:: JORDAN15 semantic presentation

REAL is non empty V32() V168() V169() V170() V174() V266() set
NAT is V168() V169() V170() V171() V172() V173() V174() V266() Element of K6(REAL)
K6(REAL) is set
omega is V168() V169() V170() V171() V172() V173() V174() V266() set
K6(omega) is set
K6(NAT) is set
COMPLEX is non empty V32() V168() V174() set
RAT is non empty V32() V168() V169() V170() V171() V174() set
INT is non empty V32() V168() V169() V170() V171() V172() V174() set
K7(COMPLEX,COMPLEX) is set
K6(K7(COMPLEX,COMPLEX)) is set
K7(K7(COMPLEX,COMPLEX),COMPLEX) is set
K6(K7(K7(COMPLEX,COMPLEX),COMPLEX)) is set
K7(REAL,REAL) is set
K6(K7(REAL,REAL)) is set
K7(K7(REAL,REAL),REAL) is set
K6(K7(K7(REAL,REAL),REAL)) is set
K7(RAT,RAT) is set
K6(K7(RAT,RAT)) is set
K7(K7(RAT,RAT),RAT) is set
K6(K7(K7(RAT,RAT),RAT)) is set
K7(INT,INT) is set
K6(K7(INT,INT)) is set
K7(K7(INT,INT),INT) is set
K6(K7(K7(INT,INT),INT)) is set
K7(NAT,NAT) is set
K7(K7(NAT,NAT),NAT) is set
K6(K7(K7(NAT,NAT),NAT)) is set
K305() is set
1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
2 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
K7(2,2) is set
K7(K7(2,2),2) is set
K6(K7(K7(2,2),2)) is set
K7(1,1) is set
K6(K7(1,1)) is set
K7(K7(1,1),1) is set
K6(K7(K7(1,1),1)) is set
K7(K7(1,1),REAL) is set
K6(K7(K7(1,1),REAL)) is set
K7(K7(2,2),REAL) is set
K6(K7(K7(2,2),REAL)) is set
TOP-REAL 2 is non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous RLTopStruct
the U1 of (TOP-REAL 2) is non empty non trivial functional set
K295( the U1 of (TOP-REAL 2)) is non empty functional FinSequence-membered M9( the U1 of (TOP-REAL 2))
K7( the U1 of (TOP-REAL 2),REAL) is set
K6(K7( the U1 of (TOP-REAL 2),REAL)) is set
K6( the U1 of (TOP-REAL 2)) is set
K7(COMPLEX,REAL) is set
K6(K7(COMPLEX,REAL)) is set
ExtREAL is non empty V169() set
{} is empty Function-like functional FinSequence-membered V168() V169() V170() V171() V172() V173() V174() set
the empty Function-like functional FinSequence-membered V168() V169() V170() V171() V172() V173() V174() set is empty Function-like functional FinSequence-membered V168() V169() V170() V171() V172() V173() V174() set
3 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Seg 1 is non empty V32() V39(1) V168() V169() V170() V171() V172() V173() Element of K6(NAT)
{1} is non empty V168() V169() V170() V171() V172() V173() set
Seg 2 is non empty V32() V39(2) V168() V169() V170() V171() V172() V173() Element of K6(NAT)
{1,2} is non empty V168() V169() V170() V171() V172() V173() set
Seg 3 is non empty V32() V39(3) V168() V169() V170() V171() V172() V173() Element of K6(NAT)
{1,2,3} is V168() V169() V170() V171() V172() V173() set
proj1 is V19() V22( the U1 of (TOP-REAL 2)) V23( REAL ) Function-like V46( the U1 of (TOP-REAL 2), REAL ) V205( TOP-REAL 2) Element of K6(K7( the U1 of (TOP-REAL 2),REAL))
proj2 is V19() V22( the U1 of (TOP-REAL 2)) V23( REAL ) Function-like V46( the U1 of (TOP-REAL 2), REAL ) V205( TOP-REAL 2) Element of K6(K7( the U1 of (TOP-REAL 2),REAL))
4 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
0 is empty ordinal natural V11() real ext-real non positive non negative Function-like functional FinSequence-membered V43() V49() V168() V169() V170() V171() V172() V173() V174() Element of NAT
n is functional Element of K6( the U1 of (TOP-REAL 2))
C is functional Element of K6( the U1 of (TOP-REAL 2))
proj1 .: n is V168() V169() V170() Element of K6(REAL)
proj1 .: C is V168() V169() V170() Element of K6(REAL)
i is set
j is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
j `1 is V11() real ext-real Element of REAL
proj1 . j is set
n is functional Element of K6( the U1 of (TOP-REAL 2))
C is functional Element of K6( the U1 of (TOP-REAL 2))
proj1 .: n is V168() V169() V170() Element of K6(REAL)
proj1 .: C is V168() V169() V170() Element of K6(REAL)
i is real set
Horizontal_Line i is functional Element of K6( the U1 of (TOP-REAL 2))
j is set
k is V11() real ext-real Element of REAL
k is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
proj1 . k is set
k `2 is V11() real ext-real Element of REAL
G is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
proj1 . G is set
G `2 is V11() real ext-real Element of REAL
G `1 is V11() real ext-real Element of REAL
|[(G `1),(k `2)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
|[k,(k `2)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
k `1 is V11() real ext-real Element of REAL
|[(k `1),(k `2)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
n is functional closed Element of K6( the U1 of (TOP-REAL 2))
proj1 .: n is V168() V169() V170() Element of K6(REAL)
Cl (proj1 .: n) is closed V168() V169() V170() Element of K6(REAL)
Cl n is functional Element of K6( the U1 of (TOP-REAL 2))
proj1 .: (Cl n) is V168() V169() V170() Element of K6(REAL)
n is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
proj1 .: n is V168() V169() V170() Element of K6(REAL)
n is V19() non empty-yielding V22( NAT ) V23(K295( the U1 of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K295( the U1 of (TOP-REAL 2))
len n is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
width n is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
C is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
i is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
k is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
k is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
j is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
n * (C,k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
n * (C,k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((n * (C,k)),(n * (C,k))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
n * (C,i) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
n * (C,j) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((n * (C,i)),(n * (C,j))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(n * (C,k)) `2 is V11() real ext-real Element of REAL
(n * (C,j)) `2 is V11() real ext-real Element of REAL
(n * (C,i)) `1 is V11() real ext-real Element of REAL
n * (C,1) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(n * (C,1)) `1 is V11() real ext-real Element of REAL
(n * (C,j)) `1 is V11() real ext-real Element of REAL
(n * (C,i)) `2 is V11() real ext-real Element of REAL
(n * (C,k)) `2 is V11() real ext-real Element of REAL
(n * (C,k)) `1 is V11() real ext-real Element of REAL
(n * (C,k)) `1 is V11() real ext-real Element of REAL
n is V19() non empty-yielding V22( NAT ) V23(K295( the U1 of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K295( the U1 of (TOP-REAL 2))
width n is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
len n is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
C is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
i is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
k is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
k is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
j is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
n * (k,C) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
n * (k,C) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((n * (k,C)),(n * (k,C))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
n * (i,C) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
n * (j,C) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((n * (i,C)),(n * (j,C))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(n * (k,C)) `1 is V11() real ext-real Element of REAL
(n * (j,C)) `1 is V11() real ext-real Element of REAL
(n * (i,C)) `2 is V11() real ext-real Element of REAL
n * (1,C) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(n * (1,C)) `2 is V11() real ext-real Element of REAL
(n * (j,C)) `2 is V11() real ext-real Element of REAL
(n * (i,C)) `1 is V11() real ext-real Element of REAL
(n * (k,C)) `1 is V11() real ext-real Element of REAL
(n * (k,C)) `2 is V11() real ext-real Element of REAL
(n * (k,C)) `2 is V11() real ext-real Element of REAL
n is V19() non empty-yielding V22( NAT ) V23(K295( the U1 of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K295( the U1 of (TOP-REAL 2))
width n is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Center n is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
C is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
j is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
k is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
i is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
n * ((Center n),j) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
n * ((Center n),k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((n * ((Center n),j)),(n * ((Center n),k))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
n * ((Center n),C) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
n * ((Center n),i) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((n * ((Center n),C)),(n * ((Center n),i))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
len n is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
n is V19() non empty-yielding V22( NAT ) V23(K295( the U1 of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K295( the U1 of (TOP-REAL 2))
len n is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
width n is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Center n is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
C is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
j is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
k is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
i is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
n * (j,(Center n)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
n * (k,(Center n)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((n * (j,(Center n))),(n * (k,(Center n)))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
n * (C,(Center n)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
n * (i,(Center n)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((n * (C,(Center n))),(n * (i,(Center n)))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
n is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
C is non empty functional closed connected bounded compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
Gauge (C,n) is V19() non empty-yielding V22( NAT ) V23(K295( the U1 of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K295( the U1 of (TOP-REAL 2))
len (Gauge (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
width (Gauge (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Lower_Seq (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
L~ (Lower_Seq (C,n)) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
i is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
j is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
k is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * (i,j) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Gauge (C,n)) * (i,k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
[i,k] is set
{i,k} is non empty V168() V169() V170() V171() V172() V173() set
{i} is non empty V168() V169() V170() V171() V172() V173() set
{{i,k},{i}} is non empty set
Indices (Gauge (C,n)) is set
LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(Gauge (C,n)) * (i,1) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (i,1)) `1 is V11() real ext-real Element of REAL
proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))) is V168() V169() V170() Element of K6(REAL)
upper_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))) is V11() real ext-real Element of REAL
[i,j] is set
{i,j} is non empty V168() V169() V170() V171() V172() V173() set
{{i,j},{i}} is non empty set
Gik is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * (i,Gik) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (i,Gik)) `2 is V11() real ext-real Element of REAL
|[(((Gauge (C,n)) * (i,1)) `1),(upper_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (i,k)) `1 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (i,j)) `1 is V11() real ext-real Element of REAL
LSeg (((Gauge (C,n)) * (i,Gik)),((Gauge (C,n)) * (i,k))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,n)) * (i,Gik)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
{((Gauge (C,n)) * (i,Gik))} is non empty functional set
j1 is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
N-most j1 is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
NW-corner j1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound j1 is V11() real ext-real Element of REAL
(TOP-REAL 2) | j1 is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | j1 is V19() V22( the U1 of ((TOP-REAL 2) | j1)) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | j1), REAL ) V205((TOP-REAL 2) | j1) Element of K6(K7( the U1 of ((TOP-REAL 2) | j1),REAL))
the U1 of ((TOP-REAL 2) | j1) is set
K7( the U1 of ((TOP-REAL 2) | j1),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | j1),REAL)) is set
lower_bound (proj1 | j1) is V11() real ext-real Element of REAL
(proj1 | j1) .: the U1 of ((TOP-REAL 2) | j1) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | j1) .: the U1 of ((TOP-REAL 2) | j1)) is V11() real ext-real Element of REAL
N-bound j1 is V11() real ext-real Element of REAL
proj2 | j1 is V19() V22( the U1 of ((TOP-REAL 2) | j1)) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | j1), REAL ) V205((TOP-REAL 2) | j1) Element of K6(K7( the U1 of ((TOP-REAL 2) | j1),REAL))
upper_bound (proj2 | j1) is V11() real ext-real Element of REAL
(proj2 | j1) .: the U1 of ((TOP-REAL 2) | j1) is V168() V169() V170() Element of K6(REAL)
upper_bound ((proj2 | j1) .: the U1 of ((TOP-REAL 2) | j1)) is V11() real ext-real Element of REAL
|[(W-bound j1),(N-bound j1)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NE-corner j1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-bound j1 is V11() real ext-real Element of REAL
upper_bound (proj1 | j1) is V11() real ext-real Element of REAL
upper_bound ((proj1 | j1) .: the U1 of ((TOP-REAL 2) | j1)) is V11() real ext-real Element of REAL
|[(E-bound j1),(N-bound j1)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((NW-corner j1),(NE-corner j1)) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((NW-corner j1),(NE-corner j1))) /\ j1 is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
Wbo is set
go is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (i,Gik)) `1 is V11() real ext-real Element of REAL
|[(((Gauge (C,n)) * (i,1)) `1),(upper_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))))]| `2 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (i,k)) `2 is V11() real ext-real Element of REAL
N-bound ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))) is strict T_2 SubSpace of TOP-REAL 2
proj2 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))) is V19() V22( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))), REAL ) V205((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))),REAL))
the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))) is set
K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))),REAL)) is set
upper_bound (proj2 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))) is V11() real ext-real Element of REAL
(proj2 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))) is V168() V169() V170() Element of K6(REAL)
upper_bound ((proj2 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))))) is V11() real ext-real Element of REAL
N-min ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))) is functional Element of K6( the U1 of (TOP-REAL 2))
NW-corner ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))) is V11() real ext-real Element of REAL
proj1 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))) is V19() V22( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))), REAL ) V205((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))),REAL))
lower_bound (proj1 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))) is V11() real ext-real Element of REAL
(proj1 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))))) is V11() real ext-real Element of REAL
|[(W-bound ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))),(N-bound ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NE-corner ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-bound ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))) is V11() real ext-real Element of REAL
upper_bound (proj1 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))) is V11() real ext-real Element of REAL
upper_bound ((proj1 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))))) is V11() real ext-real Element of REAL
|[(E-bound ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))),(N-bound ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((NW-corner ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))),(NE-corner ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((NW-corner ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))),(NE-corner ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))))) /\ ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (N-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))) is strict T_2 SubSpace of TOP-REAL 2
proj1 | (N-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))) is V19() V22( the U1 of ((TOP-REAL 2) | (N-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (N-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))))), REAL ) V205((TOP-REAL 2) | (N-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (N-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))))),REAL))
the U1 of ((TOP-REAL 2) | (N-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))))) is set
K7( the U1 of ((TOP-REAL 2) | (N-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (N-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))))),REAL)) is set
lower_bound (proj1 | (N-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))))) is V11() real ext-real Element of REAL
(proj1 | (N-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))))) .: the U1 of ((TOP-REAL 2) | (N-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | (N-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))))) .: the U1 of ((TOP-REAL 2) | (N-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (N-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))))),(N-bound ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(N-min ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))) `2 is V11() real ext-real Element of REAL
go `2 is V11() real ext-real Element of REAL
go `1 is V11() real ext-real Element of REAL
|[(((Gauge (C,n)) * (i,1)) `1),(upper_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))))]| `1 is V11() real ext-real Element of REAL
LSeg (((Gauge (C,n)) * (i,k)),|[(((Gauge (C,n)) * (i,1)) `1),(upper_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))))]|) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,n)) * (i,k)),|[(((Gauge (C,n)) * (i,1)) `1),(upper_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))))]|)) /\ (L~ (Lower_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
Gij is set
do is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
proj2 .: do is V168() V169() V170() Element of K6(REAL)
((Gauge (C,n)) * (i,j)) `2 is V11() real ext-real Element of REAL
LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,j))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
LA is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LA `2 is V11() real ext-real Element of REAL
proj2 . LA is set
pion is compact V168() V169() V170() Element of K6(REAL)
LA `1 is V11() real ext-real Element of REAL
n is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
C is non empty functional closed connected bounded compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
Gauge (C,n) is V19() non empty-yielding V22( NAT ) V23(K295( the U1 of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K295( the U1 of (TOP-REAL 2))
len (Gauge (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
width (Gauge (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Upper_Seq (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
L~ (Upper_Seq (C,n)) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
i is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
j is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
k is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * (i,k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Gauge (C,n)) * (i,j) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
[i,k] is set
{i,k} is non empty V168() V169() V170() V171() V172() V173() set
{i} is non empty V168() V169() V170() V171() V172() V173() set
{{i,k},{i}} is non empty set
Indices (Gauge (C,n)) is set
LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(Gauge (C,n)) * (i,1) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (i,1)) `1 is V11() real ext-real Element of REAL
proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))) is V168() V169() V170() Element of K6(REAL)
lower_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))) is V11() real ext-real Element of REAL
[i,j] is set
{i,j} is non empty V168() V169() V170() V171() V172() V173() set
{{i,j},{i}} is non empty set
Gik is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * (i,Gik) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (i,Gik)) `2 is V11() real ext-real Element of REAL
|[(((Gauge (C,n)) * (i,1)) `1),(lower_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (i,j)) `1 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (i,k)) `1 is V11() real ext-real Element of REAL
LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,Gik))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,Gik)))) /\ (L~ (Upper_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
{((Gauge (C,n)) * (i,Gik))} is non empty functional set
j1 is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
S-most j1 is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SW-corner j1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound j1 is V11() real ext-real Element of REAL
(TOP-REAL 2) | j1 is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | j1 is V19() V22( the U1 of ((TOP-REAL 2) | j1)) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | j1), REAL ) V205((TOP-REAL 2) | j1) Element of K6(K7( the U1 of ((TOP-REAL 2) | j1),REAL))
the U1 of ((TOP-REAL 2) | j1) is set
K7( the U1 of ((TOP-REAL 2) | j1),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | j1),REAL)) is set
lower_bound (proj1 | j1) is V11() real ext-real Element of REAL
(proj1 | j1) .: the U1 of ((TOP-REAL 2) | j1) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | j1) .: the U1 of ((TOP-REAL 2) | j1)) is V11() real ext-real Element of REAL
S-bound j1 is V11() real ext-real Element of REAL
proj2 | j1 is V19() V22( the U1 of ((TOP-REAL 2) | j1)) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | j1), REAL ) V205((TOP-REAL 2) | j1) Element of K6(K7( the U1 of ((TOP-REAL 2) | j1),REAL))
lower_bound (proj2 | j1) is V11() real ext-real Element of REAL
(proj2 | j1) .: the U1 of ((TOP-REAL 2) | j1) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | j1) .: the U1 of ((TOP-REAL 2) | j1)) is V11() real ext-real Element of REAL
|[(W-bound j1),(S-bound j1)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
SE-corner j1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-bound j1 is V11() real ext-real Element of REAL
upper_bound (proj1 | j1) is V11() real ext-real Element of REAL
upper_bound ((proj1 | j1) .: the U1 of ((TOP-REAL 2) | j1)) is V11() real ext-real Element of REAL
|[(E-bound j1),(S-bound j1)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner j1),(SE-corner j1)) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SW-corner j1),(SE-corner j1))) /\ j1 is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
Wbo is set
((Gauge (C,n)) * (i,Gik)) `1 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (i,j)) `2 is V11() real ext-real Element of REAL
|[(((Gauge (C,n)) * (i,1)) `1),(lower_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))))]| `2 is V11() real ext-real Element of REAL
|[(((Gauge (C,n)) * (i,1)) `1),(lower_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))))]| `1 is V11() real ext-real Element of REAL
go is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-bound ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))) is strict T_2 SubSpace of TOP-REAL 2
proj2 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))) is V19() V22( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))), REAL ) V205((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))),REAL))
the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))) is set
K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))),REAL)) is set
lower_bound (proj2 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))) is V11() real ext-real Element of REAL
(proj2 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))))) is V11() real ext-real Element of REAL
S-min ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))) is functional Element of K6( the U1 of (TOP-REAL 2))
SW-corner ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))) is V11() real ext-real Element of REAL
proj1 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))) is V19() V22( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))), REAL ) V205((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))),REAL))
lower_bound (proj1 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))) is V11() real ext-real Element of REAL
(proj1 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))))) is V11() real ext-real Element of REAL
|[(W-bound ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))),(S-bound ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
SE-corner ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-bound ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))) is V11() real ext-real Element of REAL
upper_bound (proj1 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))) is V11() real ext-real Element of REAL
upper_bound ((proj1 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))))) is V11() real ext-real Element of REAL
|[(E-bound ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))),(S-bound ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))),(SE-corner ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SW-corner ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))),(SE-corner ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))))) /\ ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (S-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))) is strict T_2 SubSpace of TOP-REAL 2
proj1 | (S-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))) is V19() V22( the U1 of ((TOP-REAL 2) | (S-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (S-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))))), REAL ) V205((TOP-REAL 2) | (S-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (S-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))))),REAL))
the U1 of ((TOP-REAL 2) | (S-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))))) is set
K7( the U1 of ((TOP-REAL 2) | (S-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (S-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))))),REAL)) is set
lower_bound (proj1 | (S-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))))) is V11() real ext-real Element of REAL
(proj1 | (S-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))))) .: the U1 of ((TOP-REAL 2) | (S-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | (S-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))))) .: the U1 of ((TOP-REAL 2) | (S-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (S-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))))),(S-bound ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(S-min ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))) `2 is V11() real ext-real Element of REAL
go `2 is V11() real ext-real Element of REAL
go `1 is V11() real ext-real Element of REAL
LSeg (|[(((Gauge (C,n)) * (i,1)) `1),(lower_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))))]|,((Gauge (C,n)) * (i,j))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (|[(((Gauge (C,n)) * (i,1)) `1),(lower_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))))]|,((Gauge (C,n)) * (i,j)))) /\ (L~ (Upper_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
Gij is set
do is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
proj2 .: do is V168() V169() V170() Element of K6(REAL)
((Gauge (C,n)) * (i,k)) `2 is V11() real ext-real Element of REAL
LA is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LA `2 is V11() real ext-real Element of REAL
proj2 . LA is set
pion is compact V168() V169() V170() Element of K6(REAL)
LA `1 is V11() real ext-real Element of REAL
n is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
C is non empty functional closed connected bounded compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
Gauge (C,n) is V19() non empty-yielding V22( NAT ) V23(K295( the U1 of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K295( the U1 of (TOP-REAL 2))
len (Gauge (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
width (Gauge (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Lower_Seq (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
L~ (Lower_Seq (C,n)) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
Upper_Seq (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
L~ (Upper_Seq (C,n)) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
i is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
j is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
k is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * (i,j) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Gauge (C,n)) * (i,k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
[i,j] is set
{i,j} is non empty V168() V169() V170() V171() V172() V173() set
{i} is non empty V168() V169() V170() V171() V172() V173() set
{{i,j},{i}} is non empty set
Indices (Gauge (C,n)) is set
(Gauge (C,n)) * (i,1) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (i,1)) `1 is V11() real ext-real Element of REAL
LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))) is V168() V169() V170() Element of K6(REAL)
lower_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))) is V11() real ext-real Element of REAL
[i,k] is set
{i,k} is non empty V168() V169() V170() V171() V172() V173() set
{{i,k},{i}} is non empty set
pp is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * (i,pp) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (i,pp)) `2 is V11() real ext-real Element of REAL
LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Lower_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
Gik is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
N-most Gik is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
NW-corner Gik is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound Gik is V11() real ext-real Element of REAL
(TOP-REAL 2) | Gik is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | Gik is V19() V22( the U1 of ((TOP-REAL 2) | Gik)) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | Gik), REAL ) V205((TOP-REAL 2) | Gik) Element of K6(K7( the U1 of ((TOP-REAL 2) | Gik),REAL))
the U1 of ((TOP-REAL 2) | Gik) is set
K7( the U1 of ((TOP-REAL 2) | Gik),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | Gik),REAL)) is set
lower_bound (proj1 | Gik) is V11() real ext-real Element of REAL
(proj1 | Gik) .: the U1 of ((TOP-REAL 2) | Gik) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | Gik) .: the U1 of ((TOP-REAL 2) | Gik)) is V11() real ext-real Element of REAL
N-bound Gik is V11() real ext-real Element of REAL
proj2 | Gik is V19() V22( the U1 of ((TOP-REAL 2) | Gik)) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | Gik), REAL ) V205((TOP-REAL 2) | Gik) Element of K6(K7( the U1 of ((TOP-REAL 2) | Gik),REAL))
upper_bound (proj2 | Gik) is V11() real ext-real Element of REAL
(proj2 | Gik) .: the U1 of ((TOP-REAL 2) | Gik) is V168() V169() V170() Element of K6(REAL)
upper_bound ((proj2 | Gik) .: the U1 of ((TOP-REAL 2) | Gik)) is V11() real ext-real Element of REAL
|[(W-bound Gik),(N-bound Gik)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NE-corner Gik is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-bound Gik is V11() real ext-real Element of REAL
upper_bound (proj1 | Gik) is V11() real ext-real Element of REAL
upper_bound ((proj1 | Gik) .: the U1 of ((TOP-REAL 2) | Gik)) is V11() real ext-real Element of REAL
|[(E-bound Gik),(N-bound Gik)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((NW-corner Gik),(NE-corner Gik)) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((NW-corner Gik),(NE-corner Gik))) /\ Gik is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
Wmin is set
Wbo is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
|[(((Gauge (C,n)) * (i,1)) `1),(lower_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (C,n)) * (i,j)),|[(((Gauge (C,n)) * (i,1)) `1),(lower_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))))]|) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,n)) * (i,j)),|[(((Gauge (C,n)) * (i,1)) `1),(lower_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))))]|)) /\ (L~ (Lower_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),|[(((Gauge (C,n)) * (i,1)) `1),(lower_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))))]|)) /\ (L~ (Lower_Seq (C,n)))) is V168() V169() V170() Element of K6(REAL)
upper_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),|[(((Gauge (C,n)) * (i,1)) `1),(lower_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))))]|)) /\ (L~ (Lower_Seq (C,n))))) is V11() real ext-real Element of REAL
|[(((Gauge (C,n)) * (i,1)) `1),(upper_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),|[(((Gauge (C,n)) * (i,1)) `1),(lower_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))))]|)) /\ (L~ (Lower_Seq (C,n))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (i,pp)) `1 is V11() real ext-real Element of REAL
[i,pp] is set
{i,pp} is non empty V168() V169() V170() V171() V172() V173() set
{{i,pp},{i}} is non empty set
pion is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * (i,pion) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (i,pion)) `2 is V11() real ext-real Element of REAL
{((Gauge (C,n)) * (i,pion))} is non empty functional set
LSeg (((Gauge (C,n)) * (i,pion)),((Gauge (C,n)) * (i,pp))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,n)) * (i,pion)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Lower_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,n)) * (i,pion)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Upper_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
{((Gauge (C,n)) * (i,pp))} is non empty functional set
((Gauge (C,n)) * (i,pion)) `1 is V11() real ext-real Element of REAL
|[(((Gauge (C,n)) * (i,1)) `1),(upper_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),|[(((Gauge (C,n)) * (i,1)) `1),(lower_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))))]|)) /\ (L~ (Lower_Seq (C,n))))))]| `2 is V11() real ext-real Element of REAL
|[(((Gauge (C,n)) * (i,1)) `1),(lower_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))))]| `2 is V11() real ext-real Element of REAL
N-bound ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Lower_Seq (C,n)))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Lower_Seq (C,n)))) is strict T_2 SubSpace of TOP-REAL 2
proj2 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Lower_Seq (C,n)))) is V19() V22( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Lower_Seq (C,n)))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Lower_Seq (C,n))))), REAL ) V205((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Lower_Seq (C,n))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Lower_Seq (C,n))))),REAL))
the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Lower_Seq (C,n))))) is set
K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Lower_Seq (C,n))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Lower_Seq (C,n))))),REAL)) is set
upper_bound (proj2 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Lower_Seq (C,n))))) is V11() real ext-real Element of REAL
(proj2 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Lower_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Lower_Seq (C,n))))) is V168() V169() V170() Element of K6(REAL)
upper_bound ((proj2 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Lower_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Lower_Seq (C,n)))))) is V11() real ext-real Element of REAL
N-min ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Lower_Seq (C,n)))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Lower_Seq (C,n)))) is functional Element of K6( the U1 of (TOP-REAL 2))
NW-corner ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Lower_Seq (C,n)))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Lower_Seq (C,n)))) is V11() real ext-real Element of REAL
proj1 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Lower_Seq (C,n)))) is V19() V22( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Lower_Seq (C,n)))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Lower_Seq (C,n))))), REAL ) V205((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Lower_Seq (C,n))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Lower_Seq (C,n))))),REAL))
lower_bound (proj1 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Lower_Seq (C,n))))) is V11() real ext-real Element of REAL
(proj1 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Lower_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Lower_Seq (C,n))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Lower_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Lower_Seq (C,n)))))) is V11() real ext-real Element of REAL
|[(W-bound ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Lower_Seq (C,n))))),(N-bound ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Lower_Seq (C,n)))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NE-corner ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Lower_Seq (C,n)))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-bound ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Lower_Seq (C,n)))) is V11() real ext-real Element of REAL
upper_bound (proj1 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Lower_Seq (C,n))))) is V11() real ext-real Element of REAL
upper_bound ((proj1 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Lower_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Lower_Seq (C,n)))))) is V11() real ext-real Element of REAL
|[(E-bound ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Lower_Seq (C,n))))),(N-bound ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Lower_Seq (C,n)))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((NW-corner ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Lower_Seq (C,n))))),(NE-corner ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Lower_Seq (C,n)))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((NW-corner ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Lower_Seq (C,n))))),(NE-corner ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Lower_Seq (C,n))))))) /\ ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Lower_Seq (C,n)))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (N-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Lower_Seq (C,n))))) is strict T_2 SubSpace of TOP-REAL 2
proj1 | (N-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Lower_Seq (C,n))))) is V19() V22( the U1 of ((TOP-REAL 2) | (N-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Lower_Seq (C,n))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (N-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Lower_Seq (C,n)))))), REAL ) V205((TOP-REAL 2) | (N-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Lower_Seq (C,n)))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (N-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Lower_Seq (C,n)))))),REAL))
the U1 of ((TOP-REAL 2) | (N-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Lower_Seq (C,n)))))) is set
K7( the U1 of ((TOP-REAL 2) | (N-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Lower_Seq (C,n)))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (N-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Lower_Seq (C,n)))))),REAL)) is set
lower_bound (proj1 | (N-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Lower_Seq (C,n)))))) is V11() real ext-real Element of REAL
(proj1 | (N-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Lower_Seq (C,n)))))) .: the U1 of ((TOP-REAL 2) | (N-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Lower_Seq (C,n)))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | (N-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Lower_Seq (C,n)))))) .: the U1 of ((TOP-REAL 2) | (N-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Lower_Seq (C,n))))))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (N-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Lower_Seq (C,n))))))),(N-bound ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Lower_Seq (C,n)))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(N-min ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Lower_Seq (C,n))))) `2 is V11() real ext-real Element of REAL
Wbo `2 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (i,j)) `1 is V11() real ext-real Element of REAL
|[(((Gauge (C,n)) * (i,1)) `1),(lower_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))))]| `1 is V11() real ext-real Element of REAL
Wbo `1 is V11() real ext-real Element of REAL
|[(((Gauge (C,n)) * (i,1)) `1),(upper_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),|[(((Gauge (C,n)) * (i,1)) `1),(lower_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))))]|)) /\ (L~ (Lower_Seq (C,n))))))]| `1 is V11() real ext-real Element of REAL
LSeg (|[(((Gauge (C,n)) * (i,1)) `1),(lower_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))))]|,|[(((Gauge (C,n)) * (i,1)) `1),(upper_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),|[(((Gauge (C,n)) * (i,1)) `1),(lower_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))))]|)) /\ (L~ (Lower_Seq (C,n))))))]|) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (|[(((Gauge (C,n)) * (i,1)) `1),(lower_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))))]|,|[(((Gauge (C,n)) * (i,1)) `1),(upper_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),|[(((Gauge (C,n)) * (i,1)) `1),(lower_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))))]|)) /\ (L~ (Lower_Seq (C,n))))))]|)) /\ (L~ (Lower_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
LA is set
Emax is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
proj2 .: Emax is V168() V169() V170() Element of K6(REAL)
((Gauge (C,n)) * (i,j)) `2 is V11() real ext-real Element of REAL
LSeg (|[(((Gauge (C,n)) * (i,1)) `1),(lower_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))))]|,((Gauge (C,n)) * (i,j))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
go is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
go `2 is V11() real ext-real Element of REAL
proj2 . go is set
Ebo is compact V168() V169() V170() Element of K6(REAL)
go `1 is V11() real ext-real Element of REAL
Emax is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
S-most Emax is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SW-corner Emax is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound Emax is V11() real ext-real Element of REAL
(TOP-REAL 2) | Emax is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | Emax is V19() V22( the U1 of ((TOP-REAL 2) | Emax)) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | Emax), REAL ) V205((TOP-REAL 2) | Emax) Element of K6(K7( the U1 of ((TOP-REAL 2) | Emax),REAL))
the U1 of ((TOP-REAL 2) | Emax) is set
K7( the U1 of ((TOP-REAL 2) | Emax),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | Emax),REAL)) is set
lower_bound (proj1 | Emax) is V11() real ext-real Element of REAL
(proj1 | Emax) .: the U1 of ((TOP-REAL 2) | Emax) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | Emax) .: the U1 of ((TOP-REAL 2) | Emax)) is V11() real ext-real Element of REAL
S-bound Emax is V11() real ext-real Element of REAL
proj2 | Emax is V19() V22( the U1 of ((TOP-REAL 2) | Emax)) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | Emax), REAL ) V205((TOP-REAL 2) | Emax) Element of K6(K7( the U1 of ((TOP-REAL 2) | Emax),REAL))
lower_bound (proj2 | Emax) is V11() real ext-real Element of REAL
(proj2 | Emax) .: the U1 of ((TOP-REAL 2) | Emax) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | Emax) .: the U1 of ((TOP-REAL 2) | Emax)) is V11() real ext-real Element of REAL
|[(W-bound Emax),(S-bound Emax)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
SE-corner Emax is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-bound Emax is V11() real ext-real Element of REAL
upper_bound (proj1 | Emax) is V11() real ext-real Element of REAL
upper_bound ((proj1 | Emax) .: the U1 of ((TOP-REAL 2) | Emax)) is V11() real ext-real Element of REAL
|[(E-bound Emax),(S-bound Emax)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner Emax),(SE-corner Emax)) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SW-corner Emax),(SE-corner Emax))) /\ Emax is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
Ebo is set
go is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (i,k)) `1 is V11() real ext-real Element of REAL
go `1 is V11() real ext-real Element of REAL
S-bound ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))) is strict T_2 SubSpace of TOP-REAL 2
proj2 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))) is V19() V22( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))), REAL ) V205((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))),REAL))
the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))) is set
K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))),REAL)) is set
lower_bound (proj2 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))) is V11() real ext-real Element of REAL
(proj2 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))))) is V11() real ext-real Element of REAL
S-min ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))) is functional Element of K6( the U1 of (TOP-REAL 2))
SW-corner ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))) is V11() real ext-real Element of REAL
proj1 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))) is V19() V22( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))), REAL ) V205((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))),REAL))
lower_bound (proj1 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))) is V11() real ext-real Element of REAL
(proj1 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))))) is V11() real ext-real Element of REAL
|[(W-bound ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))),(S-bound ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
SE-corner ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-bound ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))) is V11() real ext-real Element of REAL
upper_bound (proj1 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))) is V11() real ext-real Element of REAL
upper_bound ((proj1 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))))) is V11() real ext-real Element of REAL
|[(E-bound ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))),(S-bound ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))),(SE-corner ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SW-corner ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))),(SE-corner ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))))) /\ ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (S-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))) is strict T_2 SubSpace of TOP-REAL 2
proj1 | (S-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))) is V19() V22( the U1 of ((TOP-REAL 2) | (S-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (S-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))))), REAL ) V205((TOP-REAL 2) | (S-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (S-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))))),REAL))
the U1 of ((TOP-REAL 2) | (S-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))))) is set
K7( the U1 of ((TOP-REAL 2) | (S-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (S-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))))),REAL)) is set
lower_bound (proj1 | (S-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))))) is V11() real ext-real Element of REAL
