y,X)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(Cage (Y,X)) :- (E-max (L~ (Cage (Y,X)))) 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 (Y,X)) :- (E-max (L~ (Cage (Y,X))))) /. 1 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
rng ((Cage (Y,X)) :- (E-max (L~ (Cage (Y,X))))) is V26() set
len ((Cage (Y,X)) :- (E-max (L~ (Cage (Y,X))))) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
((Cage (Y,X)) :- (E-max (L~ (Cage (Y,X))))) /. (len ((Cage (Y,X)) :- (E-max (L~ (Cage (Y,X)))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
len (Cage (Y,X)) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(Cage (Y,X)) /. (len (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
{(N-min (L~ (Cage (Y,X)))),(E-max (L~ (Cage (Y,X))))} is non empty functional V26() V30() set
Ebo is set
card {(N-min (L~ (Cage (Y,X)))),(E-max (L~ (Cage (Y,X))))} is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
card (rng ((Cage (Y,X)) :- (E-max (L~ (Cage (Y,X)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(Cage (Y,X)) -: (W-min (L~ (Cage (Y,X)))) 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 (Y,X)) -: (W-min (L~ (Cage (Y,X))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
((Cage (Y,X)) -: (W-min (L~ (Cage (Y,X))))) /. (len ((Cage (Y,X)) -: (W-min (L~ (Cage (Y,X)))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
rng ((Cage (Y,X)) -: (W-min (L~ (Cage (Y,X))))) is V26() set
((Cage (Y,X)) -: (W-min (L~ (Cage (Y,X))))) /. 1 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
{(N-min (L~ (Cage (Y,X)))),(W-min (L~ (Cage (Y,X))))} is non empty functional V26() V30() set
Ebo is set
card {(N-min (L~ (Cage (Y,X)))),(W-min (L~ (Cage (Y,X))))} is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
card (rng ((Cage (Y,X)) -: (W-min (L~ (Cage (Y,X)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
dom ((Cage (Y,X)) -: (W-min (L~ (Cage (Y,X))))) is V26() V180() V181() V182() V183() V184() V185() Element of bool NAT
card (dom ((Cage (Y,X)) -: (W-min (L~ (Cage (Y,X)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(N-min (L~ (Cage (Y,X)))) `2 is V11() V12() ext-real Element of REAL
(N-max (L~ (Cage (Y,X)))) `1 is V11() V12() ext-real Element of REAL
(NE-corner (L~ (Cage (Y,X)))) `1 is V11() V12() ext-real Element of REAL
(N-min (L~ (Cage (Y,X)))) `1 is V11() V12() ext-real Element of REAL
(W-max (L~ (Cage (Y,X)))) `2 is V11() V12() ext-real Element of REAL
L~ ((Cage (Y,X)) -: (W-min (L~ (Cage (Y,X))))) is functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
(Cage (Y,X)) :- (W-min (L~ (Cage (Y,X)))) 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 (Y,X)) :- (W-min (L~ (Cage (Y,X))))) is V26() set
((Cage (Y,X)) :- (W-min (L~ (Cage (Y,X))))) /. 1 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
len ((Cage (Y,X)) :- (W-min (L~ (Cage (Y,X))))) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
((Cage (Y,X)) :- (W-min (L~ (Cage (Y,X))))) /. (len ((Cage (Y,X)) :- (W-min (L~ (Cage (Y,X)))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
Ebo is set
card (rng ((Cage (Y,X)) :- (W-min (L~ (Cage (Y,X)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
dom ((Cage (Y,X)) :- (W-min (L~ (Cage (Y,X))))) is V26() V180() V181() V182() V183() V184() V185() Element of bool NAT
card (dom ((Cage (Y,X)) :- (W-min (L~ (Cage (Y,X)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
L~ ((Cage (Y,X)) :- (W-min (L~ (Cage (Y,X))))) is functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
(L~ ((Cage (Y,X)) -: (W-min (L~ (Cage (Y,X)))))) /\ (L~ ((Cage (Y,X)) :- (W-min (L~ (Cage (Y,X)))))) is functional Element of bool the U1 of (TOP-REAL 2)
(N-max (L~ (Cage (Y,X)))) .. (Cage (Y,X)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(N-min (L~ (Cage (Y,X)))) .. (Cage (Y,X)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(E-max (L~ (Cage (Y,X)))) .. ((Cage (Y,X)) -: (W-min (L~ (Cage (Y,X))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(N-min (L~ (Cage (Y,X)))) .. ((Cage (Y,X)) -: (W-min (L~ (Cage (Y,X))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
((Cage (Y,X)) -: (W-min (L~ (Cage (Y,X))))) /^ 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 (Y,X)) -: (W-min (L~ (Cage (Y,X))))) /^ 1) is V26() set
(rng (((Cage (Y,X)) -: (W-min (L~ (Cage (Y,X))))) /^ 1)) \ (rng ((Cage (Y,X)) :- (W-min (L~ (Cage (Y,X)))))) is V26() Element of bool (rng (((Cage (Y,X)) -: (W-min (L~ (Cage (Y,X))))) /^ 1))
bool (rng (((Cage (Y,X)) -: (W-min (L~ (Cage (Y,X))))) /^ 1)) is V26() V30() set
dom ((Cage (Y,X)) :- (E-max (L~ (Cage (Y,X))))) is V26() V180() V181() V182() V183() V184() V185() Element of bool NAT
card (dom ((Cage (Y,X)) :- (E-max (L~ (Cage (Y,X)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
L~ ((Cage (Y,X)) :- (E-max (L~ (Cage (Y,X))))) is functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
(Cage (Y,X)) -: (E-max (L~ (Cage (Y,X)))) 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 (Y,X)) -: (E-max (L~ (Cage (Y,X))))) is V26() set
len ((Cage (Y,X)) -: (E-max (L~ (Cage (Y,X))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
((Cage (Y,X)) -: (E-max (L~ (Cage (Y,X))))) /. (len ((Cage (Y,X)) -: (E-max (L~ (Cage (Y,X)))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
((Cage (Y,X)) -: (E-max (L~ (Cage (Y,X))))) /. ((E-max (L~ (Cage (Y,X)))) .. (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
((Cage (Y,X)) -: (E-max (L~ (Cage (Y,X))))) /. 1 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
Ebo is set
card (rng ((Cage (Y,X)) -: (E-max (L~ (Cage (Y,X)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
dom ((Cage (Y,X)) -: (E-max (L~ (Cage (Y,X))))) is V26() V180() V181() V182() V183() V184() V185() Element of bool NAT
card (dom ((Cage (Y,X)) -: (E-max (L~ (Cage (Y,X)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
L~ ((Cage (Y,X)) -: (E-max (L~ (Cage (Y,X))))) is functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
(L~ ((Cage (Y,X)) -: (E-max (L~ (Cage (Y,X)))))) /\ (L~ ((Cage (Y,X)) :- (E-max (L~ (Cage (Y,X)))))) is functional Element of bool the U1 of (TOP-REAL 2)
(rng (Cage (Y,X))) \ (rng ((Cage (Y,X)) -: (E-max (L~ (Cage (Y,X)))))) is V26() Element of bool (rng (Cage (Y,X)))
bool (rng (Cage (Y,X))) is V26() V30() set
(Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))) -: (E-max (L~ (Cage (Y,X)))) 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 (Y,X)) :- (W-min (L~ (Cage (Y,X))))) ^ (((Cage (Y,X)) -: (W-min (L~ (Cage (Y,X))))) /^ 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 (Y,X)) :- (W-min (L~ (Cage (Y,X))))) ^ (((Cage (Y,X)) -: (W-min (L~ (Cage (Y,X))))) /^ 1)) -: (E-max (L~ (Cage (Y,X)))) 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 (Y,X)) -: (W-min (L~ (Cage (Y,X))))) /^ 1) -: (E-max (L~ (Cage (Y,X)))) 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 (Y,X)) :- (W-min (L~ (Cage (Y,X))))) ^ ((((Cage (Y,X)) -: (W-min (L~ (Cage (Y,X))))) /^ 1) -: (E-max (L~ (Cage (Y,X))))) 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 (Y,X)) -: (W-min (L~ (Cage (Y,X))))) -: (E-max (L~ (Cage (Y,X)))) 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 (Y,X)) -: (W-min (L~ (Cage (Y,X))))) -: (E-max (L~ (Cage (Y,X))))) /^ 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 (Y,X)) :- (W-min (L~ (Cage (Y,X))))) ^ ((((Cage (Y,X)) -: (W-min (L~ (Cage (Y,X))))) -: (E-max (L~ (Cage (Y,X))))) /^ 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 (Y,X)) :- (E-max (L~ (Cage (Y,X))))) :- (W-min (L~ (Cage (Y,X)))) 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 (Y,X)) :- (E-max (L~ (Cage (Y,X))))) :- (W-min (L~ (Cage (Y,X))))) ^ ((((Cage (Y,X)) -: (W-min (L~ (Cage (Y,X))))) -: (E-max (L~ (Cage (Y,X))))) /^ 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 (Y,X)) -: (E-max (L~ (Cage (Y,X))))) /^ 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 (Y,X)) :- (E-max (L~ (Cage (Y,X))))) :- (W-min (L~ (Cage (Y,X))))) ^ (((Cage (Y,X)) -: (E-max (L~ (Cage (Y,X))))) /^ 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 (Y,X)) :- (E-max (L~ (Cage (Y,X))))) ^ (((Cage (Y,X)) -: (E-max (L~ (Cage (Y,X))))) /^ 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 (Y,X)) :- (E-max (L~ (Cage (Y,X))))) ^ (((Cage (Y,X)) -: (E-max (L~ (Cage (Y,X))))) /^ 1)) :- (W-min (L~ (Cage (Y,X)))) 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)
X is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
Y is non empty functional bounded compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
Cage (Y,X) 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 (Y,X)) is non empty functional V71( TOP-REAL 2) connected bounded being_simple_closed_curve compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
W-min (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-bound (L~ (Cage (Y,X))) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (Y,X))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | (L~ (Cage (Y,X))) is V13() V16( the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))),REAL:]
the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))),REAL:] is set
K445(((TOP-REAL 2) | (L~ (Cage (Y,X)))),(proj1 | (L~ (Cage (Y,X))))) is V11() V12() ext-real Element of REAL
W-most (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
SW-corner (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Cage (Y,X))) is V11() V12() ext-real Element of REAL
proj2 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | (L~ (Cage (Y,X))) is V13() V16( the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))),REAL:]
K445(((TOP-REAL 2) | (L~ (Cage (Y,X)))),(proj2 | (L~ (Cage (Y,X))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (Y,X)))),(S-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NW-corner (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Cage (Y,X))) is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | (L~ (Cage (Y,X)))),(proj2 | (L~ (Cage (Y,X))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (Y,X)))),(N-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (Y,X)))),(NW-corner (L~ (Cage (Y,X))))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Cage (Y,X)))),(NW-corner (L~ (Cage (Y,X)))))) /\ (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ (Cage (Y,X)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Cage (Y,X)))) is V13() V16( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X)))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),REAL:]
the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))) is set
[: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),REAL:] is set
K445(((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),(proj2 | (W-most (L~ (Cage (Y,X)))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (Y,X)))),K445(((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),(proj2 | (W-most (L~ (Cage (Y,X))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
Upper_Seq (Y,X) 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 (Y,X)) is V26() set
L~ (Upper_Seq (Y,X)) is non empty functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
rng (Cage (Y,X)) is non empty non trivial V26() set
E-max (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Cage (Y,X))) is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | (L~ (Cage (Y,X)))),(proj1 | (L~ (Cage (Y,X))))) is V11() V12() ext-real Element of REAL
E-most (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
SE-corner (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
|[(E-bound (L~ (Cage (Y,X)))),(S-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NE-corner (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
|[(E-bound (L~ (Cage (Y,X)))),(N-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Cage (Y,X)))),(NE-corner (L~ (Cage (Y,X))))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SE-corner (L~ (Cage (Y,X)))),(NE-corner (L~ (Cage (Y,X)))))) /\ (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ (Cage (Y,X)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Cage (Y,X)))) is V13() V16( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X)))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),REAL:]
the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))) is set
[: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),REAL:] is set
K446(((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),(proj2 | (E-most (L~ (Cage (Y,X)))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (Y,X)))),K446(((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),(proj2 | (E-most (L~ (Cage (Y,X))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))) 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 (Y,X)),(W-min (L~ (Cage (Y,X)))))) is non empty non trivial V26() set
(Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))) -: (E-max (L~ (Cage (Y,X)))) 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 (Y,X)) /. 1 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))) /. 1 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
len (Upper_Seq (Y,X)) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
X is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
Y is non empty functional connected bounded compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
Cage (Y,X) 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 (Y,X)) is non empty functional V71( TOP-REAL 2) connected bounded being_simple_closed_curve compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
W-max (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-bound (L~ (Cage (Y,X))) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (Y,X))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | (L~ (Cage (Y,X))) is V13() V16( the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))),REAL:]
the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))),REAL:] is set
K445(((TOP-REAL 2) | (L~ (Cage (Y,X)))),(proj1 | (L~ (Cage (Y,X))))) is V11() V12() ext-real Element of REAL
W-most (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
SW-corner (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Cage (Y,X))) is V11() V12() ext-real Element of REAL
proj2 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | (L~ (Cage (Y,X))) is V13() V16( the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))),REAL:]
K445(((TOP-REAL 2) | (L~ (Cage (Y,X)))),(proj2 | (L~ (Cage (Y,X))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (Y,X)))),(S-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NW-corner (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Cage (Y,X))) is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | (L~ (Cage (Y,X)))),(proj2 | (L~ (Cage (Y,X))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (Y,X)))),(N-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (Y,X)))),(NW-corner (L~ (Cage (Y,X))))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Cage (Y,X)))),(NW-corner (L~ (Cage (Y,X)))))) /\ (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ (Cage (Y,X)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Cage (Y,X)))) is V13() V16( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X)))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),REAL:]
the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))) is set
[: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),REAL:] is set
K446(((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),(proj2 | (W-most (L~ (Cage (Y,X)))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (Y,X)))),K446(((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),(proj2 | (W-most (L~ (Cage (Y,X))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
Upper_Seq (Y,X) 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 (Y,X)) is V26() set
L~ (Upper_Seq (Y,X)) is non empty functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
W-min (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
K445(((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),(proj2 | (W-most (L~ (Cage (Y,X)))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (Y,X)))),K445(((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),(proj2 | (W-most (L~ (Cage (Y,X))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-max (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Cage (Y,X))) is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | (L~ (Cage (Y,X)))),(proj1 | (L~ (Cage (Y,X))))) is V11() V12() ext-real Element of REAL
E-most (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
SE-corner (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
|[(E-bound (L~ (Cage (Y,X)))),(S-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NE-corner (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
|[(E-bound (L~ (Cage (Y,X)))),(N-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Cage (Y,X)))),(NE-corner (L~ (Cage (Y,X))))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SE-corner (L~ (Cage (Y,X)))),(NE-corner (L~ (Cage (Y,X)))))) /\ (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ (Cage (Y,X)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Cage (Y,X)))) is V13() V16( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X)))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),REAL:]
the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))) is set
[: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),REAL:] is set
K446(((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),(proj2 | (E-most (L~ (Cage (Y,X)))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (Y,X)))),K446(((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),(proj2 | (E-most (L~ (Cage (Y,X))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))) 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 (Y,X)),(E-max (L~ (Cage (Y,X)))))) is non empty non trivial V26() set
rng (Cage (Y,X)) is non empty non trivial V26() set
L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))) is non empty functional V71( TOP-REAL 2) connected bounded being_simple_closed_curve compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
Lower_Seq (Y,X) 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)
(Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))) -: (W-min (L~ (Cage (Y,X)))) 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 (Y,X)) /. 1 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))) /. 1 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-max (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-bound (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is V13() V16( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),REAL:]
the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),REAL:] is set
K445(((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),(proj1 | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))) is V11() V12() ext-real Element of REAL
W-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is functional Element of bool the U1 of (TOP-REAL 2)
SW-corner (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is V11() V12() ext-real Element of REAL
proj2 | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is V13() V16( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),REAL:]
K445(((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),(proj2 | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),(S-bound (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NW-corner (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),(proj2 | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),(N-bound (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),(NW-corner (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),(NW-corner (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))))) /\ (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))) is V13() V16( the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))),REAL:]
the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))) is set
[: the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))),REAL:] is set
K446(((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))),(proj2 | (W-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),K446(((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))),(proj2 | (W-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(W-max (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))) .. (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
W-min (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
K445(((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))),(proj2 | (W-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),K445(((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))),(proj2 | (W-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(W-min (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))) .. (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))) :- (W-min (L~ (Cage (Y,X)))) 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 ((Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))) :- (W-min (L~ (Cage (Y,X))))) is V26() set
len (Upper_Seq (Y,X)) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
X is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
Y is non empty functional connected bounded compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
Cage (Y,X) 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 (Y,X)) is non empty functional V71( TOP-REAL 2) connected bounded being_simple_closed_curve compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
N-min (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-most (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
NW-corner (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-bound (L~ (Cage (Y,X))) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (Y,X))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | (L~ (Cage (Y,X))) is V13() V16( the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))),REAL:]
the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))),REAL:] is set
K445(((TOP-REAL 2) | (L~ (Cage (Y,X)))),(proj1 | (L~ (Cage (Y,X))))) is V11() V12() ext-real Element of REAL
N-bound (L~ (Cage (Y,X))) is V11() V12() ext-real Element of REAL
proj2 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | (L~ (Cage (Y,X))) is V13() V16( the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))),REAL:]
K446(((TOP-REAL 2) | (L~ (Cage (Y,X)))),(proj2 | (L~ (Cage (Y,X))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (Y,X)))),(N-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NE-corner (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Cage (Y,X))) is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | (L~ (Cage (Y,X)))),(proj1 | (L~ (Cage (Y,X))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (Y,X)))),(N-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((NW-corner (L~ (Cage (Y,X)))),(NE-corner (L~ (Cage (Y,X))))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((NW-corner (L~ (Cage (Y,X)))),(NE-corner (L~ (Cage (Y,X)))))) /\ (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (N-most (L~ (Cage (Y,X)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most (L~ (Cage (Y,X)))) is V13() V16( the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (Y,X)))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (Y,X))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (Y,X))))),REAL:]
the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (Y,X))))) is set
[: the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (Y,X))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (Y,X))))),REAL:] is set
K445(((TOP-REAL 2) | (N-most (L~ (Cage (Y,X))))),(proj1 | (N-most (L~ (Cage (Y,X)))))) is V11() V12() ext-real Element of REAL
|[K445(((TOP-REAL 2) | (N-most (L~ (Cage (Y,X))))),(proj1 | (N-most (L~ (Cage (Y,X)))))),(N-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
Upper_Seq (Y,X) 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 (Y,X)) is V26() set
L~ (Upper_Seq (Y,X)) is non empty functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
W-min (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-most (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
SW-corner (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Cage (Y,X))) is V11() V12() ext-real Element of REAL
K445(((TOP-REAL 2) | (L~ (Cage (Y,X)))),(proj2 | (L~ (Cage (Y,X))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (Y,X)))),(S-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (Y,X)))),(NW-corner (L~ (Cage (Y,X))))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Cage (Y,X)))),(NW-corner (L~ (Cage (Y,X)))))) /\ (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ (Cage (Y,X)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Cage (Y,X)))) is V13() V16( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X)))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),REAL:]
the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))) is set
[: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),REAL:] is set
K445(((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),(proj2 | (W-most (L~ (Cage (Y,X)))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (Y,X)))),K445(((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),(proj2 | (W-most (L~ (Cage (Y,X))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-max (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-most (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
SE-corner (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
|[(E-bound (L~ (Cage (Y,X)))),(S-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Cage (Y,X)))),(NE-corner (L~ (Cage (Y,X))))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SE-corner (L~ (Cage (Y,X)))),(NE-corner (L~ (Cage (Y,X)))))) /\ (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ (Cage (Y,X)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Cage (Y,X)))) is V13() V16( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X)))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),REAL:]
the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))) is set
[: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),REAL:] is set
K446(((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),(proj2 | (E-most (L~ (Cage (Y,X)))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (Y,X)))),K446(((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),(proj2 | (E-most (L~ (Cage (Y,X))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))) 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 (Y,X)),(E-max (L~ (Cage (Y,X)))))) is non empty non trivial V26() set
rng (Cage (Y,X)) is non empty non trivial V26() set
L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))) is non empty functional V71( TOP-REAL 2) connected bounded being_simple_closed_curve compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
Lower_Seq (Y,X) 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)
(Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))) -: (W-min (L~ (Cage (Y,X)))) 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 (Y,X)) /. 1 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))) /. 1 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-max (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-bound (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is V13() V16( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),REAL:]
the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),REAL:] is set
K445(((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),(proj1 | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))) is V11() V12() ext-real Element of REAL
W-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is functional Element of bool the U1 of (TOP-REAL 2)
SW-corner (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is V11() V12() ext-real Element of REAL
proj2 | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is V13() V16( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),REAL:]
K445(((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),(proj2 | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),(S-bound (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NW-corner (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),(proj2 | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),(N-bound (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),(NW-corner (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),(NW-corner (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))))) /\ (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))) is V13() V16( the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))),REAL:]
the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))) is set
[: the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))),REAL:] is set
K446(((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))),(proj2 | (W-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),K446(((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))),(proj2 | (W-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(W-max (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))) .. (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
N-min (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is functional Element of bool the U1 of (TOP-REAL 2)
NE-corner (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),(proj1 | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),(N-bound (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((NW-corner (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),(NE-corner (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((NW-corner (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),(NE-corner (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))))) /\ (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))) is V13() V16( the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))),REAL:]
the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))) is set
[: the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))),REAL:] is set
K445(((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))),(proj1 | (N-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))))) is V11() V12() ext-real Element of REAL
|[K445(((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))),(proj1 | (N-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))))),(N-bound (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(N-min (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))) .. (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
W-min (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
K445(((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))),(proj2 | (W-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),K445(((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))),(proj2 | (W-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(W-min (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))) .. (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))) :- (W-min (L~ (Cage (Y,X)))) 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 ((Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))) :- (W-min (L~ (Cage (Y,X))))) is V26() set
len (Upper_Seq (Y,X)) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
X is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
Y is non empty functional connected bounded compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
Cage (Y,X) 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 (Y,X)) is non empty functional V71( TOP-REAL 2) connected bounded being_simple_closed_curve compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
N-max (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-most (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
NW-corner (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-bound (L~ (Cage (Y,X))) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (Y,X))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | (L~ (Cage (Y,X))) is V13() V16( the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))),REAL:]
the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))),REAL:] is set
K445(((TOP-REAL 2) | (L~ (Cage (Y,X)))),(proj1 | (L~ (Cage (Y,X))))) is V11() V12() ext-real Element of REAL
N-bound (L~ (Cage (Y,X))) is V11() V12() ext-real Element of REAL
proj2 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | (L~ (Cage (Y,X))) is V13() V16( the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))),REAL:]
K446(((TOP-REAL 2) | (L~ (Cage (Y,X)))),(proj2 | (L~ (Cage (Y,X))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (Y,X)))),(N-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NE-corner (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Cage (Y,X))) is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | (L~ (Cage (Y,X)))),(proj1 | (L~ (Cage (Y,X))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (Y,X)))),(N-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((NW-corner (L~ (Cage (Y,X)))),(NE-corner (L~ (Cage (Y,X))))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((NW-corner (L~ (Cage (Y,X)))),(NE-corner (L~ (Cage (Y,X)))))) /\ (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (N-most (L~ (Cage (Y,X)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most (L~ (Cage (Y,X)))) is V13() V16( the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (Y,X)))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (Y,X))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (Y,X))))),REAL:]
the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (Y,X))))) is set
[: the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (Y,X))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (Y,X))))),REAL:] is set
K446(((TOP-REAL 2) | (N-most (L~ (Cage (Y,X))))),(proj1 | (N-most (L~ (Cage (Y,X)))))) is V11() V12() ext-real Element of REAL
|[K446(((TOP-REAL 2) | (N-most (L~ (Cage (Y,X))))),(proj1 | (N-most (L~ (Cage (Y,X)))))),(N-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
Upper_Seq (Y,X) 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 (Y,X)) is V26() set
L~ (Upper_Seq (Y,X)) is non empty functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
W-min (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-most (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
SW-corner (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Cage (Y,X))) is V11() V12() ext-real Element of REAL
K445(((TOP-REAL 2) | (L~ (Cage (Y,X)))),(proj2 | (L~ (Cage (Y,X))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (Y,X)))),(S-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (Y,X)))),(NW-corner (L~ (Cage (Y,X))))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Cage (Y,X)))),(NW-corner (L~ (Cage (Y,X)))))) /\ (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ (Cage (Y,X)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Cage (Y,X)))) is V13() V16( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X)))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),REAL:]
the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))) is set
[: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),REAL:] is set
K445(((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),(proj2 | (W-most (L~ (Cage (Y,X)))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (Y,X)))),K445(((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),(proj2 | (W-most (L~ (Cage (Y,X))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-max (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-most (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
SE-corner (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
|[(E-bound (L~ (Cage (Y,X)))),(S-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Cage (Y,X)))),(NE-corner (L~ (Cage (Y,X))))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SE-corner (L~ (Cage (Y,X)))),(NE-corner (L~ (Cage (Y,X)))))) /\ (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ (Cage (Y,X)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Cage (Y,X)))) is V13() V16( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X)))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),REAL:]
the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))) is set
[: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),REAL:] is set
K446(((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),(proj2 | (E-most (L~ (Cage (Y,X)))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (Y,X)))),K446(((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),(proj2 | (E-most (L~ (Cage (Y,X))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))) 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 (Y,X)),(E-max (L~ (Cage (Y,X)))))) is non empty non trivial V26() set
rng (Cage (Y,X)) is non empty non trivial V26() set
Lower_Seq (Y,X) 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 (Y,X)) /. 1 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))) is non empty functional V71( TOP-REAL 2) connected bounded being_simple_closed_curve compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
(Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))) -: (W-min (L~ (Cage (Y,X)))) 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 (Y,X)),(E-max (L~ (Cage (Y,X)))))) /. 1 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-max (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-bound (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is V13() V16( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),REAL:]
the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),REAL:] is set
K445(((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),(proj1 | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))) is V11() V12() ext-real Element of REAL
W-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is functional Element of bool the U1 of (TOP-REAL 2)
SW-corner (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is V11() V12() ext-real Element of REAL
proj2 | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is V13() V16( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),REAL:]
K445(((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),(proj2 | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),(S-bound (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NW-corner (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),(proj2 | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),(N-bound (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),(NW-corner (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),(NW-corner (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))))) /\ (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))) is V13() V16( the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))),REAL:]
the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))) is set
[: the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))),REAL:] is set
K446(((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))),(proj2 | (W-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),K446(((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))),(proj2 | (W-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(W-max (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))) .. (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
W-min (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
K445(((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))),(proj2 | (W-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),K445(((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))),(proj2 | (W-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(W-min (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))) .. (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
N-min (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is functional Element of bool the U1 of (TOP-REAL 2)
NE-corner (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),(proj1 | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),(N-bound (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((NW-corner (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),(NE-corner (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((NW-corner (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),(NE-corner (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))))) /\ (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))) is V13() V16( the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))),REAL:]
the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))) is set
[: the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))),REAL:] is set
K445(((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))),(proj1 | (N-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))))) is V11() V12() ext-real Element of REAL
|[K445(((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))),(proj1 | (N-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))))),(N-bound (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(N-min (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))) .. (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
N-max (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
K446(((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))),(proj1 | (N-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))))) is V11() V12() ext-real Element of REAL
|[K446(((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))),(proj1 | (N-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))))),(N-bound (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-max (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is functional Element of bool the U1 of (TOP-REAL 2)
SE-corner (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
|[(E-bound (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),(S-bound (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),(NE-corner (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SE-corner (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),(NE-corner (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))))) /\ (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))) is V13() V16( the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))),REAL:]
the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))) is set
[: the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))),REAL:] is set
K446(((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))),(proj2 | (E-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),K446(((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))),(proj2 | (E-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(N-max (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))) .. (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))) :- (W-min (L~ (Cage (Y,X)))) 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 ((Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))) :- (W-min (L~ (Cage (Y,X))))) is V26() set
len (Upper_Seq (Y,X)) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
N-max (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
K446(((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))),(proj1 | (N-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))))) is V11() V12() ext-real Element of REAL
|[K446(((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))),(proj1 | (N-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))))),(N-bound (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-max (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is functional Element of bool the U1 of (TOP-REAL 2)
SE-corner (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
|[(E-bound (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),(S-bound (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),(NE-corner (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SE-corner (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),(NE-corner (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))))) /\ (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))) is V13() V16( the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))),REAL:]
the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))) is set
[: the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))),REAL:] is set
K446(((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))),(proj2 | (E-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),K446(((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))),(proj2 | (E-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))) 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 (Y,X)))) .. (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
rng (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))) is non empty non trivial V26() set
(Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))) -: (E-max (L~ (Cage (Y,X)))) 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 (Y,X)) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
N-max (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
K446(((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))),(proj1 | (N-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))))) is V11() V12() ext-real Element of REAL
|[K446(((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))),(proj1 | (N-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))))),(N-bound (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-max (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is functional Element of bool the U1 of (TOP-REAL 2)
SE-corner (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
|[(E-bound (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),(S-bound (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),(NE-corner (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SE-corner (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),(NE-corner (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))))) /\ (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))) is V13() V16( the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))),REAL:]
the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))) is set
[: the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))),REAL:] is set
K446(((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))),(proj2 | (E-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),K446(((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))),(proj2 | (E-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
X is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
Y is non empty functional bounded compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
Cage (Y,X) 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 (Y,X)) is non empty functional V71( TOP-REAL 2) connected bounded being_simple_closed_curve compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
E-max (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Cage (Y,X))) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (Y,X))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | (L~ (Cage (Y,X))) is V13() V16( the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))),REAL:]
the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))),REAL:] is set
K446(((TOP-REAL 2) | (L~ (Cage (Y,X)))),(proj1 | (L~ (Cage (Y,X))))) is V11() V12() ext-real Element of REAL
E-most (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
SE-corner (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Cage (Y,X))) is V11() V12() ext-real Element of REAL
proj2 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | (L~ (Cage (Y,X))) is V13() V16( the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))),REAL:]
K445(((TOP-REAL 2) | (L~ (Cage (Y,X)))),(proj2 | (L~ (Cage (Y,X))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (Y,X)))),(S-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NE-corner (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Cage (Y,X))) is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | (L~ (Cage (Y,X)))),(proj2 | (L~ (Cage (Y,X))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (Y,X)))),(N-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Cage (Y,X)))),(NE-corner (L~ (Cage (Y,X))))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SE-corner (L~ (Cage (Y,X)))),(NE-corner (L~ (Cage (Y,X)))))) /\ (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ (Cage (Y,X)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Cage (Y,X)))) is V13() V16( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X)))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),REAL:]
the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))) is set
[: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),REAL:] is set
K446(((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),(proj2 | (E-most (L~ (Cage (Y,X)))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (Y,X)))),K446(((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),(proj2 | (E-most (L~ (Cage (Y,X))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
Upper_Seq (Y,X) 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 (Y,X)) is V26() set
L~ (Upper_Seq (Y,X)) is non empty functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
W-min (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-bound (L~ (Cage (Y,X))) is V11() V12() ext-real Element of REAL
K445(((TOP-REAL 2) | (L~ (Cage (Y,X)))),(proj1 | (L~ (Cage (Y,X))))) is V11() V12() ext-real Element of REAL
W-most (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
SW-corner (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
|[(W-bound (L~ (Cage (Y,X)))),(S-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NW-corner (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
|[(W-bound (L~ (Cage (Y,X)))),(N-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (Y,X)))),(NW-corner (L~ (Cage (Y,X))))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Cage (Y,X)))),(NW-corner (L~ (Cage (Y,X)))))) /\ (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ (Cage (Y,X)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Cage (Y,X)))) is V13() V16( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X)))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),REAL:]
the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))) is set
[: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),REAL:] is set
K445(((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),(proj2 | (W-most (L~ (Cage (Y,X)))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (Y,X)))),K445(((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),(proj2 | (W-most (L~ (Cage (Y,X))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))) 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 (Y,X)))) .. (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
rng (Cage (Y,X)) is non empty non trivial V26() set
rng (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))) is non empty non trivial V26() set
(Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))) -: (E-max (L~ (Cage (Y,X)))) 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 (Y,X)) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
X is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
Y is non empty functional bounded compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
Cage (Y,X) 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 (Y,X)) is non empty functional V71( TOP-REAL 2) connected bounded being_simple_closed_curve compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
E-max (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Cage (Y,X))) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (Y,X))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | (L~ (Cage (Y,X))) is V13() V16( the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))),REAL:]
the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))),REAL:] is set
K446(((TOP-REAL 2) | (L~ (Cage (Y,X)))),(proj1 | (L~ (Cage (Y,X))))) is V11() V12() ext-real Element of REAL
E-most (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
SE-corner (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Cage (Y,X))) is V11() V12() ext-real Element of REAL
proj2 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | (L~ (Cage (Y,X))) is V13() V16( the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))),REAL:]
K445(((TOP-REAL 2) | (L~ (Cage (Y,X)))),(proj2 | (L~ (Cage (Y,X))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (Y,X)))),(S-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NE-corner (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Cage (Y,X))) is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | (L~ (Cage (Y,X)))),(proj2 | (L~ (Cage (Y,X))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (Y,X)))),(N-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Cage (Y,X)))),(NE-corner (L~ (Cage (Y,X))))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SE-corner (L~ (Cage (Y,X)))),(NE-corner (L~ (Cage (Y,X)))))) /\ (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ (Cage (Y,X)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Cage (Y,X)))) is V13() V16( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X)))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),REAL:]
the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))) is set
[: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),REAL:] is set
K446(((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),(proj2 | (E-most (L~ (Cage (Y,X)))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (Y,X)))),K446(((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),(proj2 | (E-most (L~ (Cage (Y,X))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
Lower_Seq (Y,X) 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 (Y,X)) is V26() set
L~ (Lower_Seq (Y,X)) is non empty functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
W-min (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-bound (L~ (Cage (Y,X))) is V11() V12() ext-real Element of REAL
K445(((TOP-REAL 2) | (L~ (Cage (Y,X)))),(proj1 | (L~ (Cage (Y,X))))) is V11() V12() ext-real Element of REAL
W-most (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
SW-corner (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
|[(W-bound (L~ (Cage (Y,X)))),(S-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NW-corner (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
|[(W-bound (L~ (Cage (Y,X)))),(N-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (Y,X)))),(NW-corner (L~ (Cage (Y,X))))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Cage (Y,X)))),(NW-corner (L~ (Cage (Y,X)))))) /\ (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ (Cage (Y,X)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Cage (Y,X)))) is V13() V16( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X)))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),REAL:]
the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))) is set
[: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),REAL:] is set
K445(((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),(proj2 | (W-most (L~ (Cage (Y,X)))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (Y,X)))),K445(((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),(proj2 | (W-most (L~ (Cage (Y,X))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))) 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 (Y,X)),(W-min (L~ (Cage (Y,X)))))) :- (E-max (L~ (Cage (Y,X)))) 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 (Y,X)) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
X is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
Y is non empty functional bounded compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
Cage (Y,X) 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 (Y,X)) is non empty functional V71( TOP-REAL 2) connected bounded being_simple_closed_curve compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
E-min (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Cage (Y,X))) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (Y,X))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | (L~ (Cage (Y,X))) is V13() V16( the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))),REAL:]
the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))),REAL:] is set
K446(((TOP-REAL 2) | (L~ (Cage (Y,X)))),(proj1 | (L~ (Cage (Y,X))))) is V11() V12() ext-real Element of REAL
E-most (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
SE-corner (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Cage (Y,X))) is V11() V12() ext-real Element of REAL
proj2 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | (L~ (Cage (Y,X))) is V13() V16( the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))),REAL:]
K445(((TOP-REAL 2) | (L~ (Cage (Y,X)))),(proj2 | (L~ (Cage (Y,X))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (Y,X)))),(S-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NE-corner (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Cage (Y,X))) is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | (L~ (Cage (Y,X)))),(proj2 | (L~ (Cage (Y,X))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (Y,X)))),(N-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Cage (Y,X)))),(NE-corner (L~ (Cage (Y,X))))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SE-corner (L~ (Cage (Y,X)))),(NE-corner (L~ (Cage (Y,X)))))) /\ (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ (Cage (Y,X)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Cage (Y,X)))) is V13() V16( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X)))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),REAL:]
the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))) is set
[: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),REAL:] is set
K445(((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),(proj2 | (E-most (L~ (Cage (Y,X)))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (Y,X)))),K445(((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),(proj2 | (E-most (L~ (Cage (Y,X))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
Lower_Seq (Y,X) 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 (Y,X)) is V26() set
L~ (Lower_Seq (Y,X)) is non empty functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
E-max (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
K446(((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),(proj2 | (E-most (L~ (Cage (Y,X)))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (Y,X)))),K446(((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),(proj2 | (E-most (L~ (Cage (Y,X))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-min (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-bound (L~ (Cage (Y,X))) is V11() V12() ext-real Element of REAL
K445(((TOP-REAL 2) | (L~ (Cage (Y,X)))),(proj1 | (L~ (Cage (Y,X))))) is V11() V12() ext-real Element of REAL
W-most (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
SW-corner (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
|[(W-bound (L~ (Cage (Y,X)))),(S-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NW-corner (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
|[(W-bound (L~ (Cage (Y,X)))),(N-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (Y,X)))),(NW-corner (L~ (Cage (Y,X))))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Cage (Y,X)))),(NW-corner (L~ (Cage (Y,X)))))) /\ (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ (Cage (Y,X)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Cage (Y,X)))) is V13() V16( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X)))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),REAL:]
the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))) is set
[: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),REAL:] is set
K445(((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),(proj2 | (W-most (L~ (Cage (Y,X)))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (Y,X)))),K445(((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),(proj2 | (W-most (L~ (Cage (Y,X))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))) 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 (Y,X)),(W-min (L~ (Cage (Y,X)))))) is non empty non trivial V26() set
rng (Cage (Y,X)) is non empty non trivial V26() set
L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))) is non empty functional V71( TOP-REAL 2) connected bounded being_simple_closed_curve compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
Upper_Seq (Y,X) 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)
(Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))) -: (E-max (L~ (Cage (Y,X)))) 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 (Y,X)) /. 1 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))) /. 1 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-min (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is V13() V16( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),REAL:]
the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),REAL:] is set
K446(((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),(proj1 | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))) is V11() V12() ext-real Element of REAL
E-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is functional Element of bool the U1 of (TOP-REAL 2)
SE-corner (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is V11() V12() ext-real Element of REAL
proj2 | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is V13() V16( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),REAL:]
K445(((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),(proj2 | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),(S-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NE-corner (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),(proj2 | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),(N-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),(NE-corner (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SE-corner (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),(NE-corner (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))))) /\ (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))) is V13() V16( the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),REAL:]
the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))) is set
[: the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),REAL:] is set
K445(((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),(proj2 | (E-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),K445(((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),(proj2 | (E-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(E-min (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))) .. (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
E-max (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
K446(((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),(proj2 | (E-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),K446(((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),(proj2 | (E-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(E-max (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))) .. (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))) :- (E-max (L~ (Cage (Y,X)))) 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 ((Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))) :- (E-max (L~ (Cage (Y,X))))) is V26() set
len (Lower_Seq (Y,X)) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
X is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
Y is non empty functional bounded compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
Cage (Y,X) 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 (Y,X)) is non empty functional V71( TOP-REAL 2) connected bounded being_simple_closed_curve compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
S-max (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-most (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
SW-corner (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-bound (L~ (Cage (Y,X))) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (Y,X))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | (L~ (Cage (Y,X))) is V13() V16( the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))),REAL:]
the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))),REAL:] is set
K445(((TOP-REAL 2) | (L~ (Cage (Y,X)))),(proj1 | (L~ (Cage (Y,X))))) is V11() V12() ext-real Element of REAL
S-bound (L~ (Cage (Y,X))) is V11() V12() ext-real Element of REAL
proj2 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | (L~ (Cage (Y,X))) is V13() V16( the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))),REAL:]
K445(((TOP-REAL 2) | (L~ (Cage (Y,X)))),(proj2 | (L~ (Cage (Y,X))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (Y,X)))),(S-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
SE-corner (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Cage (Y,X))) is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | (L~ (Cage (Y,X)))),(proj1 | (L~ (Cage (Y,X))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (Y,X)))),(S-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (Y,X)))),(SE-corner (L~ (Cage (Y,X))))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Cage (Y,X)))),(SE-corner (L~ (Cage (Y,X)))))) /\ (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (S-most (L~ (Cage (Y,X)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (S-most (L~ (Cage (Y,X)))) is V13() V16( the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (Y,X)))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (Y,X))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (Y,X))))),REAL:]
the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (Y,X))))) is set
[: the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (Y,X))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (Y,X))))),REAL:] is set
K446(((TOP-REAL 2) | (S-most (L~ (Cage (Y,X))))),(proj1 | (S-most (L~ (Cage (Y,X)))))) is V11() V12() ext-real Element of REAL
|[K446(((TOP-REAL 2) | (S-most (L~ (Cage (Y,X))))),(proj1 | (S-most (L~ (Cage (Y,X)))))),(S-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
Lower_Seq (Y,X) 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 (Y,X)) is V26() set
L~ (Lower_Seq (Y,X)) is non empty functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
E-max (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-most (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
NE-corner (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Cage (Y,X))) is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | (L~ (Cage (Y,X)))),(proj2 | (L~ (Cage (Y,X))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (Y,X)))),(N-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Cage (Y,X)))),(NE-corner (L~ (Cage (Y,X))))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SE-corner (L~ (Cage (Y,X)))),(NE-corner (L~ (Cage (Y,X)))))) /\ (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ (Cage (Y,X)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Cage (Y,X)))) is V13() V16( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X)))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),REAL:]
the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))) is set
[: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),REAL:] is set
K446(((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),(proj2 | (E-most (L~ (Cage (Y,X)))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (Y,X)))),K446(((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),(proj2 | (E-most (L~ (Cage (Y,X))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-min (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-most (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
NW-corner (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
|[(W-bound (L~ (Cage (Y,X)))),(N-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (Y,X)))),(NW-corner (L~ (Cage (Y,X))))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Cage (Y,X)))),(NW-corner (L~ (Cage (Y,X)))))) /\ (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ (Cage (Y,X)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Cage (Y,X)))) is V13() V16( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X)))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),REAL:]
the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))) is set
[: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),REAL:] is set
K445(((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),(proj2 | (W-most (L~ (Cage (Y,X)))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (Y,X)))),K445(((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),(proj2 | (W-most (L~ (Cage (Y,X))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))) 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 (Y,X)),(W-min (L~ (Cage (Y,X)))))) is non empty non trivial V26() set
rng (Cage (Y,X)) is non empty non trivial V26() set
L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))) is non empty functional V71( TOP-REAL 2) connected bounded being_simple_closed_curve compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
Upper_Seq (Y,X) 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)
(Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))) -: (E-max (L~ (Cage (Y,X)))) 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 (Y,X)) /. 1 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))) /. 1 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-min (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is V13() V16( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),REAL:]
the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),REAL:] is set
K446(((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),(proj1 | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))) is V11() V12() ext-real Element of REAL
E-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is functional Element of bool the U1 of (TOP-REAL 2)
SE-corner (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is V11() V12() ext-real Element of REAL
proj2 | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is V13() V16( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),REAL:]
K445(((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),(proj2 | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),(S-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NE-corner (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),(proj2 | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),(N-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),(NE-corner (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SE-corner (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),(NE-corner (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))))) /\ (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))) is V13() V16( the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),REAL:]
the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))) is set
[: the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),REAL:] is set
K445(((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),(proj2 | (E-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),K445(((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),(proj2 | (E-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(E-min (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))) .. (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
S-max (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is functional Element of bool the U1 of (TOP-REAL 2)
SW-corner (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is V11() V12() ext-real Element of REAL
K445(((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),(proj1 | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),(S-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),(SE-corner (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),(SE-corner (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))))) /\ (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (S-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (S-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))) is V13() V16( the U1 of ((TOP-REAL 2) | (S-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (S-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (S-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),REAL:]
the U1 of ((TOP-REAL 2) | (S-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))) is set
[: the U1 of ((TOP-REAL 2) | (S-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (S-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),REAL:] is set
K446(((TOP-REAL 2) | (S-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),(proj1 | (S-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))))) is V11() V12() ext-real Element of REAL
|[K446(((TOP-REAL 2) | (S-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),(proj1 | (S-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))))),(S-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(S-max (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))) .. (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
E-max (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
K446(((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),(proj2 | (E-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),K446(((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),(proj2 | (E-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(E-max (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))) .. (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))) :- (E-max (L~ (Cage (Y,X)))) 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 ((Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))) :- (E-max (L~ (Cage (Y,X))))) is V26() set
len (Lower_Seq (Y,X)) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
X is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
Y is non empty functional bounded compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
Cage (Y,X) 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 (Y,X)) is non empty functional V71( TOP-REAL 2) connected bounded being_simple_closed_curve compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
S-min (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-most (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
SW-corner (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-bound (L~ (Cage (Y,X))) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (Y,X))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | (L~ (Cage (Y,X))) is V13() V16( the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))),REAL:]
the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))),REAL:] is set
K445(((TOP-REAL 2) | (L~ (Cage (Y,X)))),(proj1 | (L~ (Cage (Y,X))))) is V11() V12() ext-real Element of REAL
S-bound (L~ (Cage (Y,X))) is V11() V12() ext-real Element of REAL
proj2 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | (L~ (Cage (Y,X))) is V13() V16( the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))),REAL:]
K445(((TOP-REAL 2) | (L~ (Cage (Y,X)))),(proj2 | (L~ (Cage (Y,X))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (Y,X)))),(S-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
SE-corner (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Cage (Y,X))) is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | (L~ (Cage (Y,X)))),(proj1 | (L~ (Cage (Y,X))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (Y,X)))),(S-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (Y,X)))),(SE-corner (L~ (Cage (Y,X))))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Cage (Y,X)))),(SE-corner (L~ (Cage (Y,X)))))) /\ (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (S-most (L~ (Cage (Y,X)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (S-most (L~ (Cage (Y,X)))) is V13() V16( the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (Y,X)))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (Y,X))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (Y,X))))),REAL:]
the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (Y,X))))) is set
[: the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (Y,X))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (Y,X))))),REAL:] is set
K445(((TOP-REAL 2) | (S-most (L~ (Cage (Y,X))))),(proj1 | (S-most (L~ (Cage (Y,X)))))) is V11() V12() ext-real Element of REAL
|[K445(((TOP-REAL 2) | (S-most (L~ (Cage (Y,X))))),(proj1 | (S-most (L~ (Cage (Y,X)))))),(S-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
Lower_Seq (Y,X) 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 (Y,X)) is V26() set
L~ (Lower_Seq (Y,X)) is non empty functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
E-max (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-most (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
NE-corner (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Cage (Y,X))) is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | (L~ (Cage (Y,X)))),(proj2 | (L~ (Cage (Y,X))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (Y,X)))),(N-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Cage (Y,X)))),(NE-corner (L~ (Cage (Y,X))))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SE-corner (L~ (Cage (Y,X)))),(NE-corner (L~ (Cage (Y,X)))))) /\ (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ (Cage (Y,X)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Cage (Y,X)))) is V13() V16( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X)))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),REAL:]
the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))) is set
[: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),REAL:] is set
K446(((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),(proj2 | (E-most (L~ (Cage (Y,X)))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (Y,X)))),K446(((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),(proj2 | (E-most (L~ (Cage (Y,X))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-min (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-most (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
NW-corner (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
|[(W-bound (L~ (Cage (Y,X)))),(N-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (Y,X)))),(NW-corner (L~ (Cage (Y,X))))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Cage (Y,X)))),(NW-corner (L~ (Cage (Y,X)))))) /\ (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ (Cage (Y,X)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Cage (Y,X)))) is V13() V16( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X)))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),REAL:]
the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))) is set
[: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),REAL:] is set
K445(((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),(proj2 | (W-most (L~ (Cage (Y,X)))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (Y,X)))),K445(((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),(proj2 | (W-most (L~ (Cage (Y,X))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))) 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 (Y,X)),(W-min (L~ (Cage (Y,X)))))) is non empty non trivial V26() set
rng (Cage (Y,X)) is non empty non trivial V26() set
Upper_Seq (Y,X) 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 (Y,X)) /. 1 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))) is non empty functional V71( TOP-REAL 2) connected bounded being_simple_closed_curve compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
(Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))) -: (E-max (L~ (Cage (Y,X)))) 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 (Y,X)),(W-min (L~ (Cage (Y,X)))))) /. 1 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-min (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is V13() V16( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),REAL:]
the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),REAL:] is set
K446(((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),(proj1 | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))) is V11() V12() ext-real Element of REAL
E-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is functional Element of bool the U1 of (TOP-REAL 2)
SE-corner (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is V11() V12() ext-real Element of REAL
proj2 | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is V13() V16( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),REAL:]
K445(((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),(proj2 | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),(S-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NE-corner (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),(proj2 | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),(N-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),(NE-corner (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SE-corner (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),(NE-corner (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))))) /\ (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))) is V13() V16( the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),REAL:]
the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))) is set
[: the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),REAL:] is set
K445(((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),(proj2 | (E-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),K445(((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),(proj2 | (E-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(E-min (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))) .. (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
E-max (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
K446(((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),(proj2 | (E-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),K446(((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),(proj2 | (E-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(E-max (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))) .. (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
S-max (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is functional Element of bool the U1 of (TOP-REAL 2)
SW-corner (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is V11() V12() ext-real Element of REAL
K445(((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),(proj1 | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),(S-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),(SE-corner (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),(SE-corner (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))))) /\ (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (S-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (S-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))) is V13() V16( the U1 of ((TOP-REAL 2) | (S-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (S-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (S-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),REAL:]
the U1 of ((TOP-REAL 2) | (S-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))) is set
[: the U1 of ((TOP-REAL 2) | (S-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (S-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),REAL:] is set
K446(((TOP-REAL 2) | (S-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),(proj1 | (S-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))))) is V11() V12() ext-real Element of REAL
|[K446(((TOP-REAL 2) | (S-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),(proj1 | (S-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))))),(S-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(S-max (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))) .. (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
S-min (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
K445(((TOP-REAL 2) | (S-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),(proj1 | (S-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))))) is V11() V12() ext-real Element of REAL
|[K445(((TOP-REAL 2) | (S-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),(proj1 | (S-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))))),(S-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-min (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is functional Element of bool the U1 of (TOP-REAL 2)
NW-corner (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
|[(W-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),(N-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),(NW-corner (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),(NW-corner (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))))) /\ (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))) is V13() V16( the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),REAL:]
the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))) is set
[: the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),REAL:] is set
K445(((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),(proj2 | (W-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),K445(((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),(proj2 | (W-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(S-min (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))) .. (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))) :- (E-max (L~ (Cage (Y,X)))) 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 ((Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))) :- (E-max (L~ (Cage (Y,X))))) is V26() set
len (Lower_Seq (Y,X)) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
S-min (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
K445(((TOP-REAL 2) | (S-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),(proj1 | (S-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))))) is V11() V12() ext-real Element of REAL
|[K445(((TOP-REAL 2) | (S-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),(proj1 | (S-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))))),(S-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-min (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is functional Element of bool the U1 of (TOP-REAL 2)
NW-corner (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
|[(W-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),(N-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),(NW-corner (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),(NW-corner (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))))) /\ (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))) is V13() V16( the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),REAL:]
the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))) is set
[: the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),REAL:] is set
K445(((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),(proj2 | (W-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),K445(((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),(proj2 | (W-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
len (Lower_Seq (Y,X)) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(Lower_Seq (Y,X)) /. (len (Lower_Seq (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-min (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
K445(((TOP-REAL 2) | (S-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),(proj1 | (S-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))))) is V11() V12() ext-real Element of REAL
|[K445(((TOP-REAL 2) | (S-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),(proj1 | (S-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))))),(S-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-min (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is functional Element of bool the U1 of (TOP-REAL 2)
NW-corner (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
|[(W-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),(N-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),(NW-corner (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),(NW-corner (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))))) /\ (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))) is V13() V16( the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),REAL:]
the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))) is set
[: the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),REAL:] is set
K445(((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),(proj2 | (W-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),K445(((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),(proj2 | (W-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
X is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
Y is non empty functional bounded compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
Cage (Y,X) 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 (Y,X)) is non empty functional V71( TOP-REAL 2) connected bounded being_simple_closed_curve compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
W-min (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-bound (L~ (Cage (Y,X))) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (Y,X))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | (L~ (Cage (Y,X))) is V13() V16( the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))),REAL:]
the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))),REAL:] is set
K445(((TOP-REAL 2) | (L~ (Cage (Y,X)))),(proj1 | (L~ (Cage (Y,X))))) is V11() V12() ext-real Element of REAL
W-most (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
SW-corner (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Cage (Y,X))) is V11() V12() ext-real Element of REAL
proj2 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | (L~ (Cage (Y,X))) is V13() V16( the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))),REAL:]
K445(((TOP-REAL 2) | (L~ (Cage (Y,X)))),(proj2 | (L~ (Cage (Y,X))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (Y,X)))),(S-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NW-corner (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Cage (Y,X))) is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | (L~ (Cage (Y,X)))),(proj2 | (L~ (Cage (Y,X))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (Y,X)))),(N-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (Y,X)))),(NW-corner (L~ (Cage (Y,X))))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Cage (Y,X)))),(NW-corner (L~ (Cage (Y,X)))))) /\ (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ (Cage (Y,X)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Cage (Y,X)))) is V13() V16( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X)))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),REAL:]
the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))) is set
[: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),REAL:] is set
K445(((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),(proj2 | (W-most (L~ (Cage (Y,X)))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (Y,X)))),K445(((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),(proj2 | (W-most (L~ (Cage (Y,X))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
Lower_Seq (Y,X) 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 (Y,X)) is V26() set
L~ (Lower_Seq (Y,X)) is non empty functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
len (Lower_Seq (Y,X)) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(Lower_Seq (Y,X)) /. (len (Lower_Seq (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
X is non empty functional bounded compact Element of bool the U1 of (TOP-REAL 2)
Y is non empty functional bounded compact Element of bool the U1 of (TOP-REAL 2)
N-min Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-most Y is functional Element of bool the U1 of (TOP-REAL 2)
NW-corner Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-bound Y is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | Y is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | Y is V13() V16( the U1 of ((TOP-REAL 2) | Y)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | Y), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | Y),REAL:]
the U1 of ((TOP-REAL 2) | Y) is non empty set
[: the U1 of ((TOP-REAL 2) | Y),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | Y),REAL:] is set
K445(((TOP-REAL 2) | Y),(proj1 | Y)) is V11() V12() ext-real Element of REAL
N-bound Y is V11() V12() ext-real Element of REAL
proj2 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | Y is V13() V16( the U1 of ((TOP-REAL 2) | Y)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | Y), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | Y),REAL:]
K446(((TOP-REAL 2) | Y),(proj2 | Y)) is V11() V12() ext-real Element of REAL
|[(W-bound Y),(N-bound Y)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NE-corner Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-bound Y is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | Y),(proj1 | Y)) is V11() V12() ext-real Element of REAL
|[(E-bound Y),(N-bound Y)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((NW-corner Y),(NE-corner Y)) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((NW-corner Y),(NE-corner Y))) /\ Y is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (N-most Y) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most Y) is V13() V16( the U1 of ((TOP-REAL 2) | (N-most Y))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (N-most Y)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (N-most Y)),REAL:]
the U1 of ((TOP-REAL 2) | (N-most Y)) is set
[: the U1 of ((TOP-REAL 2) | (N-most Y)),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (N-most Y)),REAL:] is set
K445(((TOP-REAL 2) | (N-most Y)),(proj1 | (N-most Y))) is V11() V12() ext-real Element of REAL
|[K445(((TOP-REAL 2) | (N-most Y)),(proj1 | (N-most Y))),(N-bound Y)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-min X is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-most X is functional Element of bool the U1 of (TOP-REAL 2)
NW-corner X is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-bound X is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | X is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | X is V13() V16( the U1 of ((TOP-REAL 2) | X)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | X), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | X),REAL:]
the U1 of ((TOP-REAL 2) | X) is non empty set
[: the U1 of ((TOP-REAL 2) | X),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | X),REAL:] is set
K445(((TOP-REAL 2) | X),(proj1 | X)) is V11() V12() ext-real Element of REAL
N-bound X is V11() V12() ext-real Element of REAL
proj2 | X is V13() V16( the U1 of ((TOP-REAL 2) | X)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | X), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | X),REAL:]
K446(((TOP-REAL 2) | X),(proj2 | X)) is V11() V12() ext-real Element of REAL
|[(W-bound X),(N-bound X)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NE-corner X is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-bound X is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | X),(proj1 | X)) is V11() V12() ext-real Element of REAL
|[(E-bound X),(N-bound X)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((NW-corner X),(NE-corner X)) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((NW-corner X),(NE-corner X))) /\ X is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (N-most X) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most X) is V13() V16( the U1 of ((TOP-REAL 2) | (N-most X))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (N-most X)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (N-most X)),REAL:]
the U1 of ((TOP-REAL 2) | (N-most X)) is set
[: the U1 of ((TOP-REAL 2) | (N-most X)),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (N-most X)),REAL:] is set
K445(((TOP-REAL 2) | (N-most X)),(proj1 | (N-most X))) is V11() V12() ext-real Element of REAL
|[K445(((TOP-REAL 2) | (N-most X)),(proj1 | (N-most X))),(N-bound X)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(N-min Y) `2 is V11() V12() ext-real Element of REAL
(N-min X) `2 is V11() V12() ext-real Element of REAL
(N-min X) `1 is V11() V12() ext-real Element of REAL
(N-min Y) `1 is V11() V12() ext-real Element of REAL
X is non empty functional bounded compact Element of bool the U1 of (TOP-REAL 2)
Y is non empty functional bounded compact Element of bool the U1 of (TOP-REAL 2)
N-max Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-most Y is functional Element of bool the U1 of (TOP-REAL 2)
NW-corner Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-bound Y is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | Y is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | Y is V13() V16( the U1 of ((TOP-REAL 2) | Y)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | Y), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | Y),REAL:]
the U1 of ((TOP-REAL 2) | Y) is non empty set
[: the U1 of ((TOP-REAL 2) | Y),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | Y),REAL:] is set
K445(((TOP-REAL 2) | Y),(proj1 | Y)) is V11() V12() ext-real Element of REAL
N-bound Y is V11() V12() ext-real Element of REAL
proj2 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | Y is V13() V16( the U1 of ((TOP-REAL 2) | Y)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | Y), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | Y),REAL:]
K446(((TOP-REAL 2) | Y),(proj2 | Y)) is V11() V12() ext-real Element of REAL
|[(W-bound Y),(N-bound Y)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NE-corner Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-bound Y is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | Y),(proj1 | Y)) is V11() V12() ext-real Element of REAL
|[(E-bound Y),(N-bound Y)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((NW-corner Y),(NE-corner Y)) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((NW-corner Y),(NE-corner Y))) /\ Y is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (N-most Y) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most Y) is V13() V16( the U1 of ((TOP-REAL 2) | (N-most Y))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (N-most Y)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (N-most Y)),REAL:]
the U1 of ((TOP-REAL 2) | (N-most Y)) is set
[: the U1 of ((TOP-REAL 2) | (N-most Y)),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (N-most Y)),REAL:] is set
K446(((TOP-REAL 2) | (N-most Y)),(proj1 | (N-most Y))) is V11() V12() ext-real Element of REAL
|[K446(((TOP-REAL 2) | (N-most Y)),(proj1 | (N-most Y))),(N-bound Y)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-max X is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-most X is functional Element of bool the U1 of (TOP-REAL 2)
NW-corner X is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-bound X is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | X is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | X is V13() V16( the U1 of ((TOP-REAL 2) | X)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | X), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | X),REAL:]