(proj1 | (S-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))))) .: the U1 of ((TOP-REAL 2) | (S-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | (S-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))))) .: the U1 of ((TOP-REAL 2) | (S-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (S-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))))),(S-bound ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(S-min ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))) `2 is V11() real ext-real Element of REAL
go `2 is V11() real ext-real Element of REAL
(LSeg (|[(((Gauge (C,n)) * (i,1)) `1),(lower_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))))]|,|[(((Gauge (C,n)) * (i,1)) `1),(upper_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),|[(((Gauge (C,n)) * (i,1)) `1),(lower_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))))]|)) /\ (L~ (Lower_Seq (C,n))))))]|)) /\ (L~ (Upper_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
do is set
((Gauge (C,n)) * (i,k)) `2 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (i,j)) `2 is V11() real ext-real Element of REAL
do is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
proj2 .: do is V168() V169() V170() Element of K6(REAL)
m is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
m `2 is V11() real ext-real Element of REAL
proj2 . m is set
go is compact V168() V169() V170() Element of K6(REAL)
m `1 is V11() real ext-real Element of REAL
n is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
C is non empty functional closed connected bounded compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
Gauge (C,n) is V19() non empty-yielding V22( NAT ) V23(K295( the U1 of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K295( the U1 of (TOP-REAL 2))
len (Gauge (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
width (Gauge (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Lower_Seq (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
L~ (Lower_Seq (C,n)) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
j is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
k is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
i is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * (j,i) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Gauge (C,n)) * (k,i) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
[k,i] is set
{k,i} is non empty V168() V169() V170() V171() V172() V173() set
{k} is non empty V168() V169() V170() V171() V172() V173() set
{{k,i},{k}} is non empty set
Indices (Gauge (C,n)) is set
LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(Gauge (C,n)) * (1,i) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (1,i)) `2 is V11() real ext-real Element of REAL
proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))) is V168() V169() V170() Element of K6(REAL)
upper_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))) is V11() real ext-real Element of REAL
[j,i] is set
{j,i} is non empty V168() V169() V170() V171() V172() V173() set
{j} is non empty V168() V169() V170() V171() V172() V173() set
{{j,i},{j}} is non empty set
Gik is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * (Gik,i) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (Gik,i)) `1 is V11() real ext-real Element of REAL
|[(upper_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))),(((Gauge (C,n)) * (1,i)) `2)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (C,n)) * (Gik,i)),((Gauge (C,n)) * (k,i))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,n)) * (Gik,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
{((Gauge (C,n)) * (Gik,i))} is non empty functional set
j1 is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
E-most j1 is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SE-corner j1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-bound j1 is V11() real ext-real Element of REAL
(TOP-REAL 2) | j1 is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | j1 is V19() V22( the U1 of ((TOP-REAL 2) | j1)) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | j1), REAL ) V205((TOP-REAL 2) | j1) Element of K6(K7( the U1 of ((TOP-REAL 2) | j1),REAL))
the U1 of ((TOP-REAL 2) | j1) is set
K7( the U1 of ((TOP-REAL 2) | j1),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | j1),REAL)) is set
upper_bound (proj1 | j1) is V11() real ext-real Element of REAL
(proj1 | j1) .: the U1 of ((TOP-REAL 2) | j1) is V168() V169() V170() Element of K6(REAL)
upper_bound ((proj1 | j1) .: the U1 of ((TOP-REAL 2) | j1)) is V11() real ext-real Element of REAL
S-bound j1 is V11() real ext-real Element of REAL
proj2 | j1 is V19() V22( the U1 of ((TOP-REAL 2) | j1)) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | j1), REAL ) V205((TOP-REAL 2) | j1) Element of K6(K7( the U1 of ((TOP-REAL 2) | j1),REAL))
lower_bound (proj2 | j1) is V11() real ext-real Element of REAL
(proj2 | j1) .: the U1 of ((TOP-REAL 2) | j1) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | j1) .: the U1 of ((TOP-REAL 2) | j1)) is V11() real ext-real Element of REAL
|[(E-bound j1),(S-bound j1)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NE-corner j1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound j1 is V11() real ext-real Element of REAL
upper_bound (proj2 | j1) is V11() real ext-real Element of REAL
upper_bound ((proj2 | j1) .: the U1 of ((TOP-REAL 2) | j1)) is V11() real ext-real Element of REAL
|[(E-bound j1),(N-bound j1)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner j1),(NE-corner j1)) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SE-corner j1),(NE-corner j1))) /\ j1 is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
Wbo is set
go is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (Gik,i)) `2 is V11() real ext-real Element of REAL
|[(upper_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))),(((Gauge (C,n)) * (1,i)) `2)]| `1 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (k,i)) `1 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (k,i)) `2 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (j,i)) `2 is V11() real ext-real Element of REAL
E-bound ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))) is strict T_2 SubSpace of TOP-REAL 2
proj1 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))) is V19() V22( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))), REAL ) V205((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))),REAL))
the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))) is set
K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))),REAL)) is set
upper_bound (proj1 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))) is V11() real ext-real Element of REAL
(proj1 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))) is V168() V169() V170() Element of K6(REAL)
upper_bound ((proj1 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))) is V11() real ext-real Element of REAL
E-min ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))) is functional Element of K6( the U1 of (TOP-REAL 2))
SE-corner ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-bound ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))) is V11() real ext-real Element of REAL
proj2 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))) is V19() V22( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))), REAL ) V205((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))),REAL))
lower_bound (proj2 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))) is V11() real ext-real Element of REAL
(proj2 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))) is V11() real ext-real Element of REAL
|[(E-bound ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))),(S-bound ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NE-corner ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))) is V11() real ext-real Element of REAL
upper_bound (proj2 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))) is V11() real ext-real Element of REAL
|[(E-bound ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))),(N-bound ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))),(NE-corner ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SE-corner ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))),(NE-corner ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))))) /\ ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (E-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))) is strict T_2 SubSpace of TOP-REAL 2
proj2 | (E-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))) is V19() V22( the U1 of ((TOP-REAL 2) | (E-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (E-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))), REAL ) V205((TOP-REAL 2) | (E-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (E-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))),REAL))
the U1 of ((TOP-REAL 2) | (E-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))) is set
K7( the U1 of ((TOP-REAL 2) | (E-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (E-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))),REAL)) is set
lower_bound (proj2 | (E-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))) is V11() real ext-real Element of REAL
(proj2 | (E-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))) .: the U1 of ((TOP-REAL 2) | (E-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (E-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))) .: the U1 of ((TOP-REAL 2) | (E-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))))) is V11() real ext-real Element of REAL
|[(E-bound ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))),(lower_bound (proj2 | (E-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(E-min ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))) `1 is V11() real ext-real Element of REAL
go `1 is V11() real ext-real Element of REAL
go `2 is V11() real ext-real Element of REAL
|[(upper_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))),(((Gauge (C,n)) * (1,i)) `2)]| `2 is V11() real ext-real Element of REAL
LSeg (((Gauge (C,n)) * (k,i)),|[(upper_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))),(((Gauge (C,n)) * (1,i)) `2)]|) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,n)) * (k,i)),|[(upper_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))),(((Gauge (C,n)) * (1,i)) `2)]|)) /\ (L~ (Lower_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
Gij is set
((Gauge (C,n)) * (j,i)) `1 is V11() real ext-real Element of REAL
LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
do is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
proj1 .: do is V168() V169() V170() Element of K6(REAL)
LA is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LA `1 is V11() real ext-real Element of REAL
proj1 . LA is set
pion is compact V168() V169() V170() Element of K6(REAL)
LA `2 is V11() real ext-real Element of REAL
n is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
C is non empty functional closed connected bounded compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
Gauge (C,n) is V19() non empty-yielding V22( NAT ) V23(K295( the U1 of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K295( the U1 of (TOP-REAL 2))
len (Gauge (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
width (Gauge (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Upper_Seq (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
L~ (Upper_Seq (C,n)) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
j is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
k is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
i is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * (k,i) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Gauge (C,n)) * (j,i) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
[k,i] is set
{k,i} is non empty V168() V169() V170() V171() V172() V173() set
{k} is non empty V168() V169() V170() V171() V172() V173() set
{{k,i},{k}} is non empty set
Indices (Gauge (C,n)) is set
LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(Gauge (C,n)) * (1,i) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (1,i)) `2 is V11() real ext-real Element of REAL
proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))) is V168() V169() V170() Element of K6(REAL)
lower_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))) is V11() real ext-real Element of REAL
[j,i] is set
{j,i} is non empty V168() V169() V170() V171() V172() V173() set
{j} is non empty V168() V169() V170() V171() V172() V173() set
{{j,i},{j}} is non empty set
Gik is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * (Gik,i) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (Gik,i)) `1 is V11() real ext-real Element of REAL
|[(lower_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))),(((Gauge (C,n)) * (1,i)) `2)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (j,i)) `2 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (k,i)) `2 is V11() real ext-real Element of REAL
LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (Gik,i))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (Gik,i)))) /\ (L~ (Upper_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
{((Gauge (C,n)) * (Gik,i))} is non empty functional set
j1 is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
W-most j1 is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SW-corner j1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound j1 is V11() real ext-real Element of REAL
(TOP-REAL 2) | j1 is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | j1 is V19() V22( the U1 of ((TOP-REAL 2) | j1)) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | j1), REAL ) V205((TOP-REAL 2) | j1) Element of K6(K7( the U1 of ((TOP-REAL 2) | j1),REAL))
the U1 of ((TOP-REAL 2) | j1) is set
K7( the U1 of ((TOP-REAL 2) | j1),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | j1),REAL)) is set
lower_bound (proj1 | j1) is V11() real ext-real Element of REAL
(proj1 | j1) .: the U1 of ((TOP-REAL 2) | j1) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | j1) .: the U1 of ((TOP-REAL 2) | j1)) is V11() real ext-real Element of REAL
S-bound j1 is V11() real ext-real Element of REAL
proj2 | j1 is V19() V22( the U1 of ((TOP-REAL 2) | j1)) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | j1), REAL ) V205((TOP-REAL 2) | j1) Element of K6(K7( the U1 of ((TOP-REAL 2) | j1),REAL))
lower_bound (proj2 | j1) is V11() real ext-real Element of REAL
(proj2 | j1) .: the U1 of ((TOP-REAL 2) | j1) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | j1) .: the U1 of ((TOP-REAL 2) | j1)) is V11() real ext-real Element of REAL
|[(W-bound j1),(S-bound j1)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NW-corner j1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound j1 is V11() real ext-real Element of REAL
upper_bound (proj2 | j1) is V11() real ext-real Element of REAL
upper_bound ((proj2 | j1) .: the U1 of ((TOP-REAL 2) | j1)) is V11() real ext-real Element of REAL
|[(W-bound j1),(N-bound j1)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner j1),(NW-corner j1)) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SW-corner j1),(NW-corner j1))) /\ j1 is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
Wbo is set
((Gauge (C,n)) * (Gik,i)) `2 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (j,i)) `1 is V11() real ext-real Element of REAL
|[(lower_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))),(((Gauge (C,n)) * (1,i)) `2)]| `1 is V11() real ext-real Element of REAL
|[(lower_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))),(((Gauge (C,n)) * (1,i)) `2)]| `2 is V11() real ext-real Element of REAL
go is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))) is strict T_2 SubSpace of TOP-REAL 2
proj1 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))) is V19() V22( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))), REAL ) V205((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))),REAL))
the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))) is set
K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))),REAL)) is set
lower_bound (proj1 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))) is V11() real ext-real Element of REAL
(proj1 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))) is V11() real ext-real Element of REAL
W-min ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))) is functional Element of K6( the U1 of (TOP-REAL 2))
SW-corner ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-bound ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))) is V11() real ext-real Element of REAL
proj2 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))) is V19() V22( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))), REAL ) V205((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))),REAL))
lower_bound (proj2 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))) is V11() real ext-real Element of REAL
(proj2 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))) is V11() real ext-real Element of REAL
|[(W-bound ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))),(S-bound ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NW-corner ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))) is V11() real ext-real Element of REAL
upper_bound (proj2 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))) is V11() real ext-real Element of REAL
|[(W-bound ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))),(N-bound ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))),(NW-corner ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SW-corner ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))),(NW-corner ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))))) /\ ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (W-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))) is strict T_2 SubSpace of TOP-REAL 2
proj2 | (W-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))) is V19() V22( the U1 of ((TOP-REAL 2) | (W-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (W-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))), REAL ) V205((TOP-REAL 2) | (W-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (W-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))),REAL))
the U1 of ((TOP-REAL 2) | (W-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))) is set
K7( the U1 of ((TOP-REAL 2) | (W-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (W-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))),REAL)) is set
lower_bound (proj2 | (W-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))) is V11() real ext-real Element of REAL
(proj2 | (W-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))) .: the U1 of ((TOP-REAL 2) | (W-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (W-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))) .: the U1 of ((TOP-REAL 2) | (W-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))))) is V11() real ext-real Element of REAL
|[(W-bound ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))),(lower_bound (proj2 | (W-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(W-min ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))) `1 is V11() real ext-real Element of REAL
go `1 is V11() real ext-real Element of REAL
go `2 is V11() real ext-real Element of REAL
LSeg (|[(lower_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))),(((Gauge (C,n)) * (1,i)) `2)]|,((Gauge (C,n)) * (j,i))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (|[(lower_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))),(((Gauge (C,n)) * (1,i)) `2)]|,((Gauge (C,n)) * (j,i)))) /\ (L~ (Upper_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
Gij is set
pion is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
pion `1 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (k,i)) `1 is V11() real ext-real Element of REAL
do is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
proj1 .: do is V168() V169() V170() Element of K6(REAL)
proj1 . pion is set
LA is compact V168() V169() V170() Element of K6(REAL)
pion `2 is V11() real ext-real Element of REAL
n is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
C is non empty functional closed connected bounded compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
Gauge (C,n) is V19() non empty-yielding V22( NAT ) V23(K295( the U1 of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K295( the U1 of (TOP-REAL 2))
len (Gauge (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
width (Gauge (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Lower_Seq (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
L~ (Lower_Seq (C,n)) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
Upper_Seq (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
L~ (Upper_Seq (C,n)) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
j is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
k is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
i is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * (j,i) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Gauge (C,n)) * (k,i) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
[j,i] is set
{j,i} is non empty V168() V169() V170() V171() V172() V173() set
{j} is non empty V168() V169() V170() V171() V172() V173() set
{{j,i},{j}} is non empty set
Indices (Gauge (C,n)) is set
(Gauge (C,n)) * (1,i) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (1,i)) `2 is V11() real ext-real Element of REAL
LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))) is V168() V169() V170() Element of K6(REAL)
lower_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))) is V11() real ext-real Element of REAL
[k,i] is set
{k,i} is non empty V168() V169() V170() V171() V172() V173() set
{k} is non empty V168() V169() V170() V171() V172() V173() set
{{k,i},{k}} is non empty set
pp is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * (pp,i) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (pp,i)) `1 is V11() real ext-real Element of REAL
|[(lower_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))),(((Gauge (C,n)) * (1,i)) `2)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (C,n)) * (j,i)),|[(lower_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))),(((Gauge (C,n)) * (1,i)) `2)]|) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,n)) * (j,i)),|[(lower_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))),(((Gauge (C,n)) * (1,i)) `2)]|)) /\ (L~ (Lower_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),|[(lower_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))),(((Gauge (C,n)) * (1,i)) `2)]|)) /\ (L~ (Lower_Seq (C,n)))) is V168() V169() V170() Element of K6(REAL)
upper_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),|[(lower_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))),(((Gauge (C,n)) * (1,i)) `2)]|)) /\ (L~ (Lower_Seq (C,n))))) is V11() real ext-real Element of REAL
|[(upper_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),|[(lower_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))),(((Gauge (C,n)) * (1,i)) `2)]|)) /\ (L~ (Lower_Seq (C,n)))))),(((Gauge (C,n)) * (1,i)) `2)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
((Gauge (C,n)) * (pp,i)) `2 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (j,i)) `2 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (k,i)) `2 is V11() real ext-real Element of REAL
(LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Lower_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
go is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
E-most go is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SE-corner go is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-bound go is V11() real ext-real Element of REAL
(TOP-REAL 2) | go is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | go is V19() V22( the U1 of ((TOP-REAL 2) | go)) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | go), REAL ) V205((TOP-REAL 2) | go) Element of K6(K7( the U1 of ((TOP-REAL 2) | go),REAL))
the U1 of ((TOP-REAL 2) | go) is set
K7( the U1 of ((TOP-REAL 2) | go),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | go),REAL)) is set
upper_bound (proj1 | go) is V11() real ext-real Element of REAL
(proj1 | go) .: the U1 of ((TOP-REAL 2) | go) is V168() V169() V170() Element of K6(REAL)
upper_bound ((proj1 | go) .: the U1 of ((TOP-REAL 2) | go)) is V11() real ext-real Element of REAL
S-bound go is V11() real ext-real Element of REAL
proj2 | go is V19() V22( the U1 of ((TOP-REAL 2) | go)) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | go), REAL ) V205((TOP-REAL 2) | go) Element of K6(K7( the U1 of ((TOP-REAL 2) | go),REAL))
lower_bound (proj2 | go) is V11() real ext-real Element of REAL
(proj2 | go) .: the U1 of ((TOP-REAL 2) | go) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | go) .: the U1 of ((TOP-REAL 2) | go)) is V11() real ext-real Element of REAL
|[(E-bound go),(S-bound go)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NE-corner go is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound go is V11() real ext-real Element of REAL
upper_bound (proj2 | go) is V11() real ext-real Element of REAL
upper_bound ((proj2 | go) .: the U1 of ((TOP-REAL 2) | go)) is V11() real ext-real Element of REAL
|[(E-bound go),(N-bound go)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner go),(NE-corner go)) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SE-corner go),(NE-corner go))) /\ go is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
Gij is set
[pp,i] is set
{pp,i} is non empty V168() V169() V170() V171() V172() V173() set
{pp} is non empty V168() V169() V170() V171() V172() V173() set
{{pp,i},{pp}} is non empty set
do is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * (do,i) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (do,i)) `1 is V11() real ext-real Element of REAL
pion is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
{((Gauge (C,n)) * (do,i))} is non empty functional set
LSeg (((Gauge (C,n)) * (do,i)),((Gauge (C,n)) * (pp,i))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,n)) * (do,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Lower_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,n)) * (do,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Upper_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
{((Gauge (C,n)) * (pp,i))} is non empty functional set
((Gauge (C,n)) * (do,i)) `2 is V11() real ext-real Element of REAL
|[(upper_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),|[(lower_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))),(((Gauge (C,n)) * (1,i)) `2)]|)) /\ (L~ (Lower_Seq (C,n)))))),(((Gauge (C,n)) * (1,i)) `2)]| `1 is V11() real ext-real Element of REAL
|[(lower_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))),(((Gauge (C,n)) * (1,i)) `2)]| `1 is V11() real ext-real Element of REAL
E-bound ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Lower_Seq (C,n)))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Lower_Seq (C,n)))) is strict T_2 SubSpace of TOP-REAL 2
proj1 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Lower_Seq (C,n)))) is V19() V22( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Lower_Seq (C,n)))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Lower_Seq (C,n))))), REAL ) V205((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Lower_Seq (C,n))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Lower_Seq (C,n))))),REAL))
the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Lower_Seq (C,n))))) is set
K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Lower_Seq (C,n))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Lower_Seq (C,n))))),REAL)) is set
upper_bound (proj1 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Lower_Seq (C,n))))) is V11() real ext-real Element of REAL
(proj1 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Lower_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Lower_Seq (C,n))))) is V168() V169() V170() Element of K6(REAL)
upper_bound ((proj1 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Lower_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Lower_Seq (C,n)))))) is V11() real ext-real Element of REAL
E-min ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Lower_Seq (C,n)))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Lower_Seq (C,n)))) is functional Element of K6( the U1 of (TOP-REAL 2))
SE-corner ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Lower_Seq (C,n)))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-bound ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Lower_Seq (C,n)))) is V11() real ext-real Element of REAL
proj2 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Lower_Seq (C,n)))) is V19() V22( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Lower_Seq (C,n)))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Lower_Seq (C,n))))), REAL ) V205((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Lower_Seq (C,n))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Lower_Seq (C,n))))),REAL))
lower_bound (proj2 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Lower_Seq (C,n))))) is V11() real ext-real Element of REAL
(proj2 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Lower_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Lower_Seq (C,n))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Lower_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Lower_Seq (C,n)))))) is V11() real ext-real Element of REAL
|[(E-bound ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Lower_Seq (C,n))))),(S-bound ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Lower_Seq (C,n)))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NE-corner ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Lower_Seq (C,n)))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Lower_Seq (C,n)))) is V11() real ext-real Element of REAL
upper_bound (proj2 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Lower_Seq (C,n))))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Lower_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Lower_Seq (C,n)))))) is V11() real ext-real Element of REAL
|[(E-bound ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Lower_Seq (C,n))))),(N-bound ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Lower_Seq (C,n)))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Lower_Seq (C,n))))),(NE-corner ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Lower_Seq (C,n)))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SE-corner ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Lower_Seq (C,n))))),(NE-corner ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Lower_Seq (C,n))))))) /\ ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Lower_Seq (C,n)))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (E-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Lower_Seq (C,n))))) is strict T_2 SubSpace of TOP-REAL 2
proj2 | (E-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Lower_Seq (C,n))))) is V19() V22( the U1 of ((TOP-REAL 2) | (E-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Lower_Seq (C,n))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (E-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Lower_Seq (C,n)))))), REAL ) V205((TOP-REAL 2) | (E-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Lower_Seq (C,n)))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (E-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Lower_Seq (C,n)))))),REAL))
the U1 of ((TOP-REAL 2) | (E-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Lower_Seq (C,n)))))) is set
K7( the U1 of ((TOP-REAL 2) | (E-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Lower_Seq (C,n)))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (E-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Lower_Seq (C,n)))))),REAL)) is set
lower_bound (proj2 | (E-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Lower_Seq (C,n)))))) is V11() real ext-real Element of REAL
(proj2 | (E-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Lower_Seq (C,n)))))) .: the U1 of ((TOP-REAL 2) | (E-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Lower_Seq (C,n)))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (E-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Lower_Seq (C,n)))))) .: the U1 of ((TOP-REAL 2) | (E-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Lower_Seq (C,n))))))) is V11() real ext-real Element of REAL
|[(E-bound ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Lower_Seq (C,n))))),(lower_bound (proj2 | (E-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Lower_Seq (C,n)))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(E-min ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Lower_Seq (C,n))))) `1 is V11() real ext-real Element of REAL
pion `1 is V11() real ext-real Element of REAL
|[(lower_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))),(((Gauge (C,n)) * (1,i)) `2)]| `2 is V11() real ext-real Element of REAL
pion `2 is V11() real ext-real Element of REAL
|[(upper_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),|[(lower_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))),(((Gauge (C,n)) * (1,i)) `2)]|)) /\ (L~ (Lower_Seq (C,n)))))),(((Gauge (C,n)) * (1,i)) `2)]| `2 is V11() real ext-real Element of REAL
LSeg (|[(lower_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))),(((Gauge (C,n)) * (1,i)) `2)]|,|[(upper_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),|[(lower_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))),(((Gauge (C,n)) * (1,i)) `2)]|)) /\ (L~ (Lower_Seq (C,n)))))),(((Gauge (C,n)) * (1,i)) `2)]|) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (|[(lower_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))),(((Gauge (C,n)) * (1,i)) `2)]|,|[(upper_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),|[(lower_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))),(((Gauge (C,n)) * (1,i)) `2)]|)) /\ (L~ (Lower_Seq (C,n)))))),(((Gauge (C,n)) * (1,i)) `2)]|)) /\ (L~ (Lower_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
LA is set
Ebo is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
Ebo `1 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (j,i)) `1 is V11() real ext-real Element of REAL
Emax is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
proj1 .: Emax is V168() V169() V170() Element of K6(REAL)
LSeg (|[(lower_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))),(((Gauge (C,n)) * (1,i)) `2)]|,((Gauge (C,n)) * (j,i))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
proj1 . Ebo is set
go is compact V168() V169() V170() Element of K6(REAL)
Ebo `2 is V11() real ext-real Element of REAL
Emax is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
W-most Emax is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SW-corner Emax is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound Emax is V11() real ext-real Element of REAL
(TOP-REAL 2) | Emax is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | Emax is V19() V22( the U1 of ((TOP-REAL 2) | Emax)) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | Emax), REAL ) V205((TOP-REAL 2) | Emax) Element of K6(K7( the U1 of ((TOP-REAL 2) | Emax),REAL))
the U1 of ((TOP-REAL 2) | Emax) is set
K7( the U1 of ((TOP-REAL 2) | Emax),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | Emax),REAL)) is set
lower_bound (proj1 | Emax) is V11() real ext-real Element of REAL
(proj1 | Emax) .: the U1 of ((TOP-REAL 2) | Emax) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | Emax) .: the U1 of ((TOP-REAL 2) | Emax)) is V11() real ext-real Element of REAL
S-bound Emax is V11() real ext-real Element of REAL
proj2 | Emax is V19() V22( the U1 of ((TOP-REAL 2) | Emax)) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | Emax), REAL ) V205((TOP-REAL 2) | Emax) Element of K6(K7( the U1 of ((TOP-REAL 2) | Emax),REAL))
lower_bound (proj2 | Emax) is V11() real ext-real Element of REAL
(proj2 | Emax) .: the U1 of ((TOP-REAL 2) | Emax) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | Emax) .: the U1 of ((TOP-REAL 2) | Emax)) is V11() real ext-real Element of REAL
|[(W-bound Emax),(S-bound Emax)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NW-corner Emax is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound Emax is V11() real ext-real Element of REAL
upper_bound (proj2 | Emax) is V11() real ext-real Element of REAL
upper_bound ((proj2 | Emax) .: the U1 of ((TOP-REAL 2) | Emax)) is V11() real ext-real Element of REAL
|[(W-bound Emax),(N-bound Emax)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner Emax),(NW-corner Emax)) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SW-corner Emax),(NW-corner Emax))) /\ Emax is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
Ebo is set
go is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
go `2 is V11() real ext-real Element of REAL
W-bound ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))) is strict T_2 SubSpace of TOP-REAL 2
proj1 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))) is V19() V22( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))), REAL ) V205((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))),REAL))
the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))) is set
K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))),REAL)) is set
lower_bound (proj1 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))) is V11() real ext-real Element of REAL
(proj1 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))) is V11() real ext-real Element of REAL
W-min ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))) is functional Element of K6( the U1 of (TOP-REAL 2))
SW-corner ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-bound ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))) is V11() real ext-real Element of REAL
proj2 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))) is V19() V22( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))), REAL ) V205((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))),REAL))
lower_bound (proj2 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))) is V11() real ext-real Element of REAL
(proj2 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))) is V11() real ext-real Element of REAL
|[(W-bound ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))),(S-bound ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NW-corner ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))) is V11() real ext-real Element of REAL
upper_bound (proj2 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))) is V11() real ext-real Element of REAL
|[(W-bound ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))),(N-bound ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))),(NW-corner ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SW-corner ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))),(NW-corner ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))))) /\ ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (W-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))) is strict T_2 SubSpace of TOP-REAL 2
proj2 | (W-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))) is V19() V22( the U1 of ((TOP-REAL 2) | (W-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (W-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))), REAL ) V205((TOP-REAL 2) | (W-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (W-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))),REAL))
the U1 of ((TOP-REAL 2) | (W-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))) is set
K7( the U1 of ((TOP-REAL 2) | (W-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (W-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))),REAL)) is set
lower_bound (proj2 | (W-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))) is V11() real ext-real Element of REAL
(proj2 | (W-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))) .: the U1 of ((TOP-REAL 2) | (W-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (W-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))) .: the U1 of ((TOP-REAL 2) | (W-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))))) is V11() real ext-real Element of REAL
|[(W-bound ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))),(lower_bound (proj2 | (W-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(W-min ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))) `1 is V11() real ext-real Element of REAL
go `1 is V11() real ext-real Element of REAL
(LSeg (|[(lower_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))),(((Gauge (C,n)) * (1,i)) `2)]|,|[(upper_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),|[(lower_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))),(((Gauge (C,n)) * (1,i)) `2)]|)) /\ (L~ (Lower_Seq (C,n)))))),(((Gauge (C,n)) * (1,i)) `2)]|)) /\ (L~ (Upper_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
do is set
((Gauge (C,n)) * (k,i)) `1 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (j,i)) `1 is V11() real ext-real Element of REAL
do is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
proj1 .: do is V168() V169() V170() Element of K6(REAL)
m is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
m `1 is V11() real ext-real Element of REAL
proj1 . m is set
go is compact V168() V169() V170() Element of K6(REAL)
m `2 is V11() real ext-real Element of REAL
n is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
C is non empty functional closed connected bounded compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
Gauge (C,n) is V19() non empty-yielding V22( NAT ) V23(K295( the U1 of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K295( the U1 of (TOP-REAL 2))
len (Gauge (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
width (Gauge (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Upper_Seq (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
L~ (Upper_Seq (C,n)) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
i is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
j is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
k is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * (i,j) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Gauge (C,n)) * (i,k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
[i,k] is set
{i,k} is non empty V168() V169() V170() V171() V172() V173() set
{i} is non empty V168() V169() V170() V171() V172() V173() set
{{i,k},{i}} is non empty set
Indices (Gauge (C,n)) is set
LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(Gauge (C,n)) * (i,1) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (i,1)) `1 is V11() real ext-real Element of REAL
proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))) is V168() V169() V170() Element of K6(REAL)
upper_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))) is V11() real ext-real Element of REAL
[i,j] is set
{i,j} is non empty V168() V169() V170() V171() V172() V173() set
{{i,j},{i}} is non empty set
Gik is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * (i,Gik) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (i,Gik)) `2 is V11() real ext-real Element of REAL
|[(((Gauge (C,n)) * (i,1)) `1),(upper_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (i,k)) `1 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (i,j)) `1 is V11() real ext-real Element of REAL
LSeg (((Gauge (C,n)) * (i,Gik)),((Gauge (C,n)) * (i,k))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,n)) * (i,Gik)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
{((Gauge (C,n)) * (i,Gik))} is non empty functional set
j1 is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
N-most j1 is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
NW-corner j1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound j1 is V11() real ext-real Element of REAL
(TOP-REAL 2) | j1 is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | j1 is V19() V22( the U1 of ((TOP-REAL 2) | j1)) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | j1), REAL ) V205((TOP-REAL 2) | j1) Element of K6(K7( the U1 of ((TOP-REAL 2) | j1),REAL))
the U1 of ((TOP-REAL 2) | j1) is set
K7( the U1 of ((TOP-REAL 2) | j1),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | j1),REAL)) is set
lower_bound (proj1 | j1) is V11() real ext-real Element of REAL
(proj1 | j1) .: the U1 of ((TOP-REAL 2) | j1) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | j1) .: the U1 of ((TOP-REAL 2) | j1)) is V11() real ext-real Element of REAL
N-bound j1 is V11() real ext-real Element of REAL
proj2 | j1 is V19() V22( the U1 of ((TOP-REAL 2) | j1)) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | j1), REAL ) V205((TOP-REAL 2) | j1) Element of K6(K7( the U1 of ((TOP-REAL 2) | j1),REAL))
upper_bound (proj2 | j1) is V11() real ext-real Element of REAL
(proj2 | j1) .: the U1 of ((TOP-REAL 2) | j1) is V168() V169() V170() Element of K6(REAL)
upper_bound ((proj2 | j1) .: the U1 of ((TOP-REAL 2) | j1)) is V11() real ext-real Element of REAL
|[(W-bound j1),(N-bound j1)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NE-corner j1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-bound j1 is V11() real ext-real Element of REAL
upper_bound (proj1 | j1) is V11() real ext-real Element of REAL
upper_bound ((proj1 | j1) .: the U1 of ((TOP-REAL 2) | j1)) is V11() real ext-real Element of REAL
|[(E-bound j1),(N-bound j1)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((NW-corner j1),(NE-corner j1)) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((NW-corner j1),(NE-corner j1))) /\ j1 is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
Wbo is set
go is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (i,Gik)) `1 is V11() real ext-real Element of REAL
|[(((Gauge (C,n)) * (i,1)) `1),(upper_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))))]| `2 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (i,k)) `2 is V11() real ext-real Element of REAL
N-bound ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))) is strict T_2 SubSpace of TOP-REAL 2
proj2 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))) is V19() V22( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))), REAL ) V205((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))),REAL))
the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))) is set
K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))),REAL)) is set
upper_bound (proj2 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))) is V11() real ext-real Element of REAL
(proj2 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))) is V168() V169() V170() Element of K6(REAL)
upper_bound ((proj2 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))))) is V11() real ext-real Element of REAL
N-min ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))) is functional Element of K6( the U1 of (TOP-REAL 2))
NW-corner ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))) is V11() real ext-real Element of REAL
proj1 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))) is V19() V22( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))), REAL ) V205((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))),REAL))
lower_bound (proj1 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))) is V11() real ext-real Element of REAL
(proj1 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))))) is V11() real ext-real Element of REAL
|[(W-bound ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))),(N-bound ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NE-corner ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-bound ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))) is V11() real ext-real Element of REAL
upper_bound (proj1 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))) is V11() real ext-real Element of REAL
upper_bound ((proj1 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))))) is V11() real ext-real Element of REAL
|[(E-bound ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))),(N-bound ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((NW-corner ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))),(NE-corner ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((NW-corner ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))),(NE-corner ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))))) /\ ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (N-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))) is strict T_2 SubSpace of TOP-REAL 2
proj1 | (N-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))) is V19() V22( the U1 of ((TOP-REAL 2) | (N-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (N-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))))), REAL ) V205((TOP-REAL 2) | (N-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (N-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))))),REAL))
the U1 of ((TOP-REAL 2) | (N-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))))) is set
K7( the U1 of ((TOP-REAL 2) | (N-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (N-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))))),REAL)) is set