the U1 of ((TOP-REAL 2) | X) is non empty set
[: the U1 of ((TOP-REAL 2) | X),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | X),REAL:] is set
K445(((TOP-REAL 2) | X),(proj1 | X)) is V11() V12() ext-real Element of REAL
N-bound X is V11() V12() ext-real Element of REAL
proj2 | X is V13() V16( the U1 of ((TOP-REAL 2) | X)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | X), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | X),REAL:]
K446(((TOP-REAL 2) | X),(proj2 | X)) is V11() V12() ext-real Element of REAL
|[(W-bound X),(N-bound X)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NE-corner X is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-bound X is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | X),(proj1 | X)) is V11() V12() ext-real Element of REAL
|[(E-bound X),(N-bound X)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((NW-corner X),(NE-corner X)) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((NW-corner X),(NE-corner X))) /\ X is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (N-most X) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most X) is V13() V16( the U1 of ((TOP-REAL 2) | (N-most X))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (N-most X)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (N-most X)),REAL:]
the U1 of ((TOP-REAL 2) | (N-most X)) is set
[: the U1 of ((TOP-REAL 2) | (N-most X)),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (N-most X)),REAL:] is set
K446(((TOP-REAL 2) | (N-most X)),(proj1 | (N-most X))) is V11() V12() ext-real Element of REAL
|[K446(((TOP-REAL 2) | (N-most X)),(proj1 | (N-most X))),(N-bound X)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(N-max Y) `2 is V11() V12() ext-real Element of REAL
(N-max X) `2 is V11() V12() ext-real Element of REAL
(N-max Y) `1 is V11() V12() ext-real Element of REAL
(N-max X) `1 is V11() V12() ext-real Element of REAL
X is non empty functional bounded compact Element of bool the U1 of (TOP-REAL 2)
Y is non empty functional bounded compact Element of bool the U1 of (TOP-REAL 2)
E-min Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-bound Y is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | Y is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | Y is V13() V16( the U1 of ((TOP-REAL 2) | Y)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | Y), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | Y),REAL:]
the U1 of ((TOP-REAL 2) | Y) is non empty set
[: the U1 of ((TOP-REAL 2) | Y),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | Y),REAL:] is set
K446(((TOP-REAL 2) | Y),(proj1 | Y)) is V11() V12() ext-real Element of REAL
E-most Y is functional Element of bool the U1 of (TOP-REAL 2)
SE-corner Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-bound Y is V11() V12() ext-real Element of REAL
proj2 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | Y is V13() V16( the U1 of ((TOP-REAL 2) | Y)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | Y), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | Y),REAL:]
K445(((TOP-REAL 2) | Y),(proj2 | Y)) is V11() V12() ext-real Element of REAL
|[(E-bound Y),(S-bound Y)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NE-corner Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-bound Y is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | Y),(proj2 | Y)) is V11() V12() ext-real Element of REAL
|[(E-bound Y),(N-bound Y)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner Y),(NE-corner Y)) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SE-corner Y),(NE-corner Y))) /\ Y is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (E-most Y) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most Y) is V13() V16( the U1 of ((TOP-REAL 2) | (E-most Y))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (E-most Y)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (E-most Y)),REAL:]
the U1 of ((TOP-REAL 2) | (E-most Y)) is set
[: the U1 of ((TOP-REAL 2) | (E-most Y)),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (E-most Y)),REAL:] is set
K445(((TOP-REAL 2) | (E-most Y)),(proj2 | (E-most Y))) is V11() V12() ext-real Element of REAL
|[(E-bound Y),K445(((TOP-REAL 2) | (E-most Y)),(proj2 | (E-most Y)))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-min X is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-bound X is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | X is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | X is V13() V16( the U1 of ((TOP-REAL 2) | X)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | X), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | X),REAL:]
the U1 of ((TOP-REAL 2) | X) is non empty set
[: the U1 of ((TOP-REAL 2) | X),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | X),REAL:] is set
K446(((TOP-REAL 2) | X),(proj1 | X)) is V11() V12() ext-real Element of REAL
E-most X is functional Element of bool the U1 of (TOP-REAL 2)
SE-corner X is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-bound X is V11() V12() ext-real Element of REAL
proj2 | X is V13() V16( the U1 of ((TOP-REAL 2) | X)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | X), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | X),REAL:]
K445(((TOP-REAL 2) | X),(proj2 | X)) is V11() V12() ext-real Element of REAL
|[(E-bound X),(S-bound X)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NE-corner X is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-bound X is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | X),(proj2 | X)) is V11() V12() ext-real Element of REAL
|[(E-bound X),(N-bound X)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner X),(NE-corner X)) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SE-corner X),(NE-corner X))) /\ X is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (E-most X) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most X) is V13() V16( the U1 of ((TOP-REAL 2) | (E-most X))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (E-most X)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (E-most X)),REAL:]
the U1 of ((TOP-REAL 2) | (E-most X)) is set
[: the U1 of ((TOP-REAL 2) | (E-most X)),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (E-most X)),REAL:] is set
K445(((TOP-REAL 2) | (E-most X)),(proj2 | (E-most X))) is V11() V12() ext-real Element of REAL
|[(E-bound X),K445(((TOP-REAL 2) | (E-most X)),(proj2 | (E-most X)))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(E-min Y) `1 is V11() V12() ext-real Element of REAL
(E-min X) `1 is V11() V12() ext-real Element of REAL
(E-min X) `2 is V11() V12() ext-real Element of REAL
(E-min Y) `2 is V11() V12() ext-real Element of REAL
X is non empty functional bounded compact Element of bool the U1 of (TOP-REAL 2)
Y is non empty functional bounded compact Element of bool the U1 of (TOP-REAL 2)
E-max Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-bound Y is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | Y is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | Y is V13() V16( the U1 of ((TOP-REAL 2) | Y)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | Y), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | Y),REAL:]
the U1 of ((TOP-REAL 2) | Y) is non empty set
[: the U1 of ((TOP-REAL 2) | Y),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | Y),REAL:] is set
K446(((TOP-REAL 2) | Y),(proj1 | Y)) is V11() V12() ext-real Element of REAL
E-most Y is functional Element of bool the U1 of (TOP-REAL 2)
SE-corner Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-bound Y is V11() V12() ext-real Element of REAL
proj2 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | Y is V13() V16( the U1 of ((TOP-REAL 2) | Y)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | Y), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | Y),REAL:]
K445(((TOP-REAL 2) | Y),(proj2 | Y)) is V11() V12() ext-real Element of REAL
|[(E-bound Y),(S-bound Y)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NE-corner Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-bound Y is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | Y),(proj2 | Y)) is V11() V12() ext-real Element of REAL
|[(E-bound Y),(N-bound Y)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner Y),(NE-corner Y)) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SE-corner Y),(NE-corner Y))) /\ Y is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (E-most Y) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most Y) is V13() V16( the U1 of ((TOP-REAL 2) | (E-most Y))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (E-most Y)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (E-most Y)),REAL:]
the U1 of ((TOP-REAL 2) | (E-most Y)) is set
[: the U1 of ((TOP-REAL 2) | (E-most Y)),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (E-most Y)),REAL:] is set
K446(((TOP-REAL 2) | (E-most Y)),(proj2 | (E-most Y))) is V11() V12() ext-real Element of REAL
|[(E-bound Y),K446(((TOP-REAL 2) | (E-most Y)),(proj2 | (E-most Y)))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-max X is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-bound X is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | X is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | X is V13() V16( the U1 of ((TOP-REAL 2) | X)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | X), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | X),REAL:]
the U1 of ((TOP-REAL 2) | X) is non empty set
[: the U1 of ((TOP-REAL 2) | X),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | X),REAL:] is set
K446(((TOP-REAL 2) | X),(proj1 | X)) is V11() V12() ext-real Element of REAL
E-most X is functional Element of bool the U1 of (TOP-REAL 2)
SE-corner X is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-bound X is V11() V12() ext-real Element of REAL
proj2 | X is V13() V16( the U1 of ((TOP-REAL 2) | X)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | X), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | X),REAL:]
K445(((TOP-REAL 2) | X),(proj2 | X)) is V11() V12() ext-real Element of REAL
|[(E-bound X),(S-bound X)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NE-corner X is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-bound X is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | X),(proj2 | X)) is V11() V12() ext-real Element of REAL
|[(E-bound X),(N-bound X)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner X),(NE-corner X)) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SE-corner X),(NE-corner X))) /\ X is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (E-most X) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most X) is V13() V16( the U1 of ((TOP-REAL 2) | (E-most X))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (E-most X)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (E-most X)),REAL:]
the U1 of ((TOP-REAL 2) | (E-most X)) is set
[: the U1 of ((TOP-REAL 2) | (E-most X)),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (E-most X)),REAL:] is set
K446(((TOP-REAL 2) | (E-most X)),(proj2 | (E-most X))) is V11() V12() ext-real Element of REAL
|[(E-bound X),K446(((TOP-REAL 2) | (E-most X)),(proj2 | (E-most X)))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(E-max Y) `1 is V11() V12() ext-real Element of REAL
(E-max X) `1 is V11() V12() ext-real Element of REAL
(E-max Y) `2 is V11() V12() ext-real Element of REAL
(E-max X) `2 is V11() V12() ext-real Element of REAL
X is non empty functional bounded compact Element of bool the U1 of (TOP-REAL 2)
Y is non empty functional bounded compact Element of bool the U1 of (TOP-REAL 2)
S-min Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-most Y is functional Element of bool the U1 of (TOP-REAL 2)
SW-corner Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-bound Y is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | Y is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | Y is V13() V16( the U1 of ((TOP-REAL 2) | Y)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | Y), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | Y),REAL:]
the U1 of ((TOP-REAL 2) | Y) is non empty set
[: the U1 of ((TOP-REAL 2) | Y),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | Y),REAL:] is set
K445(((TOP-REAL 2) | Y),(proj1 | Y)) is V11() V12() ext-real Element of REAL
S-bound Y is V11() V12() ext-real Element of REAL
proj2 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | Y is V13() V16( the U1 of ((TOP-REAL 2) | Y)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | Y), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | Y),REAL:]
K445(((TOP-REAL 2) | Y),(proj2 | Y)) is V11() V12() ext-real Element of REAL
|[(W-bound Y),(S-bound Y)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
SE-corner Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-bound Y is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | Y),(proj1 | Y)) is V11() V12() ext-real Element of REAL
|[(E-bound Y),(S-bound Y)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner Y),(SE-corner Y)) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner Y),(SE-corner Y))) /\ Y is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (S-most Y) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (S-most Y) is V13() V16( the U1 of ((TOP-REAL 2) | (S-most Y))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (S-most Y)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (S-most Y)),REAL:]
the U1 of ((TOP-REAL 2) | (S-most Y)) is set
[: the U1 of ((TOP-REAL 2) | (S-most Y)),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (S-most Y)),REAL:] is set
K445(((TOP-REAL 2) | (S-most Y)),(proj1 | (S-most Y))) is V11() V12() ext-real Element of REAL
|[K445(((TOP-REAL 2) | (S-most Y)),(proj1 | (S-most Y))),(S-bound Y)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-min X is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-most X is functional Element of bool the U1 of (TOP-REAL 2)
SW-corner X is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-bound X is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | X is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | X is V13() V16( the U1 of ((TOP-REAL 2) | X)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | X), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | X),REAL:]
the U1 of ((TOP-REAL 2) | X) is non empty set
[: the U1 of ((TOP-REAL 2) | X),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | X),REAL:] is set
K445(((TOP-REAL 2) | X),(proj1 | X)) is V11() V12() ext-real Element of REAL
S-bound X is V11() V12() ext-real Element of REAL
proj2 | X is V13() V16( the U1 of ((TOP-REAL 2) | X)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | X), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | X),REAL:]
K445(((TOP-REAL 2) | X),(proj2 | X)) is V11() V12() ext-real Element of REAL
|[(W-bound X),(S-bound X)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
SE-corner X is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-bound X is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | X),(proj1 | X)) is V11() V12() ext-real Element of REAL
|[(E-bound X),(S-bound X)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner X),(SE-corner X)) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner X),(SE-corner X))) /\ X is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (S-most X) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (S-most X) is V13() V16( the U1 of ((TOP-REAL 2) | (S-most X))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (S-most X)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (S-most X)),REAL:]
the U1 of ((TOP-REAL 2) | (S-most X)) is set
[: the U1 of ((TOP-REAL 2) | (S-most X)),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (S-most X)),REAL:] is set
K445(((TOP-REAL 2) | (S-most X)),(proj1 | (S-most X))) is V11() V12() ext-real Element of REAL
|[K445(((TOP-REAL 2) | (S-most X)),(proj1 | (S-most X))),(S-bound X)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(S-min Y) `2 is V11() V12() ext-real Element of REAL
(S-min X) `2 is V11() V12() ext-real Element of REAL
(S-min X) `1 is V11() V12() ext-real Element of REAL
(S-min Y) `1 is V11() V12() ext-real Element of REAL
X is non empty functional bounded compact Element of bool the U1 of (TOP-REAL 2)
Y is non empty functional bounded compact Element of bool the U1 of (TOP-REAL 2)
S-max Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-most Y is functional Element of bool the U1 of (TOP-REAL 2)
SW-corner Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-bound Y is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | Y is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | Y is V13() V16( the U1 of ((TOP-REAL 2) | Y)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | Y), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | Y),REAL:]
the U1 of ((TOP-REAL 2) | Y) is non empty set
[: the U1 of ((TOP-REAL 2) | Y),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | Y),REAL:] is set
K445(((TOP-REAL 2) | Y),(proj1 | Y)) is V11() V12() ext-real Element of REAL
S-bound Y is V11() V12() ext-real Element of REAL
proj2 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | Y is V13() V16( the U1 of ((TOP-REAL 2) | Y)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | Y), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | Y),REAL:]
K445(((TOP-REAL 2) | Y),(proj2 | Y)) is V11() V12() ext-real Element of REAL
|[(W-bound Y),(S-bound Y)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
SE-corner Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-bound Y is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | Y),(proj1 | Y)) is V11() V12() ext-real Element of REAL
|[(E-bound Y),(S-bound Y)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner Y),(SE-corner Y)) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner Y),(SE-corner Y))) /\ Y is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (S-most Y) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (S-most Y) is V13() V16( the U1 of ((TOP-REAL 2) | (S-most Y))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (S-most Y)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (S-most Y)),REAL:]
the U1 of ((TOP-REAL 2) | (S-most Y)) is set
[: the U1 of ((TOP-REAL 2) | (S-most Y)),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (S-most Y)),REAL:] is set
K446(((TOP-REAL 2) | (S-most Y)),(proj1 | (S-most Y))) is V11() V12() ext-real Element of REAL
|[K446(((TOP-REAL 2) | (S-most Y)),(proj1 | (S-most Y))),(S-bound Y)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-max X is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-most X is functional Element of bool the U1 of (TOP-REAL 2)
SW-corner X is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-bound X is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | X is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | X is V13() V16( the U1 of ((TOP-REAL 2) | X)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | X), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | X),REAL:]
the U1 of ((TOP-REAL 2) | X) is non empty set
[: the U1 of ((TOP-REAL 2) | X),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | X),REAL:] is set
K445(((TOP-REAL 2) | X),(proj1 | X)) is V11() V12() ext-real Element of REAL
S-bound X is V11() V12() ext-real Element of REAL
proj2 | X is V13() V16( the U1 of ((TOP-REAL 2) | X)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | X), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | X),REAL:]
K445(((TOP-REAL 2) | X),(proj2 | X)) is V11() V12() ext-real Element of REAL
|[(W-bound X),(S-bound X)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
SE-corner X is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-bound X is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | X),(proj1 | X)) is V11() V12() ext-real Element of REAL
|[(E-bound X),(S-bound X)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner X),(SE-corner X)) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner X),(SE-corner X))) /\ X is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (S-most X) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (S-most X) is V13() V16( the U1 of ((TOP-REAL 2) | (S-most X))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (S-most X)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (S-most X)),REAL:]
the U1 of ((TOP-REAL 2) | (S-most X)) is set
[: the U1 of ((TOP-REAL 2) | (S-most X)),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (S-most X)),REAL:] is set
K446(((TOP-REAL 2) | (S-most X)),(proj1 | (S-most X))) is V11() V12() ext-real Element of REAL
|[K446(((TOP-REAL 2) | (S-most X)),(proj1 | (S-most X))),(S-bound X)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(S-max Y) `2 is V11() V12() ext-real Element of REAL
(S-max X) `2 is V11() V12() ext-real Element of REAL
(S-max Y) `1 is V11() V12() ext-real Element of REAL
(S-max X) `1 is V11() V12() ext-real Element of REAL
X is non empty functional bounded compact Element of bool the U1 of (TOP-REAL 2)
Y is non empty functional bounded compact Element of bool the U1 of (TOP-REAL 2)
W-min Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-bound Y is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | Y is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | Y is V13() V16( the U1 of ((TOP-REAL 2) | Y)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | Y), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | Y),REAL:]
the U1 of ((TOP-REAL 2) | Y) is non empty set
[: the U1 of ((TOP-REAL 2) | Y),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | Y),REAL:] is set
K445(((TOP-REAL 2) | Y),(proj1 | Y)) is V11() V12() ext-real Element of REAL
W-most Y is functional Element of bool the U1 of (TOP-REAL 2)
SW-corner Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-bound Y is V11() V12() ext-real Element of REAL
proj2 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | Y is V13() V16( the U1 of ((TOP-REAL 2) | Y)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | Y), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | Y),REAL:]
K445(((TOP-REAL 2) | Y),(proj2 | Y)) is V11() V12() ext-real Element of REAL
|[(W-bound Y),(S-bound Y)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NW-corner Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-bound Y is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | Y),(proj2 | Y)) is V11() V12() ext-real Element of REAL
|[(W-bound Y),(N-bound Y)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner Y),(NW-corner Y)) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner Y),(NW-corner Y))) /\ Y is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most Y) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most Y) is V13() V16( the U1 of ((TOP-REAL 2) | (W-most Y))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (W-most Y)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most Y)),REAL:]
the U1 of ((TOP-REAL 2) | (W-most Y)) is set
[: the U1 of ((TOP-REAL 2) | (W-most Y)),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (W-most Y)),REAL:] is set
K445(((TOP-REAL 2) | (W-most Y)),(proj2 | (W-most Y))) is V11() V12() ext-real Element of REAL
|[(W-bound Y),K445(((TOP-REAL 2) | (W-most Y)),(proj2 | (W-most Y)))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-min X is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-bound X is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | X is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | X is V13() V16( the U1 of ((TOP-REAL 2) | X)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | X), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | X),REAL:]
the U1 of ((TOP-REAL 2) | X) is non empty set
[: the U1 of ((TOP-REAL 2) | X),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | X),REAL:] is set
K445(((TOP-REAL 2) | X),(proj1 | X)) is V11() V12() ext-real Element of REAL
W-most X is functional Element of bool the U1 of (TOP-REAL 2)
SW-corner X is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-bound X is V11() V12() ext-real Element of REAL
proj2 | X is V13() V16( the U1 of ((TOP-REAL 2) | X)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | X), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | X),REAL:]
K445(((TOP-REAL 2) | X),(proj2 | X)) is V11() V12() ext-real Element of REAL
|[(W-bound X),(S-bound X)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NW-corner X is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-bound X is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | X),(proj2 | X)) is V11() V12() ext-real Element of REAL
|[(W-bound X),(N-bound X)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner X),(NW-corner X)) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner X),(NW-corner X))) /\ X is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most X) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most X) is V13() V16( the U1 of ((TOP-REAL 2) | (W-most X))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (W-most X)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most X)),REAL:]
the U1 of ((TOP-REAL 2) | (W-most X)) is set
[: the U1 of ((TOP-REAL 2) | (W-most X)),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (W-most X)),REAL:] is set
K445(((TOP-REAL 2) | (W-most X)),(proj2 | (W-most X))) is V11() V12() ext-real Element of REAL
|[(W-bound X),K445(((TOP-REAL 2) | (W-most X)),(proj2 | (W-most X)))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(W-min Y) `1 is V11() V12() ext-real Element of REAL
(W-min X) `1 is V11() V12() ext-real Element of REAL
(W-min X) `2 is V11() V12() ext-real Element of REAL
(W-min Y) `2 is V11() V12() ext-real Element of REAL
X is non empty functional bounded compact Element of bool the U1 of (TOP-REAL 2)
Y is non empty functional bounded compact Element of bool the U1 of (TOP-REAL 2)
W-max Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-bound Y is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | Y is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | Y is V13() V16( the U1 of ((TOP-REAL 2) | Y)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | Y), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | Y),REAL:]
the U1 of ((TOP-REAL 2) | Y) is non empty set
[: the U1 of ((TOP-REAL 2) | Y),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | Y),REAL:] is set
K445(((TOP-REAL 2) | Y),(proj1 | Y)) is V11() V12() ext-real Element of REAL
W-most Y is functional Element of bool the U1 of (TOP-REAL 2)
SW-corner Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-bound Y is V11() V12() ext-real Element of REAL
proj2 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | Y is V13() V16( the U1 of ((TOP-REAL 2) | Y)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | Y), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | Y),REAL:]
K445(((TOP-REAL 2) | Y),(proj2 | Y)) is V11() V12() ext-real Element of REAL
|[(W-bound Y),(S-bound Y)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NW-corner Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-bound Y is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | Y),(proj2 | Y)) is V11() V12() ext-real Element of REAL
|[(W-bound Y),(N-bound Y)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner Y),(NW-corner Y)) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner Y),(NW-corner Y))) /\ Y is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most Y) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most Y) is V13() V16( the U1 of ((TOP-REAL 2) | (W-most Y))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (W-most Y)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most Y)),REAL:]
the U1 of ((TOP-REAL 2) | (W-most Y)) is set
[: the U1 of ((TOP-REAL 2) | (W-most Y)),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (W-most Y)),REAL:] is set
K446(((TOP-REAL 2) | (W-most Y)),(proj2 | (W-most Y))) is V11() V12() ext-real Element of REAL
|[(W-bound Y),K446(((TOP-REAL 2) | (W-most Y)),(proj2 | (W-most Y)))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-max X is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-bound X is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | X is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | X is V13() V16( the U1 of ((TOP-REAL 2) | X)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | X), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | X),REAL:]
the U1 of ((TOP-REAL 2) | X) is non empty set
[: the U1 of ((TOP-REAL 2) | X),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | X),REAL:] is set
K445(((TOP-REAL 2) | X),(proj1 | X)) is V11() V12() ext-real Element of REAL
W-most X is functional Element of bool the U1 of (TOP-REAL 2)
SW-corner X is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-bound X is V11() V12() ext-real Element of REAL
proj2 | X is V13() V16( the U1 of ((TOP-REAL 2) | X)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | X), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | X),REAL:]
K445(((TOP-REAL 2) | X),(proj2 | X)) is V11() V12() ext-real Element of REAL
|[(W-bound X),(S-bound X)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NW-corner X is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-bound X is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | X),(proj2 | X)) is V11() V12() ext-real Element of REAL
|[(W-bound X),(N-bound X)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner X),(NW-corner X)) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner X),(NW-corner X))) /\ X is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most X) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most X) is V13() V16( the U1 of ((TOP-REAL 2) | (W-most X))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (W-most X)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most X)),REAL:]
the U1 of ((TOP-REAL 2) | (W-most X)) is set
[: the U1 of ((TOP-REAL 2) | (W-most X)),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (W-most X)),REAL:] is set
K446(((TOP-REAL 2) | (W-most X)),(proj2 | (W-most X))) is V11() V12() ext-real Element of REAL
|[(W-bound X),K446(((TOP-REAL 2) | (W-most X)),(proj2 | (W-most X)))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(W-max Y) `1 is V11() V12() ext-real Element of REAL
(W-max X) `1 is V11() V12() ext-real Element of REAL
(W-max Y) `2 is V11() V12() ext-real Element of REAL
(W-max X) `2 is V11() V12() ext-real Element of REAL
X is non empty functional bounded compact Element of bool the U1 of (TOP-REAL 2)
N-bound X is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | X is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj2 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | X is V13() V16( the U1 of ((TOP-REAL 2) | X)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | X), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | X),REAL:]
the U1 of ((TOP-REAL 2) | X) is non empty set
[: the U1 of ((TOP-REAL 2) | X),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | X),REAL:] is set
K446(((TOP-REAL 2) | X),(proj2 | X)) is V11() V12() ext-real Element of REAL
Y is non empty functional bounded compact Element of bool the U1 of (TOP-REAL 2)
N-bound Y is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | Y is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | Y is V13() V16( the U1 of ((TOP-REAL 2) | Y)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | Y), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | Y),REAL:]
the U1 of ((TOP-REAL 2) | Y) is non empty set
[: the U1 of ((TOP-REAL 2) | Y),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | Y),REAL:] is set
K446(((TOP-REAL 2) | Y),(proj2 | Y)) is V11() V12() ext-real Element of REAL
X \/ Y is non empty functional Element of bool the U1 of (TOP-REAL 2)
N-bound (X \/ Y) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (X \/ Y) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (X \/ Y) is V13() V16( the U1 of ((TOP-REAL 2) | (X \/ Y))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (X \/ Y)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (X \/ Y)),REAL:]
the U1 of ((TOP-REAL 2) | (X \/ Y)) is non empty set
[: the U1 of ((TOP-REAL 2) | (X \/ Y)),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (X \/ Y)),REAL:] is set
K446(((TOP-REAL 2) | (X \/ Y)),(proj2 | (X \/ Y))) is V11() V12() ext-real Element of REAL
max ((N-bound X),(N-bound Y)) is V11() V12() ext-real set
X is non empty functional bounded compact Element of bool the U1 of (TOP-REAL 2)
E-bound X is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | X is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | X is V13() V16( the U1 of ((TOP-REAL 2) | X)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | X), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | X),REAL:]
the U1 of ((TOP-REAL 2) | X) is non empty set
[: the U1 of ((TOP-REAL 2) | X),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | X),REAL:] is set
K446(((TOP-REAL 2) | X),(proj1 | X)) is V11() V12() ext-real Element of REAL
Y is non empty functional bounded compact Element of bool the U1 of (TOP-REAL 2)
E-bound Y is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | Y is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | Y is V13() V16( the U1 of ((TOP-REAL 2) | Y)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | Y), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | Y),REAL:]
the U1 of ((TOP-REAL 2) | Y) is non empty set
[: the U1 of ((TOP-REAL 2) | Y),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | Y),REAL:] is set
K446(((TOP-REAL 2) | Y),(proj1 | Y)) is V11() V12() ext-real Element of REAL
X \/ Y is non empty functional Element of bool the U1 of (TOP-REAL 2)
E-bound (X \/ Y) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (X \/ Y) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (X \/ Y) is V13() V16( the U1 of ((TOP-REAL 2) | (X \/ Y))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (X \/ Y)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (X \/ Y)),REAL:]
the U1 of ((TOP-REAL 2) | (X \/ Y)) is non empty set
[: the U1 of ((TOP-REAL 2) | (X \/ Y)),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (X \/ Y)),REAL:] is set
K446(((TOP-REAL 2) | (X \/ Y)),(proj1 | (X \/ Y))) is V11() V12() ext-real Element of REAL
max ((E-bound X),(E-bound Y)) is V11() V12() ext-real set
X is non empty functional bounded compact Element of bool the U1 of (TOP-REAL 2)
S-bound X is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | X is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj2 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | X is V13() V16( the U1 of ((TOP-REAL 2) | X)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | X), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | X),REAL:]
the U1 of ((TOP-REAL 2) | X) is non empty set
[: the U1 of ((TOP-REAL 2) | X),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | X),REAL:] is set
K445(((TOP-REAL 2) | X),(proj2 | X)) is V11() V12() ext-real Element of REAL
Y is non empty functional bounded compact Element of bool the U1 of (TOP-REAL 2)
S-bound Y is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | Y is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | Y is V13() V16( the U1 of ((TOP-REAL 2) | Y)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | Y), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | Y),REAL:]
the U1 of ((TOP-REAL 2) | Y) is non empty set
[: the U1 of ((TOP-REAL 2) | Y),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | Y),REAL:] is set
K445(((TOP-REAL 2) | Y),(proj2 | Y)) is V11() V12() ext-real Element of REAL
X \/ Y is non empty functional Element of bool the U1 of (TOP-REAL 2)
S-bound (X \/ Y) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (X \/ Y) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (X \/ Y) is V13() V16( the U1 of ((TOP-REAL 2) | (X \/ Y))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (X \/ Y)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (X \/ Y)),REAL:]
the U1 of ((TOP-REAL 2) | (X \/ Y)) is non empty set
[: the U1 of ((TOP-REAL 2) | (X \/ Y)),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (X \/ Y)),REAL:] is set
K445(((TOP-REAL 2) | (X \/ Y)),(proj2 | (X \/ Y))) is V11() V12() ext-real Element of REAL
min ((S-bound X),(S-bound Y)) is V11() V12() ext-real set
X is non empty functional bounded compact Element of bool the U1 of (TOP-REAL 2)
W-bound X is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | X is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | X is V13() V16( the U1 of ((TOP-REAL 2) | X)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | X), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | X),REAL:]
the U1 of ((TOP-REAL 2) | X) is non empty set
[: the U1 of ((TOP-REAL 2) | X),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | X),REAL:] is set
K445(((TOP-REAL 2) | X),(proj1 | X)) is V11() V12() ext-real Element of REAL
Y is non empty functional bounded compact Element of bool the U1 of (TOP-REAL 2)
W-bound Y is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | Y is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | Y is V13() V16( the U1 of ((TOP-REAL 2) | Y)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | Y), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | Y),REAL:]
the U1 of ((TOP-REAL 2) | Y) is non empty set
[: the U1 of ((TOP-REAL 2) | Y),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | Y),REAL:] is set
K445(((TOP-REAL 2) | Y),(proj1 | Y)) is V11() V12() ext-real Element of REAL
X \/ Y is non empty functional Element of bool the U1 of (TOP-REAL 2)
W-bound (X \/ Y) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (X \/ Y) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (X \/ Y) is V13() V16( the U1 of ((TOP-REAL 2) | (X \/ Y))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (X \/ Y)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (X \/ Y)),REAL:]
the U1 of ((TOP-REAL 2) | (X \/ Y)) is non empty set
[: the U1 of ((TOP-REAL 2) | (X \/ Y)),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (X \/ Y)),REAL:] is set
K445(((TOP-REAL 2) | (X \/ Y)),(proj1 | (X \/ Y))) is V11() V12() ext-real Element of REAL
min ((W-bound X),(W-bound Y)) is V11() V12() ext-real set
Y is non empty functional bounded compact Element of bool the U1 of (TOP-REAL 2)
N-bound Y is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | Y is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj2 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | Y is V13() V16( the U1 of ((TOP-REAL 2) | Y)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | Y), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | Y),REAL:]
the U1 of ((TOP-REAL 2) | Y) is non empty set
[: the U1 of ((TOP-REAL 2) | Y),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | Y),REAL:] is set
K446(((TOP-REAL 2) | Y),(proj2 | Y)) is V11() V12() ext-real Element of REAL
X is non empty functional bounded compact Element of bool the U1 of (TOP-REAL 2)
N-bound X is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | X is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | X is V13() V16( the U1 of ((TOP-REAL 2) | X)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | X), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | X),REAL:]
the U1 of ((TOP-REAL 2) | X) is non empty set
[: the U1 of ((TOP-REAL 2) | X),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | X),REAL:] is set
K446(((TOP-REAL 2) | X),(proj2 | X)) is V11() V12() ext-real Element of REAL
X \/ Y is non empty functional Element of bool the U1 of (TOP-REAL 2)
N-min (X \/ Y) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-most (X \/ Y) is functional Element of bool the U1 of (TOP-REAL 2)
NW-corner (X \/ Y) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-bound (X \/ Y) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (X \/ Y) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | (X \/ Y) is V13() V16( the U1 of ((TOP-REAL 2) | (X \/ Y))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (X \/ Y)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (X \/ Y)),REAL:]
the U1 of ((TOP-REAL 2) | (X \/ Y)) is non empty set
[: the U1 of ((TOP-REAL 2) | (X \/ Y)),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (X \/ Y)),REAL:] is set
K445(((TOP-REAL 2) | (X \/ Y)),(proj1 | (X \/ Y))) is V11() V12() ext-real Element of REAL
N-bound (X \/ Y) is V11() V12() ext-real Element of REAL
proj2 | (X \/ Y) is V13() V16( the U1 of ((TOP-REAL 2) | (X \/ Y))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (X \/ Y)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (X \/ Y)),REAL:]
K446(((TOP-REAL 2) | (X \/ Y)),(proj2 | (X \/ Y))) is V11() V12() ext-real Element of REAL
|[(W-bound (X \/ Y)),(N-bound (X \/ Y))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NE-corner (X \/ Y) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-bound (X \/ Y) is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | (X \/ Y)),(proj1 | (X \/ Y))) is V11() V12() ext-real Element of REAL
|[(E-bound (X \/ Y)),(N-bound (X \/ Y))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((NW-corner (X \/ Y)),(NE-corner (X \/ Y))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((NW-corner (X \/ Y)),(NE-corner (X \/ Y)))) /\ (X \/ Y) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (N-most (X \/ Y)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most (X \/ Y)) is V13() V16( the U1 of ((TOP-REAL 2) | (N-most (X \/ Y)))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (N-most (X \/ Y))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (N-most (X \/ Y))),REAL:]
the U1 of ((TOP-REAL 2) | (N-most (X \/ Y))) is set
[: the U1 of ((TOP-REAL 2) | (N-most (X \/ Y))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (N-most (X \/ Y))),REAL:] is set
K445(((TOP-REAL 2) | (N-most (X \/ Y))),(proj1 | (N-most (X \/ Y)))) is V11() V12() ext-real Element of REAL
|[K445(((TOP-REAL 2) | (N-most (X \/ Y))),(proj1 | (N-most (X \/ Y)))),(N-bound (X \/ Y))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-min Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-most Y is functional Element of bool the U1 of (TOP-REAL 2)
NW-corner Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-bound Y is V11() V12() ext-real Element of REAL
proj1 | Y is V13() V16( the U1 of ((TOP-REAL 2) | Y)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | Y), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | Y),REAL:]
K445(((TOP-REAL 2) | Y),(proj1 | Y)) is V11() V12() ext-real Element of REAL
|[(W-bound Y),(N-bound Y)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NE-corner Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-bound Y is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | Y),(proj1 | Y)) is V11() V12() ext-real Element of REAL
|[(E-bound Y),(N-bound Y)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((NW-corner Y),(NE-corner Y)) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((NW-corner Y),(NE-corner Y))) /\ Y is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (N-most Y) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most Y) is V13() V16( the U1 of ((TOP-REAL 2) | (N-most Y))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (N-most Y)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (N-most Y)),REAL:]
the U1 of ((TOP-REAL 2) | (N-most Y)) is set
[: the U1 of ((TOP-REAL 2) | (N-most Y)),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (N-most Y)),REAL:] is set
K445(((TOP-REAL 2) | (N-most Y)),(proj1 | (N-most Y))) is V11() V12() ext-real Element of REAL
|[K445(((TOP-REAL 2) | (N-most Y)),(proj1 | (N-most Y))),(N-bound Y)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(N-min (X \/ Y)) `2 is V11() V12() ext-real Element of REAL
(N-min Y) `2 is V11() V12() ext-real Element of REAL
(N-min (X \/ Y)) `1 is V11() V12() ext-real Element of REAL
(N-min Y) `1 is V11() V12() ext-real Element of REAL
Y is non empty functional bounded compact Element of bool the U1 of (TOP-REAL 2)
N-bound Y is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | Y is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj2 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | Y is V13() V16( the U1 of ((TOP-REAL 2) | Y)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | Y), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | Y),REAL:]
the U1 of ((TOP-REAL 2) | Y) is non empty set
[: the U1 of ((TOP-REAL 2) | Y),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | Y),REAL:] is set
K446(((TOP-REAL 2) | Y),(proj2 | Y)) is V11() V12() ext-real Element of REAL
X is non empty functional bounded compact Element of bool the U1 of (TOP-REAL 2)
N-bound X is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | X is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | X is V13() V16( the U1 of ((TOP-REAL 2) | X)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | X), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | X),REAL:]
the U1 of ((TOP-REAL 2) | X) is non empty set
[: the U1 of ((TOP-REAL 2) | X),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | X),REAL:] is set
K446(((TOP-REAL 2) | X),(proj2 | X)) is V11() V12() ext-real Element of REAL
X \/ Y is non empty functional Element of bool the U1 of (TOP-REAL 2)
N-max (X \/ Y) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-most (X \/ Y) is functional Element of bool the U1 of (TOP-REAL 2)
NW-corner (X \/ Y) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-bound (X \/ Y) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (X \/ Y) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | (X \/ Y) is V13() V16( the U1 of ((TOP-REAL 2) | (X \/ Y))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (X \/ Y)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (X \/ Y)),REAL:]
the U1 of ((TOP-REAL 2) | (X \/ Y)) is non empty set
[: the U1 of ((TOP-REAL 2) | (X \/ Y)),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (X \/ Y)),REAL:] is set
K445(((TOP-REAL 2) | (X \/ Y)),(proj1 | (X \/ Y))) is V11() V12() ext-real Element of REAL
N-bound (X \/ Y) is V11() V12() ext-real Element of REAL
proj2 | (X \/ Y) is V13() V16( the U1 of ((TOP-REAL 2) | (X \/ Y))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (X \/ Y)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (X \/ Y)),REAL:]
K446(((TOP-REAL 2) | (X \/ Y)),(proj2 | (X \/ Y))) is V11() V12() ext-real Element of REAL
|[(W-bound (X \/ Y)),(N-bound (X \/ Y))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NE-corner (X \/ Y) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-bound (X \/ Y) is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | (X \/ Y)),(proj1 | (X \/ Y))) is V11() V12() ext-real Element of REAL
|[(E-bound (X \/ Y)),(N-bound (X \/ Y))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((NW-corner (X \/ Y)),(NE-corner (X \/ Y))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((NW-corner (X \/ Y)),(NE-corner (X \/ Y)))) /\ (X \/ Y) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (N-most (X \/ Y)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most (X \/ Y)) is V13() V16( the U1 of ((TOP-REAL 2) | (N-most (X \/ Y)))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (N-most (X \/ Y))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (N-most (X \/ Y))),REAL:]
the U1 of ((TOP-REAL 2) | (N-most (X \/ Y))) is set
[: the U1 of ((TOP-REAL 2) | (N-most (X \/ Y))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (N-most (X \/ Y))),REAL:] is set
K446(((TOP-REAL 2) | (N-most (X \/ Y))),(proj1 | (N-most (X \/ Y)))) is V11() V12() ext-real Element of REAL
|[K446(((TOP-REAL 2) | (N-most (X \/ Y))),(proj1 | (N-most (X \/ Y)))),(N-bound (X \/ Y))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-max Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-most Y is functional Element of bool the U1 of (TOP-REAL 2)
NW-corner Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-bound Y is V11() V12() ext-real Element of REAL
proj1 | Y is V13() V16( the U1 of ((TOP-REAL 2) | Y)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | Y), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | Y),REAL:]
K445(((TOP-REAL 2) | Y),(proj1 | Y)) is V11() V12() ext-real Element of REAL
|[(W-bound Y),(N-bound Y)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NE-corner Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-bound Y is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | Y),(proj1 | Y)) is V11() V12() ext-real Element of REAL
|[(E-bound Y),(N-bound Y)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((NW-corner Y),(NE-corner Y)) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((NW-corner Y),(NE-corner Y))) /\ Y is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (N-most Y) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most Y) is V13() V16( the U1 of ((TOP-REAL 2) | (N-most Y))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (N-most Y)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (N-most Y)),REAL:]
the U1 of ((TOP-REAL 2) | (N-most Y)) is set
[: the U1 of ((TOP-REAL 2) | (N-most Y)),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (N-most Y)),REAL:] is set
K446(((TOP-REAL 2) | (N-most Y)),(proj1 | (N-most Y))) is V11() V12() ext-real Element of REAL
|[K446(((TOP-REAL 2) | (N-most Y)),(proj1 | (N-most Y))),(N-bound Y)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(N-max (X \/ Y)) `2 is V11() V12() ext-real Element of REAL