lower_bound (proj1 | (N-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))))) is V11() real ext-real Element of REAL
(proj1 | (N-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))))) .: the U1 of ((TOP-REAL 2) | (N-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | (N-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))))) .: the U1 of ((TOP-REAL 2) | (N-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (N-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))))),(N-bound ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n)))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(N-min ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))) `2 is V11() real ext-real Element of REAL
go `2 is V11() real ext-real Element of REAL
go `1 is V11() real ext-real Element of REAL
|[(((Gauge (C,n)) * (i,1)) `1),(upper_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))))]| `1 is V11() real ext-real Element of REAL
LSeg (((Gauge (C,n)) * (i,k)),|[(((Gauge (C,n)) * (i,1)) `1),(upper_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))))]|) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,n)) * (i,k)),|[(((Gauge (C,n)) * (i,1)) `1),(upper_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Upper_Seq (C,n))))))]|)) /\ (L~ (Upper_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
Gij is set
do is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
proj2 .: do is V168() V169() V170() Element of K6(REAL)
((Gauge (C,n)) * (i,j)) `2 is V11() real ext-real Element of REAL
LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,j))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
LA is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LA `2 is V11() real ext-real Element of REAL
proj2 . LA is set
pion is compact V168() V169() V170() Element of K6(REAL)
LA `1 is V11() real ext-real Element of REAL
n is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
C is non empty functional closed connected bounded compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
Gauge (C,n) is V19() non empty-yielding V22( NAT ) V23(K295( the U1 of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K295( the U1 of (TOP-REAL 2))
len (Gauge (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
width (Gauge (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Lower_Seq (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
L~ (Lower_Seq (C,n)) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
i is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
j is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
k is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * (i,k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Gauge (C,n)) * (i,j) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
[i,k] is set
{i,k} is non empty V168() V169() V170() V171() V172() V173() set
{i} is non empty V168() V169() V170() V171() V172() V173() set
{{i,k},{i}} is non empty set
Indices (Gauge (C,n)) is set
LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(Gauge (C,n)) * (i,1) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (i,1)) `1 is V11() real ext-real Element of REAL
proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))) is V168() V169() V170() Element of K6(REAL)
lower_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))) is V11() real ext-real Element of REAL
[i,j] is set
{i,j} is non empty V168() V169() V170() V171() V172() V173() set
{{i,j},{i}} is non empty set
Gik is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * (i,Gik) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (i,Gik)) `2 is V11() real ext-real Element of REAL
|[(((Gauge (C,n)) * (i,1)) `1),(lower_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (i,j)) `1 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (i,k)) `1 is V11() real ext-real Element of REAL
LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,Gik))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,Gik)))) /\ (L~ (Lower_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
{((Gauge (C,n)) * (i,Gik))} is non empty functional set
j1 is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
S-most j1 is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SW-corner j1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound j1 is V11() real ext-real Element of REAL
(TOP-REAL 2) | j1 is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | j1 is V19() V22( the U1 of ((TOP-REAL 2) | j1)) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | j1), REAL ) V205((TOP-REAL 2) | j1) Element of K6(K7( the U1 of ((TOP-REAL 2) | j1),REAL))
the U1 of ((TOP-REAL 2) | j1) is set
K7( the U1 of ((TOP-REAL 2) | j1),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | j1),REAL)) is set
lower_bound (proj1 | j1) is V11() real ext-real Element of REAL
(proj1 | j1) .: the U1 of ((TOP-REAL 2) | j1) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | j1) .: the U1 of ((TOP-REAL 2) | j1)) is V11() real ext-real Element of REAL
S-bound j1 is V11() real ext-real Element of REAL
proj2 | j1 is V19() V22( the U1 of ((TOP-REAL 2) | j1)) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | j1), REAL ) V205((TOP-REAL 2) | j1) Element of K6(K7( the U1 of ((TOP-REAL 2) | j1),REAL))
lower_bound (proj2 | j1) is V11() real ext-real Element of REAL
(proj2 | j1) .: the U1 of ((TOP-REAL 2) | j1) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | j1) .: the U1 of ((TOP-REAL 2) | j1)) is V11() real ext-real Element of REAL
|[(W-bound j1),(S-bound j1)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
SE-corner j1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-bound j1 is V11() real ext-real Element of REAL
upper_bound (proj1 | j1) is V11() real ext-real Element of REAL
upper_bound ((proj1 | j1) .: the U1 of ((TOP-REAL 2) | j1)) is V11() real ext-real Element of REAL
|[(E-bound j1),(S-bound j1)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner j1),(SE-corner j1)) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SW-corner j1),(SE-corner j1))) /\ j1 is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
Wbo is set
((Gauge (C,n)) * (i,Gik)) `1 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (i,j)) `2 is V11() real ext-real Element of REAL
|[(((Gauge (C,n)) * (i,1)) `1),(lower_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))))]| `2 is V11() real ext-real Element of REAL
|[(((Gauge (C,n)) * (i,1)) `1),(lower_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))))]| `1 is V11() real ext-real Element of REAL
go is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-bound ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))) is strict T_2 SubSpace of TOP-REAL 2
proj2 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))) is V19() V22( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))), REAL ) V205((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))),REAL))
the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))) is set
K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))),REAL)) is set
lower_bound (proj2 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))) is V11() real ext-real Element of REAL
(proj2 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))))) is V11() real ext-real Element of REAL
S-min ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))) is functional Element of K6( the U1 of (TOP-REAL 2))
SW-corner ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))) is V11() real ext-real Element of REAL
proj1 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))) is V19() V22( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))), REAL ) V205((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))),REAL))
lower_bound (proj1 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))) is V11() real ext-real Element of REAL
(proj1 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))))) is V11() real ext-real Element of REAL
|[(W-bound ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))),(S-bound ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
SE-corner ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-bound ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))) is V11() real ext-real Element of REAL
upper_bound (proj1 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))) is V11() real ext-real Element of REAL
upper_bound ((proj1 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))))) is V11() real ext-real Element of REAL
|[(E-bound ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))),(S-bound ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))),(SE-corner ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SW-corner ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))),(SE-corner ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))))) /\ ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (S-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))) is strict T_2 SubSpace of TOP-REAL 2
proj1 | (S-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))) is V19() V22( the U1 of ((TOP-REAL 2) | (S-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (S-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))))), REAL ) V205((TOP-REAL 2) | (S-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (S-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))))),REAL))
the U1 of ((TOP-REAL 2) | (S-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))))) is set
K7( the U1 of ((TOP-REAL 2) | (S-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (S-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))))),REAL)) is set
lower_bound (proj1 | (S-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))))) is V11() real ext-real Element of REAL
(proj1 | (S-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))))) .: the U1 of ((TOP-REAL 2) | (S-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | (S-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))))) .: the U1 of ((TOP-REAL 2) | (S-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (S-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))))),(S-bound ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(S-min ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))) `2 is V11() real ext-real Element of REAL
go `2 is V11() real ext-real Element of REAL
go `1 is V11() real ext-real Element of REAL
LSeg (|[(((Gauge (C,n)) * (i,1)) `1),(lower_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))))]|,((Gauge (C,n)) * (i,j))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (|[(((Gauge (C,n)) * (i,1)) `1),(lower_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))))]|,((Gauge (C,n)) * (i,j)))) /\ (L~ (Lower_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
Gij is set
do is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
proj2 .: do is V168() V169() V170() Element of K6(REAL)
((Gauge (C,n)) * (i,k)) `2 is V11() real ext-real Element of REAL
LA is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LA `2 is V11() real ext-real Element of REAL
proj2 . LA is set
pion is compact V168() V169() V170() Element of K6(REAL)
LA `1 is V11() real ext-real Element of REAL
n is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
C is non empty functional closed connected bounded compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
Gauge (C,n) is V19() non empty-yielding V22( NAT ) V23(K295( the U1 of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K295( the U1 of (TOP-REAL 2))
len (Gauge (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
width (Gauge (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Upper_Seq (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
L~ (Upper_Seq (C,n)) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
Lower_Seq (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
L~ (Lower_Seq (C,n)) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
i is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
j is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
k is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * (i,j) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Gauge (C,n)) * (i,k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
[i,j] is set
{i,j} is non empty V168() V169() V170() V171() V172() V173() set
{i} is non empty V168() V169() V170() V171() V172() V173() set
{{i,j},{i}} is non empty set
Indices (Gauge (C,n)) is set
(Gauge (C,n)) * (i,1) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (i,1)) `1 is V11() real ext-real Element of REAL
LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))) is V168() V169() V170() Element of K6(REAL)
lower_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))) is V11() real ext-real Element of REAL
[i,k] is set
{i,k} is non empty V168() V169() V170() V171() V172() V173() set
{{i,k},{i}} is non empty set
pp is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * (i,pp) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (i,pp)) `2 is V11() real ext-real Element of REAL
LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Upper_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
Gik is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
N-most Gik is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
NW-corner Gik is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound Gik is V11() real ext-real Element of REAL
(TOP-REAL 2) | Gik is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | Gik is V19() V22( the U1 of ((TOP-REAL 2) | Gik)) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | Gik), REAL ) V205((TOP-REAL 2) | Gik) Element of K6(K7( the U1 of ((TOP-REAL 2) | Gik),REAL))
the U1 of ((TOP-REAL 2) | Gik) is set
K7( the U1 of ((TOP-REAL 2) | Gik),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | Gik),REAL)) is set
lower_bound (proj1 | Gik) is V11() real ext-real Element of REAL
(proj1 | Gik) .: the U1 of ((TOP-REAL 2) | Gik) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | Gik) .: the U1 of ((TOP-REAL 2) | Gik)) is V11() real ext-real Element of REAL
N-bound Gik is V11() real ext-real Element of REAL
proj2 | Gik is V19() V22( the U1 of ((TOP-REAL 2) | Gik)) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | Gik), REAL ) V205((TOP-REAL 2) | Gik) Element of K6(K7( the U1 of ((TOP-REAL 2) | Gik),REAL))
upper_bound (proj2 | Gik) is V11() real ext-real Element of REAL
(proj2 | Gik) .: the U1 of ((TOP-REAL 2) | Gik) is V168() V169() V170() Element of K6(REAL)
upper_bound ((proj2 | Gik) .: the U1 of ((TOP-REAL 2) | Gik)) is V11() real ext-real Element of REAL
|[(W-bound Gik),(N-bound Gik)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NE-corner Gik is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-bound Gik is V11() real ext-real Element of REAL
upper_bound (proj1 | Gik) is V11() real ext-real Element of REAL
upper_bound ((proj1 | Gik) .: the U1 of ((TOP-REAL 2) | Gik)) is V11() real ext-real Element of REAL
|[(E-bound Gik),(N-bound Gik)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((NW-corner Gik),(NE-corner Gik)) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((NW-corner Gik),(NE-corner Gik))) /\ Gik is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
Wmin is set
Wbo is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
|[(((Gauge (C,n)) * (i,1)) `1),(lower_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (C,n)) * (i,j)),|[(((Gauge (C,n)) * (i,1)) `1),(lower_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))))]|) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,n)) * (i,j)),|[(((Gauge (C,n)) * (i,1)) `1),(lower_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))))]|)) /\ (L~ (Upper_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),|[(((Gauge (C,n)) * (i,1)) `1),(lower_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))))]|)) /\ (L~ (Upper_Seq (C,n)))) is V168() V169() V170() Element of K6(REAL)
upper_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),|[(((Gauge (C,n)) * (i,1)) `1),(lower_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))))]|)) /\ (L~ (Upper_Seq (C,n))))) is V11() real ext-real Element of REAL
|[(((Gauge (C,n)) * (i,1)) `1),(upper_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),|[(((Gauge (C,n)) * (i,1)) `1),(lower_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))))]|)) /\ (L~ (Upper_Seq (C,n))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (i,pp)) `1 is V11() real ext-real Element of REAL
[i,pp] is set
{i,pp} is non empty V168() V169() V170() V171() V172() V173() set
{{i,pp},{i}} is non empty set
pion is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * (i,pion) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (i,pion)) `2 is V11() real ext-real Element of REAL
{((Gauge (C,n)) * (i,pion))} is non empty functional set
LSeg (((Gauge (C,n)) * (i,pion)),((Gauge (C,n)) * (i,pp))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,n)) * (i,pion)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Upper_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,n)) * (i,pion)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Lower_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
{((Gauge (C,n)) * (i,pp))} is non empty functional set
((Gauge (C,n)) * (i,pion)) `1 is V11() real ext-real Element of REAL
|[(((Gauge (C,n)) * (i,1)) `1),(upper_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),|[(((Gauge (C,n)) * (i,1)) `1),(lower_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))))]|)) /\ (L~ (Upper_Seq (C,n))))))]| `2 is V11() real ext-real Element of REAL
|[(((Gauge (C,n)) * (i,1)) `1),(lower_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))))]| `2 is V11() real ext-real Element of REAL
N-bound ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Upper_Seq (C,n)))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Upper_Seq (C,n)))) is strict T_2 SubSpace of TOP-REAL 2
proj2 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Upper_Seq (C,n)))) is V19() V22( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Upper_Seq (C,n)))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Upper_Seq (C,n))))), REAL ) V205((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Upper_Seq (C,n))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Upper_Seq (C,n))))),REAL))
the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Upper_Seq (C,n))))) is set
K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Upper_Seq (C,n))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Upper_Seq (C,n))))),REAL)) is set
upper_bound (proj2 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Upper_Seq (C,n))))) is V11() real ext-real Element of REAL
(proj2 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Upper_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Upper_Seq (C,n))))) is V168() V169() V170() Element of K6(REAL)
upper_bound ((proj2 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Upper_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Upper_Seq (C,n)))))) is V11() real ext-real Element of REAL
N-min ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Upper_Seq (C,n)))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Upper_Seq (C,n)))) is functional Element of K6( the U1 of (TOP-REAL 2))
NW-corner ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Upper_Seq (C,n)))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Upper_Seq (C,n)))) is V11() real ext-real Element of REAL
proj1 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Upper_Seq (C,n)))) is V19() V22( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Upper_Seq (C,n)))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Upper_Seq (C,n))))), REAL ) V205((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Upper_Seq (C,n))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Upper_Seq (C,n))))),REAL))
lower_bound (proj1 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Upper_Seq (C,n))))) is V11() real ext-real Element of REAL
(proj1 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Upper_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Upper_Seq (C,n))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Upper_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Upper_Seq (C,n)))))) is V11() real ext-real Element of REAL
|[(W-bound ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Upper_Seq (C,n))))),(N-bound ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Upper_Seq (C,n)))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NE-corner ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Upper_Seq (C,n)))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-bound ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Upper_Seq (C,n)))) is V11() real ext-real Element of REAL
upper_bound (proj1 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Upper_Seq (C,n))))) is V11() real ext-real Element of REAL
upper_bound ((proj1 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Upper_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Upper_Seq (C,n)))))) is V11() real ext-real Element of REAL
|[(E-bound ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Upper_Seq (C,n))))),(N-bound ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Upper_Seq (C,n)))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((NW-corner ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Upper_Seq (C,n))))),(NE-corner ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Upper_Seq (C,n)))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((NW-corner ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Upper_Seq (C,n))))),(NE-corner ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Upper_Seq (C,n))))))) /\ ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Upper_Seq (C,n)))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (N-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Upper_Seq (C,n))))) is strict T_2 SubSpace of TOP-REAL 2
proj1 | (N-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Upper_Seq (C,n))))) is V19() V22( the U1 of ((TOP-REAL 2) | (N-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Upper_Seq (C,n))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (N-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Upper_Seq (C,n)))))), REAL ) V205((TOP-REAL 2) | (N-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Upper_Seq (C,n)))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (N-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Upper_Seq (C,n)))))),REAL))
the U1 of ((TOP-REAL 2) | (N-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Upper_Seq (C,n)))))) is set
K7( the U1 of ((TOP-REAL 2) | (N-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Upper_Seq (C,n)))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (N-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Upper_Seq (C,n)))))),REAL)) is set
lower_bound (proj1 | (N-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Upper_Seq (C,n)))))) is V11() real ext-real Element of REAL
(proj1 | (N-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Upper_Seq (C,n)))))) .: the U1 of ((TOP-REAL 2) | (N-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Upper_Seq (C,n)))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | (N-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Upper_Seq (C,n)))))) .: the U1 of ((TOP-REAL 2) | (N-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Upper_Seq (C,n))))))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (N-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Upper_Seq (C,n))))))),(N-bound ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Upper_Seq (C,n)))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(N-min ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,pp)))) /\ (L~ (Upper_Seq (C,n))))) `2 is V11() real ext-real Element of REAL
Wbo `2 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (i,j)) `1 is V11() real ext-real Element of REAL
|[(((Gauge (C,n)) * (i,1)) `1),(lower_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))))]| `1 is V11() real ext-real Element of REAL
Wbo `1 is V11() real ext-real Element of REAL
|[(((Gauge (C,n)) * (i,1)) `1),(upper_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),|[(((Gauge (C,n)) * (i,1)) `1),(lower_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))))]|)) /\ (L~ (Upper_Seq (C,n))))))]| `1 is V11() real ext-real Element of REAL
LSeg (|[(((Gauge (C,n)) * (i,1)) `1),(lower_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))))]|,|[(((Gauge (C,n)) * (i,1)) `1),(upper_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),|[(((Gauge (C,n)) * (i,1)) `1),(lower_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))))]|)) /\ (L~ (Upper_Seq (C,n))))))]|) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (|[(((Gauge (C,n)) * (i,1)) `1),(lower_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))))]|,|[(((Gauge (C,n)) * (i,1)) `1),(upper_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),|[(((Gauge (C,n)) * (i,1)) `1),(lower_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))))]|)) /\ (L~ (Upper_Seq (C,n))))))]|)) /\ (L~ (Upper_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
LA is set
Emax is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
proj2 .: Emax is V168() V169() V170() Element of K6(REAL)
((Gauge (C,n)) * (i,j)) `2 is V11() real ext-real Element of REAL
LSeg (|[(((Gauge (C,n)) * (i,1)) `1),(lower_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))))]|,((Gauge (C,n)) * (i,j))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
go is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
go `2 is V11() real ext-real Element of REAL
proj2 . go is set
Ebo is compact V168() V169() V170() Element of K6(REAL)
go `1 is V11() real ext-real Element of REAL
Emax is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
S-most Emax is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SW-corner Emax is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound Emax is V11() real ext-real Element of REAL
(TOP-REAL 2) | Emax is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | Emax is V19() V22( the U1 of ((TOP-REAL 2) | Emax)) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | Emax), REAL ) V205((TOP-REAL 2) | Emax) Element of K6(K7( the U1 of ((TOP-REAL 2) | Emax),REAL))
the U1 of ((TOP-REAL 2) | Emax) is set
K7( the U1 of ((TOP-REAL 2) | Emax),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | Emax),REAL)) is set
lower_bound (proj1 | Emax) is V11() real ext-real Element of REAL
(proj1 | Emax) .: the U1 of ((TOP-REAL 2) | Emax) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | Emax) .: the U1 of ((TOP-REAL 2) | Emax)) is V11() real ext-real Element of REAL
S-bound Emax is V11() real ext-real Element of REAL
proj2 | Emax is V19() V22( the U1 of ((TOP-REAL 2) | Emax)) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | Emax), REAL ) V205((TOP-REAL 2) | Emax) Element of K6(K7( the U1 of ((TOP-REAL 2) | Emax),REAL))
lower_bound (proj2 | Emax) is V11() real ext-real Element of REAL
(proj2 | Emax) .: the U1 of ((TOP-REAL 2) | Emax) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | Emax) .: the U1 of ((TOP-REAL 2) | Emax)) is V11() real ext-real Element of REAL
|[(W-bound Emax),(S-bound Emax)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
SE-corner Emax is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-bound Emax is V11() real ext-real Element of REAL
upper_bound (proj1 | Emax) is V11() real ext-real Element of REAL
upper_bound ((proj1 | Emax) .: the U1 of ((TOP-REAL 2) | Emax)) is V11() real ext-real Element of REAL
|[(E-bound Emax),(S-bound Emax)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner Emax),(SE-corner Emax)) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SW-corner Emax),(SE-corner Emax))) /\ Emax is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
Ebo is set
go is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (i,k)) `1 is V11() real ext-real Element of REAL
go `1 is V11() real ext-real Element of REAL
S-bound ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))) is strict T_2 SubSpace of TOP-REAL 2
proj2 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))) is V19() V22( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))), REAL ) V205((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))),REAL))
the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))) is set
K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))),REAL)) is set
lower_bound (proj2 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))) is V11() real ext-real Element of REAL
(proj2 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))))) is V11() real ext-real Element of REAL
S-min ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))) is functional Element of K6( the U1 of (TOP-REAL 2))
SW-corner ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))) is V11() real ext-real Element of REAL
proj1 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))) is V19() V22( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))), REAL ) V205((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))),REAL))
lower_bound (proj1 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))) is V11() real ext-real Element of REAL
(proj1 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))))) is V11() real ext-real Element of REAL
|[(W-bound ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))),(S-bound ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
SE-corner ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-bound ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))) is V11() real ext-real Element of REAL
upper_bound (proj1 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))) is V11() real ext-real Element of REAL
upper_bound ((proj1 | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))))) is V11() real ext-real Element of REAL
|[(E-bound ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))),(S-bound ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))),(SE-corner ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SW-corner ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))),(SE-corner ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))))) /\ ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (S-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))) is strict T_2 SubSpace of TOP-REAL 2
proj1 | (S-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))) is V19() V22( the U1 of ((TOP-REAL 2) | (S-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (S-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))))), REAL ) V205((TOP-REAL 2) | (S-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (S-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))))),REAL))
the U1 of ((TOP-REAL 2) | (S-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))))) is set
K7( the U1 of ((TOP-REAL 2) | (S-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (S-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))))),REAL)) is set
lower_bound (proj1 | (S-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))))) is V11() real ext-real Element of REAL
(proj1 | (S-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))))) .: the U1 of ((TOP-REAL 2) | (S-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | (S-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))))) .: the U1 of ((TOP-REAL 2) | (S-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (S-most ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))))),(S-bound ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n)))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(S-min ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))) `2 is V11() real ext-real Element of REAL
go `2 is V11() real ext-real Element of REAL
(LSeg (|[(((Gauge (C,n)) * (i,1)) `1),(lower_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))))]|,|[(((Gauge (C,n)) * (i,1)) `1),(upper_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),|[(((Gauge (C,n)) * (i,1)) `1),(lower_bound (proj2 .: ((LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k)))) /\ (L~ (Lower_Seq (C,n))))))]|)) /\ (L~ (Upper_Seq (C,n))))))]|)) /\ (L~ (Lower_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
do is set
((Gauge (C,n)) * (i,k)) `2 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (i,j)) `2 is V11() real ext-real Element of REAL
do is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
proj2 .: do is V168() V169() V170() Element of K6(REAL)
m is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
m `2 is V11() real ext-real Element of REAL
proj2 . m is set
go is compact V168() V169() V170() Element of K6(REAL)
m `1 is V11() real ext-real Element of REAL
n is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
C is non empty functional closed connected bounded compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
Gauge (C,n) is V19() non empty-yielding V22( NAT ) V23(K295( the U1 of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K295( the U1 of (TOP-REAL 2))
len (Gauge (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
width (Gauge (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Upper_Seq (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
L~ (Upper_Seq (C,n)) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
j is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
k is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
i is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * (j,i) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Gauge (C,n)) * (k,i) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
[k,i] is set
{k,i} is non empty V168() V169() V170() V171() V172() V173() set
{k} is non empty V168() V169() V170() V171() V172() V173() set
{{k,i},{k}} is non empty set
Indices (Gauge (C,n)) is set
LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(Gauge (C,n)) * (1,i) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (1,i)) `2 is V11() real ext-real Element of REAL
proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))) is V168() V169() V170() Element of K6(REAL)
upper_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))) is V11() real ext-real Element of REAL
[j,i] is set
{j,i} is non empty V168() V169() V170() V171() V172() V173() set
{j} is non empty V168() V169() V170() V171() V172() V173() set
{{j,i},{j}} is non empty set
Gik is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * (Gik,i) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (Gik,i)) `1 is V11() real ext-real Element of REAL
|[(upper_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))),(((Gauge (C,n)) * (1,i)) `2)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (C,n)) * (Gik,i)),((Gauge (C,n)) * (k,i))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,n)) * (Gik,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
{((Gauge (C,n)) * (Gik,i))} is non empty functional set
j1 is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
E-most j1 is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SE-corner j1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-bound j1 is V11() real ext-real Element of REAL
(TOP-REAL 2) | j1 is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | j1 is V19() V22( the U1 of ((TOP-REAL 2) | j1)) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | j1), REAL ) V205((TOP-REAL 2) | j1) Element of K6(K7( the U1 of ((TOP-REAL 2) | j1),REAL))
the U1 of ((TOP-REAL 2) | j1) is set
K7( the U1 of ((TOP-REAL 2) | j1),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | j1),REAL)) is set
upper_bound (proj1 | j1) is V11() real ext-real Element of REAL
(proj1 | j1) .: the U1 of ((TOP-REAL 2) | j1) is V168() V169() V170() Element of K6(REAL)
upper_bound ((proj1 | j1) .: the U1 of ((TOP-REAL 2) | j1)) is V11() real ext-real Element of REAL
S-bound j1 is V11() real ext-real Element of REAL
proj2 | j1 is V19() V22( the U1 of ((TOP-REAL 2) | j1)) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | j1), REAL ) V205((TOP-REAL 2) | j1) Element of K6(K7( the U1 of ((TOP-REAL 2) | j1),REAL))
lower_bound (proj2 | j1) is V11() real ext-real Element of REAL
(proj2 | j1) .: the U1 of ((TOP-REAL 2) | j1) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | j1) .: the U1 of ((TOP-REAL 2) | j1)) is V11() real ext-real Element of REAL
|[(E-bound j1),(S-bound j1)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NE-corner j1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound j1 is V11() real ext-real Element of REAL
upper_bound (proj2 | j1) is V11() real ext-real Element of REAL
upper_bound ((proj2 | j1) .: the U1 of ((TOP-REAL 2) | j1)) is V11() real ext-real Element of REAL
|[(E-bound j1),(N-bound j1)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner j1),(NE-corner j1)) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SE-corner j1),(NE-corner j1))) /\ j1 is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
Wbo is set
go is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (Gik,i)) `2 is V11() real ext-real Element of REAL
|[(upper_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))),(((Gauge (C,n)) * (1,i)) `2)]| `1 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (k,i)) `1 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (k,i)) `2 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (j,i)) `2 is V11() real ext-real Element of REAL
E-bound ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))) is strict T_2 SubSpace of TOP-REAL 2
proj1 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))) is V19() V22( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))), REAL ) V205((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))),REAL))
the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))) is set
K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))),REAL)) is set
upper_bound (proj1 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))) is V11() real ext-real Element of REAL
(proj1 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))) is V168() V169() V170() Element of K6(REAL)
upper_bound ((proj1 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))) is V11() real ext-real Element of REAL
E-min ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))) is functional Element of K6( the U1 of (TOP-REAL 2))
SE-corner ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-bound ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))) is V11() real ext-real Element of REAL
proj2 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))) is V19() V22( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))), REAL ) V205((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))),REAL))
lower_bound (proj2 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))) is V11() real ext-real Element of REAL
(proj2 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))) is V11() real ext-real Element of REAL
|[(E-bound ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))),(S-bound ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NE-corner ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))) is V11() real ext-real Element of REAL
upper_bound (proj2 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))) is V11() real ext-real Element of REAL
|[(E-bound ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))),(N-bound ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))),(NE-corner ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SE-corner ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))),(NE-corner ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))))) /\ ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (E-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))) is strict T_2 SubSpace of TOP-REAL 2
proj2 | (E-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))) is V19() V22( the U1 of ((TOP-REAL 2) | (E-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (E-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))), REAL ) V205((TOP-REAL 2) | (E-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (E-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))),REAL))
the U1 of ((TOP-REAL 2) | (E-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))) is set
K7( the U1 of ((TOP-REAL 2) | (E-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (E-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))),REAL)) is set
lower_bound (proj2 | (E-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))) is V11() real ext-real Element of REAL
(proj2 | (E-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))) .: the U1 of ((TOP-REAL 2) | (E-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (E-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))) .: the U1 of ((TOP-REAL 2) | (E-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))))) is V11() real ext-real Element of REAL
|[(E-bound ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))),(lower_bound (proj2 | (E-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(E-min ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))))) `1 is V11() real ext-real Element of REAL
go `1 is V11() real ext-real Element of REAL
go `2 is V11() real ext-real Element of REAL
|[(upper_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))),(((Gauge (C,n)) * (1,i)) `2)]| `2 is V11() real ext-real Element of REAL
LSeg (((Gauge (C,n)) * (k,i)),|[(upper_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))),(((Gauge (C,n)) * (1,i)) `2)]|) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,n)) * (k,i)),|[(upper_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n)))))),(((Gauge (C,n)) * (1,i)) `2)]|)) /\ (L~ (Upper_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
Gij is set
((Gauge (C,n)) * (j,i)) `1 is V11() real ext-real Element of REAL
LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
do is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
proj1 .: do is V168() V169() V170() Element of K6(REAL)
LA is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LA `1 is V11() real ext-real Element of REAL
proj1 . LA is set
pion is compact V168() V169() V170() Element of K6(REAL)
LA `2 is V11() real ext-real Element of REAL
n is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
C is non empty functional closed connected bounded compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
Gauge (C,n) is V19() non empty-yielding V22( NAT ) V23(K295( the U1 of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K295( the U1 of (TOP-REAL 2))
len (Gauge (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
width (Gauge (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Lower_Seq (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
L~ (Lower_Seq (C,n)) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
j is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
k is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
i is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * (k,i) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Gauge (C,n)) * (j,i) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
[k,i] is set
{k,i} is non empty V168() V169() V170() V171() V172() V173() set
{k} is non empty V168() V169() V170() V171() V172() V173() set
{{k,i},{k}} is non empty set
Indices (Gauge (C,n)) is set
LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(Gauge (C,n)) * (1,i) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (1,i)) `2 is V11() real ext-real Element of REAL
proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))) is V168() V169() V170() Element of K6(REAL)
lower_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))) is V11() real ext-real Element of REAL
[j,i] is set
{j,i} is non empty V168() V169() V170() V171() V172() V173() set
{j} is non empty V168() V169() V170() V171() V172() V173() set
{{j,i},{j}} is non empty set
Gik is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * (Gik,i) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (Gik,i)) `1 is V11() real ext-real Element of REAL
|[(lower_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))),(((Gauge (C,n)) * (1,i)) `2)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (j,i)) `2 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (k,i)) `2 is V11() real ext-real Element of REAL
LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (Gik,i))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (Gik,i)))) /\ (L~ (Lower_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
{((Gauge (C,n)) * (Gik,i))} is non empty functional set
j1 is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
W-most j1 is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SW-corner j1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound j1 is V11() real ext-real Element of REAL
(TOP-REAL 2) | j1 is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | j1 is V19() V22( the U1 of ((TOP-REAL 2) | j1)) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | j1), REAL ) V205((TOP-REAL 2) | j1) Element of K6(K7( the U1 of ((TOP-REAL 2) | j1),REAL))
the U1 of ((TOP-REAL 2) | j1) is set
K7( the U1 of ((TOP-REAL 2) | j1),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | j1),REAL)) is set
lower_bound (proj1 | j1) is V11() real ext-real Element of REAL
(proj1 | j1) .: the U1 of ((TOP-REAL 2) | j1) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | j1) .: the U1 of ((TOP-REAL 2) | j1)) is V11() real ext-real Element of REAL
S-bound j1 is V11() real ext-real Element of REAL
proj2 | j1 is V19() V22( the U1 of ((TOP-REAL 2) | j1)) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | j1), REAL ) V205((TOP-REAL 2) | j1) Element of K6(K7( the U1 of ((TOP-REAL 2) | j1),REAL))
lower_bound (proj2 | j1) is V11() real ext-real Element of REAL
(proj2 | j1) .: the U1 of ((TOP-REAL 2) | j1) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | j1) .: the U1 of ((TOP-REAL 2) | j1)) is V11() real ext-real Element of REAL
|[(W-bound j1),(S-bound j1)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NW-corner j1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound j1 is V11() real ext-real Element of REAL
upper_bound (proj2 | j1) is V11() real ext-real Element of REAL
upper_bound ((proj2 | j1) .: the U1 of ((TOP-REAL 2) | j1)) is V11() real ext-real Element of REAL
|[(W-bound j1),(N-bound j1)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner j1),(NW-corner j1)) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SW-corner j1),(NW-corner j1))) /\ j1 is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
Wbo is set
((Gauge (C,n)) * (Gik,i)) `2 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (j,i)) `1 is V11() real ext-real Element of REAL
|[(lower_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))),(((Gauge (C,n)) * (1,i)) `2)]| `1 is V11() real ext-real Element of REAL
|[(lower_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))),(((Gauge (C,n)) * (1,i)) `2)]| `2 is V11() real ext-real Element of REAL
go is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))) is strict T_2 SubSpace of TOP-REAL 2
proj1 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))) is V19() V22( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))), REAL ) V205((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))),REAL))
the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))) is set
K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))),REAL)) is set
lower_bound (proj1 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))) is V11() real ext-real Element of REAL
(proj1 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))) is V11() real ext-real Element of REAL
W-min ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))) is functional Element of K6( the U1 of (TOP-REAL 2))
SW-corner ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-bound ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))) is V11() real ext-real Element of REAL
proj2 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))) is V19() V22( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))), REAL ) V205((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))),REAL))
lower_bound (proj2 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))) is V11() real ext-real Element of REAL
(proj2 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))) is V11() real ext-real Element of REAL
|[(W-bound ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))),(S-bound ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NW-corner ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))) is V11() real ext-real Element of REAL
upper_bound (proj2 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))) is V11() real ext-real Element of REAL
|[(W-bound ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))),(N-bound ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))),(NW-corner ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SW-corner ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))),(NW-corner ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))))) /\ ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (W-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))) is strict T_2 SubSpace of TOP-REAL 2
proj2 | (W-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))) is V19() V22( the U1 of ((TOP-REAL 2) | (W-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (W-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))), REAL ) V205((TOP-REAL 2) | (W-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (W-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))),REAL))
the U1 of ((TOP-REAL 2) | (W-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))) is set
K7( the U1 of ((TOP-REAL 2) | (W-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (W-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))),REAL)) is set
lower_bound (proj2 | (W-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))) is V11() real ext-real Element of REAL
(proj2 | (W-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))) .: the U1 of ((TOP-REAL 2) | (W-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (W-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))) .: the U1 of ((TOP-REAL 2) | (W-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))))) is V11() real ext-real Element of REAL
|[(W-bound ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))),(lower_bound (proj2 | (W-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(W-min ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))) `1 is V11() real ext-real Element of REAL
go `1 is V11() real ext-real Element of REAL
go `2 is V11() real ext-real Element of REAL
LSeg (|[(lower_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))),(((Gauge (C,n)) * (1,i)) `2)]|,((Gauge (C,n)) * (j,i))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (|[(lower_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))),(((Gauge (C,n)) * (1,i)) `2)]|,((Gauge (C,n)) * (j,i)))) /\ (L~ (Lower_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
Gij is set
pion is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
pion `1 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (k,i)) `1 is V11() real ext-real Element of REAL
do is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
proj1 .: do is V168() V169() V170() Element of K6(REAL)
proj1 . pion is set
LA is compact V168() V169() V170() Element of K6(REAL)
pion `2 is V11() real ext-real Element of REAL
n is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
C is non empty functional closed connected bounded compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
Gauge (C,n) is V19() non empty-yielding V22( NAT ) V23(K295( the U1 of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K295( the U1 of (TOP-REAL 2))
len (Gauge (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
width (Gauge (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Upper_Seq (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
L~ (Upper_Seq (C,n)) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
Lower_Seq (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
L~ (Lower_Seq (C,n)) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
j is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
k is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
i is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * (j,i) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Gauge (C,n)) * (k,i) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
[j,i] is set
{j,i} is non empty V168() V169() V170() V171() V172() V173() set
{j} is non empty V168() V169() V170() V171() V172() V173() set
{{j,i},{j}} is non empty set
Indices (Gauge (C,n)) is set
(Gauge (C,n)) * (1,i) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (1,i)) `2 is V11() real ext-real Element of REAL
LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))) is V168() V169() V170() Element of K6(REAL)
lower_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))) is V11() real ext-real Element of REAL
[k,i] is set
{k,i} is non empty V168() V169() V170() V171() V172() V173() set
{k} is non empty V168() V169() V170() V171() V172() V173() set
{{k,i},{k}} is non empty set
pp is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * (pp,i) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (pp,i)) `1 is V11() real ext-real Element of REAL
|[(lower_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))),(((Gauge (C,n)) * (1,i)) `2)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (C,n)) * (j,i)),|[(lower_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))),(((Gauge (C,n)) * (1,i)) `2)]|) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,n)) * (j,i)),|[(lower_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))),(((Gauge (C,n)) * (1,i)) `2)]|)) /\ (L~ (Upper_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),|[(lower_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))),(((Gauge (C,n)) * (1,i)) `2)]|)) /\ (L~ (Upper_Seq (C,n)))) is V168() V169() V170() Element of K6(REAL)
upper_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),|[(lower_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))),(((Gauge (C,n)) * (1,i)) `2)]|)) /\ (L~ (Upper_Seq (C,n))))) is V11() real ext-real Element of REAL
|[(upper_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),|[(lower_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))),(((Gauge (C,n)) * (1,i)) `2)]|)) /\ (L~ (Upper_Seq (C,n)))))),(((Gauge (C,n)) * (1,i)) `2)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
((Gauge (C,n)) * (pp,i)) `2 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (j,i)) `2 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (k,i)) `2 is V11() real ext-real Element of REAL
(LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Upper_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
go is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
E-most go is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SE-corner go is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-bound go is V11() real ext-real Element of REAL
(TOP-REAL 2) | go is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | go is V19() V22( the U1 of ((TOP-REAL 2) | go)) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | go), REAL ) V205((TOP-REAL 2) | go) Element of K6(K7( the U1 of ((TOP-REAL 2) | go),REAL))
the U1 of ((TOP-REAL 2) | go) is set
K7( the U1 of ((TOP-REAL 2) | go),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | go),REAL)) is set
upper_bound (proj1 | go) is V11() real ext-real Element of REAL
(proj1 | go) .: the U1 of ((TOP-REAL 2) | go) is V168() V169() V170() Element of K6(REAL)
upper_bound ((proj1 | go) .: the U1 of ((TOP-REAL 2) | go)) is V11() real ext-real Element of REAL
S-bound go is V11() real ext-real Element of REAL
proj2 | go is V19() V22( the U1 of ((TOP-REAL 2) | go)) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | go), REAL ) V205((TOP-REAL 2) | go) Element of K6(K7( the U1 of ((TOP-REAL 2) | go),REAL))
lower_bound (proj2 | go) is V11() real ext-real Element of REAL
(proj2 | go) .: the U1 of ((TOP-REAL 2) | go) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | go) .: the U1 of ((TOP-REAL 2) | go)) is V11() real ext-real Element of REAL
|[(E-bound go),(S-bound go)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NE-corner go is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound go is V11() real ext-real Element of REAL
upper_bound (proj2 | go) is V11() real ext-real Element of REAL
upper_bound ((proj2 | go) .: the U1 of ((TOP-REAL 2) | go)) is V11() real ext-real Element of REAL
|[(E-bound go),(N-bound go)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner go),(NE-corner go)) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SE-corner go),(NE-corner go))) /\ go is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
Gij is set
[pp,i] is set
{pp,i} is non empty V168() V169() V170() V171() V172() V173() set
{pp} is non empty V168() V169() V170() V171() V172() V173() set
{{pp,i},{pp}} is non empty set
do is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * (do,i) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (do,i)) `1 is V11() real ext-real Element of REAL
pion is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
{((Gauge (C,n)) * (do,i))} is non empty functional set
LSeg (((Gauge (C,n)) * (do,i)),((Gauge (C,n)) * (pp,i))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,n)) * (do,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Upper_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,n)) * (do,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Lower_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
{((Gauge (C,n)) * (pp,i))} is non empty functional set
((Gauge (C,n)) * (do,i)) `2 is V11() real ext-real Element of REAL
|[(upper_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),|[(lower_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))),(((Gauge (C,n)) * (1,i)) `2)]|)) /\ (L~ (Upper_Seq (C,n)))))),(((Gauge (C,n)) * (1,i)) `2)]| `1 is V11() real ext-real Element of REAL
|[(lower_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))),(((Gauge (C,n)) * (1,i)) `2)]| `1 is V11() real ext-real Element of REAL
E-bound ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Upper_Seq (C,n)))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Upper_Seq (C,n)))) is strict T_2 SubSpace of TOP-REAL 2
proj1 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Upper_Seq (C,n)))) is V19() V22( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Upper_Seq (C,n)))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Upper_Seq (C,n))))), REAL ) V205((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Upper_Seq (C,n))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Upper_Seq (C,n))))),REAL))
the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Upper_Seq (C,n))))) is set
K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Upper_Seq (C,n))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Upper_Seq (C,n))))),REAL)) is set
upper_bound (proj1 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Upper_Seq (C,n))))) is V11() real ext-real Element of REAL
(proj1 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Upper_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Upper_Seq (C,n))))) is V168() V169() V170() Element of K6(REAL)
upper_bound ((proj1 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Upper_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Upper_Seq (C,n)))))) is V11() real ext-real Element of REAL
E-min ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Upper_Seq (C,n)))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Upper_Seq (C,n)))) is functional Element of K6( the U1 of (TOP-REAL 2))
SE-corner ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Upper_Seq (C,n)))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-bound ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Upper_Seq (C,n)))) is V11() real ext-real Element of REAL
proj2 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Upper_Seq (C,n)))) is V19() V22( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Upper_Seq (C,n)))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Upper_Seq (C,n))))), REAL ) V205((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Upper_Seq (C,n))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Upper_Seq (C,n))))),REAL))
lower_bound (proj2 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Upper_Seq (C,n))))) is V11() real ext-real Element of REAL
(proj2 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Upper_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Upper_Seq (C,n))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Upper_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Upper_Seq (C,n)))))) is V11() real ext-real Element of REAL
|[(E-bound ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Upper_Seq (C,n))))),(S-bound ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Upper_Seq (C,n)))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NE-corner ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Upper_Seq (C,n)))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Upper_Seq (C,n)))) is V11() real ext-real Element of REAL
upper_bound (proj2 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Upper_Seq (C,n))))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Upper_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Upper_Seq (C,n)))))) is V11() real ext-real Element of REAL
|[(E-bound ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Upper_Seq (C,n))))),(N-bound ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Upper_Seq (C,n)))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Upper_Seq (C,n))))),(NE-corner ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Upper_Seq (C,n)))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SE-corner ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Upper_Seq (C,n))))),(NE-corner ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Upper_Seq (C,n))))))) /\ ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Upper_Seq (C,n)))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (E-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Upper_Seq (C,n))))) is strict T_2 SubSpace of TOP-REAL 2
proj2 | (E-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Upper_Seq (C,n))))) is V19() V22( the U1 of ((TOP-REAL 2) | (E-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Upper_Seq (C,n))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (E-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Upper_Seq (C,n)))))), REAL ) V205((TOP-REAL 2) | (E-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Upper_Seq (C,n)))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (E-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Upper_Seq (C,n)))))),REAL))
the U1 of ((TOP-REAL 2) | (E-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Upper_Seq (C,n)))))) is set
K7( the U1 of ((TOP-REAL 2) | (E-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Upper_Seq (C,n)))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (E-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Upper_Seq (C,n)))))),REAL)) is set
lower_bound (proj2 | (E-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Upper_Seq (C,n)))))) is V11() real ext-real Element of REAL
(proj2 | (E-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Upper_Seq (C,n)))))) .: the U1 of ((TOP-REAL 2) | (E-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Upper_Seq (C,n)))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (E-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Upper_Seq (C,n)))))) .: the U1 of ((TOP-REAL 2) | (E-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Upper_Seq (C,n))))))) is V11() real ext-real Element of REAL
|[(E-bound ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Upper_Seq (C,n))))),(lower_bound (proj2 | (E-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Upper_Seq (C,n)))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(E-min ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (pp,i)))) /\ (L~ (Upper_Seq (C,n))))) `1 is V11() real ext-real Element of REAL
pion `1 is V11() real ext-real Element of REAL
|[(lower_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))),(((Gauge (C,n)) * (1,i)) `2)]| `2 is V11() real ext-real Element of REAL
pion `2 is V11() real ext-real Element of REAL
|[(upper_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),|[(lower_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))),(((Gauge (C,n)) * (1,i)) `2)]|)) /\ (L~ (Upper_Seq (C,n)))))),(((Gauge (C,n)) * (1,i)) `2)]| `2 is V11() real ext-real Element of REAL
LSeg (|[(lower_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))),(((Gauge (C,n)) * (1,i)) `2)]|,|[(upper_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),|[(lower_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))),(((Gauge (C,n)) * (1,i)) `2)]|)) /\ (L~ (Upper_Seq (C,n)))))),(((Gauge (C,n)) * (1,i)) `2)]|) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (|[(lower_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))),(((Gauge (C,n)) * (1,i)) `2)]|,|[(upper_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),|[(lower_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))),(((Gauge (C,n)) * (1,i)) `2)]|)) /\ (L~ (Upper_Seq (C,n)))))),(((Gauge (C,n)) * (1,i)) `2)]|)) /\ (L~ (Upper_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
LA is set
Ebo is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
Ebo `1 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (j,i)) `1 is V11() real ext-real Element of REAL
Emax is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
proj1 .: Emax is V168() V169() V170() Element of K6(REAL)
LSeg (|[(lower_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))),(((Gauge (C,n)) * (1,i)) `2)]|,((Gauge (C,n)) * (j,i))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
proj1 . Ebo is set
go is compact V168() V169() V170() Element of K6(REAL)
Ebo `2 is V11() real ext-real Element of REAL
Emax is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
W-most Emax is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SW-corner Emax is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound Emax is V11() real ext-real Element of REAL
(TOP-REAL 2) | Emax is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | Emax is V19() V22( the U1 of ((TOP-REAL 2) | Emax)) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | Emax), REAL ) V205((TOP-REAL 2) | Emax) Element of K6(K7( the U1 of ((TOP-REAL 2) | Emax),REAL))
the U1 of ((TOP-REAL 2) | Emax) is set
K7( the U1 of ((TOP-REAL 2) | Emax),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | Emax),REAL)) is set
lower_bound (proj1 | Emax) is V11() real ext-real Element of REAL
(proj1 | Emax) .: the U1 of ((TOP-REAL 2) | Emax) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | Emax) .: the U1 of ((TOP-REAL 2) | Emax)) is V11() real ext-real Element of REAL
S-bound Emax is V11() real ext-real Element of REAL
proj2 | Emax is V19() V22( the U1 of ((TOP-REAL 2) | Emax)) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | Emax), REAL ) V205((TOP-REAL 2) | Emax) Element of K6(K7( the U1 of ((TOP-REAL 2) | Emax),REAL))
lower_bound (proj2 | Emax) is V11() real ext-real Element of REAL
(proj2 | Emax) .: the U1 of ((TOP-REAL 2) | Emax) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | Emax) .: the U1 of ((TOP-REAL 2) | Emax)) is V11() real ext-real Element of REAL
|[(W-bound Emax),(S-bound Emax)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NW-corner Emax is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound Emax is V11() real ext-real Element of REAL
upper_bound (proj2 | Emax) is V11() real ext-real Element of REAL
upper_bound ((proj2 | Emax) .: the U1 of ((TOP-REAL 2) | Emax)) is V11() real ext-real Element of REAL
|[(W-bound Emax),(N-bound Emax)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner Emax),(NW-corner Emax)) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SW-corner Emax),(NW-corner Emax))) /\ Emax is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
Ebo is set
go is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
go `2 is V11() real ext-real Element of REAL
W-bound ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))) is strict T_2 SubSpace of TOP-REAL 2
proj1 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))) is V19() V22( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))), REAL ) V205((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))),REAL))
the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))) is set
K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))),REAL)) is set
lower_bound (proj1 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))) is V11() real ext-real Element of REAL
(proj1 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))) is V11() real ext-real Element of REAL
W-min ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))) is functional Element of K6( the U1 of (TOP-REAL 2))
SW-corner ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-bound ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))) is V11() real ext-real Element of REAL
proj2 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))) is V19() V22( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))), REAL ) V205((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))),REAL))
lower_bound (proj2 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))) is V11() real ext-real Element of REAL
(proj2 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))) is V11() real ext-real Element of REAL
|[(W-bound ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))),(S-bound ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NW-corner ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))) is V11() real ext-real Element of REAL
upper_bound (proj2 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))) is V11() real ext-real Element of REAL
|[(W-bound ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))),(N-bound ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))),(NW-corner ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SW-corner ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))),(NW-corner ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))))) /\ ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (W-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))) is strict T_2 SubSpace of TOP-REAL 2
proj2 | (W-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))) is V19() V22( the U1 of ((TOP-REAL 2) | (W-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (W-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))), REAL ) V205((TOP-REAL 2) | (W-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (W-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))),REAL))
the U1 of ((TOP-REAL 2) | (W-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))) is set
K7( the U1 of ((TOP-REAL 2) | (W-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (W-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))),REAL)) is set
lower_bound (proj2 | (W-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))) is V11() real ext-real Element of REAL
(proj2 | (W-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))) .: the U1 of ((TOP-REAL 2) | (W-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (W-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))) .: the U1 of ((TOP-REAL 2) | (W-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))))) is V11() real ext-real Element of REAL
|[(W-bound ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))),(lower_bound (proj2 | (W-most ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(W-min ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))))) `1 is V11() real ext-real Element of REAL
go `1 is V11() real ext-real Element of REAL
(LSeg (|[(lower_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))),(((Gauge (C,n)) * (1,i)) `2)]|,|[(upper_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),|[(lower_bound (proj1 .: ((LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n)))))),(((Gauge (C,n)) * (1,i)) `2)]|)) /\ (L~ (Upper_Seq (C,n)))))),(((Gauge (C,n)) * (1,i)) `2)]|)) /\ (L~ (Lower_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
do is set
((Gauge (C,n)) * (k,i)) `1 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (j,i)) `1 is V11() real ext-real Element of REAL
do is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
proj1 .: do is V168() V169() V170() Element of K6(REAL)
m is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
m `1 is V11() real ext-real Element of REAL
proj1 . m is set
go is compact V168() V169() V170() Element of K6(REAL)
m `2 is V11() real ext-real Element of REAL
n is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
C is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
Gauge (C,n) is V19() non empty-yielding V22( NAT ) V23(K295( the U1 of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K295( the U1 of (TOP-REAL 2))
len (Gauge (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
width (Gauge (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Upper_Seq (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
L~ (Upper_Seq (C,n)) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
Lower_Seq (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
L~ (Lower_Seq (C,n)) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
Lower_Arc C is non empty functional Element of K6( the U1 of (TOP-REAL 2))
i is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
j is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
k is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * (i,k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Gauge (C,n)) * (i,j) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
k is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
G is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * (i,k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Gauge (C,n)) * (i,G) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,G))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,G)))) /\ (L~ (Lower_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
{((Gauge (C,n)) * (i,k))} is non empty functional set
(LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,G)))) /\ (L~ (Upper_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
{((Gauge (C,n)) * (i,G))} is non empty functional set
n is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
C is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
Gauge (C,n) is V19() non empty-yielding V22( NAT ) V23(K295( the U1 of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K295( the U1 of (TOP-REAL 2))
len (Gauge (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
width (Gauge (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Upper_Seq (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
L~ (Upper_Seq (C,n)) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
Lower_Seq (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
L~ (Lower_Seq (C,n)) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
Upper_Arc C is non empty functional Element of K6( the U1 of (TOP-REAL 2))
i is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
j is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
k is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * (i,k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Gauge (C,n)) * (i,j) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
k is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
G is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * (i,k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Gauge (C,n)) * (i,G) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,G))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,G)))) /\ (L~ (Lower_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
{((Gauge (C,n)) * (i,k))} is non empty functional set
(LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,G)))) /\ (L~ (Upper_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
{((Gauge (C,n)) * (i,G))} is non empty functional set
n is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
C is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
Gauge (C,n) is V19() non empty-yielding V22( NAT ) V23(K295( the U1 of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K295( the U1 of (TOP-REAL 2))
len (Gauge (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
width (Gauge (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Cage (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
L~ (Cage (C,n)) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
Upper_Arc (L~ (Cage (C,n))) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
Lower_Arc (L~ (Cage (C,n))) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
Lower_Arc C is non empty functional Element of K6( the U1 of (TOP-REAL 2))
i is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
j is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
k is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * (i,k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Gauge (C,n)) * (i,j) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
Lower_Seq (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
L~ (Lower_Seq (C,n)) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
Upper_Seq (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
L~ (Upper_Seq (C,n)) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
n is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
C is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
Gauge (C,n) is V19() non empty-yielding V22( NAT ) V23(K295( the U1 of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K295( the U1 of (TOP-REAL 2))
len (Gauge (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
width (Gauge (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Cage (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
L~ (Cage (C,n)) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
Upper_Arc (L~ (Cage (C,n))) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
Lower_Arc (L~ (Cage (C,n))) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
Upper_Arc C is non empty functional Element of K6( the U1 of (TOP-REAL 2))
i is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
j is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
k is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * (i,k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Gauge (C,n)) * (i,j) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (C,n)) * (i,j)),((Gauge (C,n)) * (i,k))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
Lower_Seq (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
L~ (Lower_Seq (C,n)) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
Upper_Seq (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
L~ (Upper_Seq (C,n)) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
n is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
n + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
C is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
Gauge (C,(n + 1)) is V19() non empty-yielding V22( NAT ) V23(K295( the U1 of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K295( the U1 of (TOP-REAL 2))
width (Gauge (C,(n + 1))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Center (Gauge (C,(n + 1))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Cage (C,(n + 1)) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
L~ (Cage (C,(n + 1))) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
Upper_Arc (L~ (Cage (C,(n + 1)))) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
Lower_Arc (L~ (Cage (C,(n + 1)))) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
Lower_Arc C is non empty functional Element of K6( the U1 of (TOP-REAL 2))
i is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
j is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,(n + 1))) * ((Center (Gauge (C,(n + 1)))),j) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Gauge (C,(n + 1))) * ((Center (Gauge (C,(n + 1)))),i) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (C,(n + 1))) * ((Center (Gauge (C,(n + 1)))),i)),((Gauge (C,(n + 1))) * ((Center (Gauge (C,(n + 1)))),j))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
len (Gauge (C,(n + 1))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
n is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
n + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
C is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
Gauge (C,(n + 1)) is V19() non empty-yielding V22( NAT ) V23(K295( the U1 of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K295( the U1 of (TOP-REAL 2))
width (Gauge (C,(n + 1))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Center (Gauge (C,(n + 1))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Cage (C,(n + 1)) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
L~ (Cage (C,(n + 1))) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
Upper_Arc (L~ (Cage (C,(n + 1)))) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
Lower_Arc (L~ (Cage (C,(n + 1)))) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
Upper_Arc C is non empty functional Element of K6( the U1 of (TOP-REAL 2))
i is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
j is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,(n + 1))) * ((Center (Gauge (C,(n + 1)))),j) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Gauge (C,(n + 1))) * ((Center (Gauge (C,(n + 1)))),i) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (C,(n + 1))) * ((Center (Gauge (C,(n + 1)))),i)),((Gauge (C,(n + 1))) * ((Center (Gauge (C,(n + 1)))),j))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
len (Gauge (C,(n + 1))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
n is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
C is non empty functional closed connected bounded compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
Gauge (C,n) is V19() non empty-yielding V22( NAT ) V23(K295( the U1 of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K295( the U1 of (TOP-REAL 2))
len (Gauge (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
width (Gauge (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Upper_Seq (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
L~ (Upper_Seq (C,n)) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
Lower_Seq (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
L~ (Lower_Seq (C,n)) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
j is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
k is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
i is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * (k,i) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Gauge (C,n)) * (j,i) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
[j,i] is set
{j,i} is non empty V168() V169() V170() V171() V172() V173() set
{j} is non empty V168() V169() V170() V171() V172() V173() set
{{j,i},{j}} is non empty set
Indices (Gauge (C,n)) is set
(L~ (Upper_Seq (C,n))) /\ (L~ (Lower_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
Cage (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
L~ (Cage (C,n)) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
W-min (L~ (Cage (C,n))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound (L~ (Cage (C,n))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (C,n))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ (Cage (C,n))) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))), REAL ) V205((TOP-REAL 2) | (L~ (Cage (C,n)))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL))
the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))) is set
K7( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL)) is set
lower_bound (proj1 | (L~ (Cage (C,n)))) is V11() real ext-real Element of REAL
(proj1 | (L~ (Cage (C,n)))) .: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | (L~ (Cage (C,n)))) .: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n))))) is V11() real ext-real Element of REAL
W-most (L~ (Cage (C,n))) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SW-corner (L~ (Cage (C,n))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Cage (C,n))) is V11() real ext-real Element of REAL
proj2 | (L~ (Cage (C,n))) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))), REAL ) V205((TOP-REAL 2) | (L~ (Cage (C,n)))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL))
lower_bound (proj2 | (L~ (Cage (C,n)))) is V11() real ext-real Element of REAL
(proj2 | (L~ (Cage (C,n)))) .: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (L~ (Cage (C,n)))) .: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Cage (C,n)))),(S-bound (L~ (Cage (C,n))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NW-corner (L~ (Cage (C,n))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Cage (C,n))) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ (Cage (C,n)))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (L~ (Cage (C,n)))) .: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Cage (C,n)))),(N-bound (L~ (Cage (C,n))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (C,n)))),(NW-corner (L~ (Cage (C,n))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SW-corner (L~ (Cage (C,n)))),(NW-corner (L~ (Cage (C,n)))))) /\ (L~ (Cage (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (W-most (L~ (Cage (C,n)))) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Cage (C,n)))) is V19() V22( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n)))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))), REAL ) V205((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),REAL))
the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))) is set
K7( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),REAL)) is set
lower_bound (proj2 | (W-most (L~ (Cage (C,n))))) is V11() real ext-real Element of REAL
(proj2 | (W-most (L~ (Cage (C,n))))) .: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (W-most (L~ (Cage (C,n))))) .: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n)))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Cage (C,n)))),(lower_bound (proj2 | (W-most (L~ (Cage (C,n))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-max (L~ (Cage (C,n))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Cage (C,n))) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ (Cage (C,n)))) is V11() real ext-real Element of REAL
upper_bound ((proj1 | (L~ (Cage (C,n)))) .: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n))))) is V11() real ext-real Element of REAL
E-most (L~ (Cage (C,n))) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SE-corner (L~ (Cage (C,n))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
|[(E-bound (L~ (Cage (C,n)))),(S-bound (L~ (Cage (C,n))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NE-corner (L~ (Cage (C,n))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
|[(E-bound (L~ (Cage (C,n)))),(N-bound (L~ (Cage (C,n))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Cage (C,n)))),(NE-corner (L~ (Cage (C,n))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SE-corner (L~ (Cage (C,n)))),(NE-corner (L~ (Cage (C,n)))))) /\ (L~ (Cage (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (E-most (L~ (Cage (C,n)))) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Cage (C,n)))) is V19() V22( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n)))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))), REAL ) V205((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),REAL))
the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))) is set
K7( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),REAL)) is set
upper_bound (proj2 | (E-most (L~ (Cage (C,n))))) is V11() real ext-real Element of REAL
(proj2 | (E-most (L~ (Cage (C,n))))) .: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))) is V168() V169() V170() Element of K6(REAL)
upper_bound ((proj2 | (E-most (L~ (Cage (C,n))))) .: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n)))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Cage (C,n)))),(upper_bound (proj2 | (E-most (L~ (Cage (C,n))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
{(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n))))} is non empty functional set
[(len (Gauge (C,n))),i] is set
{(len (Gauge (C,n))),i} is non empty V168() V169() V170() V171() V172() V173() set
{(len (Gauge (C,n)))} is non empty V168() V169() V170() V171() V172() V173() set
{{(len (Gauge (C,n))),i},{(len (Gauge (C,n)))}} is non empty set
[1,i] is set
{1,i} is non empty V168() V169() V170() V171() V172() V173() set
{{1,i},{1}} is non empty set
(Gauge (C,n)) * (1,i) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (1,i)) `1 is V11() real ext-real Element of REAL
(W-min (L~ (Cage (C,n)))) `1 is V11() real ext-real Element of REAL
(Gauge (C,n)) * ((len (Gauge (C,n))),i) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * ((len (Gauge (C,n))),i)) `1 is V11() real ext-real Element of REAL
(E-max (L~ (Cage (C,n)))) `1 is V11() real ext-real Element of REAL
n is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
C is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
Gauge (C,n) is V19() non empty-yielding V22( NAT ) V23(K295( the U1 of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K295( the U1 of (TOP-REAL 2))
len (Gauge (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
width (Gauge (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Upper_Seq (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
L~ (Upper_Seq (C,n)) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
Lower_Seq (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
L~ (Lower_Seq (C,n)) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
Lower_Arc C is non empty functional Element of K6( the U1 of (TOP-REAL 2))
j is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
k is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
i is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * (j,i) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Gauge (C,n)) * (k,i) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
{((Gauge (C,n)) * (k,i))} is non empty functional set
(LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
{((Gauge (C,n)) * (j,i))} is non empty functional set
Cage (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
L~ (Cage (C,n)) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
W-min (L~ (Cage (C,n))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound (L~ (Cage (C,n))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (C,n))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ (Cage (C,n))) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))), REAL ) V205((TOP-REAL 2) | (L~ (Cage (C,n)))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL))
the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))) is set
K7( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL)) is set
lower_bound (proj1 | (L~ (Cage (C,n)))) is V11() real ext-real Element of REAL
(proj1 | (L~ (Cage (C,n)))) .: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | (L~ (Cage (C,n)))) .: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n))))) is V11() real ext-real Element of REAL
W-most (L~ (Cage (C,n))) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SW-corner (L~ (Cage (C,n))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Cage (C,n))) is V11() real ext-real Element of REAL
proj2 | (L~ (Cage (C,n))) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))), REAL ) V205((TOP-REAL 2) | (L~ (Cage (C,n)))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL))
lower_bound (proj2 | (L~ (Cage (C,n)))) is V11() real ext-real Element of REAL
(proj2 | (L~ (Cage (C,n)))) .: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (L~ (Cage (C,n)))) .: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Cage (C,n)))),(S-bound (L~ (Cage (C,n))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NW-corner (L~ (Cage (C,n))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Cage (C,n))) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ (Cage (C,n)))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (L~ (Cage (C,n)))) .: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Cage (C,n)))),(N-bound (L~ (Cage (C,n))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (C,n)))),(NW-corner (L~ (Cage (C,n))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SW-corner (L~ (Cage (C,n)))),(NW-corner (L~ (Cage (C,n)))))) /\ (L~ (Cage (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (W-most (L~ (Cage (C,n)))) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Cage (C,n)))) is V19() V22( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n)))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))), REAL ) V205((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),REAL))
the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))) is set
K7( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),REAL)) is set
lower_bound (proj2 | (W-most (L~ (Cage (C,n))))) is V11() real ext-real Element of REAL
(proj2 | (W-most (L~ (Cage (C,n))))) .: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (W-most (L~ (Cage (C,n))))) .: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n)))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Cage (C,n)))),(lower_bound (proj2 | (W-most (L~ (Cage (C,n))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-max (L~ (Cage (C,n))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Cage (C,n))) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ (Cage (C,n)))) is V11() real ext-real Element of REAL
upper_bound ((proj1 | (L~ (Cage (C,n)))) .: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n))))) is V11() real ext-real Element of REAL
E-most (L~ (Cage (C,n))) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SE-corner (L~ (Cage (C,n))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
|[(E-bound (L~ (Cage (C,n)))),(S-bound (L~ (Cage (C,n))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NE-corner (L~ (Cage (C,n))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
|[(E-bound (L~ (Cage (C,n)))),(N-bound (L~ (Cage (C,n))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Cage (C,n)))),(NE-corner (L~ (Cage (C,n))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SE-corner (L~ (Cage (C,n)))),(NE-corner (L~ (Cage (C,n)))))) /\ (L~ (Cage (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (E-most (L~ (Cage (C,n)))) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Cage (C,n)))) is V19() V22( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n)))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))), REAL ) V205((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),REAL))
the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))) is set
K7( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),REAL)) is set
upper_bound (proj2 | (E-most (L~ (Cage (C,n))))) is V11() real ext-real Element of REAL
(proj2 | (E-most (L~ (Cage (C,n))))) .: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))) is V168() V169() V170() Element of K6(REAL)
upper_bound ((proj2 | (E-most (L~ (Cage (C,n))))) .: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n)))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Cage (C,n)))),(upper_bound (proj2 | (E-most (L~ (Cage (C,n))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
[j,i] is set
{j,i} is non empty V168() V169() V170() V171() V172() V173() set
{j} is non empty V168() V169() V170() V171() V172() V173() set
{{j,i},{j}} is non empty set
Indices (Gauge (C,n)) is set
[k,i] is set
{k,i} is non empty V168() V169() V170() V171() V172() V173() set
{k} is non empty V168() V169() V170() V171() V172() V173() set
{{k,i},{k}} is non empty set
R_Cut ((Upper_Seq (C,n)),((Gauge (C,n)) * (k,i))) is V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
L_Cut ((Lower_Seq (C,n)),((Gauge (C,n)) * (j,i))) is V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
len (Upper_Seq (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
dom (Upper_Seq (C,n)) is non trivial V168() V169() V170() V171() V172() V173() Element of K6(NAT)
(Upper_Seq (C,n)) . 1 is V19() Function-like set
(Upper_Seq (C,n)) /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(W-min (L~ (Cage (C,n)))) `1 is V11() real ext-real Element of REAL
(Gauge (C,n)) * (1,k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (1,k)) `1 is V11() real ext-real Element of REAL
[1,k] is set
{1,k} is non empty V168() V169() V170() V171() V172() V173() set
{{1,k},{1}} is non empty set
[1,j] is set
{1,j} is non empty V168() V169() V170() V171() V172() V173() set
{{1,j},{1}} is non empty set
1 + 2 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
len (Lower_Seq (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
dom (Lower_Seq (C,n)) is non trivial V168() V169() V170() V171() V172() V173() Element of K6(NAT)
(Lower_Seq (C,n)) . (len (Lower_Seq (C,n))) is V19() Function-like set
(Lower_Seq (C,n)) /. (len (Lower_Seq (C,n))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
[(len (Gauge (C,n))),k] is set
{(len (Gauge (C,n))),k} is non empty V168() V169() V170() V171() V172() V173() set
{(len (Gauge (C,n)))} is non empty V168() V169() V170() V171() V172() V173() set
{{(len (Gauge (C,n))),k},{(len (Gauge (C,n)))}} is non empty set
(Lower_Seq (C,n)) . 1 is V19() Function-like set
(Lower_Seq (C,n)) /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(E-max (L~ (Cage (C,n)))) `1 is V11() real ext-real Element of REAL
(Gauge (C,n)) * ((len (Gauge (C,n))),k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * ((len (Gauge (C,n))),k)) `1 is V11() real ext-real Element of REAL
1 + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
do is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
len do is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
rng (Upper_Seq (C,n)) is functional Element of K6( the U1 of (TOP-REAL 2))