(N-max Y) `2 is V11() V12() ext-real Element of REAL
(N-max Y) `1 is V11() V12() ext-real Element of REAL
(N-max (X \/ Y)) `1 is V11() V12() ext-real Element of REAL
Y is non empty functional bounded compact Element of bool the U1 of (TOP-REAL 2)
E-bound Y is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | Y is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | Y is V13() V16( the U1 of ((TOP-REAL 2) | Y)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | Y), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | Y),REAL:]
the U1 of ((TOP-REAL 2) | Y) is non empty set
[: the U1 of ((TOP-REAL 2) | Y),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | Y),REAL:] is set
K446(((TOP-REAL 2) | Y),(proj1 | Y)) is V11() V12() ext-real Element of REAL
X is non empty functional bounded compact Element of bool the U1 of (TOP-REAL 2)
E-bound X is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | X is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | X is V13() V16( the U1 of ((TOP-REAL 2) | X)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | X), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | X),REAL:]
the U1 of ((TOP-REAL 2) | X) is non empty set
[: the U1 of ((TOP-REAL 2) | X),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | X),REAL:] is set
K446(((TOP-REAL 2) | X),(proj1 | X)) is V11() V12() ext-real Element of REAL
X \/ Y is non empty functional Element of bool the U1 of (TOP-REAL 2)
E-min (X \/ Y) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-bound (X \/ Y) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (X \/ Y) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (X \/ Y) is V13() V16( the U1 of ((TOP-REAL 2) | (X \/ Y))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (X \/ Y)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (X \/ Y)),REAL:]
the U1 of ((TOP-REAL 2) | (X \/ Y)) is non empty set
[: the U1 of ((TOP-REAL 2) | (X \/ Y)),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (X \/ Y)),REAL:] is set
K446(((TOP-REAL 2) | (X \/ Y)),(proj1 | (X \/ Y))) is V11() V12() ext-real Element of REAL
E-most (X \/ Y) is functional Element of bool the U1 of (TOP-REAL 2)
SE-corner (X \/ Y) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-bound (X \/ Y) is V11() V12() ext-real Element of REAL
proj2 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | (X \/ Y) is V13() V16( the U1 of ((TOP-REAL 2) | (X \/ Y))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (X \/ Y)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (X \/ Y)),REAL:]
K445(((TOP-REAL 2) | (X \/ Y)),(proj2 | (X \/ Y))) is V11() V12() ext-real Element of REAL
|[(E-bound (X \/ Y)),(S-bound (X \/ Y))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NE-corner (X \/ Y) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-bound (X \/ Y) is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | (X \/ Y)),(proj2 | (X \/ Y))) is V11() V12() ext-real Element of REAL
|[(E-bound (X \/ Y)),(N-bound (X \/ Y))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (X \/ Y)),(NE-corner (X \/ Y))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SE-corner (X \/ Y)),(NE-corner (X \/ Y)))) /\ (X \/ Y) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (X \/ Y)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (X \/ Y)) is V13() V16( the U1 of ((TOP-REAL 2) | (E-most (X \/ Y)))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (E-most (X \/ Y))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (E-most (X \/ Y))),REAL:]
the U1 of ((TOP-REAL 2) | (E-most (X \/ Y))) is set
[: the U1 of ((TOP-REAL 2) | (E-most (X \/ Y))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (E-most (X \/ Y))),REAL:] is set
K445(((TOP-REAL 2) | (E-most (X \/ Y))),(proj2 | (E-most (X \/ Y)))) is V11() V12() ext-real Element of REAL
|[(E-bound (X \/ Y)),K445(((TOP-REAL 2) | (E-most (X \/ Y))),(proj2 | (E-most (X \/ Y))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-min Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-most Y is functional Element of bool the U1 of (TOP-REAL 2)
SE-corner Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-bound Y is V11() V12() ext-real Element of REAL
proj2 | Y is V13() V16( the U1 of ((TOP-REAL 2) | Y)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | Y), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | Y),REAL:]
K445(((TOP-REAL 2) | Y),(proj2 | Y)) is V11() V12() ext-real Element of REAL
|[(E-bound Y),(S-bound Y)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NE-corner Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-bound Y is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | Y),(proj2 | Y)) is V11() V12() ext-real Element of REAL
|[(E-bound Y),(N-bound Y)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner Y),(NE-corner Y)) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SE-corner Y),(NE-corner Y))) /\ Y is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (E-most Y) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most Y) is V13() V16( the U1 of ((TOP-REAL 2) | (E-most Y))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (E-most Y)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (E-most Y)),REAL:]
the U1 of ((TOP-REAL 2) | (E-most Y)) is set
[: the U1 of ((TOP-REAL 2) | (E-most Y)),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (E-most Y)),REAL:] is set
K445(((TOP-REAL 2) | (E-most Y)),(proj2 | (E-most Y))) is V11() V12() ext-real Element of REAL
|[(E-bound Y),K445(((TOP-REAL 2) | (E-most Y)),(proj2 | (E-most Y)))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(E-min (X \/ Y)) `1 is V11() V12() ext-real Element of REAL
(E-min Y) `1 is V11() V12() ext-real Element of REAL
(E-min (X \/ Y)) `2 is V11() V12() ext-real Element of REAL
(E-min Y) `2 is V11() V12() ext-real Element of REAL
Y is non empty functional bounded compact Element of bool the U1 of (TOP-REAL 2)
E-bound Y is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | Y is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | Y is V13() V16( the U1 of ((TOP-REAL 2) | Y)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | Y), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | Y),REAL:]
the U1 of ((TOP-REAL 2) | Y) is non empty set
[: the U1 of ((TOP-REAL 2) | Y),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | Y),REAL:] is set
K446(((TOP-REAL 2) | Y),(proj1 | Y)) is V11() V12() ext-real Element of REAL
X is non empty functional bounded compact Element of bool the U1 of (TOP-REAL 2)
E-bound X is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | X is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | X is V13() V16( the U1 of ((TOP-REAL 2) | X)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | X), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | X),REAL:]
the U1 of ((TOP-REAL 2) | X) is non empty set
[: the U1 of ((TOP-REAL 2) | X),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | X),REAL:] is set
K446(((TOP-REAL 2) | X),(proj1 | X)) is V11() V12() ext-real Element of REAL
X \/ Y is non empty functional Element of bool the U1 of (TOP-REAL 2)
E-max (X \/ Y) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-bound (X \/ Y) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (X \/ Y) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (X \/ Y) is V13() V16( the U1 of ((TOP-REAL 2) | (X \/ Y))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (X \/ Y)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (X \/ Y)),REAL:]
the U1 of ((TOP-REAL 2) | (X \/ Y)) is non empty set
[: the U1 of ((TOP-REAL 2) | (X \/ Y)),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (X \/ Y)),REAL:] is set
K446(((TOP-REAL 2) | (X \/ Y)),(proj1 | (X \/ Y))) is V11() V12() ext-real Element of REAL
E-most (X \/ Y) is functional Element of bool the U1 of (TOP-REAL 2)
SE-corner (X \/ Y) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-bound (X \/ Y) is V11() V12() ext-real Element of REAL
proj2 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | (X \/ Y) is V13() V16( the U1 of ((TOP-REAL 2) | (X \/ Y))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (X \/ Y)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (X \/ Y)),REAL:]
K445(((TOP-REAL 2) | (X \/ Y)),(proj2 | (X \/ Y))) is V11() V12() ext-real Element of REAL
|[(E-bound (X \/ Y)),(S-bound (X \/ Y))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NE-corner (X \/ Y) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-bound (X \/ Y) is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | (X \/ Y)),(proj2 | (X \/ Y))) is V11() V12() ext-real Element of REAL
|[(E-bound (X \/ Y)),(N-bound (X \/ Y))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (X \/ Y)),(NE-corner (X \/ Y))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SE-corner (X \/ Y)),(NE-corner (X \/ Y)))) /\ (X \/ Y) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (X \/ Y)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (X \/ Y)) is V13() V16( the U1 of ((TOP-REAL 2) | (E-most (X \/ Y)))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (E-most (X \/ Y))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (E-most (X \/ Y))),REAL:]
the U1 of ((TOP-REAL 2) | (E-most (X \/ Y))) is set
[: the U1 of ((TOP-REAL 2) | (E-most (X \/ Y))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (E-most (X \/ Y))),REAL:] is set
K446(((TOP-REAL 2) | (E-most (X \/ Y))),(proj2 | (E-most (X \/ Y)))) is V11() V12() ext-real Element of REAL
|[(E-bound (X \/ Y)),K446(((TOP-REAL 2) | (E-most (X \/ Y))),(proj2 | (E-most (X \/ Y))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-max Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-most Y is functional Element of bool the U1 of (TOP-REAL 2)
SE-corner Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-bound Y is V11() V12() ext-real Element of REAL
proj2 | Y is V13() V16( the U1 of ((TOP-REAL 2) | Y)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | Y), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | Y),REAL:]
K445(((TOP-REAL 2) | Y),(proj2 | Y)) is V11() V12() ext-real Element of REAL
|[(E-bound Y),(S-bound Y)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NE-corner Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-bound Y is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | Y),(proj2 | Y)) is V11() V12() ext-real Element of REAL
|[(E-bound Y),(N-bound Y)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner Y),(NE-corner Y)) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SE-corner Y),(NE-corner Y))) /\ Y is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (E-most Y) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most Y) is V13() V16( the U1 of ((TOP-REAL 2) | (E-most Y))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (E-most Y)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (E-most Y)),REAL:]
the U1 of ((TOP-REAL 2) | (E-most Y)) is set
[: the U1 of ((TOP-REAL 2) | (E-most Y)),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (E-most Y)),REAL:] is set
K446(((TOP-REAL 2) | (E-most Y)),(proj2 | (E-most Y))) is V11() V12() ext-real Element of REAL
|[(E-bound Y),K446(((TOP-REAL 2) | (E-most Y)),(proj2 | (E-most Y)))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(E-max (X \/ Y)) `1 is V11() V12() ext-real Element of REAL
(E-max Y) `1 is V11() V12() ext-real Element of REAL
(E-max Y) `2 is V11() V12() ext-real Element of REAL
(E-max (X \/ Y)) `2 is V11() V12() ext-real Element of REAL
Y is non empty functional bounded compact Element of bool the U1 of (TOP-REAL 2)
S-bound Y is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | Y is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj2 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | Y is V13() V16( the U1 of ((TOP-REAL 2) | Y)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | Y), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | Y),REAL:]
the U1 of ((TOP-REAL 2) | Y) is non empty set
[: the U1 of ((TOP-REAL 2) | Y),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | Y),REAL:] is set
K445(((TOP-REAL 2) | Y),(proj2 | Y)) is V11() V12() ext-real Element of REAL
X is non empty functional bounded compact Element of bool the U1 of (TOP-REAL 2)
S-bound X is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | X is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | X is V13() V16( the U1 of ((TOP-REAL 2) | X)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | X), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | X),REAL:]
the U1 of ((TOP-REAL 2) | X) is non empty set
[: the U1 of ((TOP-REAL 2) | X),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | X),REAL:] is set
K445(((TOP-REAL 2) | X),(proj2 | X)) is V11() V12() ext-real Element of REAL
X \/ Y is non empty functional Element of bool the U1 of (TOP-REAL 2)
S-min (X \/ Y) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-most (X \/ Y) is functional Element of bool the U1 of (TOP-REAL 2)
SW-corner (X \/ Y) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-bound (X \/ Y) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (X \/ Y) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | (X \/ Y) is V13() V16( the U1 of ((TOP-REAL 2) | (X \/ Y))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (X \/ Y)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (X \/ Y)),REAL:]
the U1 of ((TOP-REAL 2) | (X \/ Y)) is non empty set
[: the U1 of ((TOP-REAL 2) | (X \/ Y)),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (X \/ Y)),REAL:] is set
K445(((TOP-REAL 2) | (X \/ Y)),(proj1 | (X \/ Y))) is V11() V12() ext-real Element of REAL
S-bound (X \/ Y) is V11() V12() ext-real Element of REAL
proj2 | (X \/ Y) is V13() V16( the U1 of ((TOP-REAL 2) | (X \/ Y))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (X \/ Y)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (X \/ Y)),REAL:]
K445(((TOP-REAL 2) | (X \/ Y)),(proj2 | (X \/ Y))) is V11() V12() ext-real Element of REAL
|[(W-bound (X \/ Y)),(S-bound (X \/ Y))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
SE-corner (X \/ Y) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-bound (X \/ Y) is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | (X \/ Y)),(proj1 | (X \/ Y))) is V11() V12() ext-real Element of REAL
|[(E-bound (X \/ Y)),(S-bound (X \/ Y))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (X \/ Y)),(SE-corner (X \/ Y))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (X \/ Y)),(SE-corner (X \/ Y)))) /\ (X \/ Y) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (S-most (X \/ Y)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (S-most (X \/ Y)) is V13() V16( the U1 of ((TOP-REAL 2) | (S-most (X \/ Y)))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (S-most (X \/ Y))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (S-most (X \/ Y))),REAL:]
the U1 of ((TOP-REAL 2) | (S-most (X \/ Y))) is set
[: the U1 of ((TOP-REAL 2) | (S-most (X \/ Y))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (S-most (X \/ Y))),REAL:] is set
K445(((TOP-REAL 2) | (S-most (X \/ Y))),(proj1 | (S-most (X \/ Y)))) is V11() V12() ext-real Element of REAL
|[K445(((TOP-REAL 2) | (S-most (X \/ Y))),(proj1 | (S-most (X \/ Y)))),(S-bound (X \/ Y))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-min X is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-most X is functional Element of bool the U1 of (TOP-REAL 2)
SW-corner X is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-bound X is V11() V12() ext-real Element of REAL
proj1 | X is V13() V16( the U1 of ((TOP-REAL 2) | X)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | X), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | X),REAL:]
K445(((TOP-REAL 2) | X),(proj1 | X)) is V11() V12() ext-real Element of REAL
|[(W-bound X),(S-bound X)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
SE-corner X is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-bound X is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | X),(proj1 | X)) is V11() V12() ext-real Element of REAL
|[(E-bound X),(S-bound X)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner X),(SE-corner X)) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner X),(SE-corner X))) /\ X is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (S-most X) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (S-most X) is V13() V16( the U1 of ((TOP-REAL 2) | (S-most X))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (S-most X)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (S-most X)),REAL:]
the U1 of ((TOP-REAL 2) | (S-most X)) is set
[: the U1 of ((TOP-REAL 2) | (S-most X)),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (S-most X)),REAL:] is set
K445(((TOP-REAL 2) | (S-most X)),(proj1 | (S-most X))) is V11() V12() ext-real Element of REAL
|[K445(((TOP-REAL 2) | (S-most X)),(proj1 | (S-most X))),(S-bound X)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(S-min (X \/ Y)) `2 is V11() V12() ext-real Element of REAL
(S-min X) `2 is V11() V12() ext-real Element of REAL
(S-min (X \/ Y)) `1 is V11() V12() ext-real Element of REAL
(S-min X) `1 is V11() V12() ext-real Element of REAL
Y is non empty functional bounded compact Element of bool the U1 of (TOP-REAL 2)
S-bound Y is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | Y is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj2 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | Y is V13() V16( the U1 of ((TOP-REAL 2) | Y)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | Y), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | Y),REAL:]
the U1 of ((TOP-REAL 2) | Y) is non empty set
[: the U1 of ((TOP-REAL 2) | Y),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | Y),REAL:] is set
K445(((TOP-REAL 2) | Y),(proj2 | Y)) is V11() V12() ext-real Element of REAL
X is non empty functional bounded compact Element of bool the U1 of (TOP-REAL 2)
S-bound X is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | X is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | X is V13() V16( the U1 of ((TOP-REAL 2) | X)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | X), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | X),REAL:]
the U1 of ((TOP-REAL 2) | X) is non empty set
[: the U1 of ((TOP-REAL 2) | X),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | X),REAL:] is set
K445(((TOP-REAL 2) | X),(proj2 | X)) is V11() V12() ext-real Element of REAL
X \/ Y is non empty functional Element of bool the U1 of (TOP-REAL 2)
S-max (X \/ Y) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-most (X \/ Y) is functional Element of bool the U1 of (TOP-REAL 2)
SW-corner (X \/ Y) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-bound (X \/ Y) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (X \/ Y) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | (X \/ Y) is V13() V16( the U1 of ((TOP-REAL 2) | (X \/ Y))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (X \/ Y)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (X \/ Y)),REAL:]
the U1 of ((TOP-REAL 2) | (X \/ Y)) is non empty set
[: the U1 of ((TOP-REAL 2) | (X \/ Y)),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (X \/ Y)),REAL:] is set
K445(((TOP-REAL 2) | (X \/ Y)),(proj1 | (X \/ Y))) is V11() V12() ext-real Element of REAL
S-bound (X \/ Y) is V11() V12() ext-real Element of REAL
proj2 | (X \/ Y) is V13() V16( the U1 of ((TOP-REAL 2) | (X \/ Y))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (X \/ Y)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (X \/ Y)),REAL:]
K445(((TOP-REAL 2) | (X \/ Y)),(proj2 | (X \/ Y))) is V11() V12() ext-real Element of REAL
|[(W-bound (X \/ Y)),(S-bound (X \/ Y))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
SE-corner (X \/ Y) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-bound (X \/ Y) is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | (X \/ Y)),(proj1 | (X \/ Y))) is V11() V12() ext-real Element of REAL
|[(E-bound (X \/ Y)),(S-bound (X \/ Y))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (X \/ Y)),(SE-corner (X \/ Y))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (X \/ Y)),(SE-corner (X \/ Y)))) /\ (X \/ Y) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (S-most (X \/ Y)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (S-most (X \/ Y)) is V13() V16( the U1 of ((TOP-REAL 2) | (S-most (X \/ Y)))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (S-most (X \/ Y))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (S-most (X \/ Y))),REAL:]
the U1 of ((TOP-REAL 2) | (S-most (X \/ Y))) is set
[: the U1 of ((TOP-REAL 2) | (S-most (X \/ Y))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (S-most (X \/ Y))),REAL:] is set
K446(((TOP-REAL 2) | (S-most (X \/ Y))),(proj1 | (S-most (X \/ Y)))) is V11() V12() ext-real Element of REAL
|[K446(((TOP-REAL 2) | (S-most (X \/ Y))),(proj1 | (S-most (X \/ Y)))),(S-bound (X \/ Y))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-max X is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-most X is functional Element of bool the U1 of (TOP-REAL 2)
SW-corner X is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-bound X is V11() V12() ext-real Element of REAL
proj1 | X is V13() V16( the U1 of ((TOP-REAL 2) | X)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | X), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | X),REAL:]
K445(((TOP-REAL 2) | X),(proj1 | X)) is V11() V12() ext-real Element of REAL
|[(W-bound X),(S-bound X)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
SE-corner X is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-bound X is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | X),(proj1 | X)) is V11() V12() ext-real Element of REAL
|[(E-bound X),(S-bound X)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner X),(SE-corner X)) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner X),(SE-corner X))) /\ X is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (S-most X) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (S-most X) is V13() V16( the U1 of ((TOP-REAL 2) | (S-most X))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (S-most X)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (S-most X)),REAL:]
the U1 of ((TOP-REAL 2) | (S-most X)) is set
[: the U1 of ((TOP-REAL 2) | (S-most X)),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (S-most X)),REAL:] is set
K446(((TOP-REAL 2) | (S-most X)),(proj1 | (S-most X))) is V11() V12() ext-real Element of REAL
|[K446(((TOP-REAL 2) | (S-most X)),(proj1 | (S-most X))),(S-bound X)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(S-max (X \/ Y)) `2 is V11() V12() ext-real Element of REAL
(S-max X) `2 is V11() V12() ext-real Element of REAL
(S-max X) `1 is V11() V12() ext-real Element of REAL
(S-max (X \/ Y)) `1 is V11() V12() ext-real Element of REAL
Y is non empty functional bounded compact Element of bool the U1 of (TOP-REAL 2)
W-bound Y is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | Y is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | Y is V13() V16( the U1 of ((TOP-REAL 2) | Y)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | Y), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | Y),REAL:]
the U1 of ((TOP-REAL 2) | Y) is non empty set
[: the U1 of ((TOP-REAL 2) | Y),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | Y),REAL:] is set
K445(((TOP-REAL 2) | Y),(proj1 | Y)) is V11() V12() ext-real Element of REAL
X is non empty functional bounded compact Element of bool the U1 of (TOP-REAL 2)
W-bound X is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | X is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | X is V13() V16( the U1 of ((TOP-REAL 2) | X)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | X), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | X),REAL:]
the U1 of ((TOP-REAL 2) | X) is non empty set
[: the U1 of ((TOP-REAL 2) | X),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | X),REAL:] is set
K445(((TOP-REAL 2) | X),(proj1 | X)) is V11() V12() ext-real Element of REAL
X \/ Y is non empty functional Element of bool the U1 of (TOP-REAL 2)
W-min (X \/ Y) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-bound (X \/ Y) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (X \/ Y) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (X \/ Y) is V13() V16( the U1 of ((TOP-REAL 2) | (X \/ Y))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (X \/ Y)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (X \/ Y)),REAL:]
the U1 of ((TOP-REAL 2) | (X \/ Y)) is non empty set
[: the U1 of ((TOP-REAL 2) | (X \/ Y)),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (X \/ Y)),REAL:] is set
K445(((TOP-REAL 2) | (X \/ Y)),(proj1 | (X \/ Y))) is V11() V12() ext-real Element of REAL
W-most (X \/ Y) is functional Element of bool the U1 of (TOP-REAL 2)
SW-corner (X \/ Y) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-bound (X \/ Y) is V11() V12() ext-real Element of REAL
proj2 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | (X \/ Y) is V13() V16( the U1 of ((TOP-REAL 2) | (X \/ Y))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (X \/ Y)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (X \/ Y)),REAL:]
K445(((TOP-REAL 2) | (X \/ Y)),(proj2 | (X \/ Y))) is V11() V12() ext-real Element of REAL
|[(W-bound (X \/ Y)),(S-bound (X \/ Y))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NW-corner (X \/ Y) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-bound (X \/ Y) is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | (X \/ Y)),(proj2 | (X \/ Y))) is V11() V12() ext-real Element of REAL
|[(W-bound (X \/ Y)),(N-bound (X \/ Y))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (X \/ Y)),(NW-corner (X \/ Y))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (X \/ Y)),(NW-corner (X \/ Y)))) /\ (X \/ Y) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (X \/ Y)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (X \/ Y)) is V13() V16( the U1 of ((TOP-REAL 2) | (W-most (X \/ Y)))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (W-most (X \/ Y))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most (X \/ Y))),REAL:]
the U1 of ((TOP-REAL 2) | (W-most (X \/ Y))) is set
[: the U1 of ((TOP-REAL 2) | (W-most (X \/ Y))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (W-most (X \/ Y))),REAL:] is set
K445(((TOP-REAL 2) | (W-most (X \/ Y))),(proj2 | (W-most (X \/ Y)))) is V11() V12() ext-real Element of REAL
|[(W-bound (X \/ Y)),K445(((TOP-REAL 2) | (W-most (X \/ Y))),(proj2 | (W-most (X \/ Y))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-min X is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-most X is functional Element of bool the U1 of (TOP-REAL 2)
SW-corner X is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-bound X is V11() V12() ext-real Element of REAL
proj2 | X is V13() V16( the U1 of ((TOP-REAL 2) | X)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | X), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | X),REAL:]
K445(((TOP-REAL 2) | X),(proj2 | X)) is V11() V12() ext-real Element of REAL
|[(W-bound X),(S-bound X)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NW-corner X is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-bound X is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | X),(proj2 | X)) is V11() V12() ext-real Element of REAL
|[(W-bound X),(N-bound X)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner X),(NW-corner X)) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner X),(NW-corner X))) /\ X is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most X) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most X) is V13() V16( the U1 of ((TOP-REAL 2) | (W-most X))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (W-most X)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most X)),REAL:]
the U1 of ((TOP-REAL 2) | (W-most X)) is set
[: the U1 of ((TOP-REAL 2) | (W-most X)),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (W-most X)),REAL:] is set
K445(((TOP-REAL 2) | (W-most X)),(proj2 | (W-most X))) is V11() V12() ext-real Element of REAL
|[(W-bound X),K445(((TOP-REAL 2) | (W-most X)),(proj2 | (W-most X)))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(W-min (X \/ Y)) `1 is V11() V12() ext-real Element of REAL
(W-min X) `1 is V11() V12() ext-real Element of REAL
(W-min (X \/ Y)) `2 is V11() V12() ext-real Element of REAL
(W-min X) `2 is V11() V12() ext-real Element of REAL
Y is non empty functional bounded compact Element of bool the U1 of (TOP-REAL 2)
W-bound Y is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | Y is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | Y is V13() V16( the U1 of ((TOP-REAL 2) | Y)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | Y), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | Y),REAL:]
the U1 of ((TOP-REAL 2) | Y) is non empty set
[: the U1 of ((TOP-REAL 2) | Y),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | Y),REAL:] is set
K445(((TOP-REAL 2) | Y),(proj1 | Y)) is V11() V12() ext-real Element of REAL
X is non empty functional bounded compact Element of bool the U1 of (TOP-REAL 2)
W-bound X is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | X is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | X is V13() V16( the U1 of ((TOP-REAL 2) | X)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | X), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | X),REAL:]
the U1 of ((TOP-REAL 2) | X) is non empty set
[: the U1 of ((TOP-REAL 2) | X),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | X),REAL:] is set
K445(((TOP-REAL 2) | X),(proj1 | X)) is V11() V12() ext-real Element of REAL
X \/ Y is non empty functional Element of bool the U1 of (TOP-REAL 2)
W-max (X \/ Y) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-bound (X \/ Y) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (X \/ Y) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (X \/ Y) is V13() V16( the U1 of ((TOP-REAL 2) | (X \/ Y))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (X \/ Y)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (X \/ Y)),REAL:]
the U1 of ((TOP-REAL 2) | (X \/ Y)) is non empty set
[: the U1 of ((TOP-REAL 2) | (X \/ Y)),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (X \/ Y)),REAL:] is set
K445(((TOP-REAL 2) | (X \/ Y)),(proj1 | (X \/ Y))) is V11() V12() ext-real Element of REAL
W-most (X \/ Y) is functional Element of bool the U1 of (TOP-REAL 2)
SW-corner (X \/ Y) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-bound (X \/ Y) is V11() V12() ext-real Element of REAL
proj2 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | (X \/ Y) is V13() V16( the U1 of ((TOP-REAL 2) | (X \/ Y))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (X \/ Y)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (X \/ Y)),REAL:]
K445(((TOP-REAL 2) | (X \/ Y)),(proj2 | (X \/ Y))) is V11() V12() ext-real Element of REAL
|[(W-bound (X \/ Y)),(S-bound (X \/ Y))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NW-corner (X \/ Y) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-bound (X \/ Y) is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | (X \/ Y)),(proj2 | (X \/ Y))) is V11() V12() ext-real Element of REAL
|[(W-bound (X \/ Y)),(N-bound (X \/ Y))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (X \/ Y)),(NW-corner (X \/ Y))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (X \/ Y)),(NW-corner (X \/ Y)))) /\ (X \/ Y) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (X \/ Y)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (X \/ Y)) is V13() V16( the U1 of ((TOP-REAL 2) | (W-most (X \/ Y)))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (W-most (X \/ Y))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most (X \/ Y))),REAL:]
the U1 of ((TOP-REAL 2) | (W-most (X \/ Y))) is set
[: the U1 of ((TOP-REAL 2) | (W-most (X \/ Y))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (W-most (X \/ Y))),REAL:] is set
K446(((TOP-REAL 2) | (W-most (X \/ Y))),(proj2 | (W-most (X \/ Y)))) is V11() V12() ext-real Element of REAL
|[(W-bound (X \/ Y)),K446(((TOP-REAL 2) | (W-most (X \/ Y))),(proj2 | (W-most (X \/ Y))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-max X is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-most X is functional Element of bool the U1 of (TOP-REAL 2)
SW-corner X is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-bound X is V11() V12() ext-real Element of REAL
proj2 | X is V13() V16( the U1 of ((TOP-REAL 2) | X)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | X), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | X),REAL:]
K445(((TOP-REAL 2) | X),(proj2 | X)) is V11() V12() ext-real Element of REAL
|[(W-bound X),(S-bound X)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NW-corner X is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-bound X is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | X),(proj2 | X)) is V11() V12() ext-real Element of REAL
|[(W-bound X),(N-bound X)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner X),(NW-corner X)) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner X),(NW-corner X))) /\ X is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most X) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most X) is V13() V16( the U1 of ((TOP-REAL 2) | (W-most X))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (W-most X)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most X)),REAL:]
the U1 of ((TOP-REAL 2) | (W-most X)) is set
[: the U1 of ((TOP-REAL 2) | (W-most X)),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (W-most X)),REAL:] is set
K446(((TOP-REAL 2) | (W-most X)),(proj2 | (W-most X))) is V11() V12() ext-real Element of REAL
|[(W-bound X),K446(((TOP-REAL 2) | (W-most X)),(proj2 | (W-most X)))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(W-max (X \/ Y)) `1 is V11() V12() ext-real Element of REAL
(W-max X) `1 is V11() V12() ext-real Element of REAL
(W-max X) `2 is V11() V12() ext-real Element of REAL
(W-max (X \/ Y)) `2 is V11() V12() ext-real Element of REAL
X 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~ X is functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
len X is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
X /. (len X) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
L_Cut (X,Y) 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 (L_Cut (X,Y)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(L_Cut (X,Y)) /. (len (L_Cut (X,Y))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
dom X is V26() V180() V181() V182() V183() V184() V185() Element of bool NAT
dom (L_Cut (X,Y)) is V26() V180() V181() V182() V183() V184() V185() Element of bool NAT
(L_Cut (X,Y)) . (len (L_Cut (X,Y))) is V13() Function-like set
X . (len X) is V13() Function-like set
X 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 FinSequence of the U1 of (TOP-REAL 2)
RightComp X is non empty functional Element of bool the U1 of (TOP-REAL 2)
LeftComp X is non empty functional Element of bool the U1 of (TOP-REAL 2)
L~ X is non empty functional V71( TOP-REAL 2) connected bounded being_simple_closed_curve compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
j is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
k is functional connected Element of bool the U1 of (TOP-REAL 2)
(L~ X) ` is non empty functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | ((L~ X) `) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
the U1 of ((TOP-REAL 2) | ((L~ X) `)) is non empty set
bool the U1 of ((TOP-REAL 2) | ((L~ X) `)) is set
Ga is Element of bool the U1 of ((TOP-REAL 2) | ((L~ X) `))
k is Element of bool the U1 of ((TOP-REAL 2) | ((L~ X) `))
Ga /\ k is Element of bool the U1 of ((TOP-REAL 2) | ((L~ X) `))
US is Element of bool the U1 of ((TOP-REAL 2) | ((L~ X) `))
US /\ k is Element of bool the U1 of ((TOP-REAL 2) | ((L~ X) `))
the V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
the non empty functional connected bounded being_simple_closed_curve compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2) is non empty functional connected bounded being_simple_closed_curve compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
Upper_Seq ( the non empty functional connected bounded being_simple_closed_curve compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2), the V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT ) 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)
Gauge ( the non empty functional connected bounded being_simple_closed_curve compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2), the V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT ) is V13() non empty-yielding V16( NAT ) V17(K233( 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 K233( the U1 of (TOP-REAL 2))
len (Upper_Seq ( the non empty functional connected bounded being_simple_closed_curve compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2), the V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT )) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
X 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 X is V26() set
len X is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
L_Cut (X,Y) 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)
Y .. X is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
mid (X,(Y .. X),(len X)) 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 X is non empty non trivial V26() V180() V181() V182() V183() V184() V185() Element of bool NAT
j is V6() V10() V11() V12() V26() cardinal ext-real non negative set
X . j is V13() Function-like set
0 + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
Index (Y,X) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(Index (Y,X)) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
mid (X,((Index (Y,X)) + 1),(len X)) 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)
X /. j is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
L_Cut (X,(X /. 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)
mid (X,1,(len X)) 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)
X is V13() non empty-yielding V16( NAT ) V17(K233( 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 K233( the U1 of (TOP-REAL 2))
Y 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 Y is V26() set
j is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
R_Cut (Y,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)
j .. Y is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
mid (Y,1,(j .. Y)) 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)
X is V13() non empty-yielding V16( NAT ) V17(K233( 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 K233( the U1 of (TOP-REAL 2))
Y 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 Y is V26() set
j is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
L_Cut (Y,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)
j .. Y is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
len Y is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
mid (Y,(j .. Y),(len Y)) 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)
X is V13() non empty-yielding V16( NAT ) V17(K233( 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 K233( the U1 of (TOP-REAL 2))
len X is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
width X is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
Y 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~ Y is functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
rng Y is V26() set
j is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
k is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
X * (j,k) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
len Y is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
k is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
k + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
Y /. k is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
Y /. (k + 1) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((Y /. k),(Y /. (k + 1))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
Indices X is set
Ga is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
US is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
[Ga,US] is non empty set
{Ga,US} is non empty V26() V30() V180() V181() V182() V183() V184() V185() set
{Ga} is non empty trivial V26() V30() 1 -element V180() V181() V182() V183() V184() V185() set
{{Ga,US},{Ga}} is non empty V26() V30() set
X * (Ga,US) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LS is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
UA is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
[LS,UA] is non empty set
{LS,UA} is non empty V26() V30() V180() V181() V182() V183() V184() V185() set
{LS} is non empty trivial V26() V30() 1 -element V180() V181() V182() V183() V184() V185() set
{{LS,UA},{LS}} is non empty V26() V30() set
X * (LS,UA) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
US + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
Ga + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
LS + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
UA + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
dom Y is V26() V180() V181() V182() V183() V184() V185() Element of bool NAT
(X * (Ga,US)) `2 is V11() V12() ext-real Element of REAL
X * (Ga,(US + 1)) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(X * (Ga,(US + 1))) `2 is V11() V12() ext-real Element of REAL
(X * (j,k)) `2 is V11() V12() ext-real Element of REAL
(X * (Ga,US)) `1 is V11() V12() ext-real Element of REAL
(X * (Ga,(US + 1))) `1 is V11() V12() ext-real Element of REAL
(X * (j,k)) `1 is V11() V12() ext-real Element of REAL
(X * (Ga,US)) `1 is V11() V12() ext-real Element of REAL
X * ((Ga + 1),US) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(X * ((Ga + 1),US)) `1 is V11() V12() ext-real Element of REAL
(X * (j,k)) `1 is V11() V12() ext-real Element of REAL
(X * (Ga,US)) `2 is V11() V12() ext-real Element of REAL
(X * ((Ga + 1),US)) `2 is V11() V12() ext-real Element of REAL
(X * (j,k)) `2 is V11() V12() ext-real Element of REAL
X * (LS,US) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(X * (LS,US)) `1 is V11() V12() ext-real Element of REAL
X * ((LS + 1),US) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(X * ((LS + 1),US)) `1 is V11() V12() ext-real Element of REAL
(X * (j,k)) `1 is V11() V12() ext-real Element of REAL
(X * (LS,US)) `2 is V11() V12() ext-real Element of REAL
(X * ((LS + 1),US)) `2 is V11() V12() ext-real Element of REAL
(X * (j,k)) `2 is V11() V12() ext-real Element of REAL
X * (Ga,UA) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(X * (Ga,UA)) `2 is V11() V12() ext-real Element of REAL
X * (Ga,(UA + 1)) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(X * (Ga,(UA + 1))) `2 is V11() V12() ext-real Element of REAL
(X * (j,k)) `2 is V11() V12() ext-real Element of REAL
(X * (Ga,UA)) `1 is V11() V12() ext-real Element of REAL
(X * (Ga,(UA + 1))) `1 is V11() V12() ext-real Element of REAL
(X * (j,k)) `1 is V11() V12() ext-real Element of REAL
X 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~ X is non empty functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
X /. 1 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
{(X /. 1)} is non empty trivial functional V26() V30() 1 -element set
len X is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
X /. (len X) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
Y 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~ Y is functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
(L~ X) /\ (L~ Y) is functional Element of bool the U1 of (TOP-REAL 2)
len Y is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
Y /. (len Y) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
Y /. 1 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((X /. (len X)),(Y /. 1)) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
X ^ Y 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)
k is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
j is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
j + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
len (X ^ Y) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
k + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
LSeg ((X ^ Y),j) is functional Element of bool the U1 of (TOP-REAL 2)
LSeg ((X ^ Y),k) is functional Element of bool the U1 of (TOP-REAL 2)
k is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
k + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
LSeg (Y,k) is functional Element of bool the U1 of (TOP-REAL 2)
(LSeg (Y,k)) /\ (LSeg ((X /. (len X)),(Y /. 1))) is functional Element of bool the U1 of (TOP-REAL 2)
k is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
k + 2 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
LSeg (X,k) is functional Element of bool the U1 of (TOP-REAL 2)
(LSeg (X,k)) /\ (LSeg ((X /. (len X)),(Y /. 1))) is functional Element of bool the U1 of (TOP-REAL 2)
(LSeg ((X ^ Y),j)) /\ (LSeg ((X ^ Y),k)) is functional Element of bool the U1 of (TOP-REAL 2)
(len X) + (len Y) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
LSeg (X,j) is functional Element of bool the U1 of (TOP-REAL 2)
LSeg (X,k) is functional Element of bool the U1 of (TOP-REAL 2)
k - (len X) is V11() V12() ext-real set
(k + 1) - (len X) is V11() V12() ext-real set
k is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
k + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(len X) + k is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(len X) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
((len X) + 1) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
1 + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(len X) + (1 + 1) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
LSeg (Y,k) is functional Element of bool the U1 of (TOP-REAL 2)
LSeg (X,j) is functional Element of bool the U1 of (TOP-REAL 2)
(j + 1) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
1 + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
j + (1 + 1) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(len X) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
LSeg ((X ^ Y),((len X) + k)) is functional Element of bool the U1 of (TOP-REAL 2)
LSeg (Y,k) is functional Element of bool the U1 of (TOP-REAL 2)
(LSeg ((X ^ Y),j)) /\ (LSeg ((X ^ Y),k)) is functional Element of bool the U1 of (TOP-REAL 2)
dom Y is V26() V180() V181() V182() V183() V184() V185() Element of bool NAT
(len X) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
LSeg ((X ^ Y),((len X) + k)) is functional Element of bool the U1 of (TOP-REAL 2)
LSeg (Y,k) is functional Element of bool the U1 of (TOP-REAL 2)
j - (len X) is V11() V12() ext-real set
Ga is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(len X) + Ga is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
LSeg ((X ^ Y),((len X) + Ga)) is functional Element of bool the U1 of (TOP-REAL 2)
LSeg (Y,Ga) is functional Element of bool the U1 of (TOP-REAL 2)
(j + 1) - (len X) is V11() V12() ext-real set
Ga + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
X is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
Y is non empty functional bounded compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
Gauge (Y,X) is V13() non empty-yielding V16( NAT ) V17(K233( 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 K233( the U1 of (TOP-REAL 2))
len (Gauge (Y,X)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
W-min Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-bound Y is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | Y is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | Y is V13() V16( the U1 of ((TOP-REAL 2) | Y)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | Y), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | Y),REAL:]
the U1 of ((TOP-REAL 2) | Y) is non empty set
[: the U1 of ((TOP-REAL 2) | Y),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | Y),REAL:] is set
K445(((TOP-REAL 2) | Y),(proj1 | Y)) is V11() V12() ext-real Element of REAL
W-most Y is functional Element of bool the U1 of (TOP-REAL 2)
SW-corner Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-bound Y is V11() V12() ext-real Element of REAL
proj2 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | Y is V13() V16( the U1 of ((TOP-REAL 2) | Y)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | Y), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | Y),REAL:]
K445(((TOP-REAL 2) | Y),(proj2 | Y)) is V11() V12() ext-real Element of REAL
|[(W-bound Y),(S-bound Y)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NW-corner Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-bound Y is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | Y),(proj2 | Y)) is V11() V12() ext-real Element of REAL
|[(W-bound Y),(N-bound Y)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner Y),(NW-corner Y)) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner Y),(NW-corner Y))) /\ Y is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most Y) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most Y) is V13() V16( the U1 of ((TOP-REAL 2) | (W-most Y))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (W-most Y)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most Y)),REAL:]
the U1 of ((TOP-REAL 2) | (W-most Y)) is set
[: the U1 of ((TOP-REAL 2) | (W-most Y)),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (W-most Y)),REAL:] is set
K445(((TOP-REAL 2) | (W-most Y)),(proj2 | (W-most Y))) is V11() V12() ext-real Element of REAL