pion is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
len pion is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
rng (Lower_Seq (C,n)) is functional Element of K6( the U1 of (TOP-REAL 2))
LA is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one non constant V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq s.c.c. FinSequence of the U1 of (TOP-REAL 2)
len LA is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
dom LA is non trivial V168() V169() V170() V171() V172() V173() Element of K6(NAT)
LA /. (len LA) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LA . (len LA) is V19() Function-like set
Emax is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one non constant V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq s.c.c. FinSequence of the U1 of (TOP-REAL 2)
len Emax is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
dom Emax is non trivial V168() V169() V170() V171() V172() V173() Element of K6(NAT)
Emax /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
Emax . 1 is V19() Function-like set
(len LA) - 1 is V11() real ext-real Element of REAL
Ebo is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Ebo + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(len LA) -' 1 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
LSeg (LA,Ebo) is functional Element of K6( the U1 of (TOP-REAL 2))
L~ LA is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (LA,Ebo)) /\ (LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i)))) is functional Element of K6( the U1 of (TOP-REAL 2))
LA /. Ebo is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((LA /. Ebo),((Gauge (C,n)) * (k,i))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
go is set
LSeg (Emax,1) is functional Element of K6( the U1 of (TOP-REAL 2))
L~ Emax is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(LSeg (Emax,1)) /\ (LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i)))) is functional Element of K6( the U1 of (TOP-REAL 2))
Emax /. (1 + 1) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (C,n)) * (j,i)),(Emax /. (1 + 1))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
go is set
(LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i)))) /\ (LSeg (Emax,1)) is functional Element of K6( the U1 of (TOP-REAL 2))
LA /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
Emax /. (len Emax) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
rng LA is non trivial functional Element of K6( the U1 of (TOP-REAL 2))
rng Emax is non trivial functional Element of K6( the U1 of (TOP-REAL 2))
{(LA /. 1)} is non empty functional set
(L~ LA) /\ (L~ Emax) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
go is set
[(len (Gauge (C,n))),j] is set
{(len (Gauge (C,n))),j} is non empty V168() V169() V170() V171() V172() V173() set
{{(len (Gauge (C,n))),j},{(len (Gauge (C,n)))}} is non empty set
go is set
(Gauge (C,n)) * ((len (Gauge (C,n))),j) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * ((len (Gauge (C,n))),j)) `1 is V11() real ext-real Element of REAL
(L~ (Upper_Seq (C,n))) /\ (L~ (Lower_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
{(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n))))} is non empty functional set
LA /. 2 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (j,i)) `1 is V11() real ext-real Element of REAL
(Gauge (C,n)) * (1,j) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (1,j)) `1 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (k,i)) .. (Upper_Seq (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
mid ((Upper_Seq (C,n)),1,(((Gauge (C,n)) * (k,i)) .. (Upper_Seq (C,n)))) is V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
(Upper_Seq (C,n)) | (((Gauge (C,n)) * (k,i)) .. (Upper_Seq (C,n))) is V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. FinSequence of the U1 of (TOP-REAL 2)
(Upper_Seq (C,n)) /. 2 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
<*((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i))*> is non empty V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() V39(2) FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
do is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
dom <*((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i))*> is V168() V169() V170() V171() V172() V173() Element of K6(NAT)
<*((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i))*> /. do is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (k,i)) `2 is V11() real ext-real Element of REAL
(Gauge (C,n)) * (1,i) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (1,i)) `2 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (j,i)) `2 is V11() real ext-real Element of REAL
L~ <*((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i))*> is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
<*((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i))*> /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
len <*((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i))*> is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
<*((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i))*> /. (len <*((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i))*>) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
do is V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
L~ do is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
do /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
len do is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
do /. (len do) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
go is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
LA ^' go is non empty V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
(LA ^' go) ^' Emax is non empty V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
len (Cage (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
len (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
len (LA ^' go) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
1 + 0 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
len ((LA ^' go) ^' Emax) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
go /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(LA ^' go) /. (len (LA ^' go)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
<*((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i))*> /. 2 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg (go,1) is functional Element of K6( the U1 of (TOP-REAL 2))
LSeg (LA,((len LA) -' 1)) is functional Element of K6( the U1 of (TOP-REAL 2))
(LSeg (LA,((len LA) -' 1))) /\ (LSeg (go,1)) is functional Element of K6( the U1 of (TOP-REAL 2))
len go is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(LSeg (LA,Ebo)) /\ (LSeg (go,1)) is functional Element of K6( the U1 of (TOP-REAL 2))
W2 is set
{(LA /. (len LA))} is non empty functional set
2 + 0 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(len go) - 2 is V11() real ext-real Element of REAL
(len (LA ^' go)) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((len (LA ^' go)) + 1) - 1 is V11() real ext-real Element of REAL
(len LA) + (len go) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((len LA) + (len go)) - 1 is V11() real ext-real Element of REAL
(len (LA ^' go)) - 1 is V11() real ext-real Element of REAL
(len LA) + ((len go) - 2) is V11() real ext-real Element of REAL
(len go) -' 2 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(len LA) + ((len go) -' 2) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(len (LA ^' go)) -' 1 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(len go) - 1 is V11() real ext-real Element of REAL
(len go) -' 1 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((len go) -' 2) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((len go) - 2) + 1 is V11() real ext-real Element of REAL
((len go) - 1) + 1 is V11() real ext-real Element of REAL
LSeg (go,((len go) -' 1)) is functional Element of K6( the U1 of (TOP-REAL 2))
(LSeg (go,((len go) -' 1))) /\ (LSeg (Emax,1)) is functional Element of K6( the U1 of (TOP-REAL 2))
W2 is set
((len go) -' 1) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
go /. (((len go) -' 1) + 1) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((LA ^' go),((len LA) + ((len go) -' 2))) is functional Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((LA ^' go),((len LA) + ((len go) -' 2)))) /\ (LSeg (Emax,1)) is functional Element of K6( the U1 of (TOP-REAL 2))
{((LA ^' go) /. (len (LA ^' go)))} is non empty functional set
rng go is functional Element of K6( the U1 of (TOP-REAL 2))
L~ go is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
{(go /. 1)} is non empty functional set
(L~ LA) /\ (L~ go) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
W2 is set
W2 is set
(L~ go) /\ (L~ (Upper_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(rng LA) /\ (rng go) is functional Element of K6( the U1 of (TOP-REAL 2))
go /. (len go) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
{(go /. (len go))} is non empty functional set
(L~ Emax) /\ (L~ go) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
W2 is set
W2 is set
(L~ go) /\ (L~ (Lower_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
L~ (LA ^' go) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(L~ (LA ^' go)) /\ (L~ Emax) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(L~ LA) \/ (L~ go) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
((L~ LA) \/ (L~ go)) /\ (L~ Emax) is functional Element of K6( the U1 of (TOP-REAL 2))
{(Emax /. 1)} is non empty functional set
{(LA /. 1)} \/ {(Emax /. 1)} is non empty set
(LA ^' go) /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
{((LA ^' go) /. 1)} is non empty functional set
{((LA ^' go) /. 1)} \/ {(Emax /. 1)} is non empty set
{((LA ^' go) /. 1),(Emax /. 1)} is non empty functional set
E-max C is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-bound C is V11() real ext-real Element of REAL
(TOP-REAL 2) | C is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | C is V19() V22( the U1 of ((TOP-REAL 2) | C)) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | C), REAL ) V205((TOP-REAL 2) | C) Element of K6(K7( the U1 of ((TOP-REAL 2) | C),REAL))
the U1 of ((TOP-REAL 2) | C) is set
K7( the U1 of ((TOP-REAL 2) | C),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | C),REAL)) is set
upper_bound (proj1 | C) is V11() real ext-real Element of REAL
(proj1 | C) .: the U1 of ((TOP-REAL 2) | C) is V168() V169() V170() Element of K6(REAL)
upper_bound ((proj1 | C) .: the U1 of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
E-most C is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SE-corner C is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-bound C is V11() real ext-real Element of REAL
proj2 | C is V19() V22( the U1 of ((TOP-REAL 2) | C)) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | C), REAL ) V205((TOP-REAL 2) | C) Element of K6(K7( the U1 of ((TOP-REAL 2) | C),REAL))
lower_bound (proj2 | C) is V11() real ext-real Element of REAL
(proj2 | C) .: the U1 of ((TOP-REAL 2) | C) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | C) .: the U1 of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
|[(E-bound C),(S-bound C)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NE-corner C is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound C is V11() real ext-real Element of REAL
upper_bound (proj2 | C) is V11() real ext-real Element of REAL
upper_bound ((proj2 | C) .: the U1 of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
|[(E-bound C),(N-bound C)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner C),(NE-corner C)) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SE-corner C),(NE-corner C))) /\ C is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (E-most C) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (E-most C) is V19() V22( the U1 of ((TOP-REAL 2) | (E-most C))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (E-most C)), REAL ) V205((TOP-REAL 2) | (E-most C)) Element of K6(K7( the U1 of ((TOP-REAL 2) | (E-most C)),REAL))
the U1 of ((TOP-REAL 2) | (E-most C)) is set
K7( the U1 of ((TOP-REAL 2) | (E-most C)),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (E-most C)),REAL)) is set
upper_bound (proj2 | (E-most C)) is V11() real ext-real Element of REAL
(proj2 | (E-most C)) .: the U1 of ((TOP-REAL 2) | (E-most C)) is V168() V169() V170() Element of K6(REAL)
upper_bound ((proj2 | (E-most C)) .: the U1 of ((TOP-REAL 2) | (E-most C))) is V11() real ext-real Element of REAL
|[(E-bound C),(upper_bound (proj2 | (E-most C)))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-min C is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound C is V11() real ext-real Element of REAL
lower_bound (proj1 | C) is V11() real ext-real Element of REAL
lower_bound ((proj1 | C) .: the U1 of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
W-most C is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SW-corner C is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
|[(W-bound C),(S-bound C)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NW-corner C is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
|[(W-bound C),(N-bound C)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner C),(NW-corner C)) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SW-corner C),(NW-corner C))) /\ C is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (W-most C) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (W-most C) is V19() V22( the U1 of ((TOP-REAL 2) | (W-most C))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (W-most C)), REAL ) V205((TOP-REAL 2) | (W-most C)) Element of K6(K7( the U1 of ((TOP-REAL 2) | (W-most C)),REAL))
the U1 of ((TOP-REAL 2) | (W-most C)) is set
K7( the U1 of ((TOP-REAL 2) | (W-most C)),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (W-most C)),REAL)) is set
lower_bound (proj2 | (W-most C)) is V11() real ext-real Element of REAL
(proj2 | (W-most C)) .: the U1 of ((TOP-REAL 2) | (W-most C)) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (W-most C)) .: the U1 of ((TOP-REAL 2) | (W-most C))) is V11() real ext-real Element of REAL
|[(W-bound C),(lower_bound (proj2 | (W-most C)))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
rng (Cage (C,n)) is non trivial functional Element of K6( the U1 of (TOP-REAL 2))
(Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
W-max (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))), REAL ) V205((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),REAL))
the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is set
K7( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),REAL)) is set
lower_bound (proj1 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is V11() real ext-real Element of REAL
(proj1 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SW-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V11() real ext-real Element of REAL
proj2 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))), REAL ) V205((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),REAL))
lower_bound (proj2 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is V11() real ext-real Element of REAL
(proj2 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),(S-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NW-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),(N-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),(NW-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SW-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),(NW-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))) /\ (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is V19() V22( the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))), REAL ) V205((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))),REAL))
the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is set
K7( the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))),REAL)) is set
upper_bound (proj2 | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
(proj2 | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) .: the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V168() V169() V170() Element of K6(REAL)
upper_bound ((proj2 | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) .: the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),(upper_bound (proj2 | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(W-max (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .. (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
N-min (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
NE-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is V11() real ext-real Element of REAL
upper_bound ((proj1 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),(N-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((NW-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),(NE-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((NW-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),(NE-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))) /\ (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is V19() V22( the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))), REAL ) V205((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))),REAL))
the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is set
K7( the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))),REAL)) is set
lower_bound (proj1 | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
(proj1 | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) .: the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) .: the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))),(N-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(N-min (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .. (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
N-max (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
upper_bound (proj1 | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
upper_bound ((proj1 | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) .: the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))) is V11() real ext-real Element of REAL
|[(upper_bound (proj1 | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))),(N-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(N-max (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .. (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(E-max (L~ (Cage (C,n)))) .. (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
W2 is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard FinSequence of the U1 of (TOP-REAL 2)
right_cell (W2,1,(Gauge (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
L~ W2 is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
(right_cell (W2,1,(Gauge (C,n)))) \ (L~ W2) is functional Element of K6( the U1 of (TOP-REAL 2))
RightComp W2 is non empty functional Element of K6( the U1 of (TOP-REAL 2))
(L~ (LA ^' go)) \/ (L~ Emax) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
((L~ LA) \/ (L~ go)) \/ (L~ Emax) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
(L~ (Upper_Seq (C,n))) \/ (L~ (Lower_Seq (C,n))) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
right_cell ((Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))),1) is functional Element of K6( the U1 of (TOP-REAL 2))
GoB (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) is V19() non empty-yielding V22( NAT ) V23(K295( the U1 of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K295( the U1 of (TOP-REAL 2))
right_cell ((Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))),1,(GoB (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is functional Element of K6( the U1 of (TOP-REAL 2))
GoB (Cage (C,n)) is V19() non empty-yielding V22( NAT ) V23(K295( the U1 of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K295( the U1 of (TOP-REAL 2))
right_cell ((Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))),1,(GoB (Cage (C,n)))) is functional Element of K6( the U1 of (TOP-REAL 2))
right_cell ((Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))),1,(Gauge (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
(Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) -: (E-max (L~ (Cage (C,n)))) is V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like special unfolded FinSequence of the U1 of (TOP-REAL 2)
right_cell (((Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) -: (E-max (L~ (Cage (C,n))))),1,(Gauge (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
right_cell ((Upper_Seq (C,n)),1,(Gauge (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
right_cell ((R_Cut ((Upper_Seq (C,n)),((Gauge (C,n)) * (k,i)))),1,(Gauge (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
right_cell ((LA ^' go),1,(Gauge (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
W2 /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W2 /. 2 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(LA ^' go) /. 2 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Upper_Seq (C,n)) ^' (Lower_Seq (C,n)) is non empty V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
((Upper_Seq (C,n)) ^' (Lower_Seq (C,n))) /. 2 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) /. 2 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(L~ LA) \/ (L~ Emax) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
W-min ((L~ LA) \/ (L~ Emax)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound ((L~ LA) \/ (L~ Emax)) is V11() real ext-real Element of REAL
(TOP-REAL 2) | ((L~ LA) \/ (L~ Emax)) is strict T_2 SubSpace of TOP-REAL 2
proj1 | ((L~ LA) \/ (L~ Emax)) is V19() V22( the U1 of ((TOP-REAL 2) | ((L~ LA) \/ (L~ Emax)))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | ((L~ LA) \/ (L~ Emax))), REAL ) V205((TOP-REAL 2) | ((L~ LA) \/ (L~ Emax))) Element of K6(K7( the U1 of ((TOP-REAL 2) | ((L~ LA) \/ (L~ Emax))),REAL))
the U1 of ((TOP-REAL 2) | ((L~ LA) \/ (L~ Emax))) is set
K7( the U1 of ((TOP-REAL 2) | ((L~ LA) \/ (L~ Emax))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | ((L~ LA) \/ (L~ Emax))),REAL)) is set
lower_bound (proj1 | ((L~ LA) \/ (L~ Emax))) is V11() real ext-real Element of REAL
(proj1 | ((L~ LA) \/ (L~ Emax))) .: the U1 of ((TOP-REAL 2) | ((L~ LA) \/ (L~ Emax))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | ((L~ LA) \/ (L~ Emax))) .: the U1 of ((TOP-REAL 2) | ((L~ LA) \/ (L~ Emax)))) is V11() real ext-real Element of REAL
W-most ((L~ LA) \/ (L~ Emax)) is functional Element of K6( the U1 of (TOP-REAL 2))
SW-corner ((L~ LA) \/ (L~ Emax)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-bound ((L~ LA) \/ (L~ Emax)) is V11() real ext-real Element of REAL
proj2 | ((L~ LA) \/ (L~ Emax)) is V19() V22( the U1 of ((TOP-REAL 2) | ((L~ LA) \/ (L~ Emax)))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | ((L~ LA) \/ (L~ Emax))), REAL ) V205((TOP-REAL 2) | ((L~ LA) \/ (L~ Emax))) Element of K6(K7( the U1 of ((TOP-REAL 2) | ((L~ LA) \/ (L~ Emax))),REAL))
lower_bound (proj2 | ((L~ LA) \/ (L~ Emax))) is V11() real ext-real Element of REAL
(proj2 | ((L~ LA) \/ (L~ Emax))) .: the U1 of ((TOP-REAL 2) | ((L~ LA) \/ (L~ Emax))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | ((L~ LA) \/ (L~ Emax))) .: the U1 of ((TOP-REAL 2) | ((L~ LA) \/ (L~ Emax)))) is V11() real ext-real Element of REAL
|[(W-bound ((L~ LA) \/ (L~ Emax))),(S-bound ((L~ LA) \/ (L~ Emax)))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NW-corner ((L~ LA) \/ (L~ Emax)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound ((L~ LA) \/ (L~ Emax)) is V11() real ext-real Element of REAL
upper_bound (proj2 | ((L~ LA) \/ (L~ Emax))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | ((L~ LA) \/ (L~ Emax))) .: the U1 of ((TOP-REAL 2) | ((L~ LA) \/ (L~ Emax)))) is V11() real ext-real Element of REAL
|[(W-bound ((L~ LA) \/ (L~ Emax))),(N-bound ((L~ LA) \/ (L~ Emax)))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner ((L~ LA) \/ (L~ Emax))),(NW-corner ((L~ LA) \/ (L~ Emax)))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SW-corner ((L~ LA) \/ (L~ Emax))),(NW-corner ((L~ LA) \/ (L~ Emax))))) /\ ((L~ LA) \/ (L~ Emax)) is functional Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (W-most ((L~ LA) \/ (L~ Emax))) is strict T_2 SubSpace of TOP-REAL 2
proj2 | (W-most ((L~ LA) \/ (L~ Emax))) is V19() V22( the U1 of ((TOP-REAL 2) | (W-most ((L~ LA) \/ (L~ Emax))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (W-most ((L~ LA) \/ (L~ Emax)))), REAL ) V205((TOP-REAL 2) | (W-most ((L~ LA) \/ (L~ Emax)))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (W-most ((L~ LA) \/ (L~ Emax)))),REAL))
the U1 of ((TOP-REAL 2) | (W-most ((L~ LA) \/ (L~ Emax)))) is set
K7( the U1 of ((TOP-REAL 2) | (W-most ((L~ LA) \/ (L~ Emax)))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (W-most ((L~ LA) \/ (L~ Emax)))),REAL)) is set
lower_bound (proj2 | (W-most ((L~ LA) \/ (L~ Emax)))) is V11() real ext-real Element of REAL
(proj2 | (W-most ((L~ LA) \/ (L~ Emax)))) .: the U1 of ((TOP-REAL 2) | (W-most ((L~ LA) \/ (L~ Emax)))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (W-most ((L~ LA) \/ (L~ Emax)))) .: the U1 of ((TOP-REAL 2) | (W-most ((L~ LA) \/ (L~ Emax))))) is V11() real ext-real Element of REAL
|[(W-bound ((L~ LA) \/ (L~ Emax))),(lower_bound (proj2 | (W-most ((L~ LA) \/ (L~ Emax)))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(W-min ((L~ LA) \/ (L~ Emax))) `1 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (k,i)) `1 is V11() real ext-real Element of REAL
W-bound (LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i)))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i)))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i)))) is V19() V22( the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i)))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i))))), REAL ) V205((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i))))),REAL))
the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i))))) is set
K7( the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i))))),REAL)) is set
lower_bound (proj1 | (LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i))))) is V11() real ext-real Element of REAL
(proj1 | (LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i))))) .: the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | (LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i))))) .: the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i)))))) is V11() real ext-real Element of REAL
W-bound (L~ go) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ go) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ go) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ go))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ go)), REAL ) V205((TOP-REAL 2) | (L~ go)) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ go)),REAL))
the U1 of ((TOP-REAL 2) | (L~ go)) is set
K7( the U1 of ((TOP-REAL 2) | (L~ go)),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (L~ go)),REAL)) is set
lower_bound (proj1 | (L~ go)) is V11() real ext-real Element of REAL
(proj1 | (L~ go)) .: the U1 of ((TOP-REAL 2) | (L~ go)) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | (L~ go)) .: the U1 of ((TOP-REAL 2) | (L~ go))) is V11() real ext-real Element of REAL
((L~ LA) \/ (L~ Emax)) \/ (L~ go) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
W-min (((L~ LA) \/ (L~ Emax)) \/ (L~ go)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound (((L~ LA) \/ (L~ Emax)) \/ (L~ go)) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (((L~ LA) \/ (L~ Emax)) \/ (L~ go)) is strict T_2 SubSpace of TOP-REAL 2
proj1 | (((L~ LA) \/ (L~ Emax)) \/ (L~ go)) is V19() V22( the U1 of ((TOP-REAL 2) | (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))), REAL ) V205((TOP-REAL 2) | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))),REAL))
the U1 of ((TOP-REAL 2) | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))) is set
K7( the U1 of ((TOP-REAL 2) | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))),REAL)) is set
lower_bound (proj1 | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))) is V11() real ext-real Element of REAL
(proj1 | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))) .: the U1 of ((TOP-REAL 2) | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))) .: the U1 of ((TOP-REAL 2) | (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))) is V11() real ext-real Element of REAL
W-most (((L~ LA) \/ (L~ Emax)) \/ (L~ go)) is functional Element of K6( the U1 of (TOP-REAL 2))
SW-corner (((L~ LA) \/ (L~ Emax)) \/ (L~ go)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-bound (((L~ LA) \/ (L~ Emax)) \/ (L~ go)) is V11() real ext-real Element of REAL
proj2 | (((L~ LA) \/ (L~ Emax)) \/ (L~ go)) is V19() V22( the U1 of ((TOP-REAL 2) | (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))), REAL ) V205((TOP-REAL 2) | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))),REAL))
lower_bound (proj2 | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))) is V11() real ext-real Element of REAL
(proj2 | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))) .: the U1 of ((TOP-REAL 2) | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))) .: the U1 of ((TOP-REAL 2) | (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))) is V11() real ext-real Element of REAL
|[(W-bound (((L~ LA) \/ (L~ Emax)) \/ (L~ go))),(S-bound (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NW-corner (((L~ LA) \/ (L~ Emax)) \/ (L~ go)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound (((L~ LA) \/ (L~ Emax)) \/ (L~ go)) is V11() real ext-real Element of REAL
upper_bound (proj2 | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))) .: the U1 of ((TOP-REAL 2) | (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))) is V11() real ext-real Element of REAL
|[(W-bound (((L~ LA) \/ (L~ Emax)) \/ (L~ go))),(N-bound (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (((L~ LA) \/ (L~ Emax)) \/ (L~ go))),(NW-corner (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SW-corner (((L~ LA) \/ (L~ Emax)) \/ (L~ go))),(NW-corner (((L~ LA) \/ (L~ Emax)) \/ (L~ go))))) /\ (((L~ LA) \/ (L~ Emax)) \/ (L~ go)) is functional Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (W-most (((L~ LA) \/ (L~ Emax)) \/ (L~ go))) is strict T_2 SubSpace of TOP-REAL 2
proj2 | (W-most (((L~ LA) \/ (L~ Emax)) \/ (L~ go))) is V19() V22( the U1 of ((TOP-REAL 2) | (W-most (((L~ LA) \/ (L~ Emax)) \/ (L~ go))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (W-most (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))), REAL ) V205((TOP-REAL 2) | (W-most (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (W-most (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))),REAL))
the U1 of ((TOP-REAL 2) | (W-most (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))) is set
K7( the U1 of ((TOP-REAL 2) | (W-most (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (W-most (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))),REAL)) is set
lower_bound (proj2 | (W-most (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))) is V11() real ext-real Element of REAL
(proj2 | (W-most (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))) .: the U1 of ((TOP-REAL 2) | (W-most (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (W-most (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))) .: the U1 of ((TOP-REAL 2) | (W-most (((L~ LA) \/ (L~ Emax)) \/ (L~ go))))) is V11() real ext-real Element of REAL
|[(W-bound (((L~ LA) \/ (L~ Emax)) \/ (L~ go))),(lower_bound (proj2 | (W-most (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-min (L~ W2) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound (L~ W2) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ W2) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ W2) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ W2))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ W2)), REAL ) V205((TOP-REAL 2) | (L~ W2)) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ W2)),REAL))
the U1 of ((TOP-REAL 2) | (L~ W2)) is set
K7( the U1 of ((TOP-REAL 2) | (L~ W2)),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (L~ W2)),REAL)) is set
lower_bound (proj1 | (L~ W2)) is V11() real ext-real Element of REAL
(proj1 | (L~ W2)) .: the U1 of ((TOP-REAL 2) | (L~ W2)) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | (L~ W2)) .: the U1 of ((TOP-REAL 2) | (L~ W2))) is V11() real ext-real Element of REAL
W-most (L~ W2) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SW-corner (L~ W2) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-bound (L~ W2) is V11() real ext-real Element of REAL
proj2 | (L~ W2) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ W2))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ W2)), REAL ) V205((TOP-REAL 2) | (L~ W2)) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ W2)),REAL))
lower_bound (proj2 | (L~ W2)) is V11() real ext-real Element of REAL
(proj2 | (L~ W2)) .: the U1 of ((TOP-REAL 2) | (L~ W2)) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (L~ W2)) .: the U1 of ((TOP-REAL 2) | (L~ W2))) is V11() real ext-real Element of REAL
|[(W-bound (L~ W2)),(S-bound (L~ W2))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NW-corner (L~ W2) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound (L~ W2) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ W2)) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (L~ W2)) .: the U1 of ((TOP-REAL 2) | (L~ W2))) is V11() real ext-real Element of REAL
|[(W-bound (L~ W2)),(N-bound (L~ W2))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ W2)),(NW-corner (L~ W2))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SW-corner (L~ W2)),(NW-corner (L~ W2)))) /\ (L~ W2) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (W-most (L~ W2)) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (W-most (L~ W2)) is V19() V22( the U1 of ((TOP-REAL 2) | (W-most (L~ W2)))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (W-most (L~ W2))), REAL ) V205((TOP-REAL 2) | (W-most (L~ W2))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (W-most (L~ W2))),REAL))
the U1 of ((TOP-REAL 2) | (W-most (L~ W2))) is set
K7( the U1 of ((TOP-REAL 2) | (W-most (L~ W2))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (W-most (L~ W2))),REAL)) is set
lower_bound (proj2 | (W-most (L~ W2))) is V11() real ext-real Element of REAL
(proj2 | (W-most (L~ W2))) .: the U1 of ((TOP-REAL 2) | (W-most (L~ W2))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (W-most (L~ W2))) .: the U1 of ((TOP-REAL 2) | (W-most (L~ W2)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ W2)),(lower_bound (proj2 | (W-most (L~ W2))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
rng W2 is non trivial functional Element of K6( the U1 of (TOP-REAL 2))
dom W2 is non trivial V168() V169() V170() V171() V172() V173() Element of K6(NAT)
(W2 /. 2) `1 is V11() real ext-real Element of REAL
(W-min (L~ W2)) `1 is V11() real ext-real Element of REAL
Rotate (W2,(W-min (L~ W2))) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard FinSequence of the U1 of (TOP-REAL 2)
(Rotate (W2,(W-min (L~ W2)))) /. 2 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Upper_Seq (C,n)) . (len (Upper_Seq (C,n))) is V19() Function-like set
(Upper_Seq (C,n)) /. (len (Upper_Seq (C,n))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
east_halfline (E-max C) is non empty functional connected V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
godo is set
godo is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(east_halfline (E-max C)) /\ (L~ (Cage (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
godo `1 is V11() real ext-real Element of REAL
pion1 is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
L~ pion1 is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
godo is set
godo is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
godo `2 is V11() real ext-real Element of REAL
(E-max C) `2 is V11() real ext-real Element of REAL
k + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(k + 1) - 1 is V11() real ext-real Element of REAL
(len (Gauge (C,n))) - 1 is V11() real ext-real Element of REAL
(len (Gauge (C,n))) -' 1 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * (((len (Gauge (C,n))) -' 1),1) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (((len (Gauge (C,n))) -' 1),1)) `1 is V11() real ext-real Element of REAL
godo `1 is V11() real ext-real Element of REAL
(E-max C) `1 is V11() real ext-real Element of REAL
godo is set
godo is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
Index (godo,Emax) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
LSeg (Emax,(Index (godo,Emax))) is functional Element of K6( the U1 of (TOP-REAL 2))
ff is ordinal natural ext-real non negative set
(Lower_Seq (C,n)) . ff is V19() Function-like set
Index (((Gauge (C,n)) * (j,i)),(Lower_Seq (C,n))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Index (((Gauge (C,n)) * (j,i)),(Lower_Seq (C,n)))) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
len (L_Cut ((Lower_Seq (C,n)),((Gauge (C,n)) * (j,i)))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(len (Lower_Seq (C,n))) - (Index (((Gauge (C,n)) * (j,i)),(Lower_Seq (C,n)))) is V11() real ext-real Element of REAL
(len (Lower_Seq (C,n))) -' (Index (((Gauge (C,n)) * (j,i)),(Lower_Seq (C,n)))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Index (godo,Emax)) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((len (Lower_Seq (C,n))) -' (Index (((Gauge (C,n)) * (j,i)),(Lower_Seq (C,n))))) - 1 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (j,i)) .. (Lower_Seq (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
mid ((Lower_Seq (C,n)),(((Gauge (C,n)) * (j,i)) .. (Lower_Seq (C,n))),(len (Lower_Seq (C,n)))) is V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
(east_halfline (E-max C)) /\ (L~ (Cage (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
godo `1 is V11() real ext-real Element of REAL
0 + (Index (((Gauge (C,n)) * (j,i)),(Lower_Seq (C,n)))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((len (Lower_Seq (C,n))) - (Index (((Gauge (C,n)) * (j,i)),(Lower_Seq (C,n))))) - 1 is V11() real ext-real Element of REAL
(len (Lower_Seq (C,n))) - (((Gauge (C,n)) * (j,i)) .. (Lower_Seq (C,n))) is V11() real ext-real Element of REAL
(len (Lower_Seq (C,n))) -' (((Gauge (C,n)) * (j,i)) .. (Lower_Seq (C,n))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((len (Lower_Seq (C,n))) -' (((Gauge (C,n)) * (j,i)) .. (Lower_Seq (C,n)))) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Index (godo,Emax)) + (((Gauge (C,n)) * (j,i)) .. (Lower_Seq (C,n))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((Index (godo,Emax)) + (((Gauge (C,n)) * (j,i)) .. (Lower_Seq (C,n)))) -' 1 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
right_cell ((Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))),1) is functional Element of K6( the U1 of (TOP-REAL 2))
GoB (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))) is V19() non empty-yielding V22( NAT ) V23(K295( the U1 of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K295( the U1 of (TOP-REAL 2))
L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
p is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * ((len (Gauge (C,n))),p) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
[(len (Gauge (C,n))),p] is set
{(len (Gauge (C,n))),p} is non empty V168() V169() V170() V171() V172() V173() set
{{(len (Gauge (C,n))),p},{(len (Gauge (C,n)))}} is non empty set
len (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))) -: (W-min (L~ (Cage (C,n)))) is V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like special unfolded FinSequence of the U1 of (TOP-REAL 2)
LSeg ((Lower_Seq (C,n)),1) is functional Element of K6( the U1 of (TOP-REAL 2))
LSeg ((Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))),1) is functional Element of K6( the U1 of (TOP-REAL 2))
(Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))) /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))) /. (1 + 1) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
t is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
tt is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
tt + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
[t,(tt + 1)] is set
{t,(tt + 1)} is non empty V168() V169() V170() V171() V172() V173() set
{t} is non empty V168() V169() V170() V171() V172() V173() set
{{t,(tt + 1)},{t}} is non empty set
[t,tt] is set
{t,tt} is non empty V168() V169() V170() V171() V172() V173() set
{{t,tt},{t}} is non empty set
(Gauge (C,n)) * (t,(tt + 1)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Gauge (C,n)) * (t,tt) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(tt + 1) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
E-max (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))), REAL ) V205((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),REAL))
the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) is set
K7( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),REAL)) is set
upper_bound (proj1 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) is V11() real ext-real Element of REAL
(proj1 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) is V168() V169() V170() Element of K6(REAL)
upper_bound ((proj1 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SE-corner (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is V11() real ext-real Element of REAL
proj2 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))), REAL ) V205((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),REAL))
lower_bound (proj2 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) is V11() real ext-real Element of REAL
(proj2 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),(S-bound (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NE-corner (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),(N-bound (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),(NE-corner (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SE-corner (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),(NE-corner (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))))) /\ (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) is V19() V22( the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))), REAL ) V205((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))),REAL))
the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) is set
K7( the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))),REAL)) is set
upper_bound (proj2 | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
(proj2 | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) .: the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) is V168() V169() V170() Element of K6(REAL)
upper_bound ((proj2 | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) .: the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),(upper_bound (proj2 | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
4 - 1 is V11() real ext-real Element of REAL
t - 1 is V11() real ext-real Element of REAL
t -' 1 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * ((len (Gauge (C,n))),tt) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * ((len (Gauge (C,n))),tt)) `1 is V11() real ext-real Element of REAL
t + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
cell ((Gauge (C,n)),(t -' 1),tt) is functional Element of K6( the U1 of (TOP-REAL 2))
(Gauge (C,n)) * ((len (Gauge (C,n))),(tt + 1)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * ((len (Gauge (C,n))),(tt + 1))) `1 is V11() real ext-real Element of REAL
(t -' 1) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * ((t -' 1),(tt + 1)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * ((t -' 1),(tt + 1))) `2 is V11() real ext-real Element of REAL
(Gauge (C,n)) * (1,(tt + 1)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (1,(tt + 1))) `2 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (t,(tt + 1))) `2 is V11() real ext-real Element of REAL
(E-max C) `2 is V11() real ext-real Element of REAL
godo `2 is V11() real ext-real Element of REAL
(Gauge (C,n)) * ((t -' 1),tt) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * ((t -' 1),tt)) `2 is V11() real ext-real Element of REAL
(Gauge (C,n)) * (1,tt) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (1,tt)) `2 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (t,tt)) `2 is V11() real ext-real Element of REAL
LSeg (((Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))) /. 1),((Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))) /. (1 + 1))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
LSeg ((mid ((Lower_Seq (C,n)),(((Gauge (C,n)) * (j,i)) .. (Lower_Seq (C,n))),(len (Lower_Seq (C,n))))),(Index (godo,Emax))) is functional Element of K6( the U1 of (TOP-REAL 2))
LSeg ((Lower_Seq (C,n)),(((Index (godo,Emax)) + (((Gauge (C,n)) * (j,i)) .. (Lower_Seq (C,n)))) -' 1)) is functional Element of K6( the U1 of (TOP-REAL 2))
(1 + 1) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((1 + 1) + 1) - 1 is V11() real ext-real Element of REAL
((Index (godo,Emax)) + (((Gauge (C,n)) * (j,i)) .. (Lower_Seq (C,n)))) - 1 is V11() real ext-real Element of REAL
(LSeg ((Lower_Seq (C,n)),1)) /\ (LSeg ((Lower_Seq (C,n)),(((Index (godo,Emax)) + (((Gauge (C,n)) * (j,i)) .. (Lower_Seq (C,n)))) -' 1))) is functional Element of K6( the U1 of (TOP-REAL 2))
(Lower_Seq (C,n)) /. 2 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
{((Lower_Seq (C,n)) /. 2)} is non empty functional set
godo .. (Lower_Seq (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * ((len (Gauge (C,n))),j) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * ((len (Gauge (C,n))),j)) `1 is V11() real ext-real Element of REAL
(L~ pion1) ` is non empty functional Element of K6( the U1 of (TOP-REAL 2))
godo is functional Element of K6( the U1 of (TOP-REAL 2))
UBD (L~ pion1) is non empty functional open connected Element of K6( the U1 of (TOP-REAL 2))
LeftComp pion1 is non empty functional Element of K6( the U1 of (TOP-REAL 2))
n is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
C is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
Gauge (C,n) is V19() non empty-yielding V22( NAT ) V23(K295( the U1 of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K295( the U1 of (TOP-REAL 2))
len (Gauge (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
width (Gauge (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Upper_Seq (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
L~ (Upper_Seq (C,n)) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
Lower_Seq (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
L~ (Lower_Seq (C,n)) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
Upper_Arc C is non empty functional Element of K6( the U1 of (TOP-REAL 2))
j is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
k is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
i is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * (j,i) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Gauge (C,n)) * (k,i) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
{((Gauge (C,n)) * (k,i))} is non empty functional set
(LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
{((Gauge (C,n)) * (j,i))} is non empty functional set
Cage (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
L~ (Cage (C,n)) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
W-min (L~ (Cage (C,n))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound (L~ (Cage (C,n))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (C,n))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ (Cage (C,n))) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))), REAL ) V205((TOP-REAL 2) | (L~ (Cage (C,n)))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL))
the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))) is set
K7( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL)) is set
lower_bound (proj1 | (L~ (Cage (C,n)))) is V11() real ext-real Element of REAL
(proj1 | (L~ (Cage (C,n)))) .: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | (L~ (Cage (C,n)))) .: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n))))) is V11() real ext-real Element of REAL
W-most (L~ (Cage (C,n))) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SW-corner (L~ (Cage (C,n))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Cage (C,n))) is V11() real ext-real Element of REAL
proj2 | (L~ (Cage (C,n))) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))), REAL ) V205((TOP-REAL 2) | (L~ (Cage (C,n)))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL))
lower_bound (proj2 | (L~ (Cage (C,n)))) is V11() real ext-real Element of REAL