|[(W-bound Y),K445(((TOP-REAL 2) | (W-most Y)),(proj2 | (W-most Y)))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(W-min Y) `2 is V11() V12() ext-real Element of REAL
k is V6() V10() V11() V12() V26() cardinal ext-real non negative set
(Gauge (Y,X)) * (2,k) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
((Gauge (Y,X)) * (2,k)) `2 is V11() V12() ext-real Element of REAL
width (Gauge (Y,X)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(SW-corner Y) `2 is V11() V12() ext-real Element of REAL
(Gauge (Y,X)) * (2,2) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
((Gauge (Y,X)) * (2,2)) `2 is V11() V12() ext-real Element of REAL
(Gauge (Y,X)) * (2,1) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
((Gauge (Y,X)) * (2,1)) `2 is V11() V12() ext-real Element of REAL
k is V6() V10() V11() V12() V26() cardinal ext-real non negative set
(Gauge (Y,X)) * (2,k) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
((Gauge (Y,X)) * (2,k)) `2 is V11() V12() ext-real Element of REAL
k is V6() V10() V11() V12() V26() cardinal ext-real non negative set
(Gauge (Y,X)) * (2,k) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
((Gauge (Y,X)) * (2,k)) `2 is V11() V12() ext-real Element of REAL
(W-min Y) `1 is V11() V12() ext-real Element of REAL
k is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(Gauge (Y,X)) * (2,k) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
((Gauge (Y,X)) * (2,k)) `1 is V11() V12() ext-real Element of REAL
k + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(Gauge (Y,X)) * (2,(k + 1)) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
((Gauge (Y,X)) * (2,(k + 1))) `1 is V11() V12() ext-real Element of REAL
(len (Gauge (Y,X))) -' 1 is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
((Gauge (Y,X)) * (2,k)) `2 is V11() V12() ext-real Element of REAL
(NW-corner Y) `2 is V11() V12() ext-real Element of REAL
((Gauge (Y,X)) * (2,(k + 1))) `2 is V11() V12() ext-real Element of REAL
LSeg (((Gauge (Y,X)) * (2,k)),((Gauge (Y,X)) * (2,(k + 1)))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
cell ((Gauge (Y,X)),1,k) is functional Element of bool the U1 of (TOP-REAL 2)
v_strip ((Gauge (Y,X)),1) is functional Element of bool the U1 of (TOP-REAL 2)
h_strip ((Gauge (Y,X)),k) is functional Element of bool the U1 of (TOP-REAL 2)
(v_strip ((Gauge (Y,X)),1)) /\ (h_strip ((Gauge (Y,X)),k)) is functional 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 V179() V180() V181() V182() V183() V184() V185() Element of NAT
(Gauge (Y,X)) * ((1 + 1),k) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(Gauge (Y,X)) * ((1 + 1),(k + 1)) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (Y,X)) * ((1 + 1),k)),((Gauge (Y,X)) * ((1 + 1),(k + 1)))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
X 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~ X is non empty functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
len X is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
X . (len X) is V13() Function-like set
Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
R_Cut (X,Y) 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 (X,Y)) is functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
Rev X 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 X) is non empty functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
(Rev X) . 1 is V13() Function-like set
L_Cut ((Rev X),Y) 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)
Rev (R_Cut (X,Y)) 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~ (L_Cut ((Rev X),Y)) is functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
X 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)
Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
R_Cut (X,Y) 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)
X . 1 is V13() Function-like set
Index (Y,X) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
mid (X,1,(Index (Y,X))) 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)
<*Y*> 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 (X,1,(Index (Y,X)))) ^ <*Y*> 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)
X . 1 is V13() Function-like set
<*Y*> 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)
X . 1 is V13() Function-like set
X 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~ X is functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
R_Cut (X,Y) 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 (R_Cut (X,Y)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(R_Cut (X,Y)) /. (len (R_Cut (X,Y))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
dom (R_Cut (X,Y)) is V26() V180() V181() V182() V183() V184() V185() Element of bool NAT
(R_Cut (X,Y)) . (len (R_Cut (X,Y))) is V13() Function-like set
X is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
Y is non empty functional connected bounded compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
Upper_Seq (Y,X) 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 (Y,X)) is non empty functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
Cage (Y,X) 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 (Y,X)) is non empty functional V71( TOP-REAL 2) connected bounded being_simple_closed_curve compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
E-bound (L~ (Cage (Y,X))) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (Y,X))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | (L~ (Cage (Y,X))) is V13() V16( the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))),REAL:]
the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))),REAL:] is set
K446(((TOP-REAL 2) | (L~ (Cage (Y,X)))),(proj1 | (L~ (Cage (Y,X))))) is V11() V12() ext-real Element of REAL
E-max (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-most (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
SE-corner (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Cage (Y,X))) is V11() V12() ext-real Element of REAL
proj2 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | (L~ (Cage (Y,X))) is V13() V16( the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))),REAL:]
K445(((TOP-REAL 2) | (L~ (Cage (Y,X)))),(proj2 | (L~ (Cage (Y,X))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (Y,X)))),(S-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NE-corner (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Cage (Y,X))) is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | (L~ (Cage (Y,X)))),(proj2 | (L~ (Cage (Y,X))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (Y,X)))),(N-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Cage (Y,X)))),(NE-corner (L~ (Cage (Y,X))))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SE-corner (L~ (Cage (Y,X)))),(NE-corner (L~ (Cage (Y,X)))))) /\ (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ (Cage (Y,X)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Cage (Y,X)))) is V13() V16( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X)))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),REAL:]
the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))) is set
[: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),REAL:] is set
K446(((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),(proj2 | (E-most (L~ (Cage (Y,X)))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (Y,X)))),K446(((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),(proj2 | (E-most (L~ (Cage (Y,X))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
j is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
j `1 is V11() V12() ext-real Element of REAL
Lower_Seq (Y,X) 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)
W-min (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-bound (L~ (Cage (Y,X))) is V11() V12() ext-real Element of REAL
K445(((TOP-REAL 2) | (L~ (Cage (Y,X)))),(proj1 | (L~ (Cage (Y,X))))) is V11() V12() ext-real Element of REAL
W-most (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
SW-corner (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
|[(W-bound (L~ (Cage (Y,X)))),(S-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NW-corner (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
|[(W-bound (L~ (Cage (Y,X)))),(N-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (Y,X)))),(NW-corner (L~ (Cage (Y,X))))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Cage (Y,X)))),(NW-corner (L~ (Cage (Y,X)))))) /\ (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ (Cage (Y,X)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Cage (Y,X)))) is V13() V16( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X)))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),REAL:]
the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))) is set
[: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),REAL:] is set
K445(((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),(proj2 | (W-most (L~ (Cage (Y,X)))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (Y,X)))),K445(((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),(proj2 | (W-most (L~ (Cage (Y,X))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-max (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-most (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (Y,X)))),(SE-corner (L~ (Cage (Y,X))))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Cage (Y,X)))),(SE-corner (L~ (Cage (Y,X)))))) /\ (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (S-most (L~ (Cage (Y,X)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (S-most (L~ (Cage (Y,X)))) is V13() V16( the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (Y,X)))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (Y,X))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (Y,X))))),REAL:]
the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (Y,X))))) is set
[: the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (Y,X))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (S-most (L~ (Cage (Y,X))))),REAL:] is set
K446(((TOP-REAL 2) | (S-most (L~ (Cage (Y,X))))),(proj1 | (S-most (L~ (Cage (Y,X)))))) is V11() V12() ext-real Element of REAL
|[K446(((TOP-REAL 2) | (S-most (L~ (Cage (Y,X))))),(proj1 | (S-most (L~ (Cage (Y,X)))))),(S-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-min (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
K445(((TOP-REAL 2) | (S-most (L~ (Cage (Y,X))))),(proj1 | (S-most (L~ (Cage (Y,X)))))) is V11() V12() ext-real Element of REAL
|[K445(((TOP-REAL 2) | (S-most (L~ (Cage (Y,X))))),(proj1 | (S-most (L~ (Cage (Y,X)))))),(S-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-min (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
K445(((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),(proj2 | (E-most (L~ (Cage (Y,X)))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (Y,X)))),K445(((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),(proj2 | (E-most (L~ (Cage (Y,X))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(Upper_Seq (Y,X)) /. 1 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
dom (Upper_Seq (Y,X)) is non empty non trivial V26() V180() V181() V182() V183() V184() V185() Element of bool NAT
(Upper_Seq (Y,X)) . 1 is V13() Function-like set
R_Cut ((Upper_Seq (Y,X)),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)
<*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)
do 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 do is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
dom do is non empty non trivial V26() V180() V181() V182() V183() V184() V185() Element of bool NAT
do /. (len do) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
do . (len do) is V13() Function-like set
do /. 1 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(do /. 1) `1 is V11() V12() ext-real Element of REAL
((Upper_Seq (Y,X)) /. 1) `1 is V11() V12() ext-real Element of REAL
(W-min (L~ (Cage (Y,X)))) `1 is V11() V12() ext-real Element of REAL
(Lower_Seq (Y,X)) /. 1 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
dom (Lower_Seq (Y,X)) is non empty non trivial V26() V180() V181() V182() V183() V184() V185() Element of bool NAT
(Lower_Seq (Y,X)) . 1 is V13() Function-like set
len (Cage (Y,X)) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
rng (Cage (Y,X)) is non empty non trivial V26() set
(NE-corner (L~ (Cage (Y,X)))) `1 is V11() V12() ext-real Element of REAL
(NE-corner (L~ (Cage (Y,X)))) `2 is V11() V12() ext-real Element of REAL
{ b<sub>1</sub> where b<sub>1</sub> is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2) : ( b<sub>1</sub> `1 = E-bound (L~ (Cage (Y,X))) & b₁ `2 <= N-bound (L~ (Cage (Y,X))) & S-bound (L~ (Cage (Y,X))) <= b<sub>1</sub> `2 ) } is set
(E-max (L~ (Cage (Y,X)))) `2 is V11() V12() ext-real Element of REAL
(E-max (L~ (Cage (Y,X)))) `1 is V11() V12() ext-real Element of REAL
rng (Lower_Seq (Y,X)) is V26() set
R_Cut ((Lower_Seq (Y,X)),(S-max (L~ (Cage (Y,X))))) 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)
(S-max (L~ (Cage (Y,X)))) .. (Lower_Seq (Y,X)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
mid ((Lower_Seq (Y,X)),1,((S-max (L~ (Cage (Y,X)))) .. (Lower_Seq (Y,X)))) 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 (R_Cut ((Lower_Seq (Y,X)),(S-max (L~ (Cage (Y,X)))))) is V26() set
{(NE-corner (L~ (Cage (Y,X))))} is non empty trivial functional V26() V30() 1 -element set
<*(NE-corner (L~ (Cage (Y,X))))*> 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)
rng <*(NE-corner (L~ (Cage (Y,X))))*> is trivial V26() set
Rev (R_Cut ((Lower_Seq (Y,X)),(S-max (L~ (Cage (Y,X)))))) 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 (Rev (R_Cut ((Lower_Seq (Y,X)),(S-max (L~ (Cage (Y,X))))))) is V26() set
(Rev (R_Cut ((Lower_Seq (Y,X)),(S-max (L~ (Cage (Y,X))))))) ^ <*(NE-corner (L~ (Cage (Y,X))))*> 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 ((Rev (R_Cut ((Lower_Seq (Y,X)),(S-max (L~ (Cage (Y,X))))))) ^ <*(NE-corner (L~ (Cage (Y,X))))*>) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
((Rev (R_Cut ((Lower_Seq (Y,X)),(S-max (L~ (Cage (Y,X))))))) ^ <*(NE-corner (L~ (Cage (Y,X))))*>) /. (len ((Rev (R_Cut ((Lower_Seq (Y,X)),(S-max (L~ (Cage (Y,X))))))) ^ <*(NE-corner (L~ (Cage (Y,X))))*>)) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(((Rev (R_Cut ((Lower_Seq (Y,X)),(S-max (L~ (Cage (Y,X))))))) ^ <*(NE-corner (L~ (Cage (Y,X))))*>) /. (len ((Rev (R_Cut ((Lower_Seq (Y,X)),(S-max (L~ (Cage (Y,X))))))) ^ <*(NE-corner (L~ (Cage (Y,X))))*>))) `2 is V11() V12() ext-real Element of REAL
len (Rev (R_Cut ((Lower_Seq (Y,X)),(S-max (L~ (Cage (Y,X))))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(len (Rev (R_Cut ((Lower_Seq (Y,X)),(S-max (L~ (Cage (Y,X)))))))) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
((Rev (R_Cut ((Lower_Seq (Y,X)),(S-max (L~ (Cage (Y,X))))))) ^ <*(NE-corner (L~ (Cage (Y,X))))*>) /. ((len (Rev (R_Cut ((Lower_Seq (Y,X)),(S-max (L~ (Cage (Y,X)))))))) + 1) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(((Rev (R_Cut ((Lower_Seq (Y,X)),(S-max (L~ (Cage (Y,X))))))) ^ <*(NE-corner (L~ (Cage (Y,X))))*>) /. ((len (Rev (R_Cut ((Lower_Seq (Y,X)),(S-max (L~ (Cage (Y,X)))))))) + 1)) `2 is V11() V12() ext-real Element of REAL
(NE-corner (L~ (Cage (Y,X)))) `2 is V11() V12() ext-real Element of REAL
(E-min (L~ (Cage (Y,X)))) `2 is V11() V12() ext-real Element of REAL
0 + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
Index ((S-max (L~ (Cage (Y,X)))),(Lower_Seq (Y,X))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(Index ((S-max (L~ (Cage (Y,X)))),(Lower_Seq (Y,X)))) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
L~ (Lower_Seq (Y,X)) is non empty functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
<*(S-max (L~ (Cage (Y,X))))*> 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)
(E-max (L~ (Cage (Y,X)))) `2 is V11() V12() ext-real Element of REAL
len (R_Cut ((Lower_Seq (Y,X)),(S-max (L~ (Cage (Y,X)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(len (R_Cut ((Lower_Seq (Y,X)),(S-max (L~ (Cage (Y,X))))))) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
((Index ((S-max (L~ (Cage (Y,X)))),(Lower_Seq (Y,X)))) + 1) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
1 + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
do 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 do 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)
dom (Rev do) is non empty non trivial V26() V180() V181() V182() V183() V184() V185() Element of bool NAT
((Rev (R_Cut ((Lower_Seq (Y,X)),(S-max (L~ (Cage (Y,X))))))) ^ <*(NE-corner (L~ (Cage (Y,X))))*>) /. 1 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(Rev do) /. 1 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(R_Cut ((Lower_Seq (Y,X)),(S-max (L~ (Cage (Y,X)))))) /. (len (R_Cut ((Lower_Seq (Y,X)),(S-max (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(((Rev (R_Cut ((Lower_Seq (Y,X)),(S-max (L~ (Cage (Y,X))))))) ^ <*(NE-corner (L~ (Cage (Y,X))))*>) /. 1) `2 is V11() V12() ext-real Element of REAL
len (Lower_Seq (Y,X)) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
len (Rev do) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(Rev do) /. (len (Rev do)) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
len do is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(Rev do) /. (len do) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
do /. 1 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
((Rev do) /. (len (Rev do))) `1 is V11() V12() ext-real Element of REAL
(NE-corner (L~ (Cage (Y,X)))) `1 is V11() V12() ext-real Element of REAL
<*(NE-corner (L~ (Cage (Y,X))))*> /. 1 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(<*(NE-corner (L~ (Cage (Y,X))))*> /. 1) `1 is V11() V12() ext-real Element of REAL
L~ do is non empty functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
L~ ((Rev (R_Cut ((Lower_Seq (Y,X)),(S-max (L~ (Cage (Y,X))))))) ^ <*(NE-corner (L~ (Cage (Y,X))))*>) is functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
go is set
L~ (Rev do) is non empty functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
LSeg (((Rev do) /. (len (Rev do))),(NE-corner (L~ (Cage (Y,X))))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(L~ (Rev do)) \/ (LSeg (((Rev do) /. (len (Rev do))),(NE-corner (L~ (Cage (Y,X)))))) is non empty functional Element of bool the U1 of (TOP-REAL 2)
L~ do is non empty functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
len (Upper_Seq (Y,X)) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
do is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(L~ (Upper_Seq (Y,X))) /\ (L~ (Lower_Seq (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
{(W-min (L~ (Cage (Y,X)))),(E-max (L~ (Cage (Y,X))))} is non empty functional V26() V30() set
(Lower_Seq (Y,X)) /. (len (Lower_Seq (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
L~ (R_Cut ((Lower_Seq (Y,X)),(S-max (L~ (Cage (Y,X)))))) is functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
(Lower_Seq (Y,X)) . (len (Lower_Seq (Y,X))) is V13() Function-like set
(S-min (L~ (Cage (Y,X)))) `1 is V11() V12() ext-real Element of REAL
(S-max (L~ (Cage (Y,X)))) `1 is V11() V12() ext-real Element of REAL
(Upper_Seq (Y,X)) /. (len (Upper_Seq (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
L~ (R_Cut ((Upper_Seq (Y,X)),j)) is functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
(Upper_Seq (Y,X)) . (len (Upper_Seq (Y,X))) is V13() Function-like set
do `2 is V11() V12() ext-real Element of REAL
(E-max (L~ (Cage (Y,X)))) `1 is V11() V12() ext-real Element of REAL
do `1 is V11() V12() ext-real Element of REAL
(L~ (Upper_Seq (Y,X))) \/ (L~ (Lower_Seq (Y,X))) is non empty functional Element of bool the U1 of (TOP-REAL 2)
(Upper_Seq (Y,X)) /. (len (Upper_Seq (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
L~ (R_Cut ((Upper_Seq (Y,X)),j)) is functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
(Upper_Seq (Y,X)) . (len (Upper_Seq (Y,X))) is V13() Function-like set
(E-min (L~ (Cage (Y,X)))) `2 is V11() V12() ext-real Element of REAL
R_Cut ((Lower_Seq (Y,X)),(S-max (L~ (Cage (Y,X))))) 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)
Rev (R_Cut ((Lower_Seq (Y,X)),(S-max (L~ (Cage (Y,X)))))) 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~ (Lower_Seq (Y,X)) is non empty functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
<*(S-max (L~ (Cage (Y,X))))*> 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)
(E-max (L~ (Cage (Y,X)))) `2 is V11() V12() ext-real Element of REAL
do 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 do 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)
dom (Rev do) is non empty non trivial V26() V180() V181() V182() V183() V184() V185() Element of bool NAT
(Rev (R_Cut ((Lower_Seq (Y,X)),(S-max (L~ (Cage (Y,X))))))) /. 1 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
len (R_Cut ((Lower_Seq (Y,X)),(S-max (L~ (Cage (Y,X)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(R_Cut ((Lower_Seq (Y,X)),(S-max (L~ (Cage (Y,X)))))) /. (len (R_Cut ((Lower_Seq (Y,X)),(S-max (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
((Rev (R_Cut ((Lower_Seq (Y,X)),(S-max (L~ (Cage (Y,X))))))) /. 1) `2 is V11() V12() ext-real Element of REAL
len do is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
len (Rev (R_Cut ((Lower_Seq (Y,X)),(S-max (L~ (Cage (Y,X))))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
len (Rev do) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(Rev do) /. (len (Rev do)) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(Rev do) /. (len do) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
do /. 1 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(Rev (R_Cut ((Lower_Seq (Y,X)),(S-max (L~ (Cage (Y,X))))))) /. (len (Rev (R_Cut ((Lower_Seq (Y,X)),(S-max (L~ (Cage (Y,X)))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
((Rev (R_Cut ((Lower_Seq (Y,X)),(S-max (L~ (Cage (Y,X))))))) /. (len (Rev (R_Cut ((Lower_Seq (Y,X)),(S-max (L~ (Cage (Y,X))))))))) `2 is V11() V12() ext-real Element of REAL
L~ do is non empty functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
L~ (Rev (R_Cut ((Lower_Seq (Y,X)),(S-max (L~ (Cage (Y,X))))))) is functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
go is set
do is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
L~ do is non empty functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
len (Upper_Seq (Y,X)) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
len (Lower_Seq (Y,X)) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(L~ (Upper_Seq (Y,X))) /\ (L~ (Lower_Seq (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
{(W-min (L~ (Cage (Y,X)))),(E-max (L~ (Cage (Y,X))))} is non empty functional V26() V30() set
(Lower_Seq (Y,X)) /. (len (Lower_Seq (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
L~ (R_Cut ((Lower_Seq (Y,X)),(S-max (L~ (Cage (Y,X)))))) is functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
(Lower_Seq (Y,X)) . (len (Lower_Seq (Y,X))) is V13() Function-like set
(S-min (L~ (Cage (Y,X)))) `1 is V11() V12() ext-real Element of REAL
(S-max (L~ (Cage (Y,X)))) `1 is V11() V12() ext-real Element of REAL
(Upper_Seq (Y,X)) /. (len (Upper_Seq (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
L~ (R_Cut ((Upper_Seq (Y,X)),j)) is functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
(Upper_Seq (Y,X)) . (len (Upper_Seq (Y,X))) is V13() Function-like set
X is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
Y is non empty functional connected bounded compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
Lower_Seq (Y,X) 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 (Y,X)) is non empty functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
Cage (Y,X) 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 (Y,X)) is non empty functional V71( TOP-REAL 2) connected bounded being_simple_closed_curve compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
W-bound (L~ (Cage (Y,X))) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (Y,X))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | (L~ (Cage (Y,X))) is V13() V16( the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))),REAL:]
the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))),REAL:] is set
K445(((TOP-REAL 2) | (L~ (Cage (Y,X)))),(proj1 | (L~ (Cage (Y,X))))) is V11() V12() ext-real Element of REAL
W-min (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-most (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
SW-corner (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Cage (Y,X))) is V11() V12() ext-real Element of REAL
proj2 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | (L~ (Cage (Y,X))) is V13() V16( the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))),REAL:]
K445(((TOP-REAL 2) | (L~ (Cage (Y,X)))),(proj2 | (L~ (Cage (Y,X))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (Y,X)))),(S-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NW-corner (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Cage (Y,X))) is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | (L~ (Cage (Y,X)))),(proj2 | (L~ (Cage (Y,X))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (Y,X)))),(N-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (Y,X)))),(NW-corner (L~ (Cage (Y,X))))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Cage (Y,X)))),(NW-corner (L~ (Cage (Y,X)))))) /\ (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ (Cage (Y,X)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Cage (Y,X)))) is V13() V16( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X)))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),REAL:]
the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))) is set
[: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),REAL:] is set
K445(((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),(proj2 | (W-most (L~ (Cage (Y,X)))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (Y,X)))),K445(((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),(proj2 | (W-most (L~ (Cage (Y,X))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
j is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
j `1 is V11() V12() ext-real Element of REAL
Upper_Seq (Y,X) 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)
E-max (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Cage (Y,X))) is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | (L~ (Cage (Y,X)))),(proj1 | (L~ (Cage (Y,X))))) is V11() V12() ext-real Element of REAL
E-most (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
SE-corner (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
|[(E-bound (L~ (Cage (Y,X)))),(S-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NE-corner (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
|[(E-bound (L~ (Cage (Y,X)))),(N-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Cage (Y,X)))),(NE-corner (L~ (Cage (Y,X))))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SE-corner (L~ (Cage (Y,X)))),(NE-corner (L~ (Cage (Y,X)))))) /\ (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ (Cage (Y,X)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Cage (Y,X)))) is V13() V16( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X)))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),REAL:]
the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))) is set
[: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),REAL:] is set
K446(((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),(proj2 | (E-most (L~ (Cage (Y,X)))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (Y,X)))),K446(((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),(proj2 | (E-most (L~ (Cage (Y,X))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-min (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-most (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
LSeg ((NW-corner (L~ (Cage (Y,X)))),(NE-corner (L~ (Cage (Y,X))))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((NW-corner (L~ (Cage (Y,X)))),(NE-corner (L~ (Cage (Y,X)))))) /\ (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (N-most (L~ (Cage (Y,X)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most (L~ (Cage (Y,X)))) is V13() V16( the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (Y,X)))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (Y,X))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (Y,X))))),REAL:]
the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (Y,X))))) is set
[: the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (Y,X))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (N-most (L~ (Cage (Y,X))))),REAL:] is set
K445(((TOP-REAL 2) | (N-most (L~ (Cage (Y,X))))),(proj1 | (N-most (L~ (Cage (Y,X)))))) is V11() V12() ext-real Element of REAL
|[K445(((TOP-REAL 2) | (N-most (L~ (Cage (Y,X))))),(proj1 | (N-most (L~ (Cage (Y,X)))))),(N-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-max (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
K446(((TOP-REAL 2) | (N-most (L~ (Cage (Y,X))))),(proj1 | (N-most (L~ (Cage (Y,X)))))) is V11() V12() ext-real Element of REAL
|[K446(((TOP-REAL 2) | (N-most (L~ (Cage (Y,X))))),(proj1 | (N-most (L~ (Cage (Y,X)))))),(N-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-max (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
K446(((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),(proj2 | (W-most (L~ (Cage (Y,X)))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (Y,X)))),K446(((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),(proj2 | (W-most (L~ (Cage (Y,X))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(Lower_Seq (Y,X)) /. 1 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
dom (Lower_Seq (Y,X)) is non empty non trivial V26() V180() V181() V182() V183() V184() V185() Element of bool NAT
(Lower_Seq (Y,X)) . 1 is V13() Function-like set
R_Cut ((Lower_Seq (Y,X)),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)
do 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 do is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
dom do is non empty non trivial V26() V180() V181() V182() V183() V184() V185() Element of bool NAT
do /. (len do) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
do . (len do) is V13() Function-like set
Rev do 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)
<*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)
go 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)
go /. 1 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
len go is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
go /. (len go) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
go /. (len do) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
do /. 1 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(do /. 1) `1 is V11() V12() ext-real Element of REAL
((Lower_Seq (Y,X)) /. 1) `1 is V11() V12() ext-real Element of REAL
(E-max (L~ (Cage (Y,X)))) `1 is V11() V12() ext-real Element of REAL
(Upper_Seq (Y,X)) /. 1 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
dom (Upper_Seq (Y,X)) is non empty non trivial V26() V180() V181() V182() V183() V184() V185() Element of bool NAT
(Upper_Seq (Y,X)) . 1 is V13() Function-like set
L~ go is non empty functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
L~ do is non empty functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
len (Cage (Y,X)) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
rng (Cage (Y,X)) is non empty non trivial V26() set
(SW-corner (L~ (Cage (Y,X)))) `1 is V11() V12() ext-real Element of REAL
(SW-corner (L~ (Cage (Y,X)))) `2 is V11() V12() ext-real Element of REAL
{ b₁ where b₁ is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2) : ( b₁ `1 = W-bound (L~ (Cage (Y,X))) & b<sub>1</sub> `2 <= N-bound (L~ (Cage (Y,X))) & S-bound (L~ (Cage (Y,X))) <= b₁ `2 ) } is set
(W-min (L~ (Cage (Y,X)))) `2 is V11() V12() ext-real Element of REAL
(W-min (L~ (Cage (Y,X)))) `1 is V11() V12() ext-real Element of REAL
rng (Upper_Seq (Y,X)) is V26() set
R_Cut ((Upper_Seq (Y,X)),(N-min (L~ (Cage (Y,X))))) 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-min (L~ (Cage (Y,X)))) .. (Upper_Seq (Y,X)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
mid ((Upper_Seq (Y,X)),1,((N-min (L~ (Cage (Y,X)))) .. (Upper_Seq (Y,X)))) 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 (R_Cut ((Upper_Seq (Y,X)),(N-min (L~ (Cage (Y,X)))))) is V26() set
{(SW-corner (L~ (Cage (Y,X))))} is non empty trivial functional V26() V30() 1 -element set
<*(SW-corner (L~ (Cage (Y,X))))*> 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)
rng <*(SW-corner (L~ (Cage (Y,X))))*> is trivial V26() set
Rev (R_Cut ((Upper_Seq (Y,X)),(N-min (L~ (Cage (Y,X)))))) 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 (Rev (R_Cut ((Upper_Seq (Y,X)),(N-min (L~ (Cage (Y,X))))))) is V26() set
(Rev (R_Cut ((Upper_Seq (Y,X)),(N-min (L~ (Cage (Y,X))))))) ^ <*(SW-corner (L~ (Cage (Y,X))))*> 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-max (L~ (Cage (Y,X)))) `2 is V11() V12() ext-real Element of REAL
L~ (Upper_Seq (Y,X)) is non empty functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
<*(N-min (L~ (Cage (Y,X))))*> 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)
(W-min (L~ (Cage (Y,X)))) `2 is V11() V12() ext-real Element of REAL
go 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 go 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 (Rev go) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(Rev go) /. (len (Rev go)) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
len go is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(Rev go) /. (len go) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
go /. 1 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
((Rev go) /. (len (Rev go))) `1 is V11() V12() ext-real Element of REAL
(SW-corner (L~ (Cage (Y,X)))) `1 is V11() V12() ext-real Element of REAL
<*(SW-corner (L~ (Cage (Y,X))))*> /. 1 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(<*(SW-corner (L~ (Cage (Y,X))))*> /. 1) `1 is V11() V12() ext-real Element of REAL
do 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 do 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)
L~ (Rev do) is functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
L~ do is functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
L~ (Rev go) is non empty functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
LSeg (((Rev go) /. (len (Rev go))),(SW-corner (L~ (Cage (Y,X))))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(L~ (Rev go)) \/ (LSeg (((Rev go) /. (len (Rev go))),(SW-corner (L~ (Cage (Y,X)))))) is non empty functional 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 V179() V180() V181() V182() V183() V184() V185() Element of NAT
Index ((N-min (L~ (Cage (Y,X)))),(Upper_Seq (Y,X))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(Index ((N-min (L~ (Cage (Y,X)))),(Upper_Seq (Y,X)))) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
len do is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
len (Rev (R_Cut ((Upper_Seq (Y,X)),(N-min (L~ (Cage (Y,X))))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(len (Rev (R_Cut ((Upper_Seq (Y,X)),(N-min (L~ (Cage (Y,X)))))))) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
len (R_Cut ((Upper_Seq (Y,X)),(N-min (L~ (Cage (Y,X)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(len (R_Cut ((Upper_Seq (Y,X)),(N-min (L~ (Cage (Y,X))))))) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
((Index ((N-min (L~ (Cage (Y,X)))),(Upper_Seq (Y,X)))) + 1) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
1 + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
len (Rev do) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(Rev do) /. 1 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
do /. (len do) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
len (Upper_Seq (Y,X)) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
dom (Rev go) is non empty non trivial V26() V180() V181() V182() V183() V184() V185() Element of bool NAT
do /. 1 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(Rev go) /. 1 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(R_Cut ((Upper_Seq (Y,X)),(N-min (L~ (Cage (Y,X)))))) /. (len (R_Cut ((Upper_Seq (Y,X)),(N-min (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(do /. 1) `2 is V11() V12() ext-real Element of REAL
(do /. (len do)) `2 is V11() V12() ext-real Element of REAL
do /. ((len (Rev (R_Cut ((Upper_Seq (Y,X)),(N-min (L~ (Cage (Y,X)))))))) + 1) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(do /. ((len (Rev (R_Cut ((Upper_Seq (Y,X)),(N-min (L~ (Cage (Y,X)))))))) + 1)) `2 is V11() V12() ext-real Element of REAL
(SW-corner (L~ (Cage (Y,X)))) `2 is V11() V12() ext-real Element of REAL
len (Lower_Seq (Y,X)) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(Rev do) /. (len (Rev do)) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(Rev do) /. (len do) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W2 is set
L~ go is non empty functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
pion is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(L~ (Lower_Seq (Y,X))) /\ (L~ (Upper_Seq (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
{(E-max (L~ (Cage (Y,X)))),(W-min (L~ (Cage (Y,X))))} is non empty functional V26() V30() set
(Upper_Seq (Y,X)) /. (len (Upper_Seq (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
L~ (R_Cut ((Upper_Seq (Y,X)),(N-min (L~ (Cage (Y,X)))))) is functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
(Upper_Seq (Y,X)) . (len (Upper_Seq (Y,X))) is V13() Function-like set
(N-max (L~ (Cage (Y,X)))) `1 is V11() V12() ext-real Element of REAL
(N-min (L~ (Cage (Y,X)))) `1 is V11() V12() ext-real Element of REAL
(Lower_Seq (Y,X)) /. (len (Lower_Seq (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
L~ (R_Cut ((Lower_Seq (Y,X)),j)) is functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
(Lower_Seq (Y,X)) . (len (Lower_Seq (Y,X))) is V13() Function-like set
pion `2 is V11() V12() ext-real Element of REAL
(W-min (L~ (Cage (Y,X)))) `1 is V11() V12() ext-real Element of REAL
pion `1 is V11() V12() ext-real Element of REAL
(L~ (Lower_Seq (Y,X))) \/ (L~ (Upper_Seq (Y,X))) is non empty functional Element of bool the U1 of (TOP-REAL 2)
(Lower_Seq (Y,X)) /. (len (Lower_Seq (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
L~ (R_Cut ((Lower_Seq (Y,X)),j)) is functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
(Lower_Seq (Y,X)) . (len (Lower_Seq (Y,X))) is V13() Function-like set
R_Cut ((Upper_Seq (Y,X)),(N-min (L~ (Cage (Y,X))))) 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)
(W-max (L~ (Cage (Y,X)))) `2 is V11() V12() ext-real Element of REAL
L~ (Upper_Seq (Y,X)) is non empty functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
<*(N-min (L~ (Cage (Y,X))))*> 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)
(W-min (L~ (Cage (Y,X)))) `2 is V11() V12() ext-real Element of REAL
go 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 go is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
len (R_Cut ((Upper_Seq (Y,X)),(N-min (L~ (Cage (Y,X)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(R_Cut ((Upper_Seq (Y,X)),(N-min (L~ (Cage (Y,X)))))) /. (len (R_Cut ((Upper_Seq (Y,X)),(N-min (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
((R_Cut ((Upper_Seq (Y,X)),(N-min (L~ (Cage (Y,X)))))) /. (len (R_Cut ((Upper_Seq (Y,X)),(N-min (L~ (Cage (Y,X)))))))) `2 is V11() V12() ext-real Element of REAL
go /. 1 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(R_Cut ((Upper_Seq (Y,X)),(N-min (L~ (Cage (Y,X)))))) /. 1 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
((R_Cut ((Upper_Seq (Y,X)),(N-min (L~ (Cage (Y,X)))))) /. 1) `2 is V11() V12() ext-real Element of REAL
L~ (R_Cut ((Upper_Seq (Y,X)),(N-min (L~ (Cage (Y,X)))))) is functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
do is set
len (Lower_Seq (Y,X)) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
len (Upper_Seq (Y,X)) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
L~ go is non empty functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
m is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(L~ (Lower_Seq (Y,X))) /\ (L~ (Upper_Seq (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
{(E-max (L~ (Cage (Y,X)))),(W-min (L~ (Cage (Y,X))))} is non empty functional V26() V30() set
(Upper_Seq (Y,X)) /. (len (Upper_Seq (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(Upper_Seq (Y,X)) . (len (Upper_Seq (Y,X))) is V13() Function-like set
(N-max (L~ (Cage (Y,X)))) `1 is V11() V12() ext-real Element of REAL
(N-min (L~ (Cage (Y,X)))) `1 is V11() V12() ext-real Element of REAL
(Lower_Seq (Y,X)) /. (len (Lower_Seq (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
L~ (R_Cut ((Lower_Seq (Y,X)),j)) is functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
(Lower_Seq (Y,X)) . (len (Lower_Seq (Y,X))) is V13() Function-like set
X is V13() non empty-yielding V16( NAT ) V17(K233( 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 K233( the U1 of (TOP-REAL 2))
Y 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 Y is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
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)
Y ^ 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)
k is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
left_cell ((Y ^ j),k,X) is functional Element of bool the U1 of (TOP-REAL 2)
left_cell (Y,k,X) is functional Element of bool the U1 of (TOP-REAL 2)
right_cell ((Y ^ j),k,X) is functional Element of bool the U1 of (TOP-REAL 2)
right_cell (Y,k,X) is functional Element of bool the U1 of (TOP-REAL 2)
k + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(Y ^ j) | (len Y) 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 j is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(len Y) + (len j) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
len (Y ^ j) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
X is set
Y is V13() V16( NAT ) V17(X) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of X
len Y is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
j is V13() V16( NAT ) V17(X) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of X
Y ^' j is V13() V16( NAT ) V17(X) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of X
k is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(Y ^' j) | k is V13() V16( NAT ) V17(X) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of X
Y | k is V13() V16( NAT ) V17(X) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of X
len (Y | k) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
0 + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
len j is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
k + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(len Y) + (len j) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
len (Y ^' j) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(len (Y ^' j)) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
len ((Y ^' j) | k) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
dom ((Y ^' j) | k) is V26() V180() V181() V182() V183() V184() V185() Element of bool NAT
Seg k is V26() k -element V180() V181() V182() V183() V184() V185() Element of bool NAT
k is V6() V10() V11() V12() V26() cardinal ext-real non negative set
((Y ^' j) | k) . k is set
(Y ^' j) | (Seg k) is V13() V16( NAT ) V17(X) Function-like V26() FinSequence-like FinSubsequence-like Element of bool [:NAT,X:]
[:NAT,X:] is set
bool [:NAT,X:] is set
((Y ^' j) | (Seg k)) . k is set
(Y ^' j) . k is set
Y . k is set
Y | (Seg k) is V13() V16( NAT ) V17(X) Function-like V26() FinSequence-like FinSubsequence-like Element of bool [:NAT,X:]
(Y | (Seg k)) . k is set
(Y | k) . k is set
X is set
Y is V13() V16( NAT ) V17(X) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of X
len Y is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
j is V13() V16( NAT ) V17(X) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of X
Y ^' j is V13() V16( NAT ) V17(X) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of X
(Y ^' j) | (len Y) is V13() V16( NAT ) V17(X) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of X
Y | (len Y) is V13() V16( NAT ) V17(X) Function-like V26() FinSequence-like FinSubsequence-like FinSequence of X
Seg (len Y) is V26() len Y -element V180() V181() V182() V183() V184() V185() Element of bool NAT
Y | (Seg (len Y)) is V13() V16( NAT ) V17(X) Function-like V26() FinSequence-like FinSubsequence-like Element of bool [:NAT,X:]
[:NAT,X:] is set
bool [:NAT,X:] is set
X is V13() non empty-yielding V16( NAT ) V17(K233( 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 K233( the U1 of (TOP-REAL 2))
Y 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 Y is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
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)
Y ^' 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)
k is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
left_cell ((Y ^' j),k,X) is functional Element of bool the U1 of (TOP-REAL 2)
left_cell (Y,k,X) is functional Element of bool the U1 of (TOP-REAL 2)
right_cell ((Y ^' j),k,X) is functional Element of bool the U1 of (TOP-REAL 2)
right_cell (Y,k,X) is functional Element of bool the U1 of (TOP-REAL 2)
k + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(Y ^' j) | (len Y) 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 (Y ^' j) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
X is V13() non empty-yielding V16( NAT ) V17(K233( 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 K233( the U1 of (TOP-REAL 2))
Y 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 Y is V26() set
j is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
j .. Y is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
R_Cut (Y,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)
k is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
left_cell ((R_Cut (Y,j)),k,X) is functional Element of bool the U1 of (TOP-REAL 2)
left_cell (Y,k,X) is functional Element of bool the U1 of (TOP-REAL 2)
right_cell ((R_Cut (Y,j)),k,X) is functional Element of bool the U1 of (TOP-REAL 2)
right_cell (Y,k,X) is functional Element of bool the U1 of (TOP-REAL 2)
Y | (j .. Y) 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)
mid (Y,1,(j .. Y)) 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)
k + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
len Y is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
X is V13() non empty-yielding V16( NAT ) V17(K233( 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 K233( the U1 of (TOP-REAL 2))
Y 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)
j is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
j .. Y is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
Y -: 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)
k is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
left_cell ((Y -: j),k,X) is functional Element of bool the U1 of (TOP-REAL 2)
left_cell (Y,k,X) is functional Element of bool the U1 of (TOP-REAL 2)
right_cell ((Y -: j),k,X) is functional Element of bool the U1 of (TOP-REAL 2)
right_cell (Y,k,X) is functional Element of bool the U1 of (TOP-REAL 2)
k + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
Y | (j .. Y) 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 Y is V26() set
len Y is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
rng Y is V26() set
X 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)
Y 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 X is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
X /. (len X) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
Y /. 1 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
L~ X is functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
L~ Y is functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
(L~ X) /\ (L~ Y) is functional Element of bool the U1 of (TOP-REAL 2)
{(Y /. 1)} is non empty trivial functional V26() V30() 1 -element set
X ^' Y 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)
k is V6() V10() V11() V12() V26() cardinal ext-real non negative set
j is V6() V10() V11() V12() V26() cardinal ext-real non negative set
j + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
LSeg ((X ^' Y),j) is functional Element of bool the U1 of (TOP-REAL 2)
LSeg (X,j) is functional Element of bool the U1 of (TOP-REAL 2)
LSeg ((X ^' Y),k) is functional Element of bool the U1 of (TOP-REAL 2)
LSeg (X,k) is functional Element of bool the U1 of (TOP-REAL 2)
k is V6() V10() V11() V12() V26() cardinal ext-real non negative set
(len X) + k is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
len Y is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
k + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
len (X ^' Y) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(len (X ^' Y)) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(len X) + (len Y) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
Ga is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
Ga + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(len X) + (Ga + 1) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(len X) + Ga is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
LSeg ((X ^' Y),((len X) + Ga)) is functional Element of bool the U1 of (TOP-REAL 2)
LSeg (Y,(Ga + 1)) is functional Element of bool the U1 of (TOP-REAL 2)
LSeg ((X ^' Y),k) is functional Element of bool the U1 of (TOP-REAL 2)
dom X is V26() V180() V181() V182() V183() V184() V185() Element of bool NAT
LSeg ((X ^' Y),j) is functional Element of bool the U1 of (TOP-REAL 2)
LSeg (X,j) is functional Element of bool the U1 of (TOP-REAL 2)
(LSeg ((X ^' Y),j)) /\ (LSeg ((X ^' Y),k)) is functional Element of bool the U1 of (TOP-REAL 2)
US is set
(len X) + 0 is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
0 + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
US is V6() V10() V11() V12() V26() cardinal ext-real non negative set
(len X) + US is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
LS is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
LS + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(len X) + (LS + 1) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(LS + 1) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(len X) + LS is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
LSeg ((X ^' Y),((len X) + LS)) is functional Element of bool the U1 of (TOP-REAL 2)
LSeg (Y,(LS + 1)) is functional Element of bool the U1 of (TOP-REAL 2)
LSeg ((X ^' Y),j) is functional Element of bool the U1 of (TOP-REAL 2)
LSeg ((X ^' Y),j) is functional Element of bool the U1 of (TOP-REAL 2)
LSeg ((X ^' Y),j) is functional Element of bool the U1 of (TOP-REAL 2)
k + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
len (X ^' Y) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
LSeg ((X ^' Y),k) is functional Element of bool the U1 of (TOP-REAL 2)
LSeg ((X ^' Y),j) is functional Element of bool the U1 of (TOP-REAL 2)
LSeg ((X ^' Y),j) is functional Element of bool the U1 of (TOP-REAL 2)
LSeg ((X ^' Y),k) is functional Element of bool the U1 of (TOP-REAL 2)
k + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
len (X ^' Y) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
LSeg ((X ^' Y),j) is functional Element of bool the U1 of (TOP-REAL 2)
LSeg ((X ^' Y),k) is functional Element of bool the U1 of (TOP-REAL 2)
LSeg ((X ^' Y),j) is functional Element of bool the U1 of (TOP-REAL 2)
LSeg ((X ^' Y),k) is functional Element of bool the U1 of (TOP-REAL 2)
LSeg ((X ^' Y),j) is functional Element of bool the U1 of (TOP-REAL 2)
LSeg ((X ^' Y),k) is functional Element of bool the U1 of (TOP-REAL 2)
LSeg ((X ^' Y),j) is functional Element of bool the U1 of (TOP-REAL 2)
LSeg ((X ^' Y),k) is functional Element of bool the U1 of (TOP-REAL 2)
X 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)
Y 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 X is V26() set
rng Y is V26() set
(rng X) /\ (rng Y) is V26() set
Y /. 1 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
{(Y /. 1)} is non empty trivial functional V26() V30() 1 -element set
X ^' Y 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 (X ^' Y) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(len (X ^' Y)) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
len X is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
len Y is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(len X) + (len Y) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
j is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
dom (X ^' Y) is V26() V180() V181() V182() V183() V184() V185() Element of bool NAT
k is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(X ^' Y) /. j is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(X ^' Y) /. k is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(len X) + 0 is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
dom Y is V26() V180() V181() V182() V183() V184() V185() Element of bool NAT
dom X is V26() V180() V181() V182() V183() V184() V185() Element of bool NAT
X /. k is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
X /. j is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
k is V6() V10() V11() V12() V26() cardinal ext-real non negative set
(len X) + k is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
Ga is V6() V10() V11() V12() V26() cardinal ext-real non negative set
(len X) + Ga is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
LS is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
0 + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
LS + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
US is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
US + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
Y /. (LS + 1) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
Y /. (US + 1) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
dom X is V26() V180() V181() V182() V183() V184() V185() Element of bool NAT
X /. j is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
k is V6() V10() V11() V12() V26() cardinal ext-real non negative set
(len X) + k is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
Ga is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
0 + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
Ga + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
Y /. (Ga + 1) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
dom X is V26() V180() V181() V182() V183() V184() V185() Element of bool NAT
X /. k is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
k is V6() V10() V11() V12() V26() cardinal ext-real non negative set
(len X) + k is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
Ga is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
0 + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
Ga + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
Y /. (Ga + 1) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
X 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 X is V26() set
X . 1 is V13() Function-like set
Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
Index (Y,X) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(Index (Y,X)) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
Y .. X is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
X . (Y .. X) is V13() Function-like set
len X is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
X is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
Y is non empty functional connected bounded compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
Gauge (Y,X) is V13() non empty-yielding V16( NAT ) V17(K233( 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 K233( the U1 of (TOP-REAL 2))
len (Gauge (Y,X)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
width (Gauge (Y,X)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
Upper_Seq (Y,X) 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 (Y,X)) is non empty functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
Lower_Seq (Y,X) 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 (Y,X)) is non empty functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
j is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
k is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
k is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(Gauge (Y,X)) * (j,k) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(Gauge (Y,X)) * (j,k) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
[j,k] is non empty set
{j,k} is non empty V26() V30() V180() V181() V182() V183() V184() V185() set
{j} is non empty trivial V26() V30() 1 -element V180() V181() V182() V183() V184() V185() set
{{j,k},{j}} is non empty V26() V30() set
Indices (Gauge (Y,X)) is set
(L~ (Upper_Seq (Y,X))) /\ (L~ (Lower_Seq (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
Cage (Y,X) 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 (Y,X)) is non empty functional V71( TOP-REAL 2) connected bounded being_simple_closed_curve compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
W-min (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-bound (L~ (Cage (Y,X))) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (Y,X))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | (L~ (Cage (Y,X))) is V13() V16( the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))),REAL:]
the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))),REAL:] is set
K445(((TOP-REAL 2) | (L~ (Cage (Y,X)))),(proj1 | (L~ (Cage (Y,X))))) is V11() V12() ext-real Element of REAL
W-most (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
SW-corner (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Cage (Y,X))) is V11() V12() ext-real Element of REAL
proj2 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | (L~ (Cage (Y,X))) is V13() V16( the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))),REAL:]
K445(((TOP-REAL 2) | (L~ (Cage (Y,X)))),(proj2 | (L~ (Cage (Y,X))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (Y,X)))),(S-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NW-corner (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Cage (Y,X))) is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | (L~ (Cage (Y,X)))),(proj2 | (L~ (Cage (Y,X))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (Y,X)))),(N-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (Y,X)))),(NW-corner (L~ (Cage (Y,X))))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Cage (Y,X)))),(NW-corner (L~ (Cage (Y,X)))))) /\ (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ (Cage (Y,X)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Cage (Y,X)))) is V13() V16( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X)))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),REAL:]
the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))) is set
[: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),REAL:] is set
K445(((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),(proj2 | (W-most (L~ (Cage (Y,X)))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (Y,X)))),K445(((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),(proj2 | (W-most (L~ (Cage (Y,X))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-max (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Cage (Y,X))) is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | (L~ (Cage (Y,X)))),(proj1 | (L~ (Cage (Y,X))))) is V11() V12() ext-real Element of REAL
E-most (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
SE-corner (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
|[(E-bound (L~ (Cage (Y,X)))),(S-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NE-corner (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
|[(E-bound (L~ (Cage (Y,X)))),(N-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Cage (Y,X)))),(NE-corner (L~ (Cage (Y,X))))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SE-corner (L~ (Cage (Y,X)))),(NE-corner (L~ (Cage (Y,X)))))) /\ (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ (Cage (Y,X)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Cage (Y,X)))) is V13() V16( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X)))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),REAL:]
the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))) is set
[: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),REAL:] is set
K446(((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),(proj2 | (E-most (L~ (Cage (Y,X)))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (Y,X)))),K446(((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),(proj2 | (E-most (L~ (Cage (Y,X))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
{(W-min (L~ (Cage (Y,X)))),(E-max (L~ (Cage (Y,X))))} is non empty functional V26() V30() set
[(len (Gauge (Y,X))),k] is non empty set
{(len (Gauge (Y,X))),k} is non empty V26() V30() V180() V181() V182() V183() V184() V185() set
{(len (Gauge (Y,X)))} is non empty trivial V26() V30() 1 -element V180() V181() V182() V183() V184() V185() set
{{(len (Gauge (Y,X))),k},{(len (Gauge (Y,X)))}} is non empty V26() V30() set
[1,k] is non empty set
{1,k} is non empty V26() V30() V180() V181() V182() V183() V184() V185() set
{{1,k},{1}} is non empty V26() V30() set
(Gauge (Y,X)) * (1,k) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
((Gauge (Y,X)) * (1,k)) `1 is V11() V12() ext-real Element of REAL
(W-min (L~ (Cage (Y,X)))) `1 is V11() V12() ext-real Element of REAL
(Gauge (Y,X)) * ((len (Gauge (Y,X))),k) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
((Gauge (Y,X)) * ((len (Gauge (Y,X))),k)) `1 is V11() V12() ext-real Element of REAL
(E-max (L~ (Cage (Y,X)))) `1 is V11() V12() ext-real Element of REAL
X is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
Y is non empty functional connected bounded being_simple_closed_curve compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
Gauge (Y,X) is V13() non empty-yielding V16( NAT ) V17(K233( 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 K233( the U1 of (TOP-REAL 2))
len (Gauge (Y,X)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
width (Gauge (Y,X)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
Upper_Seq (Y,X) 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 (Y,X)) is non empty functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
Lower_Seq (Y,X) 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 (Y,X)) is non empty functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
Lower_Arc Y is non empty functional Element of bool the U1 of (TOP-REAL 2)
j is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
k is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
k is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(Gauge (Y,X)) * (j,k) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(Gauge (Y,X)) * (j,k) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (Y,X)) * (j,k)),((Gauge (Y,X)) * (j,k))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg (((Gauge (Y,X)) * (j,k)),((Gauge (Y,X)) * (j,k)))) /\ (L~ (Upper_Seq (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
{((Gauge (Y,X)) * (j,k))} is non empty trivial functional V26() V30() 1 -element set
(LSeg (((Gauge (Y,X)) * (j,k)),((Gauge (Y,X)) * (j,k)))) /\ (L~ (Lower_Seq (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
{((Gauge (Y,X)) * (j,k))} is non empty trivial functional V26() V30() 1 -element set
Cage (Y,X) 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 (Y,X)) is non empty functional V71( TOP-REAL 2) connected bounded being_simple_closed_curve compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
W-min (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-bound (L~ (Cage (Y,X))) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (Y,X))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | (L~ (Cage (Y,X))) is V13() V16( the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))),REAL:]
the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))),REAL:] is set
K445(((TOP-REAL 2) | (L~ (Cage (Y,X)))),(proj1 | (L~ (Cage (Y,X))))) is V11() V12() ext-real Element of REAL
W-most (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
SW-corner (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Cage (Y,X))) is V11() V12() ext-real Element of REAL
proj2 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | (L~ (Cage (Y,X))) is V13() V16( the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))),REAL:]
K445(((TOP-REAL 2) | (L~ (Cage (Y,X)))),(proj2 | (L~ (Cage (Y,X))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (Y,X)))),(S-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NW-corner (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Cage (Y,X))) is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | (L~ (Cage (Y,X)))),(proj2 | (L~ (Cage (Y,X))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (Y,X)))),(N-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (Y,X)))),(NW-corner (L~ (Cage (Y,X))))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Cage (Y,X)))),(NW-corner (L~ (Cage (Y,X)))))) /\ (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ (Cage (Y,X)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Cage (Y,X)))) is V13() V16( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X)))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),REAL:]
the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))) is set
[: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),REAL:] is set
K445(((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),(proj2 | (W-most (L~ (Cage (Y,X)))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (Y,X)))),K445(((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),(proj2 | (W-most (L~ (Cage (Y,X))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-max (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Cage (Y,X))) is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | (L~ (Cage (Y,X)))),(proj1 | (L~ (Cage (Y,X))))) is V11() V12() ext-real Element of REAL
E-most (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
SE-corner (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
|[(E-bound (L~ (Cage (Y,X)))),(S-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NE-corner (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
|[(E-bound (L~ (Cage (Y,X)))),(N-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Cage (Y,X)))),(NE-corner (L~ (Cage (Y,X))))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SE-corner (L~ (Cage (Y,X)))),(NE-corner (L~ (Cage (Y,X)))))) /\ (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ (Cage (Y,X)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Cage (Y,X)))) is V13() V16( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X)))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),REAL:]
the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))) is set
[: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),REAL:] is set
K446(((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),(proj2 | (E-most (L~ (Cage (Y,X)))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (Y,X)))),K446(((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),(proj2 | (E-most (L~ (Cage (Y,X))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
[j,k] is non empty set
{j,k} is non empty V26() V30() V180() V181() V182() V183() V184() V185() set
{j} is non empty trivial V26() V30() 1 -element V180() V181() V182() V183() V184() V185() set
{{j,k},{j}} is non empty V26() V30() set
Indices (Gauge (Y,X)) is set
[j,k] is non empty set
{j,k} is non empty V26() V30() V180() V181() V182() V183() V184() V185() set
{{j,k},{j}} is non empty V26() V30() set
R_Cut ((Upper_Seq (Y,X)),((Gauge (Y,X)) * (j,k))) 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_Cut ((Lower_Seq (Y,X)),((Gauge (Y,X)) * (j,k))) 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 (Upper_Seq (Y,X)) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
dom (Upper_Seq (Y,X)) is non empty non trivial V26() V180() V181() V182() V183() V184() V185() Element of bool NAT
(Upper_Seq (Y,X)) . 1 is V13() Function-like set
(Upper_Seq (Y,X)) /. 1 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(W-min (L~ (Cage (Y,X)))) `1 is V11() V12() ext-real Element of REAL
(Gauge (Y,X)) * (1,k) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
((Gauge (Y,X)) * (1,k)) `1 is V11() V12() ext-real Element of REAL
[1,k] is non empty set
{1,k} is non empty V26() V30() V180() V181() V182() V183() V184() V185() set
{{1,k},{1}} is non empty V26() V30() set
1 + 2 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
len (Lower_Seq (Y,X)) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
dom (Lower_Seq (Y,X)) is non empty non trivial V26() V180() V181() V182() V183() V184() V185() Element of bool NAT
(Lower_Seq (Y,X)) . (len (Lower_Seq (Y,X))) is V13() Function-like set
(Lower_Seq (Y,X)) /. (len (Lower_Seq (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
[(len (Gauge (Y,X))),k] is non empty set
{(len (Gauge (Y,X))),k} is non empty V26() V30() V180() V181() V182() V183() V184() V185() set
{(len (Gauge (Y,X)))} is non empty trivial V26() V30() 1 -element V180() V181() V182() V183() V184() V185() set
{{(len (Gauge (Y,X))),k},{(len (Gauge (Y,X)))}} is non empty V26() V30() set
(Lower_Seq (Y,X)) . 1 is V13() Function-like set
(Lower_Seq (Y,X)) /. 1 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(E-max (L~ (Cage (Y,X)))) `1 is V11() V12() ext-real Element of REAL
(Gauge (Y,X)) * ((len (Gauge (Y,X))),k) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
((Gauge (Y,X)) * ((len (Gauge (Y,X))),k)) `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 V179() V180() V181() V182() V183() V184() V185() Element of NAT
go 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 go is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
rng (Upper_Seq (Y,X)) is V26() set
do 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 do is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
rng (Lower_Seq (Y,X)) is V26() set
go is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like one-to-one non constant V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq s.c.c. FinSequence of the U1 of (TOP-REAL 2)
len go is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
dom go is non empty non trivial V26() V180() V181() V182() V183() V184() V185() Element of bool NAT
go /. (len go) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
go . (len go) is V13() Function-like set
do is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like one-to-one non constant V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq s.c.c. FinSequence of the U1 of (TOP-REAL 2)
len do is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
dom do is non empty non trivial V26() V180() V181() V182() V183() V184() V185() Element of bool NAT
do /. 1 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
do . 1 is V13() Function-like set
(len go) - 1 is V11() V12() ext-real set
m is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
m + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(len go) -' 1 is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
LSeg (go,m) is functional Element of bool the U1 of (TOP-REAL 2)
L~ go is non empty functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
LSeg (((Gauge (Y,X)) * (j,k)),((Gauge (Y,X)) * (j,k))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg (go,m)) /\ (LSeg (((Gauge (Y,X)) * (j,k)),((Gauge (Y,X)) * (j,k)))) is functional Element of bool the U1 of (TOP-REAL 2)
go /. m is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((go /. m),((Gauge (Y,X)) * (j,k))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
W2 is set
LSeg (do,1) is functional Element of bool the U1 of (TOP-REAL 2)
L~ do is non empty functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
(LSeg (do,1)) /\ (LSeg (((Gauge (Y,X)) * (j,k)),((Gauge (Y,X)) * (j,k)))) is functional Element of bool the U1 of (TOP-REAL 2)
do /. (1 + 1) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (Y,X)) * (j,k)),(do /. (1 + 1))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
W2 is set
(LSeg (((Gauge (Y,X)) * (j,k)),((Gauge (Y,X)) * (j,k)))) /\ (LSeg (do,1)) is functional Element of bool the U1 of (TOP-REAL 2)
go /. 1 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
do /. (len do) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
rng go is non empty non trivial V26() set
rng do is non empty non trivial V26() set
{(go /. 1)} is non empty trivial functional V26() V30() 1 -element set
(L~ go) /\ (L~ do) is functional Element of bool the U1 of (TOP-REAL 2)
W2 is set
[(len (Gauge (Y,X))),k] is non empty set
{(len (Gauge (Y,X))),k} is non empty V26() V30() V180() V181() V182() V183() V184() V185() set
{{(len (Gauge (Y,X))),k},{(len (Gauge (Y,X)))}} is non empty V26() V30() set
W2 is set
(Gauge (Y,X)) * ((len (Gauge (Y,X))),k) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
((Gauge (Y,X)) * ((len (Gauge (Y,X))),k)) `1 is V11() V12() ext-real Element of REAL
(L~ (Upper_Seq (Y,X))) /\ (L~ (Lower_Seq (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
{(W-min (L~ (Cage (Y,X)))),(E-max (L~ (Cage (Y,X))))} is non empty functional V26() V30() set
go /. 2 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
((Gauge (Y,X)) * (j,k)) `1 is V11() V12() ext-real Element of REAL
((Gauge (Y,X)) * (j,k)) .. (Upper_Seq (Y,X)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
mid ((Upper_Seq (Y,X)),1,(((Gauge (Y,X)) * (j,k)) .. (Upper_Seq (Y,X)))) 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 (Y,X)) | (((Gauge (Y,X)) * (j,k)) .. (Upper_Seq (Y,X))) 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)
(Upper_Seq (Y,X)) /. 2 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
<*((Gauge (Y,X)) * (j,k)),((Gauge (Y,X)) * (j,k))*> 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)
pion1 is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
dom <*((Gauge (Y,X)) * (j,k)),((Gauge (Y,X)) * (j,k))*> is non empty non trivial V26() 2 -element V180() V181() V182() V183() V184() V185() Element of bool NAT
<*((Gauge (Y,X)) * (j,k)),((Gauge (Y,X)) * (j,k))*> /. pion1 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(Gauge (Y,X)) * (j,1) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
((Gauge (Y,X)) * (j,1)) `1 is V11() V12() ext-real Element of REAL
((Gauge (Y,X)) * (j,k)) `1 is V11() V12() ext-real Element of REAL
L~ <*((Gauge (Y,X)) * (j,k)),((Gauge (Y,X)) * (j,k))*> is non empty functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
<*((Gauge (Y,X)) * (j,k)),((Gauge (Y,X)) * (j,k))*> /. 1 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
len <*((Gauge (Y,X)) * (j,k)),((Gauge (Y,X)) * (j,k))*> is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
<*((Gauge (Y,X)) * (j,k)),((Gauge (Y,X)) * (j,k))*> /. (len <*((Gauge (Y,X)) * (j,k)),((Gauge (Y,X)) * (j,k))*>) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
pion1 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~ pion1 is functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
pion1 /. 1 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
len pion1 is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
pion1 /. (len pion1) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
pion1 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)
go ^' pion1 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)
(go ^' pion1) ^' do 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 (Y,X)) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))) 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)
len (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
len (go ^' pion1) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
1 + 0 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
len ((go ^' pion1) ^' do) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
pion1 /. 1 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(go ^' pion1) /. (len (go ^' pion1)) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
<*((Gauge (Y,X)) * (j,k)),((Gauge (Y,X)) * (j,k))*> /. 2 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg (pion1,1) is functional Element of bool the U1 of (TOP-REAL 2)
LSeg (go,((len go) -' 1)) is functional Element of bool the U1 of (TOP-REAL 2)
(LSeg (go,((len go) -' 1))) /\ (LSeg (pion1,1)) is functional Element of bool the U1 of (TOP-REAL 2)
len pion1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(LSeg (go,m)) /\ (LSeg (pion1,1)) is functional Element of bool the U1 of (TOP-REAL 2)
godo is set
{(go /. (len go))} is non empty trivial functional V26() V30() 1 -element set
2 + 0 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(len pion1) - 2 is V11() V12() ext-real set
(len (go ^' pion1)) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
((len (go ^' pion1)) + 1) - 1 is V11() V12() ext-real set
(len go) + (len pion1) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
((len go) + (len pion1)) - 1 is V11() V12() ext-real set
(len (go ^' pion1)) - 1 is V11() V12() ext-real set
(len go) + ((len pion1) - 2) is V11() V12() ext-real set
(len pion1) -' 2 is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(len go) + ((len pion1) -' 2) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(len (go ^' pion1)) -' 1 is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(len pion1) - 1 is V11() V12() ext-real set
(len pion1) -' 1 is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
((len pion1) -' 2) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
((len pion1) - 2) + 1 is V11() V12() ext-real set
((len pion1) - 1) + 1 is V11() V12() ext-real set
LSeg (pion1,((len pion1) -' 1)) is functional Element of bool the U1 of (TOP-REAL 2)
(LSeg (pion1,((len pion1) -' 1))) /\ (LSeg (do,1)) is functional Element of bool the U1 of (TOP-REAL 2)
godo is set
((len pion1) -' 1) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
pion1 /. (((len pion1) -' 1) + 1) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((go ^' pion1),((len go) + ((len pion1) -' 2))) is functional Element of bool the U1 of (TOP-REAL 2)
(LSeg ((go ^' pion1),((len go) + ((len pion1) -' 2)))) /\ (LSeg (do,1)) is functional Element of bool the U1 of (TOP-REAL 2)
{((go ^' pion1) /. (len (go ^' pion1)))} is non empty trivial functional V26() V30() 1 -element set
rng pion1 is V26() set
L~ pion1 is non empty functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
{(pion1 /. 1)} is non empty trivial functional V26() V30() 1 -element set
(L~ go) /\ (L~ pion1) is functional Element of bool the U1 of (TOP-REAL 2)
godo is set
godo is set
(L~ pion1) /\ (L~ (Upper_Seq (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
(rng go) /\ (rng pion1) is V26() set
pion1 /. (len pion1) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
{(pion1 /. (len pion1))} is non empty trivial functional V26() V30() 1 -element set
(L~ do) /\ (L~ pion1) is functional Element of bool the U1 of (TOP-REAL 2)
godo is set
godo is set
(L~ pion1) /\ (L~ (Lower_Seq (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
L~ (go ^' pion1) is functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
(L~ (go ^' pion1)) /\ (L~ do) is functional Element of bool the U1 of (TOP-REAL 2)
(L~ go) \/ (L~ pion1) is non empty functional Element of bool the U1 of (TOP-REAL 2)
((L~ go) \/ (L~ pion1)) /\ (L~ do) is functional Element of bool the U1 of (TOP-REAL 2)
{(do /. 1)} is non empty trivial functional V26() V30() 1 -element set
{(go /. 1)} \/ {(do /. 1)} is non empty V26() V30() set
(go ^' pion1) /. 1 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
{((go ^' pion1) /. 1)} is non empty trivial functional V26() V30() 1 -element set
{((go ^' pion1) /. 1)} \/ {(do /. 1)} is non empty V26() V30() set
{((go ^' pion1) /. 1),(do /. 1)} is non empty functional V26() V30() set
E-max Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-bound Y is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | Y is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | Y is V13() V16( the U1 of ((TOP-REAL 2) | Y)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | Y), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | Y),REAL:]
the U1 of ((TOP-REAL 2) | Y) is non empty set
[: the U1 of ((TOP-REAL 2) | Y),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | Y),REAL:] is set
K446(((TOP-REAL 2) | Y),(proj1 | Y)) is V11() V12() ext-real Element of REAL
E-most Y is functional Element of bool the U1 of (TOP-REAL 2)
SE-corner Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-bound Y is V11() V12() ext-real Element of REAL
proj2 | Y is V13() V16( the U1 of ((TOP-REAL 2) | Y)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | Y), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | Y),REAL:]
K445(((TOP-REAL 2) | Y),(proj2 | Y)) is V11() V12() ext-real Element of REAL
|[(E-bound Y),(S-bound Y)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NE-corner Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-bound Y is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | Y),(proj2 | Y)) is V11() V12() ext-real Element of REAL
|[(E-bound Y),(N-bound Y)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner Y),(NE-corner Y)) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SE-corner Y),(NE-corner Y))) /\ Y is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (E-most Y) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most Y) is V13() V16( the U1 of ((TOP-REAL 2) | (E-most Y))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (E-most Y)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (E-most Y)),REAL:]
the U1 of ((TOP-REAL 2) | (E-most Y)) is set
[: the U1 of ((TOP-REAL 2) | (E-most Y)),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (E-most Y)),REAL:] is set
K446(((TOP-REAL 2) | (E-most Y)),(proj2 | (E-most Y))) is V11() V12() ext-real Element of REAL
|[(E-bound Y),K446(((TOP-REAL 2) | (E-most Y)),(proj2 | (E-most Y)))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-min Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-bound Y is V11() V12() ext-real Element of REAL
K445(((TOP-REAL 2) | Y),(proj1 | Y)) is V11() V12() ext-real Element of REAL
W-most Y is functional Element of bool the U1 of (TOP-REAL 2)
SW-corner Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
|[(W-bound Y),(S-bound Y)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NW-corner Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
|[(W-bound Y),(N-bound Y)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner Y),(NW-corner Y)) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner Y),(NW-corner Y))) /\ Y is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most Y) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most Y) is V13() V16( the U1 of ((TOP-REAL 2) | (W-most Y))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (W-most Y)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most Y)),REAL:]
the U1 of ((TOP-REAL 2) | (W-most Y)) is set
[: the U1 of ((TOP-REAL 2) | (W-most Y)),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (W-most Y)),REAL:] is set
K445(((TOP-REAL 2) | (W-most Y)),(proj2 | (W-most Y))) is V11() V12() ext-real Element of REAL
|[(W-bound Y),K445(((TOP-REAL 2) | (W-most Y)),(proj2 | (W-most Y)))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
rng (Cage (Y,X)) is non empty non trivial V26() set
(Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))) /. 1 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))) is non empty functional V71( TOP-REAL 2) connected bounded being_simple_closed_curve compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
W-max (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is V13() V16( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),REAL:]
the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),REAL:] is set
K445(((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),(proj1 | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))) is V11() V12() ext-real Element of REAL
W-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is functional Element of bool the U1 of (TOP-REAL 2)
SW-corner (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is V11() V12() ext-real Element of REAL
proj2 | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is V13() V16( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),REAL:]
K445(((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),(proj2 | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),(S-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NW-corner (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),(proj2 | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),(N-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),(NW-corner (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),(NW-corner (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))))) /\ (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))) is V13() V16( the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),REAL:]
the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))) is set
[: the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),REAL:] is set
K446(((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),(proj2 | (W-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),K446(((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),(proj2 | (W-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(W-max (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))) .. (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
N-min (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is functional Element of bool the U1 of (TOP-REAL 2)
NE-corner (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),(proj1 | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),(N-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((NW-corner (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),(NE-corner (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((NW-corner (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),(NE-corner (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))))) /\ (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))) is V13() V16( the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),REAL:]
the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))) is set
[: the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),REAL:] is set
K445(((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),(proj1 | (N-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))))) is V11() V12() ext-real Element of REAL
|[K445(((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),(proj1 | (N-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))))),(N-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(N-min (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))) .. (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
N-max (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
K446(((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),(proj1 | (N-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))))) is V11() V12() ext-real Element of REAL
|[K446(((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),(proj1 | (N-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))))),(N-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(N-max (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))) .. (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(E-max (L~ (Cage (Y,X)))) .. (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
godo 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 FinSequence of the U1 of (TOP-REAL 2)
right_cell (godo,1,(Gauge (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
L~ godo is non empty functional V71( TOP-REAL 2) connected bounded being_simple_closed_curve compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
(right_cell (godo,1,(Gauge (Y,X)))) \ (L~ godo) is functional Element of bool the U1 of (TOP-REAL 2)
RightComp godo is non empty functional Element of bool the U1 of (TOP-REAL 2)
(L~ (go ^' pion1)) \/ (L~ do) is non empty functional Element of bool the U1 of (TOP-REAL 2)
((L~ go) \/ (L~ pion1)) \/ (L~ do) is non empty functional Element of bool the U1 of (TOP-REAL 2)
(L~ (Upper_Seq (Y,X))) \/ (L~ (Lower_Seq (Y,X))) is non empty functional Element of bool the U1 of (TOP-REAL 2)
right_cell ((Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))),1) is functional Element of bool the U1 of (TOP-REAL 2)
GoB (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))) is V13() non empty-yielding V16( NAT ) V17(K233( 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 K233( the U1 of (TOP-REAL 2))
right_cell ((Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))),1,(GoB (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))) is functional Element of bool the U1 of (TOP-REAL 2)
GoB (Cage (Y,X)) is V13() non empty-yielding V16( NAT ) V17(K233( 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 K233( the U1 of (TOP-REAL 2))
right_cell ((Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))),1,(GoB (Cage (Y,X)))) is functional Element of bool the U1 of (TOP-REAL 2)
right_cell ((Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))),1,(Gauge (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
(Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))) -: (E-max (L~ (Cage (Y,X)))) 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)
right_cell (((Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))) -: (E-max (L~ (Cage (Y,X))))),1,(Gauge (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
right_cell ((Upper_Seq (Y,X)),1,(Gauge (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
right_cell ((R_Cut ((Upper_Seq (Y,X)),((Gauge (Y,X)) * (j,k)))),1,(Gauge (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
right_cell ((go ^' pion1),1,(Gauge (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
godo /. 1 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
godo /. 2 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(go ^' pion1) /. 2 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(Upper_Seq (Y,X)) ^' (Lower_Seq (Y,X)) 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 (Y,X)) ^' (Lower_Seq (Y,X))) /. 2 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))) /. 2 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(L~ go) \/ (L~ do) is non empty functional Element of bool the U1 of (TOP-REAL 2)
W-min ((L~ go) \/ (L~ do)) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-bound ((L~ go) \/ (L~ do)) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | ((L~ go) \/ (L~ do)) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | ((L~ go) \/ (L~ do)) is V13() V16( the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ do)))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ do))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ do))),REAL:]
the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ do))) is non empty set
[: the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ do))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ do))),REAL:] is set
K445(((TOP-REAL 2) | ((L~ go) \/ (L~ do))),(proj1 | ((L~ go) \/ (L~ do)))) is V11() V12() ext-real Element of REAL
W-most ((L~ go) \/ (L~ do)) is functional Element of bool the U1 of (TOP-REAL 2)
SW-corner ((L~ go) \/ (L~ do)) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-bound ((L~ go) \/ (L~ do)) is V11() V12() ext-real Element of REAL
proj2 | ((L~ go) \/ (L~ do)) is V13() V16( the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ do)))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ do))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ do))),REAL:]
K445(((TOP-REAL 2) | ((L~ go) \/ (L~ do))),(proj2 | ((L~ go) \/ (L~ do)))) is V11() V12() ext-real Element of REAL
|[(W-bound ((L~ go) \/ (L~ do))),(S-bound ((L~ go) \/ (L~ do)))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NW-corner ((L~ go) \/ (L~ do)) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-bound ((L~ go) \/ (L~ do)) is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | ((L~ go) \/ (L~ do))),(proj2 | ((L~ go) \/ (L~ do)))) is V11() V12() ext-real Element of REAL
|[(W-bound ((L~ go) \/ (L~ do))),(N-bound ((L~ go) \/ (L~ do)))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner ((L~ go) \/ (L~ do))),(NW-corner ((L~ go) \/ (L~ do)))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner ((L~ go) \/ (L~ do))),(NW-corner ((L~ go) \/ (L~ do))))) /\ ((L~ go) \/ (L~ do)) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most ((L~ go) \/ (L~ do))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most ((L~ go) \/ (L~ do))) is V13() V16( the U1 of ((TOP-REAL 2) | (W-most ((L~ go) \/ (L~ do))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (W-most ((L~ go) \/ (L~ do)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most ((L~ go) \/ (L~ do)))),REAL:]
the U1 of ((TOP-REAL 2) | (W-most ((L~ go) \/ (L~ do)))) is set
[: the U1 of ((TOP-REAL 2) | (W-most ((L~ go) \/ (L~ do)))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (W-most ((L~ go) \/ (L~ do)))),REAL:] is set
K445(((TOP-REAL 2) | (W-most ((L~ go) \/ (L~ do)))),(proj2 | (W-most ((L~ go) \/ (L~ do))))) is V11() V12() ext-real Element of REAL
|[(W-bound ((L~ go) \/ (L~ do))),K445(((TOP-REAL 2) | (W-most ((L~ go) \/ (L~ do)))),(proj2 | (W-most ((L~ go) \/ (L~ do)))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(W-min ((L~ go) \/ (L~ do))) `1 is V11() V12() ext-real Element of REAL
W-bound (LSeg (((Gauge (Y,X)) * (j,k)),((Gauge (Y,X)) * (j,k)))) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (LSeg (((Gauge (Y,X)) * (j,k)),((Gauge (Y,X)) * (j,k)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (LSeg (((Gauge (Y,X)) * (j,k)),((Gauge (Y,X)) * (j,k)))) is V13() V16( the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (Y,X)) * (j,k)),((Gauge (Y,X)) * (j,k)))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (Y,X)) * (j,k)),((Gauge (Y,X)) * (j,k))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (Y,X)) * (j,k)),((Gauge (Y,X)) * (j,k))))),REAL:]
the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (Y,X)) * (j,k)),((Gauge (Y,X)) * (j,k))))) is set
[: the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (Y,X)) * (j,k)),((Gauge (Y,X)) * (j,k))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (Y,X)) * (j,k)),((Gauge (Y,X)) * (j,k))))),REAL:] is set
K445(((TOP-REAL 2) | (LSeg (((Gauge (Y,X)) * (j,k)),((Gauge (Y,X)) * (j,k))))),(proj1 | (LSeg (((Gauge (Y,X)) * (j,k)),((Gauge (Y,X)) * (j,k)))))) is V11() V12() ext-real Element of REAL
W-bound (L~ pion1) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ pion1) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ pion1) is V13() V16( the U1 of ((TOP-REAL 2) | (L~ pion1))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (L~ pion1)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ pion1)),REAL:]
the U1 of ((TOP-REAL 2) | (L~ pion1)) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ pion1)),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (L~ pion1)),REAL:] is set
K445(((TOP-REAL 2) | (L~ pion1)),(proj1 | (L~ pion1))) is V11() V12() ext-real Element of REAL
((L~ go) \/ (L~ do)) \/ (L~ pion1) is non empty functional Element of bool the U1 of (TOP-REAL 2)
W-min (((L~ go) \/ (L~ do)) \/ (L~ pion1)) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-bound (((L~ go) \/ (L~ do)) \/ (L~ pion1)) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (((L~ go) \/ (L~ do)) \/ (L~ pion1)) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (((L~ go) \/ (L~ do)) \/ (L~ pion1)) is V13() V16( the U1 of ((TOP-REAL 2) | (((L~ go) \/ (L~ do)) \/ (L~ pion1)))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (((L~ go) \/ (L~ do)) \/ (L~ pion1))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (((L~ go) \/ (L~ do)) \/ (L~ pion1))),REAL:]
the U1 of ((TOP-REAL 2) | (((L~ go) \/ (L~ do)) \/ (L~ pion1))) is non empty set
[: the U1 of ((TOP-REAL 2) | (((L~ go) \/ (L~ do)) \/ (L~ pion1))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (((L~ go) \/ (L~ do)) \/ (L~ pion1))),REAL:] is set
K445(((TOP-REAL 2) | (((L~ go) \/ (L~ do)) \/ (L~ pion1))),(proj1 | (((L~ go) \/ (L~ do)) \/ (L~ pion1)))) is V11() V12() ext-real Element of REAL
W-most (((L~ go) \/ (L~ do)) \/ (L~ pion1)) is functional Element of bool the U1 of (TOP-REAL 2)
SW-corner (((L~ go) \/ (L~ do)) \/ (L~ pion1)) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-bound (((L~ go) \/ (L~ do)) \/ (L~ pion1)) is V11() V12() ext-real Element of REAL
proj2 | (((L~ go) \/ (L~ do)) \/ (L~ pion1)) is V13() V16( the U1 of ((TOP-REAL 2) | (((L~ go) \/ (L~ do)) \/ (L~ pion1)))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (((L~ go) \/ (L~ do)) \/ (L~ pion1))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (((L~ go) \/ (L~ do)) \/ (L~ pion1))),REAL:]
K445(((TOP-REAL 2) | (((L~ go) \/ (L~ do)) \/ (L~ pion1))),(proj2 | (((L~ go) \/ (L~ do)) \/ (L~ pion1)))) is V11() V12() ext-real Element of REAL
|[(W-bound (((L~ go) \/ (L~ do)) \/ (L~ pion1))),(S-bound (((L~ go) \/ (L~ do)) \/ (L~ pion1)))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NW-corner (((L~ go) \/ (L~ do)) \/ (L~ pion1)) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-bound (((L~ go) \/ (L~ do)) \/ (L~ pion1)) is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | (((L~ go) \/ (L~ do)) \/ (L~ pion1))),(proj2 | (((L~ go) \/ (L~ do)) \/ (L~ pion1)))) is V11() V12() ext-real Element of REAL
|[(W-bound (((L~ go) \/ (L~ do)) \/ (L~ pion1))),(N-bound (((L~ go) \/ (L~ do)) \/ (L~ pion1)))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (((L~ go) \/ (L~ do)) \/ (L~ pion1))),(NW-corner (((L~ go) \/ (L~ do)) \/ (L~ pion1)))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (((L~ go) \/ (L~ do)) \/ (L~ pion1))),(NW-corner (((L~ go) \/ (L~ do)) \/ (L~ pion1))))) /\ (((L~ go) \/ (L~ do)) \/ (L~ pion1)) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (((L~ go) \/ (L~ do)) \/ (L~ pion1))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (((L~ go) \/ (L~ do)) \/ (L~ pion1))) is V13() V16( the U1 of ((TOP-REAL 2) | (W-most (((L~ go) \/ (L~ do)) \/ (L~ pion1))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (W-most (((L~ go) \/ (L~ do)) \/ (L~ pion1)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most (((L~ go) \/ (L~ do)) \/ (L~ pion1)))),REAL:]
the U1 of ((TOP-REAL 2) | (W-most (((L~ go) \/ (L~ do)) \/ (L~ pion1)))) is set
[: the U1 of ((TOP-REAL 2) | (W-most (((L~ go) \/ (L~ do)) \/ (L~ pion1)))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (W-most (((L~ go) \/ (L~ do)) \/ (L~ pion1)))),REAL:] is set
K445(((TOP-REAL 2) | (W-most (((L~ go) \/ (L~ do)) \/ (L~ pion1)))),(proj2 | (W-most (((L~ go) \/ (L~ do)) \/ (L~ pion1))))) is V11() V12() ext-real Element of REAL