(proj2 | (L~ (Cage (C,n)))) .: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (L~ (Cage (C,n)))) .: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Cage (C,n)))),(S-bound (L~ (Cage (C,n))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NW-corner (L~ (Cage (C,n))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Cage (C,n))) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ (Cage (C,n)))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (L~ (Cage (C,n)))) .: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Cage (C,n)))),(N-bound (L~ (Cage (C,n))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (C,n)))),(NW-corner (L~ (Cage (C,n))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SW-corner (L~ (Cage (C,n)))),(NW-corner (L~ (Cage (C,n)))))) /\ (L~ (Cage (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (W-most (L~ (Cage (C,n)))) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Cage (C,n)))) is V19() V22( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n)))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))), REAL ) V205((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),REAL))
the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))) is set
K7( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),REAL)) is set
lower_bound (proj2 | (W-most (L~ (Cage (C,n))))) is V11() real ext-real Element of REAL
(proj2 | (W-most (L~ (Cage (C,n))))) .: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (W-most (L~ (Cage (C,n))))) .: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n)))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Cage (C,n)))),(lower_bound (proj2 | (W-most (L~ (Cage (C,n))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-max (L~ (Cage (C,n))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Cage (C,n))) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ (Cage (C,n)))) is V11() real ext-real Element of REAL
upper_bound ((proj1 | (L~ (Cage (C,n)))) .: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n))))) is V11() real ext-real Element of REAL
E-most (L~ (Cage (C,n))) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SE-corner (L~ (Cage (C,n))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
|[(E-bound (L~ (Cage (C,n)))),(S-bound (L~ (Cage (C,n))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NE-corner (L~ (Cage (C,n))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
|[(E-bound (L~ (Cage (C,n)))),(N-bound (L~ (Cage (C,n))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Cage (C,n)))),(NE-corner (L~ (Cage (C,n))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SE-corner (L~ (Cage (C,n)))),(NE-corner (L~ (Cage (C,n)))))) /\ (L~ (Cage (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (E-most (L~ (Cage (C,n)))) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Cage (C,n)))) is V19() V22( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n)))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))), REAL ) V205((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),REAL))
the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))) is set
K7( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),REAL)) is set
upper_bound (proj2 | (E-most (L~ (Cage (C,n))))) is V11() real ext-real Element of REAL
(proj2 | (E-most (L~ (Cage (C,n))))) .: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))) is V168() V169() V170() Element of K6(REAL)
upper_bound ((proj2 | (E-most (L~ (Cage (C,n))))) .: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n)))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Cage (C,n)))),(upper_bound (proj2 | (E-most (L~ (Cage (C,n))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
[j,i] is set
{j,i} is non empty V168() V169() V170() V171() V172() V173() set
{j} is non empty V168() V169() V170() V171() V172() V173() set
{{j,i},{j}} is non empty set
Indices (Gauge (C,n)) is set
[k,i] is set
{k,i} is non empty V168() V169() V170() V171() V172() V173() set
{k} is non empty V168() V169() V170() V171() V172() V173() set
{{k,i},{k}} is non empty set
R_Cut ((Upper_Seq (C,n)),((Gauge (C,n)) * (k,i))) is V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
L_Cut ((Lower_Seq (C,n)),((Gauge (C,n)) * (j,i))) is V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
len (Upper_Seq (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
dom (Upper_Seq (C,n)) is non trivial V168() V169() V170() V171() V172() V173() Element of K6(NAT)
(Upper_Seq (C,n)) . 1 is V19() Function-like set
(Upper_Seq (C,n)) /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(W-min (L~ (Cage (C,n)))) `1 is V11() real ext-real Element of REAL
(Gauge (C,n)) * (1,k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (1,k)) `1 is V11() real ext-real Element of REAL
[1,k] is set
{1,k} is non empty V168() V169() V170() V171() V172() V173() set
{{1,k},{1}} is non empty set
[1,j] is set
{1,j} is non empty V168() V169() V170() V171() V172() V173() set
{{1,j},{1}} is non empty set
1 + 2 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
len (Lower_Seq (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
dom (Lower_Seq (C,n)) is non trivial V168() V169() V170() V171() V172() V173() Element of K6(NAT)
(Lower_Seq (C,n)) . (len (Lower_Seq (C,n))) is V19() Function-like set
(Lower_Seq (C,n)) /. (len (Lower_Seq (C,n))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
[(len (Gauge (C,n))),k] is set
{(len (Gauge (C,n))),k} is non empty V168() V169() V170() V171() V172() V173() set
{(len (Gauge (C,n)))} is non empty V168() V169() V170() V171() V172() V173() set
{{(len (Gauge (C,n))),k},{(len (Gauge (C,n)))}} is non empty set
(Lower_Seq (C,n)) . 1 is V19() Function-like set
(Lower_Seq (C,n)) /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(E-max (L~ (Cage (C,n)))) `1 is V11() real ext-real Element of REAL
(Gauge (C,n)) * ((len (Gauge (C,n))),k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * ((len (Gauge (C,n))),k)) `1 is V11() real ext-real Element of REAL
1 + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
do is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
len do is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
rng (Upper_Seq (C,n)) is functional Element of K6( the U1 of (TOP-REAL 2))
pion is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
len pion is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
rng (Lower_Seq (C,n)) is functional Element of K6( the U1 of (TOP-REAL 2))
LA is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one non constant V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq s.c.c. FinSequence of the U1 of (TOP-REAL 2)
len LA is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
dom LA is non trivial V168() V169() V170() V171() V172() V173() Element of K6(NAT)
LA /. (len LA) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LA . (len LA) is V19() Function-like set
Emax is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one non constant V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq s.c.c. FinSequence of the U1 of (TOP-REAL 2)
len Emax is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
dom Emax is non trivial V168() V169() V170() V171() V172() V173() Element of K6(NAT)
Emax /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
Emax . 1 is V19() Function-like set
(len LA) - 1 is V11() real ext-real Element of REAL
Ebo is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Ebo + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(len LA) -' 1 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
LSeg (LA,Ebo) is functional Element of K6( the U1 of (TOP-REAL 2))
L~ LA is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (LA,Ebo)) /\ (LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i)))) is functional Element of K6( the U1 of (TOP-REAL 2))
LA /. Ebo is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((LA /. Ebo),((Gauge (C,n)) * (k,i))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
go is set
LSeg (Emax,1) is functional Element of K6( the U1 of (TOP-REAL 2))
L~ Emax is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(LSeg (Emax,1)) /\ (LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i)))) is functional Element of K6( the U1 of (TOP-REAL 2))
Emax /. (1 + 1) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (C,n)) * (j,i)),(Emax /. (1 + 1))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
go is set
(LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i)))) /\ (LSeg (Emax,1)) is functional Element of K6( the U1 of (TOP-REAL 2))
LA /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
Emax /. (len Emax) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
rng LA is non trivial functional Element of K6( the U1 of (TOP-REAL 2))
rng Emax is non trivial functional Element of K6( the U1 of (TOP-REAL 2))
{(LA /. 1)} is non empty functional set
(L~ LA) /\ (L~ Emax) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
go is set
[(len (Gauge (C,n))),j] is set
{(len (Gauge (C,n))),j} is non empty V168() V169() V170() V171() V172() V173() set
{{(len (Gauge (C,n))),j},{(len (Gauge (C,n)))}} is non empty set
go is set
(Gauge (C,n)) * ((len (Gauge (C,n))),j) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * ((len (Gauge (C,n))),j)) `1 is V11() real ext-real Element of REAL
(L~ (Upper_Seq (C,n))) /\ (L~ (Lower_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
{(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n))))} is non empty functional set
LA /. 2 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (j,i)) `1 is V11() real ext-real Element of REAL
(Gauge (C,n)) * (1,j) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (1,j)) `1 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (k,i)) .. (Upper_Seq (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
mid ((Upper_Seq (C,n)),1,(((Gauge (C,n)) * (k,i)) .. (Upper_Seq (C,n)))) is V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
(Upper_Seq (C,n)) | (((Gauge (C,n)) * (k,i)) .. (Upper_Seq (C,n))) is V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. FinSequence of the U1 of (TOP-REAL 2)
(Upper_Seq (C,n)) /. 2 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
<*((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i))*> is non empty V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() V39(2) FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
do is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
dom <*((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i))*> is V168() V169() V170() V171() V172() V173() Element of K6(NAT)
<*((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i))*> /. do is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (k,i)) `2 is V11() real ext-real Element of REAL
(Gauge (C,n)) * (1,i) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (1,i)) `2 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (j,i)) `2 is V11() real ext-real Element of REAL
L~ <*((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i))*> is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
<*((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i))*> /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
len <*((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i))*> is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
<*((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i))*> /. (len <*((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i))*>) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
do is V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
L~ do is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
do /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
len do is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
do /. (len do) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
go is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
LA ^' go is non empty V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
(LA ^' go) ^' Emax is non empty V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
len (Cage (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
len (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
len (LA ^' go) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
1 + 0 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
len ((LA ^' go) ^' Emax) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
go /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(LA ^' go) /. (len (LA ^' go)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
<*((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i))*> /. 2 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg (go,1) is functional Element of K6( the U1 of (TOP-REAL 2))
LSeg (LA,((len LA) -' 1)) is functional Element of K6( the U1 of (TOP-REAL 2))
(LSeg (LA,((len LA) -' 1))) /\ (LSeg (go,1)) is functional Element of K6( the U1 of (TOP-REAL 2))
len go is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(LSeg (LA,Ebo)) /\ (LSeg (go,1)) is functional Element of K6( the U1 of (TOP-REAL 2))
W2 is set
{(LA /. (len LA))} is non empty functional set
2 + 0 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(len go) - 2 is V11() real ext-real Element of REAL
(len (LA ^' go)) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((len (LA ^' go)) + 1) - 1 is V11() real ext-real Element of REAL
(len LA) + (len go) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((len LA) + (len go)) - 1 is V11() real ext-real Element of REAL
(len (LA ^' go)) - 1 is V11() real ext-real Element of REAL
(len LA) + ((len go) - 2) is V11() real ext-real Element of REAL
(len go) -' 2 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(len LA) + ((len go) -' 2) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(len (LA ^' go)) -' 1 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(len go) - 1 is V11() real ext-real Element of REAL
(len go) -' 1 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((len go) -' 2) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((len go) - 2) + 1 is V11() real ext-real Element of REAL
((len go) - 1) + 1 is V11() real ext-real Element of REAL
LSeg (go,((len go) -' 1)) is functional Element of K6( the U1 of (TOP-REAL 2))
(LSeg (go,((len go) -' 1))) /\ (LSeg (Emax,1)) is functional Element of K6( the U1 of (TOP-REAL 2))
W2 is set
((len go) -' 1) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
go /. (((len go) -' 1) + 1) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((LA ^' go),((len LA) + ((len go) -' 2))) is functional Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((LA ^' go),((len LA) + ((len go) -' 2)))) /\ (LSeg (Emax,1)) is functional Element of K6( the U1 of (TOP-REAL 2))
{((LA ^' go) /. (len (LA ^' go)))} is non empty functional set
rng go is functional Element of K6( the U1 of (TOP-REAL 2))
L~ go is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
{(go /. 1)} is non empty functional set
(L~ LA) /\ (L~ go) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
W2 is set
W2 is set
(L~ go) /\ (L~ (Upper_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(rng LA) /\ (rng go) is functional Element of K6( the U1 of (TOP-REAL 2))
go /. (len go) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
{(go /. (len go))} is non empty functional set
(L~ Emax) /\ (L~ go) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
W2 is set
W2 is set
(L~ go) /\ (L~ (Lower_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
L~ (LA ^' go) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(L~ (LA ^' go)) /\ (L~ Emax) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(L~ LA) \/ (L~ go) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
((L~ LA) \/ (L~ go)) /\ (L~ Emax) is functional Element of K6( the U1 of (TOP-REAL 2))
{(Emax /. 1)} is non empty functional set
{(LA /. 1)} \/ {(Emax /. 1)} is non empty set
(LA ^' go) /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
{((LA ^' go) /. 1)} is non empty functional set
{((LA ^' go) /. 1)} \/ {(Emax /. 1)} is non empty set
{((LA ^' go) /. 1),(Emax /. 1)} is non empty functional set
W-min C is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound C is V11() real ext-real Element of REAL
(TOP-REAL 2) | C is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | C is V19() V22( the U1 of ((TOP-REAL 2) | C)) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | C), REAL ) V205((TOP-REAL 2) | C) Element of K6(K7( the U1 of ((TOP-REAL 2) | C),REAL))
the U1 of ((TOP-REAL 2) | C) is set
K7( the U1 of ((TOP-REAL 2) | C),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | C),REAL)) is set
lower_bound (proj1 | C) is V11() real ext-real Element of REAL
(proj1 | C) .: the U1 of ((TOP-REAL 2) | C) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | C) .: the U1 of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
W-most C is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SW-corner C is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-bound C is V11() real ext-real Element of REAL
proj2 | C is V19() V22( the U1 of ((TOP-REAL 2) | C)) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | C), REAL ) V205((TOP-REAL 2) | C) Element of K6(K7( the U1 of ((TOP-REAL 2) | C),REAL))
lower_bound (proj2 | C) is V11() real ext-real Element of REAL
(proj2 | C) .: the U1 of ((TOP-REAL 2) | C) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | C) .: the U1 of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
|[(W-bound C),(S-bound C)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NW-corner C is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound C is V11() real ext-real Element of REAL
upper_bound (proj2 | C) is V11() real ext-real Element of REAL
upper_bound ((proj2 | C) .: the U1 of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
|[(W-bound C),(N-bound C)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner C),(NW-corner C)) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SW-corner C),(NW-corner C))) /\ C is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (W-most C) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (W-most C) is V19() V22( the U1 of ((TOP-REAL 2) | (W-most C))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (W-most C)), REAL ) V205((TOP-REAL 2) | (W-most C)) Element of K6(K7( the U1 of ((TOP-REAL 2) | (W-most C)),REAL))
the U1 of ((TOP-REAL 2) | (W-most C)) is set
K7( the U1 of ((TOP-REAL 2) | (W-most C)),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (W-most C)),REAL)) is set
lower_bound (proj2 | (W-most C)) is V11() real ext-real Element of REAL
(proj2 | (W-most C)) .: the U1 of ((TOP-REAL 2) | (W-most C)) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (W-most C)) .: the U1 of ((TOP-REAL 2) | (W-most C))) is V11() real ext-real Element of REAL
|[(W-bound C),(lower_bound (proj2 | (W-most C)))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-max C is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-bound C is V11() real ext-real Element of REAL
upper_bound (proj1 | C) is V11() real ext-real Element of REAL
upper_bound ((proj1 | C) .: the U1 of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
E-most C is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SE-corner C is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
|[(E-bound C),(S-bound C)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NE-corner C is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
|[(E-bound C),(N-bound C)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner C),(NE-corner C)) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SE-corner C),(NE-corner C))) /\ C is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (E-most C) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (E-most C) is V19() V22( the U1 of ((TOP-REAL 2) | (E-most C))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (E-most C)), REAL ) V205((TOP-REAL 2) | (E-most C)) Element of K6(K7( the U1 of ((TOP-REAL 2) | (E-most C)),REAL))
the U1 of ((TOP-REAL 2) | (E-most C)) is set
K7( the U1 of ((TOP-REAL 2) | (E-most C)),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (E-most C)),REAL)) is set
upper_bound (proj2 | (E-most C)) is V11() real ext-real Element of REAL
(proj2 | (E-most C)) .: the U1 of ((TOP-REAL 2) | (E-most C)) is V168() V169() V170() Element of K6(REAL)
upper_bound ((proj2 | (E-most C)) .: the U1 of ((TOP-REAL 2) | (E-most C))) is V11() real ext-real Element of REAL
|[(E-bound C),(upper_bound (proj2 | (E-most C)))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
rng (Cage (C,n)) is non trivial functional Element of K6( the U1 of (TOP-REAL 2))
(Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
W-max (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))), REAL ) V205((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),REAL))
the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is set
K7( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),REAL)) is set
lower_bound (proj1 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is V11() real ext-real Element of REAL
(proj1 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SW-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V11() real ext-real Element of REAL
proj2 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))), REAL ) V205((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),REAL))
lower_bound (proj2 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is V11() real ext-real Element of REAL
(proj2 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),(S-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NW-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),(N-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),(NW-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SW-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),(NW-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))) /\ (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is V19() V22( the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))), REAL ) V205((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))),REAL))
the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is set
K7( the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))),REAL)) is set
upper_bound (proj2 | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
(proj2 | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) .: the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V168() V169() V170() Element of K6(REAL)
upper_bound ((proj2 | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) .: the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),(upper_bound (proj2 | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(W-max (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .. (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
N-min (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
NE-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is V11() real ext-real Element of REAL
upper_bound ((proj1 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),(N-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((NW-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),(NE-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((NW-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),(NE-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))) /\ (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is V19() V22( the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))), REAL ) V205((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))),REAL))
the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is set
K7( the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))),REAL)) is set
lower_bound (proj1 | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
(proj1 | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) .: the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) .: the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))),(N-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(N-min (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .. (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
N-max (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
upper_bound (proj1 | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
upper_bound ((proj1 | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) .: the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))) is V11() real ext-real Element of REAL
|[(upper_bound (proj1 | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))),(N-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(N-max (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .. (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(E-max (L~ (Cage (C,n)))) .. (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
W2 is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard FinSequence of the U1 of (TOP-REAL 2)
right_cell (W2,1,(Gauge (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
L~ W2 is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
(right_cell (W2,1,(Gauge (C,n)))) \ (L~ W2) is functional Element of K6( the U1 of (TOP-REAL 2))
RightComp W2 is non empty functional Element of K6( the U1 of (TOP-REAL 2))
(L~ (LA ^' go)) \/ (L~ Emax) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
((L~ LA) \/ (L~ go)) \/ (L~ Emax) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
(L~ (Upper_Seq (C,n))) \/ (L~ (Lower_Seq (C,n))) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
right_cell ((Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))),1) is functional Element of K6( the U1 of (TOP-REAL 2))
GoB (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) is V19() non empty-yielding V22( NAT ) V23(K295( the U1 of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K295( the U1 of (TOP-REAL 2))
right_cell ((Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))),1,(GoB (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is functional Element of K6( the U1 of (TOP-REAL 2))
GoB (Cage (C,n)) is V19() non empty-yielding V22( NAT ) V23(K295( the U1 of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K295( the U1 of (TOP-REAL 2))
right_cell ((Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))),1,(GoB (Cage (C,n)))) is functional Element of K6( the U1 of (TOP-REAL 2))
right_cell ((Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))),1,(Gauge (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
(Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) -: (E-max (L~ (Cage (C,n)))) is V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like special unfolded FinSequence of the U1 of (TOP-REAL 2)
right_cell (((Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) -: (E-max (L~ (Cage (C,n))))),1,(Gauge (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
right_cell ((Upper_Seq (C,n)),1,(Gauge (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
right_cell ((R_Cut ((Upper_Seq (C,n)),((Gauge (C,n)) * (k,i)))),1,(Gauge (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
right_cell ((LA ^' go),1,(Gauge (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
W2 /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W2 /. 2 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(LA ^' go) /. 2 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Upper_Seq (C,n)) ^' (Lower_Seq (C,n)) is non empty V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
((Upper_Seq (C,n)) ^' (Lower_Seq (C,n))) /. 2 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) /. 2 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(L~ LA) \/ (L~ Emax) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
W-min ((L~ LA) \/ (L~ Emax)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound ((L~ LA) \/ (L~ Emax)) is V11() real ext-real Element of REAL
(TOP-REAL 2) | ((L~ LA) \/ (L~ Emax)) is strict T_2 SubSpace of TOP-REAL 2
proj1 | ((L~ LA) \/ (L~ Emax)) is V19() V22( the U1 of ((TOP-REAL 2) | ((L~ LA) \/ (L~ Emax)))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | ((L~ LA) \/ (L~ Emax))), REAL ) V205((TOP-REAL 2) | ((L~ LA) \/ (L~ Emax))) Element of K6(K7( the U1 of ((TOP-REAL 2) | ((L~ LA) \/ (L~ Emax))),REAL))
the U1 of ((TOP-REAL 2) | ((L~ LA) \/ (L~ Emax))) is set
K7( the U1 of ((TOP-REAL 2) | ((L~ LA) \/ (L~ Emax))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | ((L~ LA) \/ (L~ Emax))),REAL)) is set
lower_bound (proj1 | ((L~ LA) \/ (L~ Emax))) is V11() real ext-real Element of REAL
(proj1 | ((L~ LA) \/ (L~ Emax))) .: the U1 of ((TOP-REAL 2) | ((L~ LA) \/ (L~ Emax))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | ((L~ LA) \/ (L~ Emax))) .: the U1 of ((TOP-REAL 2) | ((L~ LA) \/ (L~ Emax)))) is V11() real ext-real Element of REAL
W-most ((L~ LA) \/ (L~ Emax)) is functional Element of K6( the U1 of (TOP-REAL 2))
SW-corner ((L~ LA) \/ (L~ Emax)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-bound ((L~ LA) \/ (L~ Emax)) is V11() real ext-real Element of REAL
proj2 | ((L~ LA) \/ (L~ Emax)) is V19() V22( the U1 of ((TOP-REAL 2) | ((L~ LA) \/ (L~ Emax)))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | ((L~ LA) \/ (L~ Emax))), REAL ) V205((TOP-REAL 2) | ((L~ LA) \/ (L~ Emax))) Element of K6(K7( the U1 of ((TOP-REAL 2) | ((L~ LA) \/ (L~ Emax))),REAL))
lower_bound (proj2 | ((L~ LA) \/ (L~ Emax))) is V11() real ext-real Element of REAL
(proj2 | ((L~ LA) \/ (L~ Emax))) .: the U1 of ((TOP-REAL 2) | ((L~ LA) \/ (L~ Emax))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | ((L~ LA) \/ (L~ Emax))) .: the U1 of ((TOP-REAL 2) | ((L~ LA) \/ (L~ Emax)))) is V11() real ext-real Element of REAL
|[(W-bound ((L~ LA) \/ (L~ Emax))),(S-bound ((L~ LA) \/ (L~ Emax)))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NW-corner ((L~ LA) \/ (L~ Emax)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound ((L~ LA) \/ (L~ Emax)) is V11() real ext-real Element of REAL
upper_bound (proj2 | ((L~ LA) \/ (L~ Emax))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | ((L~ LA) \/ (L~ Emax))) .: the U1 of ((TOP-REAL 2) | ((L~ LA) \/ (L~ Emax)))) is V11() real ext-real Element of REAL
|[(W-bound ((L~ LA) \/ (L~ Emax))),(N-bound ((L~ LA) \/ (L~ Emax)))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner ((L~ LA) \/ (L~ Emax))),(NW-corner ((L~ LA) \/ (L~ Emax)))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SW-corner ((L~ LA) \/ (L~ Emax))),(NW-corner ((L~ LA) \/ (L~ Emax))))) /\ ((L~ LA) \/ (L~ Emax)) is functional Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (W-most ((L~ LA) \/ (L~ Emax))) is strict T_2 SubSpace of TOP-REAL 2
proj2 | (W-most ((L~ LA) \/ (L~ Emax))) is V19() V22( the U1 of ((TOP-REAL 2) | (W-most ((L~ LA) \/ (L~ Emax))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (W-most ((L~ LA) \/ (L~ Emax)))), REAL ) V205((TOP-REAL 2) | (W-most ((L~ LA) \/ (L~ Emax)))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (W-most ((L~ LA) \/ (L~ Emax)))),REAL))
the U1 of ((TOP-REAL 2) | (W-most ((L~ LA) \/ (L~ Emax)))) is set
K7( the U1 of ((TOP-REAL 2) | (W-most ((L~ LA) \/ (L~ Emax)))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (W-most ((L~ LA) \/ (L~ Emax)))),REAL)) is set
lower_bound (proj2 | (W-most ((L~ LA) \/ (L~ Emax)))) is V11() real ext-real Element of REAL
(proj2 | (W-most ((L~ LA) \/ (L~ Emax)))) .: the U1 of ((TOP-REAL 2) | (W-most ((L~ LA) \/ (L~ Emax)))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (W-most ((L~ LA) \/ (L~ Emax)))) .: the U1 of ((TOP-REAL 2) | (W-most ((L~ LA) \/ (L~ Emax))))) is V11() real ext-real Element of REAL
|[(W-bound ((L~ LA) \/ (L~ Emax))),(lower_bound (proj2 | (W-most ((L~ LA) \/ (L~ Emax)))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(W-min ((L~ LA) \/ (L~ Emax))) `1 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (k,i)) `1 is V11() real ext-real Element of REAL
W-bound (LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i)))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i)))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i)))) is V19() V22( the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i)))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i))))), REAL ) V205((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i))))),REAL))
the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i))))) is set
K7( the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i))))),REAL)) is set
lower_bound (proj1 | (LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i))))) is V11() real ext-real Element of REAL
(proj1 | (LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i))))) .: the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | (LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i))))) .: the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i)))))) is V11() real ext-real Element of REAL
W-bound (L~ go) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ go) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ go) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ go))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ go)), REAL ) V205((TOP-REAL 2) | (L~ go)) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ go)),REAL))
the U1 of ((TOP-REAL 2) | (L~ go)) is set
K7( the U1 of ((TOP-REAL 2) | (L~ go)),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (L~ go)),REAL)) is set
lower_bound (proj1 | (L~ go)) is V11() real ext-real Element of REAL
(proj1 | (L~ go)) .: the U1 of ((TOP-REAL 2) | (L~ go)) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | (L~ go)) .: the U1 of ((TOP-REAL 2) | (L~ go))) is V11() real ext-real Element of REAL
((L~ LA) \/ (L~ Emax)) \/ (L~ go) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
W-min (((L~ LA) \/ (L~ Emax)) \/ (L~ go)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound (((L~ LA) \/ (L~ Emax)) \/ (L~ go)) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (((L~ LA) \/ (L~ Emax)) \/ (L~ go)) is strict T_2 SubSpace of TOP-REAL 2
proj1 | (((L~ LA) \/ (L~ Emax)) \/ (L~ go)) is V19() V22( the U1 of ((TOP-REAL 2) | (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))), REAL ) V205((TOP-REAL 2) | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))),REAL))
the U1 of ((TOP-REAL 2) | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))) is set
K7( the U1 of ((TOP-REAL 2) | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))),REAL)) is set
lower_bound (proj1 | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))) is V11() real ext-real Element of REAL
(proj1 | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))) .: the U1 of ((TOP-REAL 2) | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))) .: the U1 of ((TOP-REAL 2) | (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))) is V11() real ext-real Element of REAL
W-most (((L~ LA) \/ (L~ Emax)) \/ (L~ go)) is functional Element of K6( the U1 of (TOP-REAL 2))
SW-corner (((L~ LA) \/ (L~ Emax)) \/ (L~ go)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-bound (((L~ LA) \/ (L~ Emax)) \/ (L~ go)) is V11() real ext-real Element of REAL
proj2 | (((L~ LA) \/ (L~ Emax)) \/ (L~ go)) is V19() V22( the U1 of ((TOP-REAL 2) | (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))), REAL ) V205((TOP-REAL 2) | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))),REAL))
lower_bound (proj2 | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))) is V11() real ext-real Element of REAL
(proj2 | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))) .: the U1 of ((TOP-REAL 2) | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))) .: the U1 of ((TOP-REAL 2) | (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))) is V11() real ext-real Element of REAL
|[(W-bound (((L~ LA) \/ (L~ Emax)) \/ (L~ go))),(S-bound (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NW-corner (((L~ LA) \/ (L~ Emax)) \/ (L~ go)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound (((L~ LA) \/ (L~ Emax)) \/ (L~ go)) is V11() real ext-real Element of REAL
upper_bound (proj2 | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))) .: the U1 of ((TOP-REAL 2) | (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))) is V11() real ext-real Element of REAL
|[(W-bound (((L~ LA) \/ (L~ Emax)) \/ (L~ go))),(N-bound (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (((L~ LA) \/ (L~ Emax)) \/ (L~ go))),(NW-corner (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SW-corner (((L~ LA) \/ (L~ Emax)) \/ (L~ go))),(NW-corner (((L~ LA) \/ (L~ Emax)) \/ (L~ go))))) /\ (((L~ LA) \/ (L~ Emax)) \/ (L~ go)) is functional Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (W-most (((L~ LA) \/ (L~ Emax)) \/ (L~ go))) is strict T_2 SubSpace of TOP-REAL 2
proj2 | (W-most (((L~ LA) \/ (L~ Emax)) \/ (L~ go))) is V19() V22( the U1 of ((TOP-REAL 2) | (W-most (((L~ LA) \/ (L~ Emax)) \/ (L~ go))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (W-most (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))), REAL ) V205((TOP-REAL 2) | (W-most (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (W-most (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))),REAL))
the U1 of ((TOP-REAL 2) | (W-most (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))) is set
K7( the U1 of ((TOP-REAL 2) | (W-most (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (W-most (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))),REAL)) is set
lower_bound (proj2 | (W-most (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))) is V11() real ext-real Element of REAL
(proj2 | (W-most (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))) .: the U1 of ((TOP-REAL 2) | (W-most (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (W-most (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))) .: the U1 of ((TOP-REAL 2) | (W-most (((L~ LA) \/ (L~ Emax)) \/ (L~ go))))) is V11() real ext-real Element of REAL
|[(W-bound (((L~ LA) \/ (L~ Emax)) \/ (L~ go))),(lower_bound (proj2 | (W-most (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-min (L~ W2) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound (L~ W2) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ W2) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ W2) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ W2))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ W2)), REAL ) V205((TOP-REAL 2) | (L~ W2)) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ W2)),REAL))
the U1 of ((TOP-REAL 2) | (L~ W2)) is set
K7( the U1 of ((TOP-REAL 2) | (L~ W2)),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (L~ W2)),REAL)) is set
lower_bound (proj1 | (L~ W2)) is V11() real ext-real Element of REAL
(proj1 | (L~ W2)) .: the U1 of ((TOP-REAL 2) | (L~ W2)) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | (L~ W2)) .: the U1 of ((TOP-REAL 2) | (L~ W2))) is V11() real ext-real Element of REAL
W-most (L~ W2) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SW-corner (L~ W2) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-bound (L~ W2) is V11() real ext-real Element of REAL
proj2 | (L~ W2) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ W2))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ W2)), REAL ) V205((TOP-REAL 2) | (L~ W2)) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ W2)),REAL))
lower_bound (proj2 | (L~ W2)) is V11() real ext-real Element of REAL
(proj2 | (L~ W2)) .: the U1 of ((TOP-REAL 2) | (L~ W2)) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (L~ W2)) .: the U1 of ((TOP-REAL 2) | (L~ W2))) is V11() real ext-real Element of REAL
|[(W-bound (L~ W2)),(S-bound (L~ W2))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NW-corner (L~ W2) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound (L~ W2) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ W2)) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (L~ W2)) .: the U1 of ((TOP-REAL 2) | (L~ W2))) is V11() real ext-real Element of REAL
|[(W-bound (L~ W2)),(N-bound (L~ W2))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ W2)),(NW-corner (L~ W2))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SW-corner (L~ W2)),(NW-corner (L~ W2)))) /\ (L~ W2) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (W-most (L~ W2)) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (W-most (L~ W2)) is V19() V22( the U1 of ((TOP-REAL 2) | (W-most (L~ W2)))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (W-most (L~ W2))), REAL ) V205((TOP-REAL 2) | (W-most (L~ W2))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (W-most (L~ W2))),REAL))
the U1 of ((TOP-REAL 2) | (W-most (L~ W2))) is set
K7( the U1 of ((TOP-REAL 2) | (W-most (L~ W2))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (W-most (L~ W2))),REAL)) is set
lower_bound (proj2 | (W-most (L~ W2))) is V11() real ext-real Element of REAL
(proj2 | (W-most (L~ W2))) .: the U1 of ((TOP-REAL 2) | (W-most (L~ W2))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (W-most (L~ W2))) .: the U1 of ((TOP-REAL 2) | (W-most (L~ W2)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ W2)),(lower_bound (proj2 | (W-most (L~ W2))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
rng W2 is non trivial functional Element of K6( the U1 of (TOP-REAL 2))
dom W2 is non trivial V168() V169() V170() V171() V172() V173() Element of K6(NAT)
(W2 /. 2) `1 is V11() real ext-real Element of REAL
(W-min (L~ W2)) `1 is V11() real ext-real Element of REAL
Rotate (W2,(W-min (L~ W2))) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard FinSequence of the U1 of (TOP-REAL 2)
(Rotate (W2,(W-min (L~ W2)))) /. 2 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Upper_Seq (C,n)) . (len (Upper_Seq (C,n))) is V19() Function-like set
(Upper_Seq (C,n)) /. (len (Upper_Seq (C,n))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
east_halfline (E-max C) is non empty functional connected V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
godo is set
godo is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(east_halfline (E-max C)) /\ (L~ (Cage (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
godo `1 is V11() real ext-real Element of REAL
pion1 is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
L~ pion1 is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
godo is set
godo is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
godo `2 is V11() real ext-real Element of REAL
(E-max C) `2 is V11() real ext-real Element of REAL
k + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(k + 1) - 1 is V11() real ext-real Element of REAL
(len (Gauge (C,n))) - 1 is V11() real ext-real Element of REAL
(len (Gauge (C,n))) -' 1 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * (((len (Gauge (C,n))) -' 1),1) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (((len (Gauge (C,n))) -' 1),1)) `1 is V11() real ext-real Element of REAL
godo `1 is V11() real ext-real Element of REAL
(E-max C) `1 is V11() real ext-real Element of REAL
godo is set
godo is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
Index (godo,Emax) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
LSeg (Emax,(Index (godo,Emax))) is functional Element of K6( the U1 of (TOP-REAL 2))
ff is ordinal natural ext-real non negative set
(Lower_Seq (C,n)) . ff is V19() Function-like set
Index (((Gauge (C,n)) * (j,i)),(Lower_Seq (C,n))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Index (((Gauge (C,n)) * (j,i)),(Lower_Seq (C,n)))) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
len (L_Cut ((Lower_Seq (C,n)),((Gauge (C,n)) * (j,i)))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(len (Lower_Seq (C,n))) - (Index (((Gauge (C,n)) * (j,i)),(Lower_Seq (C,n)))) is V11() real ext-real Element of REAL
(len (Lower_Seq (C,n))) -' (Index (((Gauge (C,n)) * (j,i)),(Lower_Seq (C,n)))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Index (godo,Emax)) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((len (Lower_Seq (C,n))) -' (Index (((Gauge (C,n)) * (j,i)),(Lower_Seq (C,n))))) - 1 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (j,i)) .. (Lower_Seq (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
mid ((Lower_Seq (C,n)),(((Gauge (C,n)) * (j,i)) .. (Lower_Seq (C,n))),(len (Lower_Seq (C,n)))) is V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
(east_halfline (E-max C)) /\ (L~ (Cage (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
godo `1 is V11() real ext-real Element of REAL
0 + (Index (((Gauge (C,n)) * (j,i)),(Lower_Seq (C,n)))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((len (Lower_Seq (C,n))) - (Index (((Gauge (C,n)) * (j,i)),(Lower_Seq (C,n))))) - 1 is V11() real ext-real Element of REAL
(len (Lower_Seq (C,n))) - (((Gauge (C,n)) * (j,i)) .. (Lower_Seq (C,n))) is V11() real ext-real Element of REAL
(len (Lower_Seq (C,n))) -' (((Gauge (C,n)) * (j,i)) .. (Lower_Seq (C,n))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((len (Lower_Seq (C,n))) -' (((Gauge (C,n)) * (j,i)) .. (Lower_Seq (C,n)))) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Index (godo,Emax)) + (((Gauge (C,n)) * (j,i)) .. (Lower_Seq (C,n))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((Index (godo,Emax)) + (((Gauge (C,n)) * (j,i)) .. (Lower_Seq (C,n)))) -' 1 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
right_cell ((Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))),1) is functional Element of K6( the U1 of (TOP-REAL 2))
GoB (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))) is V19() non empty-yielding V22( NAT ) V23(K295( the U1 of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K295( the U1 of (TOP-REAL 2))
L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
p is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * ((len (Gauge (C,n))),p) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
[(len (Gauge (C,n))),p] is set
{(len (Gauge (C,n))),p} is non empty V168() V169() V170() V171() V172() V173() set
{{(len (Gauge (C,n))),p},{(len (Gauge (C,n)))}} is non empty set
len (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))) -: (W-min (L~ (Cage (C,n)))) is V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like special unfolded FinSequence of the U1 of (TOP-REAL 2)
LSeg ((Lower_Seq (C,n)),1) is functional Element of K6( the U1 of (TOP-REAL 2))
LSeg ((Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))),1) is functional Element of K6( the U1 of (TOP-REAL 2))
(Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))) /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))) /. (1 + 1) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
t is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
tt is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
tt + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
[t,(tt + 1)] is set
{t,(tt + 1)} is non empty V168() V169() V170() V171() V172() V173() set
{t} is non empty V168() V169() V170() V171() V172() V173() set
{{t,(tt + 1)},{t}} is non empty set
[t,tt] is set
{t,tt} is non empty V168() V169() V170() V171() V172() V173() set
{{t,tt},{t}} is non empty set
(Gauge (C,n)) * (t,(tt + 1)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Gauge (C,n)) * (t,tt) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(tt + 1) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
E-max (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))), REAL ) V205((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),REAL))
the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) is set
K7( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),REAL)) is set
upper_bound (proj1 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) is V11() real ext-real Element of REAL
(proj1 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) is V168() V169() V170() Element of K6(REAL)
upper_bound ((proj1 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SE-corner (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is V11() real ext-real Element of REAL
proj2 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))), REAL ) V205((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),REAL))
lower_bound (proj2 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) is V11() real ext-real Element of REAL
(proj2 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),(S-bound (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NE-corner (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),(N-bound (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),(NE-corner (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SE-corner (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),(NE-corner (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))))) /\ (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) is V19() V22( the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))), REAL ) V205((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))),REAL))
the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) is set
K7( the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))),REAL)) is set
upper_bound (proj2 | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
(proj2 | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) .: the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) is V168() V169() V170() Element of K6(REAL)
upper_bound ((proj2 | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) .: the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),(upper_bound (proj2 | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