|[(W-bound (((L~ go) \/ (L~ do)) \/ (L~ pion1))),K445(((TOP-REAL 2) | (W-most (((L~ go) \/ (L~ do)) \/ (L~ pion1)))),(proj2 | (W-most (((L~ go) \/ (L~ do)) \/ (L~ pion1)))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-min (L~ godo) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-bound (L~ godo) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ godo) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ godo) is V13() V16( the U1 of ((TOP-REAL 2) | (L~ godo))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (L~ godo)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ godo)),REAL:]
the U1 of ((TOP-REAL 2) | (L~ godo)) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ godo)),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (L~ godo)),REAL:] is set
K445(((TOP-REAL 2) | (L~ godo)),(proj1 | (L~ godo))) is V11() V12() ext-real Element of REAL
W-most (L~ godo) is functional Element of bool the U1 of (TOP-REAL 2)
SW-corner (L~ godo) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-bound (L~ godo) is V11() V12() ext-real Element of REAL
proj2 | (L~ godo) is V13() V16( the U1 of ((TOP-REAL 2) | (L~ godo))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (L~ godo)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ godo)),REAL:]
K445(((TOP-REAL 2) | (L~ godo)),(proj2 | (L~ godo))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ godo)),(S-bound (L~ godo))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NW-corner (L~ godo) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-bound (L~ godo) is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | (L~ godo)),(proj2 | (L~ godo))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ godo)),(N-bound (L~ godo))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ godo)),(NW-corner (L~ godo))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ godo)),(NW-corner (L~ godo)))) /\ (L~ godo) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ godo)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ godo)) is V13() V16( the U1 of ((TOP-REAL 2) | (W-most (L~ godo)))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (W-most (L~ godo))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ godo))),REAL:]
the U1 of ((TOP-REAL 2) | (W-most (L~ godo))) is set
[: the U1 of ((TOP-REAL 2) | (W-most (L~ godo))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ godo))),REAL:] is set
K445(((TOP-REAL 2) | (W-most (L~ godo))),(proj2 | (W-most (L~ godo)))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ godo)),K445(((TOP-REAL 2) | (W-most (L~ godo))),(proj2 | (W-most (L~ godo))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
rng godo is non empty non trivial V26() set
dom godo is non empty non trivial V26() V180() V181() V182() V183() V184() V185() Element of bool NAT
(godo /. 2) `1 is V11() V12() ext-real Element of REAL
(W-min (L~ godo)) `1 is V11() V12() ext-real Element of REAL
Rotate (godo,(W-min (L~ godo))) 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 FinSequence of the U1 of (TOP-REAL 2)
(Rotate (godo,(W-min (L~ godo)))) /. 2 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(Upper_Seq (Y,X)) . (len (Upper_Seq (Y,X))) is V13() Function-like set
(Upper_Seq (Y,X)) /. (len (Upper_Seq (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
east_halfline (E-max Y) is non empty functional connected V259( TOP-REAL 2) Element of bool the U1 of (TOP-REAL 2)
W is set
p is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(east_halfline (E-max Y)) /\ (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
p `1 is V11() V12() ext-real Element of REAL
godo 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~ godo is non empty functional V71( TOP-REAL 2) connected bounded being_simple_closed_curve compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
W is set
p is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
p `2 is V11() V12() ext-real Element of REAL
(E-max Y) `2 is V11() V12() ext-real Element of REAL
j + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(j + 1) - 1 is V11() V12() ext-real set
(len (Gauge (Y,X))) - 1 is V11() V12() ext-real set
(len (Gauge (Y,X))) -' 1 is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
p `1 is V11() V12() ext-real Element of REAL
(Gauge (Y,X)) * (((len (Gauge (Y,X))) -' 1),1) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
((Gauge (Y,X)) * (((len (Gauge (Y,X))) -' 1),1)) `1 is V11() V12() ext-real Element of REAL
(E-max Y) `1 is V11() V12() ext-real Element of REAL
W is set
(E-max Y) `2 is V11() V12() ext-real Element of REAL
p is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
p `2 is V11() V12() ext-real Element of REAL
Index (p,do) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
((Gauge (Y,X)) * (j,k)) .. (Lower_Seq (Y,X)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(Index (p,do)) + (((Gauge (Y,X)) * (j,k)) .. (Lower_Seq (Y,X))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
((Index (p,do)) + (((Gauge (Y,X)) * (j,k)) .. (Lower_Seq (Y,X)))) -' 1 is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))) 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 (Y,X)),(E-max (L~ (Cage (Y,X)))))) is non empty functional V71( TOP-REAL 2) connected bounded being_simple_closed_curve compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
t is V6() V10() V11() V12() V26() cardinal ext-real non negative set
(Lower_Seq (Y,X)) . t is V13() Function-like set
Index (((Gauge (Y,X)) * (j,k)),(Lower_Seq (Y,X))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(Index (((Gauge (Y,X)) * (j,k)),(Lower_Seq (Y,X)))) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
len (L_Cut ((Lower_Seq (Y,X)),((Gauge (Y,X)) * (j,k)))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(len (Lower_Seq (Y,X))) - (Index (((Gauge (Y,X)) * (j,k)),(Lower_Seq (Y,X)))) is V11() V12() ext-real set
(len (Lower_Seq (Y,X))) -' (Index (((Gauge (Y,X)) * (j,k)),(Lower_Seq (Y,X)))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(Index (p,do)) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
((len (Lower_Seq (Y,X))) -' (Index (((Gauge (Y,X)) * (j,k)),(Lower_Seq (Y,X))))) - 1 is V11() V12() ext-real set
mid ((Lower_Seq (Y,X)),(((Gauge (Y,X)) * (j,k)) .. (Lower_Seq (Y,X))),(len (Lower_Seq (Y,X)))) 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 (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(east_halfline (E-max Y)) /\ (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
p `1 is V11() V12() ext-real Element of REAL
GoB (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))) is V13() non empty-yielding V16( NAT ) V17(K233( 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 K233( the U1 of (TOP-REAL 2))
jj2 is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(Gauge (Y,X)) * ((len (Gauge (Y,X))),jj2) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
[(len (Gauge (Y,X))),jj2] is non empty set
{(len (Gauge (Y,X))),jj2} is non empty V26() V30() V180() V181() V182() V183() V184() V185() set
{{(len (Gauge (Y,X))),jj2},{(len (Gauge (Y,X)))}} is non empty V26() V30() set
(Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))) -: (W-min (L~ (Cage (Y,X)))) 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)
LSeg ((Lower_Seq (Y,X)),1) is functional Element of bool the U1 of (TOP-REAL 2)
LSeg ((Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))),1) is functional Element of bool the U1 of (TOP-REAL 2)
(Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))) /. 1 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))) /. (1 + 1) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
ii is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
jj is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
jj + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
[ii,(jj + 1)] is non empty set
{ii,(jj + 1)} is non empty V26() V30() V180() V181() V182() V183() V184() V185() set
{ii} is non empty trivial V26() V30() 1 -element V180() V181() V182() V183() V184() V185() set
{{ii,(jj + 1)},{ii}} is non empty V26() V30() set
[ii,jj] is non empty set
{ii,jj} is non empty V26() V30() V180() V181() V182() V183() V184() V185() set
{{ii,jj},{ii}} is non empty V26() V30() set
(Gauge (Y,X)) * (ii,(jj + 1)) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(Gauge (Y,X)) * (ii,jj) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(jj + 1) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
E-max (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is V13() V16( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),REAL:]
the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),REAL:] is set
K446(((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),(proj1 | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))) is V11() V12() ext-real Element of REAL
E-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is functional Element of bool the U1 of (TOP-REAL 2)
SE-corner (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is V11() V12() ext-real Element of REAL
proj2 | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is V13() V16( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),REAL:]
K445(((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),(proj2 | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),(S-bound (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NE-corner (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),(proj2 | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),(N-bound (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),(NE-corner (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SE-corner (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),(NE-corner (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))))) /\ (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))) is V13() V16( the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))),REAL:]
the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))) is set
[: the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))),REAL:] is set
K446(((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))),(proj2 | (E-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),K446(((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))),(proj2 | (E-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
4 - 1 is V11() V12() ext-real set
ii - 1 is V11() V12() ext-real set
ii -' 1 is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(Gauge (Y,X)) * ((len (Gauge (Y,X))),jj) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
((Gauge (Y,X)) * ((len (Gauge (Y,X))),jj)) `1 is V11() V12() ext-real Element of REAL
ii + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
right_cell ((Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))),1) is functional Element of bool the U1 of (TOP-REAL 2)
cell ((Gauge (Y,X)),(ii -' 1),jj) is functional Element of bool the U1 of (TOP-REAL 2)
v_strip ((Gauge (Y,X)),(ii -' 1)) is functional Element of bool the U1 of (TOP-REAL 2)
h_strip ((Gauge (Y,X)),jj) is functional Element of bool the U1 of (TOP-REAL 2)
(v_strip ((Gauge (Y,X)),(ii -' 1))) /\ (h_strip ((Gauge (Y,X)),jj)) is functional Element of bool the U1 of (TOP-REAL 2)
(Gauge (Y,X)) * ((len (Gauge (Y,X))),(jj + 1)) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
((Gauge (Y,X)) * ((len (Gauge (Y,X))),(jj + 1))) `1 is V11() V12() ext-real Element of REAL
(ii -' 1) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(Gauge (Y,X)) * ((ii -' 1),(jj + 1)) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
((Gauge (Y,X)) * ((ii -' 1),(jj + 1))) `2 is V11() V12() ext-real Element of REAL
(Gauge (Y,X)) * (1,(jj + 1)) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
((Gauge (Y,X)) * (1,(jj + 1))) `2 is V11() V12() ext-real Element of REAL
((Gauge (Y,X)) * (ii,(jj + 1))) `2 is V11() V12() ext-real Element of REAL
(Gauge (Y,X)) * ((ii -' 1),jj) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
((Gauge (Y,X)) * ((ii -' 1),jj)) `2 is V11() V12() ext-real Element of REAL
(Gauge (Y,X)) * (1,jj) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
((Gauge (Y,X)) * (1,jj)) `2 is V11() V12() ext-real Element of REAL
((Gauge (Y,X)) * (ii,jj)) `2 is V11() V12() ext-real Element of REAL
LSeg (((Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))) /. 1),((Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))) /. (1 + 1))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
0 + (Index (((Gauge (Y,X)) * (j,k)),(Lower_Seq (Y,X)))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
((len (Lower_Seq (Y,X))) - (Index (((Gauge (Y,X)) * (j,k)),(Lower_Seq (Y,X))))) - 1 is V11() V12() ext-real set
(len (Lower_Seq (Y,X))) - (((Gauge (Y,X)) * (j,k)) .. (Lower_Seq (Y,X))) is V11() V12() ext-real set
(len (Lower_Seq (Y,X))) -' (((Gauge (Y,X)) * (j,k)) .. (Lower_Seq (Y,X))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
((len (Lower_Seq (Y,X))) -' (((Gauge (Y,X)) * (j,k)) .. (Lower_Seq (Y,X)))) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
LSeg (do,(Index (p,do))) is functional Element of bool the U1 of (TOP-REAL 2)
LSeg ((mid ((Lower_Seq (Y,X)),(((Gauge (Y,X)) * (j,k)) .. (Lower_Seq (Y,X))),(len (Lower_Seq (Y,X))))),(Index (p,do))) is functional Element of bool the U1 of (TOP-REAL 2)
LSeg ((Lower_Seq (Y,X)),(((Index (p,do)) + (((Gauge (Y,X)) * (j,k)) .. (Lower_Seq (Y,X)))) -' 1)) is functional Element of bool the U1 of (TOP-REAL 2)
(1 + 1) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
((1 + 1) + 1) - 1 is V11() V12() ext-real set
((Index (p,do)) + (((Gauge (Y,X)) * (j,k)) .. (Lower_Seq (Y,X)))) - 1 is V11() V12() ext-real set
(LSeg ((Lower_Seq (Y,X)),1)) /\ (LSeg ((Lower_Seq (Y,X)),(((Index (p,do)) + (((Gauge (Y,X)) * (j,k)) .. (Lower_Seq (Y,X)))) -' 1))) is functional Element of bool the U1 of (TOP-REAL 2)
(Lower_Seq (Y,X)) /. 2 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
{((Lower_Seq (Y,X)) /. 2)} is non empty trivial functional V26() V30() 1 -element set
p .. (Lower_Seq (Y,X)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(Gauge (Y,X)) * ((len (Gauge (Y,X))),k) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
((Gauge (Y,X)) * ((len (Gauge (Y,X))),k)) `1 is V11() V12() ext-real Element of REAL
(L~ godo) ` is non empty functional Element of bool the U1 of (TOP-REAL 2)
W is functional Element of bool the U1 of (TOP-REAL 2)
UBD (L~ godo) is non empty functional connected Element of bool the U1 of (TOP-REAL 2)
LeftComp godo is non empty functional Element of bool the U1 of (TOP-REAL 2)
X is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
Y is non empty functional connected bounded being_simple_closed_curve compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
Gauge (Y,X) is V13() non empty-yielding V16( NAT ) V17(K233( 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 K233( the U1 of (TOP-REAL 2))
len (Gauge (Y,X)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
width (Gauge (Y,X)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
Upper_Seq (Y,X) 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 (Y,X)) is non empty functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
Lower_Seq (Y,X) 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 (Y,X)) is non empty functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
Upper_Arc Y is non empty functional Element of bool the U1 of (TOP-REAL 2)
j is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
k is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
k is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(Gauge (Y,X)) * (j,k) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(Gauge (Y,X)) * (j,k) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (Y,X)) * (j,k)),((Gauge (Y,X)) * (j,k))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg (((Gauge (Y,X)) * (j,k)),((Gauge (Y,X)) * (j,k)))) /\ (L~ (Upper_Seq (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
{((Gauge (Y,X)) * (j,k))} is non empty trivial functional V26() V30() 1 -element set
(LSeg (((Gauge (Y,X)) * (j,k)),((Gauge (Y,X)) * (j,k)))) /\ (L~ (Lower_Seq (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
{((Gauge (Y,X)) * (j,k))} is non empty trivial functional V26() V30() 1 -element set
Cage (Y,X) 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 (Y,X)) is non empty functional V71( TOP-REAL 2) connected bounded being_simple_closed_curve compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
W-min (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-bound (L~ (Cage (Y,X))) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (Y,X))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | (L~ (Cage (Y,X))) is V13() V16( the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))),REAL:]
the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))),REAL:] is set
K445(((TOP-REAL 2) | (L~ (Cage (Y,X)))),(proj1 | (L~ (Cage (Y,X))))) is V11() V12() ext-real Element of REAL
W-most (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
SW-corner (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Cage (Y,X))) is V11() V12() ext-real Element of REAL
proj2 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | (L~ (Cage (Y,X))) is V13() V16( the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Cage (Y,X)))),REAL:]
K445(((TOP-REAL 2) | (L~ (Cage (Y,X)))),(proj2 | (L~ (Cage (Y,X))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (Y,X)))),(S-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NW-corner (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Cage (Y,X))) is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | (L~ (Cage (Y,X)))),(proj2 | (L~ (Cage (Y,X))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (Y,X)))),(N-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (Y,X)))),(NW-corner (L~ (Cage (Y,X))))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Cage (Y,X)))),(NW-corner (L~ (Cage (Y,X)))))) /\ (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ (Cage (Y,X)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Cage (Y,X)))) is V13() V16( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X)))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),REAL:]
the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))) is set
[: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),REAL:] is set
K445(((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),(proj2 | (W-most (L~ (Cage (Y,X)))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Cage (Y,X)))),K445(((TOP-REAL 2) | (W-most (L~ (Cage (Y,X))))),(proj2 | (W-most (L~ (Cage (Y,X))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-max (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Cage (Y,X))) is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | (L~ (Cage (Y,X)))),(proj1 | (L~ (Cage (Y,X))))) is V11() V12() ext-real Element of REAL
E-most (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
SE-corner (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
|[(E-bound (L~ (Cage (Y,X)))),(S-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NE-corner (L~ (Cage (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
|[(E-bound (L~ (Cage (Y,X)))),(N-bound (L~ (Cage (Y,X))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Cage (Y,X)))),(NE-corner (L~ (Cage (Y,X))))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SE-corner (L~ (Cage (Y,X)))),(NE-corner (L~ (Cage (Y,X)))))) /\ (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ (Cage (Y,X)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Cage (Y,X)))) is V13() V16( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X)))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),REAL:]
the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))) is set
[: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),REAL:] is set
K446(((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),(proj2 | (E-most (L~ (Cage (Y,X)))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Cage (Y,X)))),K446(((TOP-REAL 2) | (E-most (L~ (Cage (Y,X))))),(proj2 | (E-most (L~ (Cage (Y,X))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
[j,k] is non empty set
{j,k} is non empty V26() V30() V180() V181() V182() V183() V184() V185() set
{j} is non empty trivial V26() V30() 1 -element V180() V181() V182() V183() V184() V185() set
{{j,k},{j}} is non empty V26() V30() set
Indices (Gauge (Y,X)) is set
[j,k] is non empty set
{j,k} is non empty V26() V30() V180() V181() V182() V183() V184() V185() set
{{j,k},{j}} is non empty V26() V30() set
R_Cut ((Upper_Seq (Y,X)),((Gauge (Y,X)) * (j,k))) 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_Cut ((Lower_Seq (Y,X)),((Gauge (Y,X)) * (j,k))) 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 (Upper_Seq (Y,X)) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
dom (Upper_Seq (Y,X)) is non empty non trivial V26() V180() V181() V182() V183() V184() V185() Element of bool NAT
(Upper_Seq (Y,X)) . 1 is V13() Function-like set
(Upper_Seq (Y,X)) /. 1 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(W-min (L~ (Cage (Y,X)))) `1 is V11() V12() ext-real Element of REAL
(Gauge (Y,X)) * (1,k) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
((Gauge (Y,X)) * (1,k)) `1 is V11() V12() ext-real Element of REAL
[1,k] is non empty set
{1,k} is non empty V26() V30() V180() V181() V182() V183() V184() V185() set
{{1,k},{1}} is non empty V26() V30() set
1 + 2 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
len (Lower_Seq (Y,X)) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
dom (Lower_Seq (Y,X)) is non empty non trivial V26() V180() V181() V182() V183() V184() V185() Element of bool NAT
(Lower_Seq (Y,X)) . (len (Lower_Seq (Y,X))) is V13() Function-like set
(Lower_Seq (Y,X)) /. (len (Lower_Seq (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
[(len (Gauge (Y,X))),k] is non empty set
{(len (Gauge (Y,X))),k} is non empty V26() V30() V180() V181() V182() V183() V184() V185() set
{(len (Gauge (Y,X)))} is non empty trivial V26() V30() 1 -element V180() V181() V182() V183() V184() V185() set
{{(len (Gauge (Y,X))),k},{(len (Gauge (Y,X)))}} is non empty V26() V30() set
(Lower_Seq (Y,X)) . 1 is V13() Function-like set
(Lower_Seq (Y,X)) /. 1 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(E-max (L~ (Cage (Y,X)))) `1 is V11() V12() ext-real Element of REAL
(Gauge (Y,X)) * ((len (Gauge (Y,X))),k) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
((Gauge (Y,X)) * ((len (Gauge (Y,X))),k)) `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 V179() V180() V181() V182() V183() V184() V185() Element of NAT
go 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 go is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
rng (Upper_Seq (Y,X)) is V26() set
do 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 do is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
rng (Lower_Seq (Y,X)) is V26() set
go is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like one-to-one non constant V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq s.c.c. FinSequence of the U1 of (TOP-REAL 2)
len go is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
dom go is non empty non trivial V26() V180() V181() V182() V183() V184() V185() Element of bool NAT
go /. (len go) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
go . (len go) is V13() Function-like set
do is non empty non trivial V13() V16( NAT ) V17( the U1 of (TOP-REAL 2)) Function-like one-to-one non constant V26() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq s.c.c. FinSequence of the U1 of (TOP-REAL 2)
len do is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
dom do is non empty non trivial V26() V180() V181() V182() V183() V184() V185() Element of bool NAT
do /. 1 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
do . 1 is V13() Function-like set
(len go) - 1 is V11() V12() ext-real set
m is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
m + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(len go) -' 1 is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
LSeg (go,m) is functional Element of bool the U1 of (TOP-REAL 2)
L~ go is non empty functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
LSeg (((Gauge (Y,X)) * (j,k)),((Gauge (Y,X)) * (j,k))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg (go,m)) /\ (LSeg (((Gauge (Y,X)) * (j,k)),((Gauge (Y,X)) * (j,k)))) is functional Element of bool the U1 of (TOP-REAL 2)
go /. m is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((go /. m),((Gauge (Y,X)) * (j,k))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
W2 is set
LSeg (do,1) is functional Element of bool the U1 of (TOP-REAL 2)
L~ do is non empty functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
(LSeg (do,1)) /\ (LSeg (((Gauge (Y,X)) * (j,k)),((Gauge (Y,X)) * (j,k)))) is functional Element of bool the U1 of (TOP-REAL 2)
do /. (1 + 1) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (Y,X)) * (j,k)),(do /. (1 + 1))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
W2 is set
(LSeg (((Gauge (Y,X)) * (j,k)),((Gauge (Y,X)) * (j,k)))) /\ (LSeg (do,1)) is functional Element of bool the U1 of (TOP-REAL 2)
go /. 1 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
do /. (len do) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
rng go is non empty non trivial V26() set
rng do is non empty non trivial V26() set
{(go /. 1)} is non empty trivial functional V26() V30() 1 -element set
(L~ go) /\ (L~ do) is functional Element of bool the U1 of (TOP-REAL 2)
W2 is set
[(len (Gauge (Y,X))),k] is non empty set
{(len (Gauge (Y,X))),k} is non empty V26() V30() V180() V181() V182() V183() V184() V185() set
{{(len (Gauge (Y,X))),k},{(len (Gauge (Y,X)))}} is non empty V26() V30() set
W2 is set
(Gauge (Y,X)) * ((len (Gauge (Y,X))),k) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
((Gauge (Y,X)) * ((len (Gauge (Y,X))),k)) `1 is V11() V12() ext-real Element of REAL
(L~ (Upper_Seq (Y,X))) /\ (L~ (Lower_Seq (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
{(W-min (L~ (Cage (Y,X)))),(E-max (L~ (Cage (Y,X))))} is non empty functional V26() V30() set
go /. 2 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
((Gauge (Y,X)) * (j,k)) `1 is V11() V12() ext-real Element of REAL
((Gauge (Y,X)) * (j,k)) .. (Upper_Seq (Y,X)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
mid ((Upper_Seq (Y,X)),1,(((Gauge (Y,X)) * (j,k)) .. (Upper_Seq (Y,X)))) 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 (Y,X)) | (((Gauge (Y,X)) * (j,k)) .. (Upper_Seq (Y,X))) 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)
(Upper_Seq (Y,X)) /. 2 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
<*((Gauge (Y,X)) * (j,k)),((Gauge (Y,X)) * (j,k))*> 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)
pion1 is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
dom <*((Gauge (Y,X)) * (j,k)),((Gauge (Y,X)) * (j,k))*> is non empty non trivial V26() 2 -element V180() V181() V182() V183() V184() V185() Element of bool NAT
<*((Gauge (Y,X)) * (j,k)),((Gauge (Y,X)) * (j,k))*> /. pion1 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(Gauge (Y,X)) * (j,1) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
((Gauge (Y,X)) * (j,1)) `1 is V11() V12() ext-real Element of REAL
((Gauge (Y,X)) * (j,k)) `1 is V11() V12() ext-real Element of REAL
L~ <*((Gauge (Y,X)) * (j,k)),((Gauge (Y,X)) * (j,k))*> is non empty functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
<*((Gauge (Y,X)) * (j,k)),((Gauge (Y,X)) * (j,k))*> /. 1 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
len <*((Gauge (Y,X)) * (j,k)),((Gauge (Y,X)) * (j,k))*> is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
<*((Gauge (Y,X)) * (j,k)),((Gauge (Y,X)) * (j,k))*> /. (len <*((Gauge (Y,X)) * (j,k)),((Gauge (Y,X)) * (j,k))*>) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
pion1 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~ pion1 is functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
pion1 /. 1 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
len pion1 is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
pion1 /. (len pion1) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
pion1 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)
go ^' pion1 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)
(go ^' pion1) ^' do 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 (Y,X)) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))) 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)
len (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
len (go ^' pion1) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
1 + 0 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
len ((go ^' pion1) ^' do) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
pion1 /. 1 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(go ^' pion1) /. (len (go ^' pion1)) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
<*((Gauge (Y,X)) * (j,k)),((Gauge (Y,X)) * (j,k))*> /. 2 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg (pion1,1) is functional Element of bool the U1 of (TOP-REAL 2)
LSeg (go,((len go) -' 1)) is functional Element of bool the U1 of (TOP-REAL 2)
(LSeg (go,((len go) -' 1))) /\ (LSeg (pion1,1)) is functional Element of bool the U1 of (TOP-REAL 2)
len pion1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(LSeg (go,m)) /\ (LSeg (pion1,1)) is functional Element of bool the U1 of (TOP-REAL 2)
godo is set
{(go /. (len go))} is non empty trivial functional V26() V30() 1 -element set
2 + 0 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(len pion1) - 2 is V11() V12() ext-real set
(len (go ^' pion1)) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
((len (go ^' pion1)) + 1) - 1 is V11() V12() ext-real set
(len go) + (len pion1) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
((len go) + (len pion1)) - 1 is V11() V12() ext-real set
(len (go ^' pion1)) - 1 is V11() V12() ext-real set
(len go) + ((len pion1) - 2) is V11() V12() ext-real set
(len pion1) -' 2 is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(len go) + ((len pion1) -' 2) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(len (go ^' pion1)) -' 1 is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(len pion1) - 1 is V11() V12() ext-real set
(len pion1) -' 1 is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
((len pion1) -' 2) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
((len pion1) - 2) + 1 is V11() V12() ext-real set
((len pion1) - 1) + 1 is V11() V12() ext-real set
LSeg (pion1,((len pion1) -' 1)) is functional Element of bool the U1 of (TOP-REAL 2)
(LSeg (pion1,((len pion1) -' 1))) /\ (LSeg (do,1)) is functional Element of bool the U1 of (TOP-REAL 2)
godo is set
((len pion1) -' 1) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
pion1 /. (((len pion1) -' 1) + 1) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((go ^' pion1),((len go) + ((len pion1) -' 2))) is functional Element of bool the U1 of (TOP-REAL 2)
(LSeg ((go ^' pion1),((len go) + ((len pion1) -' 2)))) /\ (LSeg (do,1)) is functional Element of bool the U1 of (TOP-REAL 2)
{((go ^' pion1) /. (len (go ^' pion1)))} is non empty trivial functional V26() V30() 1 -element set
rng pion1 is V26() set
L~ pion1 is non empty functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
{(pion1 /. 1)} is non empty trivial functional V26() V30() 1 -element set
(L~ go) /\ (L~ pion1) is functional Element of bool the U1 of (TOP-REAL 2)
godo is set
godo is set
(L~ pion1) /\ (L~ (Upper_Seq (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
(rng go) /\ (rng pion1) is V26() set
pion1 /. (len pion1) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
{(pion1 /. (len pion1))} is non empty trivial functional V26() V30() 1 -element set
(L~ do) /\ (L~ pion1) is functional Element of bool the U1 of (TOP-REAL 2)
godo is set
godo is set
(L~ pion1) /\ (L~ (Lower_Seq (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
L~ (go ^' pion1) is functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
(L~ (go ^' pion1)) /\ (L~ do) is functional Element of bool the U1 of (TOP-REAL 2)
(L~ go) \/ (L~ pion1) is non empty functional Element of bool the U1 of (TOP-REAL 2)
((L~ go) \/ (L~ pion1)) /\ (L~ do) is functional Element of bool the U1 of (TOP-REAL 2)
{(do /. 1)} is non empty trivial functional V26() V30() 1 -element set
{(go /. 1)} \/ {(do /. 1)} is non empty V26() V30() set
(go ^' pion1) /. 1 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
{((go ^' pion1) /. 1)} is non empty trivial functional V26() V30() 1 -element set
{((go ^' pion1) /. 1)} \/ {(do /. 1)} is non empty V26() V30() set
{((go ^' pion1) /. 1),(do /. 1)} is non empty functional V26() V30() set
W-min Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-bound Y is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | Y is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | Y is V13() V16( the U1 of ((TOP-REAL 2) | Y)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | Y), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | Y),REAL:]
the U1 of ((TOP-REAL 2) | Y) is non empty set
[: the U1 of ((TOP-REAL 2) | Y),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | Y),REAL:] is set
K445(((TOP-REAL 2) | Y),(proj1 | Y)) is V11() V12() ext-real Element of REAL
W-most Y is functional Element of bool the U1 of (TOP-REAL 2)
SW-corner Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-bound Y is V11() V12() ext-real Element of REAL
proj2 | Y is V13() V16( the U1 of ((TOP-REAL 2) | Y)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | Y), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | Y),REAL:]
K445(((TOP-REAL 2) | Y),(proj2 | Y)) is V11() V12() ext-real Element of REAL
|[(W-bound Y),(S-bound Y)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NW-corner Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-bound Y is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | Y),(proj2 | Y)) is V11() V12() ext-real Element of REAL
|[(W-bound Y),(N-bound Y)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner Y),(NW-corner Y)) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner Y),(NW-corner Y))) /\ Y is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most Y) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most Y) is V13() V16( the U1 of ((TOP-REAL 2) | (W-most Y))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (W-most Y)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most Y)),REAL:]
the U1 of ((TOP-REAL 2) | (W-most Y)) is set
[: the U1 of ((TOP-REAL 2) | (W-most Y)),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (W-most Y)),REAL:] is set
K445(((TOP-REAL 2) | (W-most Y)),(proj2 | (W-most Y))) is V11() V12() ext-real Element of REAL
|[(W-bound Y),K445(((TOP-REAL 2) | (W-most Y)),(proj2 | (W-most Y)))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-max Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-bound Y is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | Y),(proj1 | Y)) is V11() V12() ext-real Element of REAL
E-most Y is functional Element of bool the U1 of (TOP-REAL 2)
SE-corner Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
|[(E-bound Y),(S-bound Y)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NE-corner Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
|[(E-bound Y),(N-bound Y)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner Y),(NE-corner Y)) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SE-corner Y),(NE-corner Y))) /\ Y is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (E-most Y) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most Y) is V13() V16( the U1 of ((TOP-REAL 2) | (E-most Y))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (E-most Y)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (E-most Y)),REAL:]
the U1 of ((TOP-REAL 2) | (E-most Y)) is set
[: the U1 of ((TOP-REAL 2) | (E-most Y)),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (E-most Y)),REAL:] is set
K446(((TOP-REAL 2) | (E-most Y)),(proj2 | (E-most Y))) is V11() V12() ext-real Element of REAL
|[(E-bound Y),K446(((TOP-REAL 2) | (E-most Y)),(proj2 | (E-most Y)))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
rng (Cage (Y,X)) is non empty non trivial V26() set
(Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))) /. 1 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))) is non empty functional V71( TOP-REAL 2) connected bounded being_simple_closed_curve compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
W-max (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is V13() V16( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),REAL:]
the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),REAL:] is set
K445(((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),(proj1 | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))) is V11() V12() ext-real Element of REAL
W-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is functional Element of bool the U1 of (TOP-REAL 2)
SW-corner (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is V11() V12() ext-real Element of REAL
proj2 | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is V13() V16( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),REAL:]
K445(((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),(proj2 | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),(S-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NW-corner (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),(proj2 | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),(N-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),(NW-corner (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),(NW-corner (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))))) /\ (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))) is V13() V16( the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),REAL:]
the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))) is set
[: the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),REAL:] is set
K446(((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),(proj2 | (W-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),K446(((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),(proj2 | (W-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(W-max (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))) .. (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
N-min (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is functional Element of bool the U1 of (TOP-REAL 2)
NE-corner (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),(proj1 | (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),(N-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((NW-corner (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),(NE-corner (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((NW-corner (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))),(NE-corner (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))))) /\ (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))) is V13() V16( the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),REAL:]
the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))) is set
[: the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),REAL:] is set
K445(((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),(proj1 | (N-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))))) is V11() V12() ext-real Element of REAL
|[K445(((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),(proj1 | (N-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))))),(N-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(N-min (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))) .. (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
N-max (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
K446(((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),(proj1 | (N-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))))) is V11() V12() ext-real Element of REAL
|[K446(((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))),(proj1 | (N-most (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))))),(N-bound (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X))))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(N-max (L~ (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))) .. (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(E-max (L~ (Cage (Y,X)))) .. (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
godo 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 FinSequence of the U1 of (TOP-REAL 2)
right_cell (godo,1,(Gauge (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
L~ godo is non empty functional V71( TOP-REAL 2) connected bounded being_simple_closed_curve compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
(right_cell (godo,1,(Gauge (Y,X)))) \ (L~ godo) is functional Element of bool the U1 of (TOP-REAL 2)
RightComp godo is non empty functional Element of bool the U1 of (TOP-REAL 2)
(L~ (go ^' pion1)) \/ (L~ do) is non empty functional Element of bool the U1 of (TOP-REAL 2)
((L~ go) \/ (L~ pion1)) \/ (L~ do) is non empty functional Element of bool the U1 of (TOP-REAL 2)
(L~ (Upper_Seq (Y,X))) \/ (L~ (Lower_Seq (Y,X))) is non empty functional Element of bool the U1 of (TOP-REAL 2)
right_cell ((Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))),1) is functional Element of bool the U1 of (TOP-REAL 2)
GoB (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))) is V13() non empty-yielding V16( NAT ) V17(K233( 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 K233( the U1 of (TOP-REAL 2))
right_cell ((Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))),1,(GoB (Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))))) is functional Element of bool the U1 of (TOP-REAL 2)
GoB (Cage (Y,X)) is V13() non empty-yielding V16( NAT ) V17(K233( 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 K233( the U1 of (TOP-REAL 2))
right_cell ((Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))),1,(GoB (Cage (Y,X)))) is functional Element of bool the U1 of (TOP-REAL 2)
right_cell ((Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))),1,(Gauge (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
(Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))) -: (E-max (L~ (Cage (Y,X)))) 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)
right_cell (((Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))) -: (E-max (L~ (Cage (Y,X))))),1,(Gauge (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
right_cell ((Upper_Seq (Y,X)),1,(Gauge (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
right_cell ((R_Cut ((Upper_Seq (Y,X)),((Gauge (Y,X)) * (j,k)))),1,(Gauge (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
right_cell ((go ^' pion1),1,(Gauge (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
godo /. 1 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
godo /. 2 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(go ^' pion1) /. 2 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(Upper_Seq (Y,X)) ^' (Lower_Seq (Y,X)) 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 (Y,X)) ^' (Lower_Seq (Y,X))) /. 2 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(Rotate ((Cage (Y,X)),(W-min (L~ (Cage (Y,X)))))) /. 2 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(L~ go) \/ (L~ do) is non empty functional Element of bool the U1 of (TOP-REAL 2)
W-min ((L~ go) \/ (L~ do)) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-bound ((L~ go) \/ (L~ do)) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | ((L~ go) \/ (L~ do)) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | ((L~ go) \/ (L~ do)) is V13() V16( the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ do)))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ do))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ do))),REAL:]
the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ do))) is non empty set
[: the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ do))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ do))),REAL:] is set
K445(((TOP-REAL 2) | ((L~ go) \/ (L~ do))),(proj1 | ((L~ go) \/ (L~ do)))) is V11() V12() ext-real Element of REAL
W-most ((L~ go) \/ (L~ do)) is functional Element of bool the U1 of (TOP-REAL 2)
SW-corner ((L~ go) \/ (L~ do)) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-bound ((L~ go) \/ (L~ do)) is V11() V12() ext-real Element of REAL
proj2 | ((L~ go) \/ (L~ do)) is V13() V16( the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ do)))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ do))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ do))),REAL:]
K445(((TOP-REAL 2) | ((L~ go) \/ (L~ do))),(proj2 | ((L~ go) \/ (L~ do)))) is V11() V12() ext-real Element of REAL
|[(W-bound ((L~ go) \/ (L~ do))),(S-bound ((L~ go) \/ (L~ do)))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NW-corner ((L~ go) \/ (L~ do)) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-bound ((L~ go) \/ (L~ do)) is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | ((L~ go) \/ (L~ do))),(proj2 | ((L~ go) \/ (L~ do)))) is V11() V12() ext-real Element of REAL
|[(W-bound ((L~ go) \/ (L~ do))),(N-bound ((L~ go) \/ (L~ do)))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner ((L~ go) \/ (L~ do))),(NW-corner ((L~ go) \/ (L~ do)))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner ((L~ go) \/ (L~ do))),(NW-corner ((L~ go) \/ (L~ do))))) /\ ((L~ go) \/ (L~ do)) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most ((L~ go) \/ (L~ do))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most ((L~ go) \/ (L~ do))) is V13() V16( the U1 of ((TOP-REAL 2) | (W-most ((L~ go) \/ (L~ do))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (W-most ((L~ go) \/ (L~ do)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most ((L~ go) \/ (L~ do)))),REAL:]
the U1 of ((TOP-REAL 2) | (W-most ((L~ go) \/ (L~ do)))) is set
[: the U1 of ((TOP-REAL 2) | (W-most ((L~ go) \/ (L~ do)))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (W-most ((L~ go) \/ (L~ do)))),REAL:] is set
K445(((TOP-REAL 2) | (W-most ((L~ go) \/ (L~ do)))),(proj2 | (W-most ((L~ go) \/ (L~ do))))) is V11() V12() ext-real Element of REAL
|[(W-bound ((L~ go) \/ (L~ do))),K445(((TOP-REAL 2) | (W-most ((L~ go) \/ (L~ do)))),(proj2 | (W-most ((L~ go) \/ (L~ do)))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(W-min ((L~ go) \/ (L~ do))) `1 is V11() V12() ext-real Element of REAL
W-bound (LSeg (((Gauge (Y,X)) * (j,k)),((Gauge (Y,X)) * (j,k)))) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (LSeg (((Gauge (Y,X)) * (j,k)),((Gauge (Y,X)) * (j,k)))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (LSeg (((Gauge (Y,X)) * (j,k)),((Gauge (Y,X)) * (j,k)))) is V13() V16( the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (Y,X)) * (j,k)),((Gauge (Y,X)) * (j,k)))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (Y,X)) * (j,k)),((Gauge (Y,X)) * (j,k))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (Y,X)) * (j,k)),((Gauge (Y,X)) * (j,k))))),REAL:]
the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (Y,X)) * (j,k)),((Gauge (Y,X)) * (j,k))))) is set
[: the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (Y,X)) * (j,k)),((Gauge (Y,X)) * (j,k))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (Y,X)) * (j,k)),((Gauge (Y,X)) * (j,k))))),REAL:] is set
K445(((TOP-REAL 2) | (LSeg (((Gauge (Y,X)) * (j,k)),((Gauge (Y,X)) * (j,k))))),(proj1 | (LSeg (((Gauge (Y,X)) * (j,k)),((Gauge (Y,X)) * (j,k)))))) is V11() V12() ext-real Element of REAL
W-bound (L~ pion1) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ pion1) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ pion1) is V13() V16( the U1 of ((TOP-REAL 2) | (L~ pion1))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (L~ pion1)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ pion1)),REAL:]
the U1 of ((TOP-REAL 2) | (L~ pion1)) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ pion1)),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (L~ pion1)),REAL:] is set
K445(((TOP-REAL 2) | (L~ pion1)),(proj1 | (L~ pion1))) is V11() V12() ext-real Element of REAL
((L~ go) \/ (L~ do)) \/ (L~ pion1) is non empty functional Element of bool the U1 of (TOP-REAL 2)
W-min (((L~ go) \/ (L~ do)) \/ (L~ pion1)) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-bound (((L~ go) \/ (L~ do)) \/ (L~ pion1)) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (((L~ go) \/ (L~ do)) \/ (L~ pion1)) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (((L~ go) \/ (L~ do)) \/ (L~ pion1)) is V13() V16( the U1 of ((TOP-REAL 2) | (((L~ go) \/ (L~ do)) \/ (L~ pion1)))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (((L~ go) \/ (L~ do)) \/ (L~ pion1))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (((L~ go) \/ (L~ do)) \/ (L~ pion1))),REAL:]
the U1 of ((TOP-REAL 2) | (((L~ go) \/ (L~ do)) \/ (L~ pion1))) is non empty set
[: the U1 of ((TOP-REAL 2) | (((L~ go) \/ (L~ do)) \/ (L~ pion1))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (((L~ go) \/ (L~ do)) \/ (L~ pion1))),REAL:] is set
K445(((TOP-REAL 2) | (((L~ go) \/ (L~ do)) \/ (L~ pion1))),(proj1 | (((L~ go) \/ (L~ do)) \/ (L~ pion1)))) is V11() V12() ext-real Element of REAL
W-most (((L~ go) \/ (L~ do)) \/ (L~ pion1)) is functional Element of bool the U1 of (TOP-REAL 2)
SW-corner (((L~ go) \/ (L~ do)) \/ (L~ pion1)) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-bound (((L~ go) \/ (L~ do)) \/ (L~ pion1)) is V11() V12() ext-real Element of REAL
proj2 | (((L~ go) \/ (L~ do)) \/ (L~ pion1)) is V13() V16( the U1 of ((TOP-REAL 2) | (((L~ go) \/ (L~ do)) \/ (L~ pion1)))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (((L~ go) \/ (L~ do)) \/ (L~ pion1))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (((L~ go) \/ (L~ do)) \/ (L~ pion1))),REAL:]
K445(((TOP-REAL 2) | (((L~ go) \/ (L~ do)) \/ (L~ pion1))),(proj2 | (((L~ go) \/ (L~ do)) \/ (L~ pion1)))) is V11() V12() ext-real Element of REAL
|[(W-bound (((L~ go) \/ (L~ do)) \/ (L~ pion1))),(S-bound (((L~ go) \/ (L~ do)) \/ (L~ pion1)))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NW-corner (((L~ go) \/ (L~ do)) \/ (L~ pion1)) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-bound (((L~ go) \/ (L~ do)) \/ (L~ pion1)) is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | (((L~ go) \/ (L~ do)) \/ (L~ pion1))),(proj2 | (((L~ go) \/ (L~ do)) \/ (L~ pion1)))) is V11() V12() ext-real Element of REAL
|[(W-bound (((L~ go) \/ (L~ do)) \/ (L~ pion1))),(N-bound (((L~ go) \/ (L~ do)) \/ (L~ pion1)))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (((L~ go) \/ (L~ do)) \/ (L~ pion1))),(NW-corner (((L~ go) \/ (L~ do)) \/ (L~ pion1)))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (((L~ go) \/ (L~ do)) \/ (L~ pion1))),(NW-corner (((L~ go) \/ (L~ do)) \/ (L~ pion1))))) /\ (((L~ go) \/ (L~ do)) \/ (L~ pion1)) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (((L~ go) \/ (L~ do)) \/ (L~ pion1))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (((L~ go) \/ (L~ do)) \/ (L~ pion1))) is V13() V16( the U1 of ((TOP-REAL 2) | (W-most (((L~ go) \/ (L~ do)) \/ (L~ pion1))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (W-most (((L~ go) \/ (L~ do)) \/ (L~ pion1)))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most (((L~ go) \/ (L~ do)) \/ (L~ pion1)))),REAL:]
the U1 of ((TOP-REAL 2) | (W-most (((L~ go) \/ (L~ do)) \/ (L~ pion1)))) is set
[: the U1 of ((TOP-REAL 2) | (W-most (((L~ go) \/ (L~ do)) \/ (L~ pion1)))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (W-most (((L~ go) \/ (L~ do)) \/ (L~ pion1)))),REAL:] is set
K445(((TOP-REAL 2) | (W-most (((L~ go) \/ (L~ do)) \/ (L~ pion1)))),(proj2 | (W-most (((L~ go) \/ (L~ do)) \/ (L~ pion1))))) is V11() V12() ext-real Element of REAL
|[(W-bound (((L~ go) \/ (L~ do)) \/ (L~ pion1))),K445(((TOP-REAL 2) | (W-most (((L~ go) \/ (L~ do)) \/ (L~ pion1)))),(proj2 | (W-most (((L~ go) \/ (L~ do)) \/ (L~ pion1)))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-min (L~ godo) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-bound (L~ godo) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ godo) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ godo) is V13() V16( the U1 of ((TOP-REAL 2) | (L~ godo))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (L~ godo)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ godo)),REAL:]
the U1 of ((TOP-REAL 2) | (L~ godo)) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ godo)),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (L~ godo)),REAL:] is set
K445(((TOP-REAL 2) | (L~ godo)),(proj1 | (L~ godo))) is V11() V12() ext-real Element of REAL
W-most (L~ godo) is functional Element of bool the U1 of (TOP-REAL 2)
SW-corner (L~ godo) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-bound (L~ godo) is V11() V12() ext-real Element of REAL
proj2 | (L~ godo) is V13() V16( the U1 of ((TOP-REAL 2) | (L~ godo))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (L~ godo)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ godo)),REAL:]
K445(((TOP-REAL 2) | (L~ godo)),(proj2 | (L~ godo))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ godo)),(S-bound (L~ godo))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NW-corner (L~ godo) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-bound (L~ godo) is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | (L~ godo)),(proj2 | (L~ godo))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ godo)),(N-bound (L~ godo))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ godo)),(NW-corner (L~ godo))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner (L~ godo)),(NW-corner (L~ godo)))) /\ (L~ godo) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ godo)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ godo)) is V13() V16( the U1 of ((TOP-REAL 2) | (W-most (L~ godo)))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (W-most (L~ godo))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ godo))),REAL:]
the U1 of ((TOP-REAL 2) | (W-most (L~ godo))) is set
[: the U1 of ((TOP-REAL 2) | (W-most (L~ godo))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (W-most (L~ godo))),REAL:] is set
K445(((TOP-REAL 2) | (W-most (L~ godo))),(proj2 | (W-most (L~ godo)))) is V11() V12() ext-real Element of REAL
|[(W-bound (L~ godo)),K445(((TOP-REAL 2) | (W-most (L~ godo))),(proj2 | (W-most (L~ godo))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
rng godo is non empty non trivial V26() set
dom godo is non empty non trivial V26() V180() V181() V182() V183() V184() V185() Element of bool NAT
(godo /. 2) `1 is V11() V12() ext-real Element of REAL
(W-min (L~ godo)) `1 is V11() V12() ext-real Element of REAL
Rotate (godo,(W-min (L~ godo))) 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 FinSequence of the U1 of (TOP-REAL 2)
(Rotate (godo,(W-min (L~ godo)))) /. 2 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(Upper_Seq (Y,X)) . (len (Upper_Seq (Y,X))) is V13() Function-like set
(Upper_Seq (Y,X)) /. (len (Upper_Seq (Y,X))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
east_halfline (E-max Y) is non empty functional connected V259( TOP-REAL 2) Element of bool the U1 of (TOP-REAL 2)
W is set
p is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(east_halfline (E-max Y)) /\ (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
p `1 is V11() V12() ext-real Element of REAL
godo 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~ godo is non empty functional V71( TOP-REAL 2) connected bounded being_simple_closed_curve compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
W is set
p is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
p `2 is V11() V12() ext-real Element of REAL
(E-max Y) `2 is V11() V12() ext-real Element of REAL
j + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(j + 1) - 1 is V11() V12() ext-real set
(len (Gauge (Y,X))) - 1 is V11() V12() ext-real set
(len (Gauge (Y,X))) -' 1 is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
p `1 is V11() V12() ext-real Element of REAL
(Gauge (Y,X)) * (((len (Gauge (Y,X))) -' 1),1) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
((Gauge (Y,X)) * (((len (Gauge (Y,X))) -' 1),1)) `1 is V11() V12() ext-real Element of REAL
(E-max Y) `1 is V11() V12() ext-real Element of REAL
W is set
(E-max Y) `2 is V11() V12() ext-real Element of REAL
p is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
p `2 is V11() V12() ext-real Element of REAL
Index (p,do) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
((Gauge (Y,X)) * (j,k)) .. (Lower_Seq (Y,X)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(Index (p,do)) + (((Gauge (Y,X)) * (j,k)) .. (Lower_Seq (Y,X))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
((Index (p,do)) + (((Gauge (Y,X)) * (j,k)) .. (Lower_Seq (Y,X)))) -' 1 is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))) 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 (Y,X)),(E-max (L~ (Cage (Y,X)))))) is non empty functional V71( TOP-REAL 2) connected bounded being_simple_closed_curve compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
t is V6() V10() V11() V12() V26() cardinal ext-real non negative set
(Lower_Seq (Y,X)) . t is V13() Function-like set
Index (((Gauge (Y,X)) * (j,k)),(Lower_Seq (Y,X))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(Index (((Gauge (Y,X)) * (j,k)),(Lower_Seq (Y,X)))) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
len (L_Cut ((Lower_Seq (Y,X)),((Gauge (Y,X)) * (j,k)))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(len (Lower_Seq (Y,X))) - (Index (((Gauge (Y,X)) * (j,k)),(Lower_Seq (Y,X)))) is V11() V12() ext-real set
(len (Lower_Seq (Y,X))) -' (Index (((Gauge (Y,X)) * (j,k)),(Lower_Seq (Y,X)))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(Index (p,do)) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
((len (Lower_Seq (Y,X))) -' (Index (((Gauge (Y,X)) * (j,k)),(Lower_Seq (Y,X))))) - 1 is V11() V12() ext-real set
mid ((Lower_Seq (Y,X)),(((Gauge (Y,X)) * (j,k)) .. (Lower_Seq (Y,X))),(len (Lower_Seq (Y,X)))) 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 (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))) is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(east_halfline (E-max Y)) /\ (L~ (Cage (Y,X))) is functional Element of bool the U1 of (TOP-REAL 2)
p `1 is V11() V12() ext-real Element of REAL
GoB (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))) is V13() non empty-yielding V16( NAT ) V17(K233( 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 K233( the U1 of (TOP-REAL 2))
jj2 is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(Gauge (Y,X)) * ((len (Gauge (Y,X))),jj2) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
[(len (Gauge (Y,X))),jj2] is non empty set
{(len (Gauge (Y,X))),jj2} is non empty V26() V30() V180() V181() V182() V183() V184() V185() set
{{(len (Gauge (Y,X))),jj2},{(len (Gauge (Y,X)))}} is non empty V26() V30() set
(Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))) -: (W-min (L~ (Cage (Y,X)))) 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)
LSeg ((Lower_Seq (Y,X)),1) is functional Element of bool the U1 of (TOP-REAL 2)
LSeg ((Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))),1) is functional Element of bool the U1 of (TOP-REAL 2)
(Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))) /. 1 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))) /. (1 + 1) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
ii is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
jj is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
jj + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
[ii,(jj + 1)] is non empty set
{ii,(jj + 1)} is non empty V26() V30() V180() V181() V182() V183() V184() V185() set
{ii} is non empty trivial V26() V30() 1 -element V180() V181() V182() V183() V184() V185() set
{{ii,(jj + 1)},{ii}} is non empty V26() V30() set
[ii,jj] is non empty set
{ii,jj} is non empty V26() V30() V180() V181() V182() V183() V184() V185() set
{{ii,jj},{ii}} is non empty V26() V30() set
(Gauge (Y,X)) * (ii,(jj + 1)) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(Gauge (Y,X)) * (ii,jj) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(jj + 1) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
E-max (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is V13() V16( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),REAL:]
the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))) is non empty set
[: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),REAL:] is set
K446(((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),(proj1 | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))) is V11() V12() ext-real Element of REAL
E-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is functional Element of bool the U1 of (TOP-REAL 2)
SE-corner (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is V11() V12() ext-real Element of REAL
proj2 | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is V13() V16( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),REAL:]
K445(((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),(proj2 | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),(S-bound (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NE-corner (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),(proj2 | (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),(N-bound (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),(NE-corner (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SE-corner (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),(NE-corner (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))))) /\ (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))) is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))) is V13() V16( the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))),REAL:]
the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))) is set
[: the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))),REAL:] is set
K446(((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))),(proj2 | (E-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))))) is V11() V12() ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))))),K446(((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))),(proj2 | (E-most (L~ (Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X))))))))))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
4 - 1 is V11() V12() ext-real set
ii - 1 is V11() V12() ext-real set
ii -' 1 is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(Gauge (Y,X)) * ((len (Gauge (Y,X))),jj) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
((Gauge (Y,X)) * ((len (Gauge (Y,X))),jj)) `1 is V11() V12() ext-real Element of REAL
ii + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
right_cell ((Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))),1) is functional Element of bool the U1 of (TOP-REAL 2)
cell ((Gauge (Y,X)),(ii -' 1),jj) is functional Element of bool the U1 of (TOP-REAL 2)
v_strip ((Gauge (Y,X)),(ii -' 1)) is functional Element of bool the U1 of (TOP-REAL 2)
h_strip ((Gauge (Y,X)),jj) is functional Element of bool the U1 of (TOP-REAL 2)
(v_strip ((Gauge (Y,X)),(ii -' 1))) /\ (h_strip ((Gauge (Y,X)),jj)) is functional Element of bool the U1 of (TOP-REAL 2)
(Gauge (Y,X)) * ((len (Gauge (Y,X))),(jj + 1)) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
((Gauge (Y,X)) * ((len (Gauge (Y,X))),(jj + 1))) `1 is V11() V12() ext-real Element of REAL
(ii -' 1) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(Gauge (Y,X)) * ((ii -' 1),(jj + 1)) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
((Gauge (Y,X)) * ((ii -' 1),(jj + 1))) `2 is V11() V12() ext-real Element of REAL
(Gauge (Y,X)) * (1,(jj + 1)) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
((Gauge (Y,X)) * (1,(jj + 1))) `2 is V11() V12() ext-real Element of REAL
((Gauge (Y,X)) * (ii,(jj + 1))) `2 is V11() V12() ext-real Element of REAL
(Gauge (Y,X)) * ((ii -' 1),jj) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
((Gauge (Y,X)) * ((ii -' 1),jj)) `2 is V11() V12() ext-real Element of REAL
(Gauge (Y,X)) * (1,jj) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
((Gauge (Y,X)) * (1,jj)) `2 is V11() V12() ext-real Element of REAL
((Gauge (Y,X)) * (ii,jj)) `2 is V11() V12() ext-real Element of REAL
LSeg (((Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))) /. 1),((Rotate ((Cage (Y,X)),(E-max (L~ (Cage (Y,X)))))) /. (1 + 1))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
0 + (Index (((Gauge (Y,X)) * (j,k)),(Lower_Seq (Y,X)))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
((len (Lower_Seq (Y,X))) - (Index (((Gauge (Y,X)) * (j,k)),(Lower_Seq (Y,X))))) - 1 is V11() V12() ext-real set
(len (Lower_Seq (Y,X))) - (((Gauge (Y,X)) * (j,k)) .. (Lower_Seq (Y,X))) is V11() V12() ext-real set
(len (Lower_Seq (Y,X))) -' (((Gauge (Y,X)) * (j,k)) .. (Lower_Seq (Y,X))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
((len (Lower_Seq (Y,X))) -' (((Gauge (Y,X)) * (j,k)) .. (Lower_Seq (Y,X)))) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
LSeg (do,(Index (p,do))) is functional Element of bool the U1 of (TOP-REAL 2)
LSeg ((mid ((Lower_Seq (Y,X)),(((Gauge (Y,X)) * (j,k)) .. (Lower_Seq (Y,X))),(len (Lower_Seq (Y,X))))),(Index (p,do))) is functional Element of bool the U1 of (TOP-REAL 2)
LSeg ((Lower_Seq (Y,X)),(((Index (p,do)) + (((Gauge (Y,X)) * (j,k)) .. (Lower_Seq (Y,X)))) -' 1)) is functional Element of bool the U1 of (TOP-REAL 2)
(1 + 1) + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
((1 + 1) + 1) - 1 is V11() V12() ext-real set
((Index (p,do)) + (((Gauge (Y,X)) * (j,k)) .. (Lower_Seq (Y,X)))) - 1 is V11() V12() ext-real set
(LSeg ((Lower_Seq (Y,X)),1)) /\ (LSeg ((Lower_Seq (Y,X)),(((Index (p,do)) + (((Gauge (Y,X)) * (j,k)) .. (Lower_Seq (Y,X)))) -' 1))) is functional Element of bool the U1 of (TOP-REAL 2)
(Lower_Seq (Y,X)) /. 2 is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
{((Lower_Seq (Y,X)) /. 2)} is non empty trivial functional V26() V30() 1 -element set
p .. (Lower_Seq (Y,X)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(Gauge (Y,X)) * ((len (Gauge (Y,X))),k) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
((Gauge (Y,X)) * ((len (Gauge (Y,X))),k)) `1 is V11() V12() ext-real Element of REAL
(L~ godo) ` is non empty functional Element of bool the U1 of (TOP-REAL 2)
W is functional Element of bool the U1 of (TOP-REAL 2)
UBD (L~ godo) is non empty functional connected Element of bool the U1 of (TOP-REAL 2)
LeftComp godo is non empty functional Element of bool the U1 of (TOP-REAL 2)
X is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
Y is non empty functional connected bounded being_simple_closed_curve compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
Gauge (Y,X) is V13() non empty-yielding V16( NAT ) V17(K233( 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 K233( the U1 of (TOP-REAL 2))
len (Gauge (Y,X)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
width (Gauge (Y,X)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
Cage (Y,X) 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 (Y,X)) is non empty functional V71( TOP-REAL 2) connected bounded being_simple_closed_curve compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
Upper_Arc (L~ (Cage (Y,X))) is non empty functional Element of bool the U1 of (TOP-REAL 2)
Lower_Arc (L~ (Cage (Y,X))) is non empty functional Element of bool the U1 of (TOP-REAL 2)
Lower_Arc Y is non empty functional Element of bool the U1 of (TOP-REAL 2)
j is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
k is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
k is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(Gauge (Y,X)) * (j,k) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(Gauge (Y,X)) * (j,k) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (Y,X)) * (j,k)),((Gauge (Y,X)) * (j,k))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg (((Gauge (Y,X)) * (j,k)),((Gauge (Y,X)) * (j,k)))) /\ (Upper_Arc (L~ (Cage (Y,X)))) is functional Element of bool the U1 of (TOP-REAL 2)
{((Gauge (Y,X)) * (j,k))} is non empty trivial functional V26() V30() 1 -element set
(LSeg (((Gauge (Y,X)) * (j,k)),((Gauge (Y,X)) * (j,k)))) /\ (Lower_Arc (L~ (Cage (Y,X)))) is functional Element of bool the U1 of (TOP-REAL 2)
{((Gauge (Y,X)) * (j,k))} is non empty trivial functional V26() V30() 1 -element set
Lower_Seq (Y,X) 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 (Y,X)) is non empty functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
Upper_Seq (Y,X) 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 (Y,X)) is non empty functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
X is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
Y is non empty functional connected bounded being_simple_closed_curve compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
Gauge (Y,X) is V13() non empty-yielding V16( NAT ) V17(K233( 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 K233( the U1 of (TOP-REAL 2))
len (Gauge (Y,X)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
width (Gauge (Y,X)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
Cage (Y,X) 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 (Y,X)) is non empty functional V71( TOP-REAL 2) connected bounded being_simple_closed_curve compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
Upper_Arc (L~ (Cage (Y,X))) is non empty functional Element of bool the U1 of (TOP-REAL 2)
Lower_Arc (L~ (Cage (Y,X))) is non empty functional Element of bool the U1 of (TOP-REAL 2)
Upper_Arc Y is non empty functional Element of bool the U1 of (TOP-REAL 2)
j is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
k is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
k is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(Gauge (Y,X)) * (j,k) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(Gauge (Y,X)) * (j,k) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (Y,X)) * (j,k)),((Gauge (Y,X)) * (j,k))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg (((Gauge (Y,X)) * (j,k)),((Gauge (Y,X)) * (j,k)))) /\ (Upper_Arc (L~ (Cage (Y,X)))) is functional Element of bool the U1 of (TOP-REAL 2)
{((Gauge (Y,X)) * (j,k))} is non empty trivial functional V26() V30() 1 -element set
(LSeg (((Gauge (Y,X)) * (j,k)),((Gauge (Y,X)) * (j,k)))) /\ (Lower_Arc (L~ (Cage (Y,X)))) is functional Element of bool the U1 of (TOP-REAL 2)
{((Gauge (Y,X)) * (j,k))} is non empty trivial functional V26() V30() 1 -element set
Lower_Seq (Y,X) 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 (Y,X)) is non empty functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
Upper_Seq (Y,X) 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 (Y,X)) is non empty functional V71( TOP-REAL 2) bounded compact Element of bool the U1 of (TOP-REAL 2)
X is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
X + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
Y is non empty functional connected bounded compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
Gauge (Y,(X + 1)) is V13() non empty-yielding V16( NAT ) V17(K233( 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 K233( the U1 of (TOP-REAL 2))
Center (Gauge (Y,(X + 1))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
Cage (Y,(X + 1)) 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 (Y,(X + 1))) is non empty functional V71( TOP-REAL 2) connected bounded being_simple_closed_curve compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
Upper_Arc (L~ (Cage (Y,(X + 1)))) is non empty functional Element of bool the U1 of (TOP-REAL 2)
width (Gauge (Y,(X + 1))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
Gauge (Y,1) is V13() non empty-yielding V16( NAT ) V17(K233( 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 K233( the U1 of (TOP-REAL 2))
Center (Gauge (Y,1)) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(Gauge (Y,1)) * ((Center (Gauge (Y,1))),1) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
Lower_Arc (L~ (Cage (Y,(X + 1)))) is non empty functional Element of bool the U1 of (TOP-REAL 2)
j is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(Gauge (Y,(X + 1))) * ((Center (Gauge (Y,(X + 1)))),j) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (Y,1)) * ((Center (Gauge (Y,1))),1)),((Gauge (Y,(X + 1))) * ((Center (Gauge (Y,(X + 1)))),j))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
len (Gauge (Y,(X + 1))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
0 + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(Gauge (Y,(X + 1))) * ((Center (Gauge (Y,(X + 1)))),1) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (Y,(X + 1))) * ((Center (Gauge (Y,(X + 1)))),1)),((Gauge (Y,(X + 1))) * ((Center (Gauge (Y,(X + 1)))),j))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
X is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
X + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
Y is non empty functional connected bounded being_simple_closed_curve compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
Gauge (Y,(X + 1)) is V13() non empty-yielding V16( NAT ) V17(K233( 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 K233( the U1 of (TOP-REAL 2))
width (Gauge (Y,(X + 1))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
Center (Gauge (Y,(X + 1))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
Cage (Y,(X + 1)) 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 (Y,(X + 1))) is non empty functional V71( TOP-REAL 2) connected bounded being_simple_closed_curve compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
Upper_Arc (L~ (Cage (Y,(X + 1)))) is non empty functional Element of bool the U1 of (TOP-REAL 2)
Lower_Arc (L~ (Cage (Y,(X + 1)))) is non empty functional Element of bool the U1 of (TOP-REAL 2)
Lower_Arc Y is non empty functional Element of bool the U1 of (TOP-REAL 2)
j is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
k is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(Gauge (Y,(X + 1))) * ((Center (Gauge (Y,(X + 1)))),j) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(Gauge (Y,(X + 1))) * ((Center (Gauge (Y,(X + 1)))),k) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (Y,(X + 1))) * ((Center (Gauge (Y,(X + 1)))),j)),((Gauge (Y,(X + 1))) * ((Center (Gauge (Y,(X + 1)))),k))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg (((Gauge (Y,(X + 1))) * ((Center (Gauge (Y,(X + 1)))),j)),((Gauge (Y,(X + 1))) * ((Center (Gauge (Y,(X + 1)))),k)))) /\ (Upper_Arc (L~ (Cage (Y,(X + 1))))) is functional Element of bool the U1 of (TOP-REAL 2)
{((Gauge (Y,(X + 1))) * ((Center (Gauge (Y,(X + 1)))),k))} is non empty trivial functional V26() V30() 1 -element set
(LSeg (((Gauge (Y,(X + 1))) * ((Center (Gauge (Y,(X + 1)))),j)),((Gauge (Y,(X + 1))) * ((Center (Gauge (Y,(X + 1)))),k)))) /\ (Lower_Arc (L~ (Cage (Y,(X + 1))))) is functional Element of bool the U1 of (TOP-REAL 2)
{((Gauge (Y,(X + 1))) * ((Center (Gauge (Y,(X + 1)))),j))} is non empty trivial functional V26() V30() 1 -element set
len (Gauge (Y,(X + 1))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
X is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
X + 1 is non empty V6() V10() V11() V12() V26() cardinal V37() ext-real positive non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
Y is non empty functional connected bounded being_simple_closed_curve compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
Gauge (Y,(X + 1)) is V13() non empty-yielding V16( NAT ) V17(K233( 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 K233( the U1 of (TOP-REAL 2))
width (Gauge (Y,(X + 1))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
Center (Gauge (Y,(X + 1))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
Cage (Y,(X + 1)) 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 (Y,(X + 1))) is non empty functional V71( TOP-REAL 2) connected bounded being_simple_closed_curve compact non horizontal non vertical Element of bool the U1 of (TOP-REAL 2)
Upper_Arc (L~ (Cage (Y,(X + 1)))) is non empty functional Element of bool the U1 of (TOP-REAL 2)
Lower_Arc (L~ (Cage (Y,(X + 1)))) is non empty functional Element of bool the U1 of (TOP-REAL 2)
Upper_Arc Y is non empty functional Element of bool the U1 of (TOP-REAL 2)
j is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
k is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
(Gauge (Y,(X + 1))) * ((Center (Gauge (Y,(X + 1)))),j) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(Gauge (Y,(X + 1))) * ((Center (Gauge (Y,(X + 1)))),k) is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (Y,(X + 1))) * ((Center (Gauge (Y,(X + 1)))),j)),((Gauge (Y,(X + 1))) * ((Center (Gauge (Y,(X + 1)))),k))) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg (((Gauge (Y,(X + 1))) * ((Center (Gauge (Y,(X + 1)))),j)),((Gauge (Y,(X + 1))) * ((Center (Gauge (Y,(X + 1)))),k)))) /\ (Upper_Arc (L~ (Cage (Y,(X + 1))))) is functional Element of bool the U1 of (TOP-REAL 2)
{((Gauge (Y,(X + 1))) * ((Center (Gauge (Y,(X + 1)))),k))} is non empty trivial functional V26() V30() 1 -element set
(LSeg (((Gauge (Y,(X + 1))) * ((Center (Gauge (Y,(X + 1)))),j)),((Gauge (Y,(X + 1))) * ((Center (Gauge (Y,(X + 1)))),k)))) /\ (Lower_Arc (L~ (Cage (Y,(X + 1))))) is functional Element of bool the U1 of (TOP-REAL 2)
{((Gauge (Y,(X + 1))) * ((Center (Gauge (Y,(X + 1)))),j))} is non empty trivial functional V26() V30() 1 -element set
len (Gauge (Y,(X + 1))) is V6() V10() V11() V12() V26() cardinal V37() ext-real non negative V179() V180() V181() V182() V183() V184() V185() Element of NAT
X is non empty functional bounded compact Element of bool the U1 of (TOP-REAL 2)
Y is non empty functional bounded compact Element of bool the U1 of (TOP-REAL 2)
W-min Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-bound Y is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | Y is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | Y is V13() V16( the U1 of ((TOP-REAL 2) | Y)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | Y), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | Y),REAL:]
the U1 of ((TOP-REAL 2) | Y) is non empty set
[: the U1 of ((TOP-REAL 2) | Y),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | Y),REAL:] is set
K445(((TOP-REAL 2) | Y),(proj1 | Y)) is V11() V12() ext-real Element of REAL
W-most Y is functional Element of bool the U1 of (TOP-REAL 2)
SW-corner Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-bound Y is V11() V12() ext-real Element of REAL
proj2 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | Y is V13() V16( the U1 of ((TOP-REAL 2) | Y)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | Y), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | Y),REAL:]
K445(((TOP-REAL 2) | Y),(proj2 | Y)) is V11() V12() ext-real Element of REAL
|[(W-bound Y),(S-bound Y)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NW-corner Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-bound Y is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | Y),(proj2 | Y)) is V11() V12() ext-real Element of REAL
|[(W-bound Y),(N-bound Y)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner Y),(NW-corner Y)) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner Y),(NW-corner Y))) /\ Y is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most Y) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most Y) is V13() V16( the U1 of ((TOP-REAL 2) | (W-most Y))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (W-most Y)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most Y)),REAL:]
the U1 of ((TOP-REAL 2) | (W-most Y)) is set
[: the U1 of ((TOP-REAL 2) | (W-most Y)),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (W-most Y)),REAL:] is set
K445(((TOP-REAL 2) | (W-most Y)),(proj2 | (W-most Y))) is V11() V12() ext-real Element of REAL
|[(W-bound Y),K445(((TOP-REAL 2) | (W-most Y)),(proj2 | (W-most Y)))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-max Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
K446(((TOP-REAL 2) | (W-most Y)),(proj2 | (W-most Y))) is V11() V12() ext-real Element of REAL
|[(W-bound Y),K446(((TOP-REAL 2) | (W-most Y)),(proj2 | (W-most Y)))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-bound X is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | X is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | X is V13() V16( the U1 of ((TOP-REAL 2) | X)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | X), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | X),REAL:]
the U1 of ((TOP-REAL 2) | X) is non empty set
[: the U1 of ((TOP-REAL 2) | X),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | X),REAL:] is set
K445(((TOP-REAL 2) | X),(proj1 | X)) is V11() V12() ext-real Element of REAL
W-max X is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-most X is functional Element of bool the U1 of (TOP-REAL 2)
SW-corner X is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-bound X is V11() V12() ext-real Element of REAL
proj2 | X is V13() V16( the U1 of ((TOP-REAL 2) | X)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | X), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | X),REAL:]
K445(((TOP-REAL 2) | X),(proj2 | X)) is V11() V12() ext-real Element of REAL
|[(W-bound X),(S-bound X)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NW-corner X is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-bound X is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | X),(proj2 | X)) is V11() V12() ext-real Element of REAL
|[(W-bound X),(N-bound X)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner X),(NW-corner X)) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner X),(NW-corner X))) /\ X is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (W-most X) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most X) is V13() V16( the U1 of ((TOP-REAL 2) | (W-most X))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (W-most X)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (W-most X)),REAL:]
the U1 of ((TOP-REAL 2) | (W-most X)) is set
[: the U1 of ((TOP-REAL 2) | (W-most X)),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (W-most X)),REAL:] is set
K446(((TOP-REAL 2) | (W-most X)),(proj2 | (W-most X))) is V11() V12() ext-real Element of REAL
|[(W-bound X),K446(((TOP-REAL 2) | (W-most X)),(proj2 | (W-most X)))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(W-max X) `1 is V11() V12() ext-real Element of REAL
(W-max Y) `1 is V11() V12() ext-real Element of REAL
(W-min Y) `1 is V11() V12() ext-real Element of REAL
W-min X is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
K445(((TOP-REAL 2) | (W-most X)),(proj2 | (W-most X))) is V11() V12() ext-real Element of REAL
|[(W-bound X),K445(((TOP-REAL 2) | (W-most X)),(proj2 | (W-most X)))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(W-min X) `1 is V11() V12() ext-real Element of REAL
X is non empty functional bounded compact Element of bool the U1 of (TOP-REAL 2)
Y is non empty functional bounded compact Element of bool the U1 of (TOP-REAL 2)
E-min Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-bound Y is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | Y is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | Y is V13() V16( the U1 of ((TOP-REAL 2) | Y)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | Y), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | Y),REAL:]
the U1 of ((TOP-REAL 2) | Y) is non empty set
[: the U1 of ((TOP-REAL 2) | Y),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | Y),REAL:] is set
K446(((TOP-REAL 2) | Y),(proj1 | Y)) is V11() V12() ext-real Element of REAL
E-most Y is functional Element of bool the U1 of (TOP-REAL 2)
SE-corner Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-bound Y is V11() V12() ext-real Element of REAL
proj2 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | Y is V13() V16( the U1 of ((TOP-REAL 2) | Y)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | Y), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | Y),REAL:]
K445(((TOP-REAL 2) | Y),(proj2 | Y)) is V11() V12() ext-real Element of REAL
|[(E-bound Y),(S-bound Y)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NE-corner Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-bound Y is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | Y),(proj2 | Y)) is V11() V12() ext-real Element of REAL
|[(E-bound Y),(N-bound Y)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner Y),(NE-corner Y)) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SE-corner Y),(NE-corner Y))) /\ Y is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (E-most Y) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most Y) is V13() V16( the U1 of ((TOP-REAL 2) | (E-most Y))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (E-most Y)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (E-most Y)),REAL:]
the U1 of ((TOP-REAL 2) | (E-most Y)) is set
[: the U1 of ((TOP-REAL 2) | (E-most Y)),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (E-most Y)),REAL:] is set
K445(((TOP-REAL 2) | (E-most Y)),(proj2 | (E-most Y))) is V11() V12() ext-real Element of REAL
|[(E-bound Y),K445(((TOP-REAL 2) | (E-most Y)),(proj2 | (E-most Y)))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-max Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
K446(((TOP-REAL 2) | (E-most Y)),(proj2 | (E-most Y))) is V11() V12() ext-real Element of REAL
|[(E-bound Y),K446(((TOP-REAL 2) | (E-most Y)),(proj2 | (E-most Y)))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-bound X is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | X is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | X is V13() V16( the U1 of ((TOP-REAL 2) | X)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | X), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | X),REAL:]
the U1 of ((TOP-REAL 2) | X) is non empty set
[: the U1 of ((TOP-REAL 2) | X),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | X),REAL:] is set
K446(((TOP-REAL 2) | X),(proj1 | X)) is V11() V12() ext-real Element of REAL
E-max X is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-most X is functional Element of bool the U1 of (TOP-REAL 2)
SE-corner X is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-bound X is V11() V12() ext-real Element of REAL
proj2 | X is V13() V16( the U1 of ((TOP-REAL 2) | X)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | X), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | X),REAL:]
K445(((TOP-REAL 2) | X),(proj2 | X)) is V11() V12() ext-real Element of REAL
|[(E-bound X),(S-bound X)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NE-corner X is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-bound X is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | X),(proj2 | X)) is V11() V12() ext-real Element of REAL
|[(E-bound X),(N-bound X)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner X),(NE-corner X)) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SE-corner X),(NE-corner X))) /\ X is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (E-most X) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most X) is V13() V16( the U1 of ((TOP-REAL 2) | (E-most X))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (E-most X)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (E-most X)),REAL:]
the U1 of ((TOP-REAL 2) | (E-most X)) is set
[: the U1 of ((TOP-REAL 2) | (E-most X)),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (E-most X)),REAL:] is set
K446(((TOP-REAL 2) | (E-most X)),(proj2 | (E-most X))) is V11() V12() ext-real Element of REAL
|[(E-bound X),K446(((TOP-REAL 2) | (E-most X)),(proj2 | (E-most X)))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(E-max X) `1 is V11() V12() ext-real Element of REAL
(E-max Y) `1 is V11() V12() ext-real Element of REAL
(E-min Y) `1 is V11() V12() ext-real Element of REAL
E-min X is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
K445(((TOP-REAL 2) | (E-most X)),(proj2 | (E-most X))) is V11() V12() ext-real Element of REAL
|[(E-bound X),K445(((TOP-REAL 2) | (E-most X)),(proj2 | (E-most X)))]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(E-min X) `1 is V11() V12() ext-real Element of REAL
X is non empty functional bounded compact Element of bool the U1 of (TOP-REAL 2)
Y is non empty functional bounded compact Element of bool the U1 of (TOP-REAL 2)
N-min Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-most Y is functional Element of bool the U1 of (TOP-REAL 2)
NW-corner Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-bound Y is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | Y is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | Y is V13() V16( the U1 of ((TOP-REAL 2) | Y)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | Y), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | Y),REAL:]
the U1 of ((TOP-REAL 2) | Y) is non empty set
[: the U1 of ((TOP-REAL 2) | Y),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | Y),REAL:] is set
K445(((TOP-REAL 2) | Y),(proj1 | Y)) is V11() V12() ext-real Element of REAL
N-bound Y is V11() V12() ext-real Element of REAL
proj2 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | Y is V13() V16( the U1 of ((TOP-REAL 2) | Y)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | Y), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | Y),REAL:]
K446(((TOP-REAL 2) | Y),(proj2 | Y)) is V11() V12() ext-real Element of REAL
|[(W-bound Y),(N-bound Y)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NE-corner Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-bound Y is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | Y),(proj1 | Y)) is V11() V12() ext-real Element of REAL
|[(E-bound Y),(N-bound Y)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((NW-corner Y),(NE-corner Y)) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((NW-corner Y),(NE-corner Y))) /\ Y is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (N-most Y) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most Y) is V13() V16( the U1 of ((TOP-REAL 2) | (N-most Y))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (N-most Y)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (N-most Y)),REAL:]
the U1 of ((TOP-REAL 2) | (N-most Y)) is set
[: the U1 of ((TOP-REAL 2) | (N-most Y)),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (N-most Y)),REAL:] is set
K445(((TOP-REAL 2) | (N-most Y)),(proj1 | (N-most Y))) is V11() V12() ext-real Element of REAL
|[K445(((TOP-REAL 2) | (N-most Y)),(proj1 | (N-most Y))),(N-bound Y)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-max Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
K446(((TOP-REAL 2) | (N-most Y)),(proj1 | (N-most Y))) is V11() V12() ext-real Element of REAL
|[K446(((TOP-REAL 2) | (N-most Y)),(proj1 | (N-most Y))),(N-bound Y)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-bound X is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | X is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | X is V13() V16( the U1 of ((TOP-REAL 2) | X)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | X), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | X),REAL:]
the U1 of ((TOP-REAL 2) | X) is non empty set
[: the U1 of ((TOP-REAL 2) | X),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | X),REAL:] is set
K446(((TOP-REAL 2) | X),(proj2 | X)) is V11() V12() ext-real Element of REAL
N-max X is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
N-most X is functional Element of bool the U1 of (TOP-REAL 2)
NW-corner X is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-bound X is V11() V12() ext-real Element of REAL
proj1 | X is V13() V16( the U1 of ((TOP-REAL 2) | X)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | X), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | X),REAL:]
K445(((TOP-REAL 2) | X),(proj1 | X)) is V11() V12() ext-real Element of REAL
|[(W-bound X),(N-bound X)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
NE-corner X is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-bound X is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | X),(proj1 | X)) is V11() V12() ext-real Element of REAL
|[(E-bound X),(N-bound X)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((NW-corner X),(NE-corner X)) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((NW-corner X),(NE-corner X))) /\ X is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (N-most X) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most X) is V13() V16( the U1 of ((TOP-REAL 2) | (N-most X))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (N-most X)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (N-most X)),REAL:]
the U1 of ((TOP-REAL 2) | (N-most X)) is set
[: the U1 of ((TOP-REAL 2) | (N-most X)),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (N-most X)),REAL:] is set
K446(((TOP-REAL 2) | (N-most X)),(proj1 | (N-most X))) is V11() V12() ext-real Element of REAL
|[K446(((TOP-REAL 2) | (N-most X)),(proj1 | (N-most X))),(N-bound X)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(N-max X) `2 is V11() V12() ext-real Element of REAL
(N-max Y) `2 is V11() V12() ext-real Element of REAL
(N-min Y) `2 is V11() V12() ext-real Element of REAL
N-min X is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
K445(((TOP-REAL 2) | (N-most X)),(proj1 | (N-most X))) is V11() V12() ext-real Element of REAL
|[K445(((TOP-REAL 2) | (N-most X)),(proj1 | (N-most X))),(N-bound X)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(N-min X) `2 is V11() V12() ext-real Element of REAL
X is non empty functional bounded compact Element of bool the U1 of (TOP-REAL 2)
Y is non empty functional bounded compact Element of bool the U1 of (TOP-REAL 2)
S-min Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-most Y is functional Element of bool the U1 of (TOP-REAL 2)
SW-corner Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-bound Y is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | Y is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj1 | Y is V13() V16( the U1 of ((TOP-REAL 2) | Y)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | Y), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | Y),REAL:]
the U1 of ((TOP-REAL 2) | Y) is non empty set
[: the U1 of ((TOP-REAL 2) | Y),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | Y),REAL:] is set
K445(((TOP-REAL 2) | Y),(proj1 | Y)) is V11() V12() ext-real Element of REAL
S-bound Y is V11() V12() ext-real Element of REAL
proj2 is V13() V16( the U1 of (TOP-REAL 2)) V17( REAL ) Function-like V40( the U1 of (TOP-REAL 2), REAL ) Element of bool [: the U1 of (TOP-REAL 2),REAL:]
proj2 | Y is V13() V16( the U1 of ((TOP-REAL 2) | Y)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | Y), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | Y),REAL:]
K445(((TOP-REAL 2) | Y),(proj2 | Y)) is V11() V12() ext-real Element of REAL
|[(W-bound Y),(S-bound Y)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
SE-corner Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-bound Y is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | Y),(proj1 | Y)) is V11() V12() ext-real Element of REAL
|[(E-bound Y),(S-bound Y)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner Y),(SE-corner Y)) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner Y),(SE-corner Y))) /\ Y is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (S-most Y) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (S-most Y) is V13() V16( the U1 of ((TOP-REAL 2) | (S-most Y))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (S-most Y)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (S-most Y)),REAL:]
the U1 of ((TOP-REAL 2) | (S-most Y)) is set
[: the U1 of ((TOP-REAL 2) | (S-most Y)),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (S-most Y)),REAL:] is set
K445(((TOP-REAL 2) | (S-most Y)),(proj1 | (S-most Y))) is V11() V12() ext-real Element of REAL
|[K445(((TOP-REAL 2) | (S-most Y)),(proj1 | (S-most Y))),(S-bound Y)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-max Y is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
K446(((TOP-REAL 2) | (S-most Y)),(proj1 | (S-most Y))) is V11() V12() ext-real Element of REAL
|[K446(((TOP-REAL 2) | (S-most Y)),(proj1 | (S-most Y))),(S-bound Y)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-bound X is V11() V12() ext-real Element of REAL
(TOP-REAL 2) | X is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | X is V13() V16( the U1 of ((TOP-REAL 2) | X)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | X), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | X),REAL:]
the U1 of ((TOP-REAL 2) | X) is non empty set
[: the U1 of ((TOP-REAL 2) | X),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | X),REAL:] is set
K445(((TOP-REAL 2) | X),(proj2 | X)) is V11() V12() ext-real Element of REAL
S-max X is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
S-most X is functional Element of bool the U1 of (TOP-REAL 2)
SW-corner X is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
W-bound X is V11() V12() ext-real Element of REAL
proj1 | X is V13() V16( the U1 of ((TOP-REAL 2) | X)) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | X), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | X),REAL:]
K445(((TOP-REAL 2) | X),(proj1 | X)) is V11() V12() ext-real Element of REAL
|[(W-bound X),(S-bound X)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
SE-corner X is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
E-bound X is V11() V12() ext-real Element of REAL
K446(((TOP-REAL 2) | X),(proj1 | X)) is V11() V12() ext-real Element of REAL
|[(E-bound X),(S-bound X)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner X),(SE-corner X)) is functional V71( TOP-REAL 2) connected bounded bounded compact compact Element of bool the U1 of (TOP-REAL 2)
(LSeg ((SW-corner X),(SE-corner X))) /\ X is functional Element of bool the U1 of (TOP-REAL 2)
(TOP-REAL 2) | (S-most X) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (S-most X) is V13() V16( the U1 of ((TOP-REAL 2) | (S-most X))) V17( REAL ) Function-like V40( the U1 of ((TOP-REAL 2) | (S-most X)), REAL ) Element of bool [: the U1 of ((TOP-REAL 2) | (S-most X)),REAL:]
the U1 of ((TOP-REAL 2) | (S-most X)) is set
[: the U1 of ((TOP-REAL 2) | (S-most X)),REAL:] is set
bool [: the U1 of ((TOP-REAL 2) | (S-most X)),REAL:] is set
K446(((TOP-REAL 2) | (S-most X)),(proj1 | (S-most X))) is V11() V12() ext-real Element of REAL
|[K446(((TOP-REAL 2) | (S-most X)),(proj1 | (S-most X))),(S-bound X)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(S-max X) `2 is V11() V12() ext-real Element of REAL
(S-max Y) `2 is V11() V12() ext-real Element of REAL
(S-min Y) `2 is V11() V12() ext-real Element of REAL
S-min X is V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
K445(((TOP-REAL 2) | (S-most X)),(proj1 | (S-most X))) is V11() V12() ext-real Element of REAL
|[K445(((TOP-REAL 2) | (S-most X)),(proj1 | (S-most X))),(S-bound X)]| is non empty non trivial V13() V16( NAT ) Function-like V26() 2 -element FinSequence-like FinSubsequence-like V171() Element of the U1 of (TOP-REAL 2)
(S-min X) `2 is V11() V12() ext-real Element of REAL