4 - 1 is V11() real ext-real Element of REAL
t - 1 is V11() real ext-real Element of REAL
t -' 1 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * ((len (Gauge (C,n))),tt) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * ((len (Gauge (C,n))),tt)) `1 is V11() real ext-real Element of REAL
t + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
cell ((Gauge (C,n)),(t -' 1),tt) is functional Element of K6( the U1 of (TOP-REAL 2))
(Gauge (C,n)) * ((len (Gauge (C,n))),(tt + 1)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * ((len (Gauge (C,n))),(tt + 1))) `1 is V11() real ext-real Element of REAL
(t -' 1) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * ((t -' 1),(tt + 1)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * ((t -' 1),(tt + 1))) `2 is V11() real ext-real Element of REAL
(Gauge (C,n)) * (1,(tt + 1)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (1,(tt + 1))) `2 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (t,(tt + 1))) `2 is V11() real ext-real Element of REAL
(E-max C) `2 is V11() real ext-real Element of REAL
godo `2 is V11() real ext-real Element of REAL
(Gauge (C,n)) * ((t -' 1),tt) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * ((t -' 1),tt)) `2 is V11() real ext-real Element of REAL
(Gauge (C,n)) * (1,tt) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (1,tt)) `2 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (t,tt)) `2 is V11() real ext-real Element of REAL
LSeg (((Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))) /. 1),((Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))) /. (1 + 1))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
LSeg ((mid ((Lower_Seq (C,n)),(((Gauge (C,n)) * (j,i)) .. (Lower_Seq (C,n))),(len (Lower_Seq (C,n))))),(Index (godo,Emax))) is functional Element of K6( the U1 of (TOP-REAL 2))
LSeg ((Lower_Seq (C,n)),(((Index (godo,Emax)) + (((Gauge (C,n)) * (j,i)) .. (Lower_Seq (C,n)))) -' 1)) is functional Element of K6( the U1 of (TOP-REAL 2))
(1 + 1) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((1 + 1) + 1) - 1 is V11() real ext-real Element of REAL
((Index (godo,Emax)) + (((Gauge (C,n)) * (j,i)) .. (Lower_Seq (C,n)))) - 1 is V11() real ext-real Element of REAL
(LSeg ((Lower_Seq (C,n)),1)) /\ (LSeg ((Lower_Seq (C,n)),(((Index (godo,Emax)) + (((Gauge (C,n)) * (j,i)) .. (Lower_Seq (C,n)))) -' 1))) is functional Element of K6( the U1 of (TOP-REAL 2))
(Lower_Seq (C,n)) /. 2 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
{((Lower_Seq (C,n)) /. 2)} is non empty functional set
godo .. (Lower_Seq (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * ((len (Gauge (C,n))),j) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * ((len (Gauge (C,n))),j)) `1 is V11() real ext-real Element of REAL
(L~ pion1) ` is non empty functional Element of K6( the U1 of (TOP-REAL 2))
godo is functional Element of K6( the U1 of (TOP-REAL 2))
UBD (L~ pion1) is non empty functional open connected Element of K6( the U1 of (TOP-REAL 2))
LeftComp pion1 is non empty functional Element of K6( the U1 of (TOP-REAL 2))
n is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
C is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
Gauge (C,n) is V19() non empty-yielding V22( NAT ) V23(K295( the U1 of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K295( the U1 of (TOP-REAL 2))
len (Gauge (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
width (Gauge (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Upper_Seq (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
L~ (Upper_Seq (C,n)) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
Lower_Seq (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
L~ (Lower_Seq (C,n)) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
Lower_Arc C is non empty functional Element of K6( the U1 of (TOP-REAL 2))
j is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
k is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
i is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * (k,i) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Gauge (C,n)) * (j,i) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
k is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
G is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * (k,i) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Gauge (C,n)) * (G,i) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (G,i))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (G,i)))) /\ (L~ (Lower_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
{((Gauge (C,n)) * (k,i))} is non empty functional set
(LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (G,i)))) /\ (L~ (Upper_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
{((Gauge (C,n)) * (G,i))} is non empty functional set
n is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
C is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
Gauge (C,n) is V19() non empty-yielding V22( NAT ) V23(K295( the U1 of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K295( the U1 of (TOP-REAL 2))
len (Gauge (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
width (Gauge (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Upper_Seq (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
L~ (Upper_Seq (C,n)) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
Lower_Seq (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
L~ (Lower_Seq (C,n)) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
Upper_Arc C is non empty functional Element of K6( the U1 of (TOP-REAL 2))
j is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
k is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
i is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * (k,i) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Gauge (C,n)) * (j,i) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
k is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
G is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * (k,i) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Gauge (C,n)) * (G,i) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (G,i))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (G,i)))) /\ (L~ (Lower_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
{((Gauge (C,n)) * (k,i))} is non empty functional set
(LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (G,i)))) /\ (L~ (Upper_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
{((Gauge (C,n)) * (G,i))} is non empty functional set
n is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
C is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
Gauge (C,n) is V19() non empty-yielding V22( NAT ) V23(K295( the U1 of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K295( the U1 of (TOP-REAL 2))
len (Gauge (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
width (Gauge (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Cage (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
L~ (Cage (C,n)) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
Upper_Arc (L~ (Cage (C,n))) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
Lower_Arc (L~ (Cage (C,n))) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
Lower_Arc C is non empty functional Element of K6( the U1 of (TOP-REAL 2))
j is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
k is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
i is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * (k,i) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Gauge (C,n)) * (j,i) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
Lower_Seq (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
L~ (Lower_Seq (C,n)) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
Upper_Seq (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
L~ (Upper_Seq (C,n)) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
n is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
C is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
Gauge (C,n) is V19() non empty-yielding V22( NAT ) V23(K295( the U1 of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K295( the U1 of (TOP-REAL 2))
len (Gauge (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
width (Gauge (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Cage (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
L~ (Cage (C,n)) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
Upper_Arc (L~ (Cage (C,n))) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
Lower_Arc (L~ (Cage (C,n))) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
Upper_Arc C is non empty functional Element of K6( the U1 of (TOP-REAL 2))
j is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
k is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
i is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * (k,i) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Gauge (C,n)) * (j,i) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
Lower_Seq (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
L~ (Lower_Seq (C,n)) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
Upper_Seq (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
L~ (Upper_Seq (C,n)) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
n is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
n + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
C is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
Gauge (C,(n + 1)) is V19() non empty-yielding V22( NAT ) V23(K295( the U1 of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K295( the U1 of (TOP-REAL 2))
len (Gauge (C,(n + 1))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Center (Gauge (C,(n + 1))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Cage (C,(n + 1)) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
L~ (Cage (C,(n + 1))) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
Upper_Arc (L~ (Cage (C,(n + 1)))) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
Lower_Arc (L~ (Cage (C,(n + 1)))) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
Lower_Arc C is non empty functional Element of K6( the U1 of (TOP-REAL 2))
i is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
j is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,(n + 1))) * (j,(Center (Gauge (C,(n + 1))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Gauge (C,(n + 1))) * (i,(Center (Gauge (C,(n + 1))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (C,(n + 1))) * (i,(Center (Gauge (C,(n + 1)))))),((Gauge (C,(n + 1))) * (j,(Center (Gauge (C,(n + 1))))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
width (Gauge (C,(n + 1))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
n is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
n + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
C is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
Gauge (C,(n + 1)) is V19() non empty-yielding V22( NAT ) V23(K295( the U1 of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K295( the U1 of (TOP-REAL 2))
len (Gauge (C,(n + 1))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Center (Gauge (C,(n + 1))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Cage (C,(n + 1)) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
L~ (Cage (C,(n + 1))) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
Upper_Arc (L~ (Cage (C,(n + 1)))) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
Lower_Arc (L~ (Cage (C,(n + 1)))) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
Upper_Arc C is non empty functional Element of K6( the U1 of (TOP-REAL 2))
i is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
j is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,(n + 1))) * (j,(Center (Gauge (C,(n + 1))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Gauge (C,(n + 1))) * (i,(Center (Gauge (C,(n + 1))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (C,(n + 1))) * (i,(Center (Gauge (C,(n + 1)))))),((Gauge (C,(n + 1))) * (j,(Center (Gauge (C,(n + 1))))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
width (Gauge (C,(n + 1))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
n is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
C is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
Gauge (C,n) is V19() non empty-yielding V22( NAT ) V23(K295( the U1 of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K295( the U1 of (TOP-REAL 2))
len (Gauge (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
width (Gauge (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Upper_Seq (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
L~ (Upper_Seq (C,n)) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
Lower_Seq (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
L~ (Lower_Seq (C,n)) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
Lower_Arc C is non empty functional Element of K6( the U1 of (TOP-REAL 2))
j is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
k is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
i is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * (j,i) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Gauge (C,n)) * (k,i) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
{((Gauge (C,n)) * (j,i))} is non empty functional set
(LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
{((Gauge (C,n)) * (k,i))} is non empty functional set
Cage (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
L~ (Cage (C,n)) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
W-min (L~ (Cage (C,n))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound (L~ (Cage (C,n))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (C,n))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ (Cage (C,n))) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))), REAL ) V205((TOP-REAL 2) | (L~ (Cage (C,n)))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL))
the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))) is set
K7( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL)) is set
lower_bound (proj1 | (L~ (Cage (C,n)))) is V11() real ext-real Element of REAL
(proj1 | (L~ (Cage (C,n)))) .: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | (L~ (Cage (C,n)))) .: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n))))) is V11() real ext-real Element of REAL
W-most (L~ (Cage (C,n))) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SW-corner (L~ (Cage (C,n))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Cage (C,n))) is V11() real ext-real Element of REAL
proj2 | (L~ (Cage (C,n))) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))), REAL ) V205((TOP-REAL 2) | (L~ (Cage (C,n)))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL))
lower_bound (proj2 | (L~ (Cage (C,n)))) is V11() real ext-real Element of REAL
(proj2 | (L~ (Cage (C,n)))) .: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (L~ (Cage (C,n)))) .: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Cage (C,n)))),(S-bound (L~ (Cage (C,n))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NW-corner (L~ (Cage (C,n))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Cage (C,n))) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ (Cage (C,n)))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (L~ (Cage (C,n)))) .: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Cage (C,n)))),(N-bound (L~ (Cage (C,n))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (C,n)))),(NW-corner (L~ (Cage (C,n))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SW-corner (L~ (Cage (C,n)))),(NW-corner (L~ (Cage (C,n)))))) /\ (L~ (Cage (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (W-most (L~ (Cage (C,n)))) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Cage (C,n)))) is V19() V22( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n)))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))), REAL ) V205((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),REAL))
the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))) is set
K7( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),REAL)) is set
lower_bound (proj2 | (W-most (L~ (Cage (C,n))))) is V11() real ext-real Element of REAL
(proj2 | (W-most (L~ (Cage (C,n))))) .: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (W-most (L~ (Cage (C,n))))) .: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n)))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Cage (C,n)))),(lower_bound (proj2 | (W-most (L~ (Cage (C,n))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-max (L~ (Cage (C,n))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Cage (C,n))) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ (Cage (C,n)))) is V11() real ext-real Element of REAL
upper_bound ((proj1 | (L~ (Cage (C,n)))) .: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n))))) is V11() real ext-real Element of REAL
E-most (L~ (Cage (C,n))) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SE-corner (L~ (Cage (C,n))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
|[(E-bound (L~ (Cage (C,n)))),(S-bound (L~ (Cage (C,n))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NE-corner (L~ (Cage (C,n))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
|[(E-bound (L~ (Cage (C,n)))),(N-bound (L~ (Cage (C,n))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Cage (C,n)))),(NE-corner (L~ (Cage (C,n))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SE-corner (L~ (Cage (C,n)))),(NE-corner (L~ (Cage (C,n)))))) /\ (L~ (Cage (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (E-most (L~ (Cage (C,n)))) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Cage (C,n)))) is V19() V22( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n)))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))), REAL ) V205((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),REAL))
the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))) is set
K7( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),REAL)) is set
upper_bound (proj2 | (E-most (L~ (Cage (C,n))))) is V11() real ext-real Element of REAL
(proj2 | (E-most (L~ (Cage (C,n))))) .: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))) is V168() V169() V170() Element of K6(REAL)
upper_bound ((proj2 | (E-most (L~ (Cage (C,n))))) .: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n)))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Cage (C,n)))),(upper_bound (proj2 | (E-most (L~ (Cage (C,n))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
[j,i] is set
{j,i} is non empty V168() V169() V170() V171() V172() V173() set
{j} is non empty V168() V169() V170() V171() V172() V173() set
{{j,i},{j}} is non empty set
Indices (Gauge (C,n)) is set
[k,i] is set
{k,i} is non empty V168() V169() V170() V171() V172() V173() set
{k} is non empty V168() V169() V170() V171() V172() V173() set
{{k,i},{k}} is non empty set
R_Cut ((Upper_Seq (C,n)),((Gauge (C,n)) * (j,i))) is V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
L_Cut ((Lower_Seq (C,n)),((Gauge (C,n)) * (k,i))) is V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
len (Upper_Seq (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
dom (Upper_Seq (C,n)) is non trivial V168() V169() V170() V171() V172() V173() Element of K6(NAT)
(Upper_Seq (C,n)) . 1 is V19() Function-like set
(Upper_Seq (C,n)) /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(W-min (L~ (Cage (C,n)))) `1 is V11() real ext-real Element of REAL
(Gauge (C,n)) * (1,i) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (1,i)) `1 is V11() real ext-real Element of REAL
[1,k] is set
{1,k} is non empty V168() V169() V170() V171() V172() V173() set
{{1,k},{1}} is non empty set
[1,i] is set
{1,i} is non empty V168() V169() V170() V171() V172() V173() set
{{1,i},{1}} is non empty set
1 + 2 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
len (Lower_Seq (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
dom (Lower_Seq (C,n)) is non trivial V168() V169() V170() V171() V172() V173() Element of K6(NAT)
(Lower_Seq (C,n)) . (len (Lower_Seq (C,n))) is V19() Function-like set
(Lower_Seq (C,n)) /. (len (Lower_Seq (C,n))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
[(len (Gauge (C,n))),k] is set
{(len (Gauge (C,n))),k} is non empty V168() V169() V170() V171() V172() V173() set
{(len (Gauge (C,n)))} is non empty V168() V169() V170() V171() V172() V173() set
{{(len (Gauge (C,n))),k},{(len (Gauge (C,n)))}} is non empty set
(Lower_Seq (C,n)) . 1 is V19() Function-like set
(Lower_Seq (C,n)) /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(E-max (L~ (Cage (C,n)))) `1 is V11() real ext-real Element of REAL
(Gauge (C,n)) * ((len (Gauge (C,n))),k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * ((len (Gauge (C,n))),k)) `1 is V11() real ext-real Element of REAL
1 + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
do is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
len do is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
rng (Upper_Seq (C,n)) is functional Element of K6( the U1 of (TOP-REAL 2))
pion is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
len pion is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
rng (Lower_Seq (C,n)) is functional Element of K6( the U1 of (TOP-REAL 2))
LA is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one non constant V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq s.c.c. FinSequence of the U1 of (TOP-REAL 2)
len LA is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
dom LA is non trivial V168() V169() V170() V171() V172() V173() Element of K6(NAT)
LA /. (len LA) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LA . (len LA) is V19() Function-like set
Emax is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one non constant V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq s.c.c. FinSequence of the U1 of (TOP-REAL 2)
len Emax is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
dom Emax is non trivial V168() V169() V170() V171() V172() V173() Element of K6(NAT)
Emax /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
Emax . 1 is V19() Function-like set
(len LA) - 1 is V11() real ext-real Element of REAL
Ebo is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Ebo + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(len LA) -' 1 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
LSeg (LA,Ebo) is functional Element of K6( the U1 of (TOP-REAL 2))
L~ LA is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (LA,Ebo)) /\ (LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i)))) is functional Element of K6( the U1 of (TOP-REAL 2))
LA /. Ebo is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((LA /. Ebo),((Gauge (C,n)) * (j,i))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
go is set
LSeg (Emax,1) is functional Element of K6( the U1 of (TOP-REAL 2))
L~ Emax is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(LSeg (Emax,1)) /\ (LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i)))) is functional Element of K6( the U1 of (TOP-REAL 2))
Emax /. (1 + 1) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (C,n)) * (k,i)),(Emax /. (1 + 1))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
go is set
(LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i)))) /\ (LSeg (Emax,1)) is functional Element of K6( the U1 of (TOP-REAL 2))
LA /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
Emax /. (len Emax) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
rng LA is non trivial functional Element of K6( the U1 of (TOP-REAL 2))
rng Emax is non trivial functional Element of K6( the U1 of (TOP-REAL 2))
{(LA /. 1)} is non empty functional set
(L~ LA) /\ (L~ Emax) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
go is set
[(len (Gauge (C,n))),j] is set
{(len (Gauge (C,n))),j} is non empty V168() V169() V170() V171() V172() V173() set
{{(len (Gauge (C,n))),j},{(len (Gauge (C,n)))}} is non empty set
go is set
(Gauge (C,n)) * ((len (Gauge (C,n))),j) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * ((len (Gauge (C,n))),j)) `1 is V11() real ext-real Element of REAL
(L~ (Upper_Seq (C,n))) /\ (L~ (Lower_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
{(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n))))} is non empty functional set
LA /. 2 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (j,i)) `1 is V11() real ext-real Element of REAL
(Gauge (C,n)) * (1,k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (1,k)) `1 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (j,i)) .. (Upper_Seq (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
mid ((Upper_Seq (C,n)),1,(((Gauge (C,n)) * (j,i)) .. (Upper_Seq (C,n)))) is V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
(Upper_Seq (C,n)) | (((Gauge (C,n)) * (j,i)) .. (Upper_Seq (C,n))) is V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. FinSequence of the U1 of (TOP-REAL 2)
(Upper_Seq (C,n)) /. 2 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
<*((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i))*> is non empty V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() V39(2) FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
do is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
dom <*((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i))*> is V168() V169() V170() V171() V172() V173() Element of K6(NAT)
<*((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i))*> /. do is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (k,i)) `2 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (1,i)) `2 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (j,i)) `2 is V11() real ext-real Element of REAL
L~ <*((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i))*> is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
<*((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i))*> /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
len <*((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i))*> is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
<*((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i))*> /. (len <*((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i))*>) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
do is V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
L~ do is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
do /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
len do is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
do /. (len do) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
go is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
LA ^' go is non empty V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
(LA ^' go) ^' Emax is non empty V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
len (Cage (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
len (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
len (LA ^' go) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
1 + 0 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
len ((LA ^' go) ^' Emax) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
go /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(LA ^' go) /. (len (LA ^' go)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
<*((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i))*> /. 2 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg (go,1) is functional Element of K6( the U1 of (TOP-REAL 2))
LSeg (LA,((len LA) -' 1)) is functional Element of K6( the U1 of (TOP-REAL 2))
(LSeg (LA,((len LA) -' 1))) /\ (LSeg (go,1)) is functional Element of K6( the U1 of (TOP-REAL 2))
len go is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(LSeg (LA,Ebo)) /\ (LSeg (go,1)) is functional Element of K6( the U1 of (TOP-REAL 2))
W2 is set
{(LA /. (len LA))} is non empty functional set
2 + 0 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(len go) - 2 is V11() real ext-real Element of REAL
(len (LA ^' go)) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((len (LA ^' go)) + 1) - 1 is V11() real ext-real Element of REAL
(len LA) + (len go) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((len LA) + (len go)) - 1 is V11() real ext-real Element of REAL
(len (LA ^' go)) - 1 is V11() real ext-real Element of REAL
(len LA) + ((len go) - 2) is V11() real ext-real Element of REAL
(len go) -' 2 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(len LA) + ((len go) -' 2) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(len (LA ^' go)) -' 1 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(len go) - 1 is V11() real ext-real Element of REAL
(len go) -' 1 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((len go) -' 2) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((len go) - 2) + 1 is V11() real ext-real Element of REAL
((len go) - 1) + 1 is V11() real ext-real Element of REAL
LSeg (go,((len go) -' 1)) is functional Element of K6( the U1 of (TOP-REAL 2))
(LSeg (go,((len go) -' 1))) /\ (LSeg (Emax,1)) is functional Element of K6( the U1 of (TOP-REAL 2))
W2 is set
((len go) -' 1) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
go /. (((len go) -' 1) + 1) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((LA ^' go),((len LA) + ((len go) -' 2))) is functional Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((LA ^' go),((len LA) + ((len go) -' 2)))) /\ (LSeg (Emax,1)) is functional Element of K6( the U1 of (TOP-REAL 2))
{((LA ^' go) /. (len (LA ^' go)))} is non empty functional set
rng go is functional Element of K6( the U1 of (TOP-REAL 2))
L~ go is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
{(go /. 1)} is non empty functional set
(L~ LA) /\ (L~ go) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
W2 is set
W2 is set
(L~ go) /\ (L~ (Upper_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(rng LA) /\ (rng go) is functional Element of K6( the U1 of (TOP-REAL 2))
go /. (len go) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
{(go /. (len go))} is non empty functional set
(L~ Emax) /\ (L~ go) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
W2 is set
W2 is set
(L~ go) /\ (L~ (Lower_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
L~ (LA ^' go) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(L~ (LA ^' go)) /\ (L~ Emax) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(L~ LA) \/ (L~ go) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
((L~ LA) \/ (L~ go)) /\ (L~ Emax) is functional Element of K6( the U1 of (TOP-REAL 2))
{(Emax /. 1)} is non empty functional set
{(LA /. 1)} \/ {(Emax /. 1)} is non empty set
(LA ^' go) /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
{((LA ^' go) /. 1)} is non empty functional set
{((LA ^' go) /. 1)} \/ {(Emax /. 1)} is non empty set
{((LA ^' go) /. 1),(Emax /. 1)} is non empty functional set
E-max C is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-bound C is V11() real ext-real Element of REAL
(TOP-REAL 2) | C is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | C is V19() V22( the U1 of ((TOP-REAL 2) | C)) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | C), REAL ) V205((TOP-REAL 2) | C) Element of K6(K7( the U1 of ((TOP-REAL 2) | C),REAL))
the U1 of ((TOP-REAL 2) | C) is set
K7( the U1 of ((TOP-REAL 2) | C),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | C),REAL)) is set
upper_bound (proj1 | C) is V11() real ext-real Element of REAL
(proj1 | C) .: the U1 of ((TOP-REAL 2) | C) is V168() V169() V170() Element of K6(REAL)
upper_bound ((proj1 | C) .: the U1 of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
E-most C is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SE-corner C is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-bound C is V11() real ext-real Element of REAL
proj2 | C is V19() V22( the U1 of ((TOP-REAL 2) | C)) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | C), REAL ) V205((TOP-REAL 2) | C) Element of K6(K7( the U1 of ((TOP-REAL 2) | C),REAL))
lower_bound (proj2 | C) is V11() real ext-real Element of REAL
(proj2 | C) .: the U1 of ((TOP-REAL 2) | C) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | C) .: the U1 of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
|[(E-bound C),(S-bound C)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NE-corner C is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound C is V11() real ext-real Element of REAL
upper_bound (proj2 | C) is V11() real ext-real Element of REAL
upper_bound ((proj2 | C) .: the U1 of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
|[(E-bound C),(N-bound C)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner C),(NE-corner C)) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SE-corner C),(NE-corner C))) /\ C is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (E-most C) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (E-most C) is V19() V22( the U1 of ((TOP-REAL 2) | (E-most C))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (E-most C)), REAL ) V205((TOP-REAL 2) | (E-most C)) Element of K6(K7( the U1 of ((TOP-REAL 2) | (E-most C)),REAL))
the U1 of ((TOP-REAL 2) | (E-most C)) is set
K7( the U1 of ((TOP-REAL 2) | (E-most C)),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (E-most C)),REAL)) is set
upper_bound (proj2 | (E-most C)) is V11() real ext-real Element of REAL
(proj2 | (E-most C)) .: the U1 of ((TOP-REAL 2) | (E-most C)) is V168() V169() V170() Element of K6(REAL)
upper_bound ((proj2 | (E-most C)) .: the U1 of ((TOP-REAL 2) | (E-most C))) is V11() real ext-real Element of REAL
|[(E-bound C),(upper_bound (proj2 | (E-most C)))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-min C is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound C is V11() real ext-real Element of REAL
lower_bound (proj1 | C) is V11() real ext-real Element of REAL
lower_bound ((proj1 | C) .: the U1 of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
W-most C is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SW-corner C is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
|[(W-bound C),(S-bound C)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NW-corner C is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
|[(W-bound C),(N-bound C)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner C),(NW-corner C)) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SW-corner C),(NW-corner C))) /\ C is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (W-most C) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (W-most C) is V19() V22( the U1 of ((TOP-REAL 2) | (W-most C))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (W-most C)), REAL ) V205((TOP-REAL 2) | (W-most C)) Element of K6(K7( the U1 of ((TOP-REAL 2) | (W-most C)),REAL))
the U1 of ((TOP-REAL 2) | (W-most C)) is set
K7( the U1 of ((TOP-REAL 2) | (W-most C)),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (W-most C)),REAL)) is set
lower_bound (proj2 | (W-most C)) is V11() real ext-real Element of REAL
(proj2 | (W-most C)) .: the U1 of ((TOP-REAL 2) | (W-most C)) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (W-most C)) .: the U1 of ((TOP-REAL 2) | (W-most C))) is V11() real ext-real Element of REAL
|[(W-bound C),(lower_bound (proj2 | (W-most C)))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
rng (Cage (C,n)) is non trivial functional Element of K6( the U1 of (TOP-REAL 2))
(Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
W-max (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))), REAL ) V205((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),REAL))
the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is set
K7( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),REAL)) is set
lower_bound (proj1 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is V11() real ext-real Element of REAL
(proj1 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SW-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V11() real ext-real Element of REAL
proj2 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))), REAL ) V205((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),REAL))
lower_bound (proj2 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is V11() real ext-real Element of REAL
(proj2 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),(S-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NW-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),(N-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),(NW-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SW-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),(NW-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))) /\ (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is V19() V22( the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))), REAL ) V205((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))),REAL))
the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is set
K7( the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))),REAL)) is set
upper_bound (proj2 | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
(proj2 | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) .: the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V168() V169() V170() Element of K6(REAL)
upper_bound ((proj2 | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) .: the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),(upper_bound (proj2 | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(W-max (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .. (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
N-min (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
NE-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is V11() real ext-real Element of REAL
upper_bound ((proj1 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),(N-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((NW-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),(NE-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((NW-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),(NE-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))) /\ (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is V19() V22( the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))), REAL ) V205((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))),REAL))
the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is set
K7( the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))),REAL)) is set
lower_bound (proj1 | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
(proj1 | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) .: the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) .: the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))),(N-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(N-min (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .. (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
N-max (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
upper_bound (proj1 | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
upper_bound ((proj1 | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) .: the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))) is V11() real ext-real Element of REAL
|[(upper_bound (proj1 | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))),(N-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(N-max (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .. (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(E-max (L~ (Cage (C,n)))) .. (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
W2 is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard FinSequence of the U1 of (TOP-REAL 2)
right_cell (W2,1,(Gauge (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
L~ W2 is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
(right_cell (W2,1,(Gauge (C,n)))) \ (L~ W2) is functional Element of K6( the U1 of (TOP-REAL 2))
RightComp W2 is non empty functional Element of K6( the U1 of (TOP-REAL 2))
(L~ (LA ^' go)) \/ (L~ Emax) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
((L~ LA) \/ (L~ go)) \/ (L~ Emax) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
(L~ (Upper_Seq (C,n))) \/ (L~ (Lower_Seq (C,n))) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
right_cell ((Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))),1) is functional Element of K6( the U1 of (TOP-REAL 2))
GoB (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) is V19() non empty-yielding V22( NAT ) V23(K295( the U1 of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K295( the U1 of (TOP-REAL 2))
right_cell ((Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))),1,(GoB (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is functional Element of K6( the U1 of (TOP-REAL 2))
GoB (Cage (C,n)) is V19() non empty-yielding V22( NAT ) V23(K295( the U1 of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K295( the U1 of (TOP-REAL 2))
right_cell ((Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))),1,(GoB (Cage (C,n)))) is functional Element of K6( the U1 of (TOP-REAL 2))
right_cell ((Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))),1,(Gauge (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
(Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) -: (E-max (L~ (Cage (C,n)))) is V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like special unfolded FinSequence of the U1 of (TOP-REAL 2)
right_cell (((Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) -: (E-max (L~ (Cage (C,n))))),1,(Gauge (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
right_cell ((Upper_Seq (C,n)),1,(Gauge (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
right_cell ((R_Cut ((Upper_Seq (C,n)),((Gauge (C,n)) * (j,i)))),1,(Gauge (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
right_cell ((LA ^' go),1,(Gauge (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
W2 /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W2 /. 2 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(LA ^' go) /. 2 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Upper_Seq (C,n)) ^' (Lower_Seq (C,n)) is non empty V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
((Upper_Seq (C,n)) ^' (Lower_Seq (C,n))) /. 2 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) /. 2 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(L~ LA) \/ (L~ Emax) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
W-min ((L~ LA) \/ (L~ Emax)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound ((L~ LA) \/ (L~ Emax)) is V11() real ext-real Element of REAL
(TOP-REAL 2) | ((L~ LA) \/ (L~ Emax)) is strict T_2 SubSpace of TOP-REAL 2
proj1 | ((L~ LA) \/ (L~ Emax)) is V19() V22( the U1 of ((TOP-REAL 2) | ((L~ LA) \/ (L~ Emax)))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | ((L~ LA) \/ (L~ Emax))), REAL ) V205((TOP-REAL 2) | ((L~ LA) \/ (L~ Emax))) Element of K6(K7( the U1 of ((TOP-REAL 2) | ((L~ LA) \/ (L~ Emax))),REAL))
the U1 of ((TOP-REAL 2) | ((L~ LA) \/ (L~ Emax))) is set
K7( the U1 of ((TOP-REAL 2) | ((L~ LA) \/ (L~ Emax))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | ((L~ LA) \/ (L~ Emax))),REAL)) is set
lower_bound (proj1 | ((L~ LA) \/ (L~ Emax))) is V11() real ext-real Element of REAL
(proj1 | ((L~ LA) \/ (L~ Emax))) .: the U1 of ((TOP-REAL 2) | ((L~ LA) \/ (L~ Emax))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | ((L~ LA) \/ (L~ Emax))) .: the U1 of ((TOP-REAL 2) | ((L~ LA) \/ (L~ Emax)))) is V11() real ext-real Element of REAL
W-most ((L~ LA) \/ (L~ Emax)) is functional Element of K6( the U1 of (TOP-REAL 2))
SW-corner ((L~ LA) \/ (L~ Emax)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-bound ((L~ LA) \/ (L~ Emax)) is V11() real ext-real Element of REAL
proj2 | ((L~ LA) \/ (L~ Emax)) is V19() V22( the U1 of ((TOP-REAL 2) | ((L~ LA) \/ (L~ Emax)))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | ((L~ LA) \/ (L~ Emax))), REAL ) V205((TOP-REAL 2) | ((L~ LA) \/ (L~ Emax))) Element of K6(K7( the U1 of ((TOP-REAL 2) | ((L~ LA) \/ (L~ Emax))),REAL))
lower_bound (proj2 | ((L~ LA) \/ (L~ Emax))) is V11() real ext-real Element of REAL
(proj2 | ((L~ LA) \/ (L~ Emax))) .: the U1 of ((TOP-REAL 2) | ((L~ LA) \/ (L~ Emax))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | ((L~ LA) \/ (L~ Emax))) .: the U1 of ((TOP-REAL 2) | ((L~ LA) \/ (L~ Emax)))) is V11() real ext-real Element of REAL
|[(W-bound ((L~ LA) \/ (L~ Emax))),(S-bound ((L~ LA) \/ (L~ Emax)))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NW-corner ((L~ LA) \/ (L~ Emax)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound ((L~ LA) \/ (L~ Emax)) is V11() real ext-real Element of REAL
upper_bound (proj2 | ((L~ LA) \/ (L~ Emax))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | ((L~ LA) \/ (L~ Emax))) .: the U1 of ((TOP-REAL 2) | ((L~ LA) \/ (L~ Emax)))) is V11() real ext-real Element of REAL
|[(W-bound ((L~ LA) \/ (L~ Emax))),(N-bound ((L~ LA) \/ (L~ Emax)))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner ((L~ LA) \/ (L~ Emax))),(NW-corner ((L~ LA) \/ (L~ Emax)))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SW-corner ((L~ LA) \/ (L~ Emax))),(NW-corner ((L~ LA) \/ (L~ Emax))))) /\ ((L~ LA) \/ (L~ Emax)) is functional Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (W-most ((L~ LA) \/ (L~ Emax))) is strict T_2 SubSpace of TOP-REAL 2
proj2 | (W-most ((L~ LA) \/ (L~ Emax))) is V19() V22( the U1 of ((TOP-REAL 2) | (W-most ((L~ LA) \/ (L~ Emax))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (W-most ((L~ LA) \/ (L~ Emax)))), REAL ) V205((TOP-REAL 2) | (W-most ((L~ LA) \/ (L~ Emax)))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (W-most ((L~ LA) \/ (L~ Emax)))),REAL))
the U1 of ((TOP-REAL 2) | (W-most ((L~ LA) \/ (L~ Emax)))) is set
K7( the U1 of ((TOP-REAL 2) | (W-most ((L~ LA) \/ (L~ Emax)))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (W-most ((L~ LA) \/ (L~ Emax)))),REAL)) is set
lower_bound (proj2 | (W-most ((L~ LA) \/ (L~ Emax)))) is V11() real ext-real Element of REAL
(proj2 | (W-most ((L~ LA) \/ (L~ Emax)))) .: the U1 of ((TOP-REAL 2) | (W-most ((L~ LA) \/ (L~ Emax)))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (W-most ((L~ LA) \/ (L~ Emax)))) .: the U1 of ((TOP-REAL 2) | (W-most ((L~ LA) \/ (L~ Emax))))) is V11() real ext-real Element of REAL
|[(W-bound ((L~ LA) \/ (L~ Emax))),(lower_bound (proj2 | (W-most ((L~ LA) \/ (L~ Emax)))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(W-min ((L~ LA) \/ (L~ Emax))) `1 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (k,i)) `1 is V11() real ext-real Element of REAL
W-bound (LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i)))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i)))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i)))) is V19() V22( the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i)))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i))))), REAL ) V205((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i))))),REAL))
the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i))))) is set
K7( the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i))))),REAL)) is set
lower_bound (proj1 | (LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i))))) is V11() real ext-real Element of REAL
(proj1 | (LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i))))) .: the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | (LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i))))) .: the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i)))))) is V11() real ext-real Element of REAL
W-bound (L~ go) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ go) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ go) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ go))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ go)), REAL ) V205((TOP-REAL 2) | (L~ go)) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ go)),REAL))
the U1 of ((TOP-REAL 2) | (L~ go)) is set
K7( the U1 of ((TOP-REAL 2) | (L~ go)),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (L~ go)),REAL)) is set
lower_bound (proj1 | (L~ go)) is V11() real ext-real Element of REAL
(proj1 | (L~ go)) .: the U1 of ((TOP-REAL 2) | (L~ go)) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | (L~ go)) .: the U1 of ((TOP-REAL 2) | (L~ go))) is V11() real ext-real Element of REAL
((L~ LA) \/ (L~ Emax)) \/ (L~ go) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
W-min (((L~ LA) \/ (L~ Emax)) \/ (L~ go)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound (((L~ LA) \/ (L~ Emax)) \/ (L~ go)) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (((L~ LA) \/ (L~ Emax)) \/ (L~ go)) is strict T_2 SubSpace of TOP-REAL 2
proj1 | (((L~ LA) \/ (L~ Emax)) \/ (L~ go)) is V19() V22( the U1 of ((TOP-REAL 2) | (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))), REAL ) V205((TOP-REAL 2) | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))),REAL))
the U1 of ((TOP-REAL 2) | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))) is set
K7( the U1 of ((TOP-REAL 2) | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))),REAL)) is set
lower_bound (proj1 | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))) is V11() real ext-real Element of REAL
(proj1 | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))) .: the U1 of ((TOP-REAL 2) | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))) .: the U1 of ((TOP-REAL 2) | (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))) is V11() real ext-real Element of REAL
W-most (((L~ LA) \/ (L~ Emax)) \/ (L~ go)) is functional Element of K6( the U1 of (TOP-REAL 2))
SW-corner (((L~ LA) \/ (L~ Emax)) \/ (L~ go)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-bound (((L~ LA) \/ (L~ Emax)) \/ (L~ go)) is V11() real ext-real Element of REAL
proj2 | (((L~ LA) \/ (L~ Emax)) \/ (L~ go)) is V19() V22( the U1 of ((TOP-REAL 2) | (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))), REAL ) V205((TOP-REAL 2) | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))),REAL))
lower_bound (proj2 | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))) is V11() real ext-real Element of REAL
(proj2 | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))) .: the U1 of ((TOP-REAL 2) | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))) .: the U1 of ((TOP-REAL 2) | (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))) is V11() real ext-real Element of REAL
|[(W-bound (((L~ LA) \/ (L~ Emax)) \/ (L~ go))),(S-bound (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NW-corner (((L~ LA) \/ (L~ Emax)) \/ (L~ go)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound (((L~ LA) \/ (L~ Emax)) \/ (L~ go)) is V11() real ext-real Element of REAL
upper_bound (proj2 | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))) .: the U1 of ((TOP-REAL 2) | (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))) is V11() real ext-real Element of REAL
|[(W-bound (((L~ LA) \/ (L~ Emax)) \/ (L~ go))),(N-bound (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (((L~ LA) \/ (L~ Emax)) \/ (L~ go))),(NW-corner (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SW-corner (((L~ LA) \/ (L~ Emax)) \/ (L~ go))),(NW-corner (((L~ LA) \/ (L~ Emax)) \/ (L~ go))))) /\ (((L~ LA) \/ (L~ Emax)) \/ (L~ go)) is functional Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (W-most (((L~ LA) \/ (L~ Emax)) \/ (L~ go))) is strict T_2 SubSpace of TOP-REAL 2
proj2 | (W-most (((L~ LA) \/ (L~ Emax)) \/ (L~ go))) is V19() V22( the U1 of ((TOP-REAL 2) | (W-most (((L~ LA) \/ (L~ Emax)) \/ (L~ go))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (W-most (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))), REAL ) V205((TOP-REAL 2) | (W-most (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (W-most (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))),REAL))
the U1 of ((TOP-REAL 2) | (W-most (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))) is set
K7( the U1 of ((TOP-REAL 2) | (W-most (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (W-most (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))),REAL)) is set
lower_bound (proj2 | (W-most (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))) is V11() real ext-real Element of REAL
(proj2 | (W-most (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))) .: the U1 of ((TOP-REAL 2) | (W-most (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (W-most (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))) .: the U1 of ((TOP-REAL 2) | (W-most (((L~ LA) \/ (L~ Emax)) \/ (L~ go))))) is V11() real ext-real Element of REAL
|[(W-bound (((L~ LA) \/ (L~ Emax)) \/ (L~ go))),(lower_bound (proj2 | (W-most (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-min (L~ W2) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound (L~ W2) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ W2) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ W2) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ W2))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ W2)), REAL ) V205((TOP-REAL 2) | (L~ W2)) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ W2)),REAL))
the U1 of ((TOP-REAL 2) | (L~ W2)) is set
K7( the U1 of ((TOP-REAL 2) | (L~ W2)),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (L~ W2)),REAL)) is set
lower_bound (proj1 | (L~ W2)) is V11() real ext-real Element of REAL
(proj1 | (L~ W2)) .: the U1 of ((TOP-REAL 2) | (L~ W2)) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | (L~ W2)) .: the U1 of ((TOP-REAL 2) | (L~ W2))) is V11() real ext-real Element of REAL
W-most (L~ W2) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SW-corner (L~ W2) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-bound (L~ W2) is V11() real ext-real Element of REAL
proj2 | (L~ W2) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ W2))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ W2)), REAL ) V205((TOP-REAL 2) | (L~ W2)) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ W2)),REAL))
lower_bound (proj2 | (L~ W2)) is V11() real ext-real Element of REAL
(proj2 | (L~ W2)) .: the U1 of ((TOP-REAL 2) | (L~ W2)) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (L~ W2)) .: the U1 of ((TOP-REAL 2) | (L~ W2))) is V11() real ext-real Element of REAL
|[(W-bound (L~ W2)),(S-bound (L~ W2))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NW-corner (L~ W2) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound (L~ W2) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ W2)) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (L~ W2)) .: the U1 of ((TOP-REAL 2) | (L~ W2))) is V11() real ext-real Element of REAL
|[(W-bound (L~ W2)),(N-bound (L~ W2))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ W2)),(NW-corner (L~ W2))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SW-corner (L~ W2)),(NW-corner (L~ W2)))) /\ (L~ W2) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (W-most (L~ W2)) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (W-most (L~ W2)) is V19() V22( the U1 of ((TOP-REAL 2) | (W-most (L~ W2)))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (W-most (L~ W2))), REAL ) V205((TOP-REAL 2) | (W-most (L~ W2))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (W-most (L~ W2))),REAL))
the U1 of ((TOP-REAL 2) | (W-most (L~ W2))) is set
K7( the U1 of ((TOP-REAL 2) | (W-most (L~ W2))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (W-most (L~ W2))),REAL)) is set
lower_bound (proj2 | (W-most (L~ W2))) is V11() real ext-real Element of REAL
(proj2 | (W-most (L~ W2))) .: the U1 of ((TOP-REAL 2) | (W-most (L~ W2))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (W-most (L~ W2))) .: the U1 of ((TOP-REAL 2) | (W-most (L~ W2)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ W2)),(lower_bound (proj2 | (W-most (L~ W2))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
rng W2 is non trivial functional Element of K6( the U1 of (TOP-REAL 2))
dom W2 is non trivial V168() V169() V170() V171() V172() V173() Element of K6(NAT)
(W2 /. 2) `1 is V11() real ext-real Element of REAL
(W-min (L~ W2)) `1 is V11() real ext-real Element of REAL
Rotate (W2,(W-min (L~ W2))) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard FinSequence of the U1 of (TOP-REAL 2)
(Rotate (W2,(W-min (L~ W2)))) /. 2 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Upper_Seq (C,n)) . (len (Upper_Seq (C,n))) is V19() Function-like set
(Upper_Seq (C,n)) /. (len (Upper_Seq (C,n))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
east_halfline (E-max C) is non empty functional connected V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
godo is set
godo is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(east_halfline (E-max C)) /\ (L~ (Cage (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
godo `1 is V11() real ext-real Element of REAL
pion1 is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
L~ pion1 is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
godo is set
godo is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
godo `2 is V11() real ext-real Element of REAL
(E-max C) `2 is V11() real ext-real Element of REAL
k + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(k + 1) - 1 is V11() real ext-real Element of REAL
(len (Gauge (C,n))) - 1 is V11() real ext-real Element of REAL
(len (Gauge (C,n))) -' 1 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * (((len (Gauge (C,n))) -' 1),1) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (((len (Gauge (C,n))) -' 1),1)) `1 is V11() real ext-real Element of REAL
godo `1 is V11() real ext-real Element of REAL
(E-max C) `1 is V11() real ext-real Element of REAL
godo is set
godo is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
Index (godo,Emax) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
LSeg (Emax,(Index (godo,Emax))) is functional Element of K6( the U1 of (TOP-REAL 2))
ff is ordinal natural ext-real non negative set
(Lower_Seq (C,n)) . ff is V19() Function-like set
Index (((Gauge (C,n)) * (k,i)),(Lower_Seq (C,n))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Index (((Gauge (C,n)) * (k,i)),(Lower_Seq (C,n)))) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
len (L_Cut ((Lower_Seq (C,n)),((Gauge (C,n)) * (k,i)))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(len (Lower_Seq (C,n))) - (Index (((Gauge (C,n)) * (k,i)),(Lower_Seq (C,n)))) is V11() real ext-real Element of REAL
(len (Lower_Seq (C,n))) -' (Index (((Gauge (C,n)) * (k,i)),(Lower_Seq (C,n)))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Index (godo,Emax)) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((len (Lower_Seq (C,n))) -' (Index (((Gauge (C,n)) * (k,i)),(Lower_Seq (C,n))))) - 1 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (k,i)) .. (Lower_Seq (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
mid ((Lower_Seq (C,n)),(((Gauge (C,n)) * (k,i)) .. (Lower_Seq (C,n))),(len (Lower_Seq (C,n)))) is V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
(east_halfline (E-max C)) /\ (L~ (Cage (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
godo `1 is V11() real ext-real Element of REAL
0 + (Index (((Gauge (C,n)) * (k,i)),(Lower_Seq (C,n)))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((len (Lower_Seq (C,n))) - (Index (((Gauge (C,n)) * (k,i)),(Lower_Seq (C,n))))) - 1 is V11() real ext-real Element of REAL
(len (Lower_Seq (C,n))) - (((Gauge (C,n)) * (k,i)) .. (Lower_Seq (C,n))) is V11() real ext-real Element of REAL
(len (Lower_Seq (C,n))) -' (((Gauge (C,n)) * (k,i)) .. (Lower_Seq (C,n))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((len (Lower_Seq (C,n))) -' (((Gauge (C,n)) * (k,i)) .. (Lower_Seq (C,n)))) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Index (godo,Emax)) + (((Gauge (C,n)) * (k,i)) .. (Lower_Seq (C,n))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((Index (godo,Emax)) + (((Gauge (C,n)) * (k,i)) .. (Lower_Seq (C,n)))) -' 1 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
right_cell ((Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))),1) is functional Element of K6( the U1 of (TOP-REAL 2))
GoB (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))) is V19() non empty-yielding V22( NAT ) V23(K295( the U1 of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K295( the U1 of (TOP-REAL 2))
L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
p is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * ((len (Gauge (C,n))),p) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
[(len (Gauge (C,n))),p] is set
{(len (Gauge (C,n))),p} is non empty V168() V169() V170() V171() V172() V173() set
{{(len (Gauge (C,n))),p},{(len (Gauge (C,n)))}} is non empty set
len (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))) -: (W-min (L~ (Cage (C,n)))) is V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like special unfolded FinSequence of the U1 of (TOP-REAL 2)
LSeg ((Lower_Seq (C,n)),1) is functional Element of K6( the U1 of (TOP-REAL 2))
LSeg ((Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))),1) is functional Element of K6( the U1 of (TOP-REAL 2))
(Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))) /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))) /. (1 + 1) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
t is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
tt is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
tt + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
[t,(tt + 1)] is set
{t,(tt + 1)} is non empty V168() V169() V170() V171() V172() V173() set
{t} is non empty V168() V169() V170() V171() V172() V173() set
{{t,(tt + 1)},{t}} is non empty set
[t,tt] is set
{t,tt} is non empty V168() V169() V170() V171() V172() V173() set
{{t,tt},{t}} is non empty set
(Gauge (C,n)) * (t,(tt + 1)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Gauge (C,n)) * (t,tt) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(tt + 1) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
E-max (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))), REAL ) V205((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),REAL))
the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) is set
K7( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),REAL)) is set
upper_bound (proj1 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) is V11() real ext-real Element of REAL
(proj1 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) is V168() V169() V170() Element of K6(REAL)
upper_bound ((proj1 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SE-corner (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is V11() real ext-real Element of REAL
proj2 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))), REAL ) V205((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),REAL))
lower_bound (proj2 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) is V11() real ext-real Element of REAL
(proj2 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),(S-bound (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NE-corner (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),(N-bound (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),(NE-corner (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SE-corner (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),(NE-corner (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))))) /\ (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) is V19() V22( the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))), REAL ) V205((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))),REAL))
the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) is set
K7( the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))),REAL)) is set
upper_bound (proj2 | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
(proj2 | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) .: the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) is V168() V169() V170() Element of K6(REAL)
upper_bound ((proj2 | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) .: the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),(upper_bound (proj2 | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
4 - 1 is V11() real ext-real Element of REAL
t - 1 is V11() real ext-real Element of REAL
t -' 1 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * ((len (Gauge (C,n))),tt) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * ((len (Gauge (C,n))),tt)) `1 is V11() real ext-real Element of REAL
t + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
cell ((Gauge (C,n)),(t -' 1),tt) is functional Element of K6( the U1 of (TOP-REAL 2))
(Gauge (C,n)) * ((len (Gauge (C,n))),(tt + 1)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * ((len (Gauge (C,n))),(tt + 1))) `1 is V11() real ext-real Element of REAL
(t -' 1) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * ((t -' 1),(tt + 1)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * ((t -' 1),(tt + 1))) `2 is V11() real ext-real Element of REAL
(Gauge (C,n)) * (1,(tt + 1)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (1,(tt + 1))) `2 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (t,(tt + 1))) `2 is V11() real ext-real Element of REAL
(E-max C) `2 is V11() real ext-real Element of REAL
godo `2 is V11() real ext-real Element of REAL
(Gauge (C,n)) * ((t -' 1),tt) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * ((t -' 1),tt)) `2 is V11() real ext-real Element of REAL
(Gauge (C,n)) * (1,tt) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (1,tt)) `2 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (t,tt)) `2 is V11() real ext-real Element of REAL
LSeg (((Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))) /. 1),((Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))) /. (1 + 1))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
LSeg ((mid ((Lower_Seq (C,n)),(((Gauge (C,n)) * (k,i)) .. (Lower_Seq (C,n))),(len (Lower_Seq (C,n))))),(Index (godo,Emax))) is functional Element of K6( the U1 of (TOP-REAL 2))
LSeg ((Lower_Seq (C,n)),(((Index (godo,Emax)) + (((Gauge (C,n)) * (k,i)) .. (Lower_Seq (C,n)))) -' 1)) is functional Element of K6( the U1 of (TOP-REAL 2))
(1 + 1) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((1 + 1) + 1) - 1 is V11() real ext-real Element of REAL
((Index (godo,Emax)) + (((Gauge (C,n)) * (k,i)) .. (Lower_Seq (C,n)))) - 1 is V11() real ext-real Element of REAL
(LSeg ((Lower_Seq (C,n)),1)) /\ (LSeg ((Lower_Seq (C,n)),(((Index (godo,Emax)) + (((Gauge (C,n)) * (k,i)) .. (Lower_Seq (C,n)))) -' 1))) is functional Element of K6( the U1 of (TOP-REAL 2))
(Lower_Seq (C,n)) /. 2 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
{((Lower_Seq (C,n)) /. 2)} is non empty functional set
godo .. (Lower_Seq (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * ((len (Gauge (C,n))),j) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * ((len (Gauge (C,n))),j)) `1 is V11() real ext-real Element of REAL
(L~ pion1) ` is non empty functional Element of K6( the U1 of (TOP-REAL 2))
godo is functional Element of K6( the U1 of (TOP-REAL 2))
UBD (L~ pion1) is non empty functional open connected Element of K6( the U1 of (TOP-REAL 2))
LeftComp pion1 is non empty functional Element of K6( the U1 of (TOP-REAL 2))
n is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
C is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
Gauge (C,n) is V19() non empty-yielding V22( NAT ) V23(K295( the U1 of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K295( the U1 of (TOP-REAL 2))
len (Gauge (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
width (Gauge (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Upper_Seq (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
L~ (Upper_Seq (C,n)) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
Lower_Seq (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
L~ (Lower_Seq (C,n)) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
Upper_Arc C is non empty functional Element of K6( the U1 of (TOP-REAL 2))
j is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
k is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
i is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * (j,i) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Gauge (C,n)) * (k,i) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Upper_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
{((Gauge (C,n)) * (j,i))} is non empty functional set
(LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i)))) /\ (L~ (Lower_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
{((Gauge (C,n)) * (k,i))} is non empty functional set
Cage (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
L~ (Cage (C,n)) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
W-min (L~ (Cage (C,n))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound (L~ (Cage (C,n))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (C,n))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ (Cage (C,n))) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))), REAL ) V205((TOP-REAL 2) | (L~ (Cage (C,n)))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL))
the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))) is set
K7( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL)) is set
lower_bound (proj1 | (L~ (Cage (C,n)))) is V11() real ext-real Element of REAL
(proj1 | (L~ (Cage (C,n)))) .: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | (L~ (Cage (C,n)))) .: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n))))) is V11() real ext-real Element of REAL
W-most (L~ (Cage (C,n))) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SW-corner (L~ (Cage (C,n))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Cage (C,n))) is V11() real ext-real Element of REAL
proj2 | (L~ (Cage (C,n))) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))), REAL ) V205((TOP-REAL 2) | (L~ (Cage (C,n)))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL))
lower_bound (proj2 | (L~ (Cage (C,n)))) is V11() real ext-real Element of REAL
(proj2 | (L~ (Cage (C,n)))) .: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (L~ (Cage (C,n)))) .: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Cage (C,n)))),(S-bound (L~ (Cage (C,n))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NW-corner (L~ (Cage (C,n))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Cage (C,n))) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ (Cage (C,n)))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (L~ (Cage (C,n)))) .: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Cage (C,n)))),(N-bound (L~ (Cage (C,n))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (C,n)))),(NW-corner (L~ (Cage (C,n))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SW-corner (L~ (Cage (C,n)))),(NW-corner (L~ (Cage (C,n)))))) /\ (L~ (Cage (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (W-most (L~ (Cage (C,n)))) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Cage (C,n)))) is V19() V22( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n)))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))), REAL ) V205((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),REAL))
the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))) is set
K7( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),REAL)) is set
lower_bound (proj2 | (W-most (L~ (Cage (C,n))))) is V11() real ext-real Element of REAL
(proj2 | (W-most (L~ (Cage (C,n))))) .: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (W-most (L~ (Cage (C,n))))) .: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n)))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Cage (C,n)))),(lower_bound (proj2 | (W-most (L~ (Cage (C,n))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-max (L~ (Cage (C,n))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Cage (C,n))) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ (Cage (C,n)))) is V11() real ext-real Element of REAL
upper_bound ((proj1 | (L~ (Cage (C,n)))) .: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n))))) is V11() real ext-real Element of REAL
E-most (L~ (Cage (C,n))) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SE-corner (L~ (Cage (C,n))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
|[(E-bound (L~ (Cage (C,n)))),(S-bound (L~ (Cage (C,n))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NE-corner (L~ (Cage (C,n))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
|[(E-bound (L~ (Cage (C,n)))),(N-bound (L~ (Cage (C,n))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Cage (C,n)))),(NE-corner (L~ (Cage (C,n))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SE-corner (L~ (Cage (C,n)))),(NE-corner (L~ (Cage (C,n)))))) /\ (L~ (Cage (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (E-most (L~ (Cage (C,n)))) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Cage (C,n)))) is V19() V22( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n)))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))), REAL ) V205((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),REAL))
the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))) is set
K7( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),REAL)) is set
upper_bound (proj2 | (E-most (L~ (Cage (C,n))))) is V11() real ext-real Element of REAL
(proj2 | (E-most (L~ (Cage (C,n))))) .: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))) is V168() V169() V170() Element of K6(REAL)
upper_bound ((proj2 | (E-most (L~ (Cage (C,n))))) .: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n)))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Cage (C,n)))),(upper_bound (proj2 | (E-most (L~ (Cage (C,n))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
[j,i] is set
{j,i} is non empty V168() V169() V170() V171() V172() V173() set
{j} is non empty V168() V169() V170() V171() V172() V173() set
{{j,i},{j}} is non empty set
Indices (Gauge (C,n)) is set
[k,i] is set
{k,i} is non empty V168() V169() V170() V171() V172() V173() set
{k} is non empty V168() V169() V170() V171() V172() V173() set
{{k,i},{k}} is non empty set
R_Cut ((Upper_Seq (C,n)),((Gauge (C,n)) * (j,i))) is V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
L_Cut ((Lower_Seq (C,n)),((Gauge (C,n)) * (k,i))) is V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
len (Upper_Seq (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
dom (Upper_Seq (C,n)) is non trivial V168() V169() V170() V171() V172() V173() Element of K6(NAT)
(Upper_Seq (C,n)) . 1 is V19() Function-like set
(Upper_Seq (C,n)) /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(W-min (L~ (Cage (C,n)))) `1 is V11() real ext-real Element of REAL
(Gauge (C,n)) * (1,i) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (1,i)) `1 is V11() real ext-real Element of REAL
[1,k] is set
{1,k} is non empty V168() V169() V170() V171() V172() V173() set
{{1,k},{1}} is non empty set
[1,i] is set
{1,i} is non empty V168() V169() V170() V171() V172() V173() set
{{1,i},{1}} is non empty set
1 + 2 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
len (Lower_Seq (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
dom (Lower_Seq (C,n)) is non trivial V168() V169() V170() V171() V172() V173() Element of K6(NAT)
(Lower_Seq (C,n)) . (len (Lower_Seq (C,n))) is V19() Function-like set
(Lower_Seq (C,n)) /. (len (Lower_Seq (C,n))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
[(len (Gauge (C,n))),k] is set
{(len (Gauge (C,n))),k} is non empty V168() V169() V170() V171() V172() V173() set
{(len (Gauge (C,n)))} is non empty V168() V169() V170() V171() V172() V173() set
{{(len (Gauge (C,n))),k},{(len (Gauge (C,n)))}} is non empty set
(Lower_Seq (C,n)) . 1 is V19() Function-like set
(Lower_Seq (C,n)) /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(E-max (L~ (Cage (C,n)))) `1 is V11() real ext-real Element of REAL
(Gauge (C,n)) * ((len (Gauge (C,n))),k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * ((len (Gauge (C,n))),k)) `1 is V11() real ext-real Element of REAL
1 + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
do is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
len do is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
rng (Upper_Seq (C,n)) is functional Element of K6( the U1 of (TOP-REAL 2))
pion is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
len pion is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
rng (Lower_Seq (C,n)) is functional Element of K6( the U1 of (TOP-REAL 2))
LA is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one non constant V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq s.c.c. FinSequence of the U1 of (TOP-REAL 2)
len LA is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
dom LA is non trivial V168() V169() V170() V171() V172() V173() Element of K6(NAT)
LA /. (len LA) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LA . (len LA) is V19() Function-like set
Emax is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one non constant V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq s.c.c. FinSequence of the U1 of (TOP-REAL 2)
len Emax is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
dom Emax is non trivial V168() V169() V170() V171() V172() V173() Element of K6(NAT)
Emax /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
Emax . 1 is V19() Function-like set
(len LA) - 1 is V11() real ext-real Element of REAL
Ebo is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Ebo + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(len LA) -' 1 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
LSeg (LA,Ebo) is functional Element of K6( the U1 of (TOP-REAL 2))
L~ LA is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (LA,Ebo)) /\ (LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i)))) is functional Element of K6( the U1 of (TOP-REAL 2))
LA /. Ebo is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((LA /. Ebo),((Gauge (C,n)) * (j,i))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
go is set
LSeg (Emax,1) is functional Element of K6( the U1 of (TOP-REAL 2))
L~ Emax is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(LSeg (Emax,1)) /\ (LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i)))) is functional Element of K6( the U1 of (TOP-REAL 2))
Emax /. (1 + 1) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (C,n)) * (k,i)),(Emax /. (1 + 1))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
go is set
(LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i)))) /\ (LSeg (Emax,1)) is functional Element of K6( the U1 of (TOP-REAL 2))
LA /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
Emax /. (len Emax) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
rng LA is non trivial functional Element of K6( the U1 of (TOP-REAL 2))
rng Emax is non trivial functional Element of K6( the U1 of (TOP-REAL 2))
{(LA /. 1)} is non empty functional set
(L~ LA) /\ (L~ Emax) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
go is set
[(len (Gauge (C,n))),j] is set
{(len (Gauge (C,n))),j} is non empty V168() V169() V170() V171() V172() V173() set
{{(len (Gauge (C,n))),j},{(len (Gauge (C,n)))}} is non empty set
go is set
(Gauge (C,n)) * ((len (Gauge (C,n))),j) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * ((len (Gauge (C,n))),j)) `1 is V11() real ext-real Element of REAL
(L~ (Upper_Seq (C,n))) /\ (L~ (Lower_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
{(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n))))} is non empty functional set
LA /. 2 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (j,i)) `1 is V11() real ext-real Element of REAL
(Gauge (C,n)) * (1,k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (1,k)) `1 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (j,i)) .. (Upper_Seq (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
mid ((Upper_Seq (C,n)),1,(((Gauge (C,n)) * (j,i)) .. (Upper_Seq (C,n)))) is V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
(Upper_Seq (C,n)) | (((Gauge (C,n)) * (j,i)) .. (Upper_Seq (C,n))) is V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. FinSequence of the U1 of (TOP-REAL 2)
(Upper_Seq (C,n)) /. 2 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
<*((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i))*> is non empty V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() V39(2) FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
do is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
dom <*((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i))*> is V168() V169() V170() V171() V172() V173() Element of K6(NAT)
<*((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i))*> /. do is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (k,i)) `2 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (1,i)) `2 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (j,i)) `2 is V11() real ext-real Element of REAL
L~ <*((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i))*> is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
<*((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i))*> /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
len <*((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i))*> is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
<*((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i))*> /. (len <*((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i))*>) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
do is V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
L~ do is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
do /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
len do is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
do /. (len do) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
go is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
LA ^' go is non empty V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
(LA ^' go) ^' Emax is non empty V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
len (Cage (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
len (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
len (LA ^' go) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
1 + 0 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
len ((LA ^' go) ^' Emax) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
go /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(LA ^' go) /. (len (LA ^' go)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
<*((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i))*> /. 2 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg (go,1) is functional Element of K6( the U1 of (TOP-REAL 2))
LSeg (LA,((len LA) -' 1)) is functional Element of K6( the U1 of (TOP-REAL 2))
(LSeg (LA,((len LA) -' 1))) /\ (LSeg (go,1)) is functional Element of K6( the U1 of (TOP-REAL 2))
len go is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(LSeg (LA,Ebo)) /\ (LSeg (go,1)) is functional Element of K6( the U1 of (TOP-REAL 2))
W2 is set
{(LA /. (len LA))} is non empty functional set
2 + 0 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(len go) - 2 is V11() real ext-real Element of REAL
(len (LA ^' go)) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((len (LA ^' go)) + 1) - 1 is V11() real ext-real Element of REAL
(len LA) + (len go) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((len LA) + (len go)) - 1 is V11() real ext-real Element of REAL
(len (LA ^' go)) - 1 is V11() real ext-real Element of REAL
(len LA) + ((len go) - 2) is V11() real ext-real Element of REAL
(len go) -' 2 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(len LA) + ((len go) -' 2) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(len (LA ^' go)) -' 1 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(len go) - 1 is V11() real ext-real Element of REAL
(len go) -' 1 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((len go) -' 2) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((len go) - 2) + 1 is V11() real ext-real Element of REAL
((len go) - 1) + 1 is V11() real ext-real Element of REAL
LSeg (go,((len go) -' 1)) is functional Element of K6( the U1 of (TOP-REAL 2))
(LSeg (go,((len go) -' 1))) /\ (LSeg (Emax,1)) is functional Element of K6( the U1 of (TOP-REAL 2))
W2 is set
((len go) -' 1) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
go /. (((len go) -' 1) + 1) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((LA ^' go),((len LA) + ((len go) -' 2))) is functional Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((LA ^' go),((len LA) + ((len go) -' 2)))) /\ (LSeg (Emax,1)) is functional Element of K6( the U1 of (TOP-REAL 2))
{((LA ^' go) /. (len (LA ^' go)))} is non empty functional set
rng go is functional Element of K6( the U1 of (TOP-REAL 2))
L~ go is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
{(go /. 1)} is non empty functional set
(L~ LA) /\ (L~ go) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
W2 is set
W2 is set
(L~ go) /\ (L~ (Upper_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(rng LA) /\ (rng go) is functional Element of K6( the U1 of (TOP-REAL 2))
go /. (len go) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
{(go /. (len go))} is non empty functional set
(L~ Emax) /\ (L~ go) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
W2 is set
W2 is set
(L~ go) /\ (L~ (Lower_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
L~ (LA ^' go) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(L~ (LA ^' go)) /\ (L~ Emax) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(L~ LA) \/ (L~ go) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
((L~ LA) \/ (L~ go)) /\ (L~ Emax) is functional Element of K6( the U1 of (TOP-REAL 2))
{(Emax /. 1)} is non empty functional set
{(LA /. 1)} \/ {(Emax /. 1)} is non empty set
(LA ^' go) /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
{((LA ^' go) /. 1)} is non empty functional set
{((LA ^' go) /. 1)} \/ {(Emax /. 1)} is non empty set
{((LA ^' go) /. 1),(Emax /. 1)} is non empty functional set
W-min C is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound C is V11() real ext-real Element of REAL
(TOP-REAL 2) | C is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | C is V19() V22( the U1 of ((TOP-REAL 2) | C)) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | C), REAL ) V205((TOP-REAL 2) | C) Element of K6(K7( the U1 of ((TOP-REAL 2) | C),REAL))
the U1 of ((TOP-REAL 2) | C) is set
K7( the U1 of ((TOP-REAL 2) | C),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | C),REAL)) is set
lower_bound (proj1 | C) is V11() real ext-real Element of REAL
(proj1 | C) .: the U1 of ((TOP-REAL 2) | C) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | C) .: the U1 of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
W-most C is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SW-corner C is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-bound C is V11() real ext-real Element of REAL
proj2 | C is V19() V22( the U1 of ((TOP-REAL 2) | C)) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | C), REAL ) V205((TOP-REAL 2) | C) Element of K6(K7( the U1 of ((TOP-REAL 2) | C),REAL))
lower_bound (proj2 | C) is V11() real ext-real Element of REAL
(proj2 | C) .: the U1 of ((TOP-REAL 2) | C) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | C) .: the U1 of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
|[(W-bound C),(S-bound C)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NW-corner C is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound C is V11() real ext-real Element of REAL
upper_bound (proj2 | C) is V11() real ext-real Element of REAL
upper_bound ((proj2 | C) .: the U1 of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
|[(W-bound C),(N-bound C)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner C),(NW-corner C)) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SW-corner C),(NW-corner C))) /\ C is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (W-most C) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (W-most C) is V19() V22( the U1 of ((TOP-REAL 2) | (W-most C))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (W-most C)), REAL ) V205((TOP-REAL 2) | (W-most C)) Element of K6(K7( the U1 of ((TOP-REAL 2) | (W-most C)),REAL))
the U1 of ((TOP-REAL 2) | (W-most C)) is set
K7( the U1 of ((TOP-REAL 2) | (W-most C)),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (W-most C)),REAL)) is set
lower_bound (proj2 | (W-most C)) is V11() real ext-real Element of REAL
(proj2 | (W-most C)) .: the U1 of ((TOP-REAL 2) | (W-most C)) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (W-most C)) .: the U1 of ((TOP-REAL 2) | (W-most C))) is V11() real ext-real Element of REAL
|[(W-bound C),(lower_bound (proj2 | (W-most C)))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-max C is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-bound C is V11() real ext-real Element of REAL
upper_bound (proj1 | C) is V11() real ext-real Element of REAL
upper_bound ((proj1 | C) .: the U1 of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
E-most C is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SE-corner C is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
|[(E-bound C),(S-bound C)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NE-corner C is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
|[(E-bound C),(N-bound C)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner C),(NE-corner C)) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SE-corner C),(NE-corner C))) /\ C is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (E-most C) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (E-most C) is V19() V22( the U1 of ((TOP-REAL 2) | (E-most C))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (E-most C)), REAL ) V205((TOP-REAL 2) | (E-most C)) Element of K6(K7( the U1 of ((TOP-REAL 2) | (E-most C)),REAL))
the U1 of ((TOP-REAL 2) | (E-most C)) is set
K7( the U1 of ((TOP-REAL 2) | (E-most C)),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (E-most C)),REAL)) is set
upper_bound (proj2 | (E-most C)) is V11() real ext-real Element of REAL
(proj2 | (E-most C)) .: the U1 of ((TOP-REAL 2) | (E-most C)) is V168() V169() V170() Element of K6(REAL)
upper_bound ((proj2 | (E-most C)) .: the U1 of ((TOP-REAL 2) | (E-most C))) is V11() real ext-real Element of REAL
|[(E-bound C),(upper_bound (proj2 | (E-most C)))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
rng (Cage (C,n)) is non trivial functional Element of K6( the U1 of (TOP-REAL 2))
(Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
W-max (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))), REAL ) V205((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),REAL))
the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is set
K7( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),REAL)) is set
lower_bound (proj1 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is V11() real ext-real Element of REAL
(proj1 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SW-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V11() real ext-real Element of REAL
proj2 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))), REAL ) V205((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),REAL))
lower_bound (proj2 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is V11() real ext-real Element of REAL
(proj2 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),(S-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NW-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),(N-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),(NW-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SW-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),(NW-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))) /\ (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is V19() V22( the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))), REAL ) V205((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))),REAL))
the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is set
K7( the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))),REAL)) is set
upper_bound (proj2 | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
(proj2 | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) .: the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V168() V169() V170() Element of K6(REAL)
upper_bound ((proj2 | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) .: the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),(upper_bound (proj2 | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(W-max (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .. (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
N-min (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
NE-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is V11() real ext-real Element of REAL
upper_bound ((proj1 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),(N-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((NW-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),(NE-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((NW-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),(NE-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))) /\ (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is V19() V22( the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))), REAL ) V205((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))),REAL))
the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is set
K7( the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))),REAL)) is set
lower_bound (proj1 | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
(proj1 | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) .: the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) .: the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))),(N-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(N-min (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .. (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
N-max (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
upper_bound (proj1 | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
upper_bound ((proj1 | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) .: the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))) is V11() real ext-real Element of REAL
|[(upper_bound (proj1 | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))),(N-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(N-max (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .. (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(E-max (L~ (Cage (C,n)))) .. (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
W2 is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard FinSequence of the U1 of (TOP-REAL 2)
right_cell (W2,1,(Gauge (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
L~ W2 is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
(right_cell (W2,1,(Gauge (C,n)))) \ (L~ W2) is functional Element of K6( the U1 of (TOP-REAL 2))
RightComp W2 is non empty functional Element of K6( the U1 of (TOP-REAL 2))
(L~ (LA ^' go)) \/ (L~ Emax) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
((L~ LA) \/ (L~ go)) \/ (L~ Emax) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
(L~ (Upper_Seq (C,n))) \/ (L~ (Lower_Seq (C,n))) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
right_cell ((Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))),1) is functional Element of K6( the U1 of (TOP-REAL 2))
GoB (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) is V19() non empty-yielding V22( NAT ) V23(K295( the U1 of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K295( the U1 of (TOP-REAL 2))
right_cell ((Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))),1,(GoB (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is functional Element of K6( the U1 of (TOP-REAL 2))
GoB (Cage (C,n)) is V19() non empty-yielding V22( NAT ) V23(K295( the U1 of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K295( the U1 of (TOP-REAL 2))
right_cell ((Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))),1,(GoB (Cage (C,n)))) is functional Element of K6( the U1 of (TOP-REAL 2))
right_cell ((Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))),1,(Gauge (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
(Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) -: (E-max (L~ (Cage (C,n)))) is V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like special unfolded FinSequence of the U1 of (TOP-REAL 2)
right_cell (((Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) -: (E-max (L~ (Cage (C,n))))),1,(Gauge (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
right_cell ((Upper_Seq (C,n)),1,(Gauge (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
right_cell ((R_Cut ((Upper_Seq (C,n)),((Gauge (C,n)) * (j,i)))),1,(Gauge (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
right_cell ((LA ^' go),1,(Gauge (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
W2 /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W2 /. 2 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(LA ^' go) /. 2 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Upper_Seq (C,n)) ^' (Lower_Seq (C,n)) is non empty V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
((Upper_Seq (C,n)) ^' (Lower_Seq (C,n))) /. 2 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) /. 2 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(L~ LA) \/ (L~ Emax) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
W-min ((L~ LA) \/ (L~ Emax)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound ((L~ LA) \/ (L~ Emax)) is V11() real ext-real Element of REAL
(TOP-REAL 2) | ((L~ LA) \/ (L~ Emax)) is strict T_2 SubSpace of TOP-REAL 2
proj1 | ((L~ LA) \/ (L~ Emax)) is V19() V22( the U1 of ((TOP-REAL 2) | ((L~ LA) \/ (L~ Emax)))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | ((L~ LA) \/ (L~ Emax))), REAL ) V205((TOP-REAL 2) | ((L~ LA) \/ (L~ Emax))) Element of K6(K7( the U1 of ((TOP-REAL 2) | ((L~ LA) \/ (L~ Emax))),REAL))
the U1 of ((TOP-REAL 2) | ((L~ LA) \/ (L~ Emax))) is set
K7( the U1 of ((TOP-REAL 2) | ((L~ LA) \/ (L~ Emax))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | ((L~ LA) \/ (L~ Emax))),REAL)) is set
lower_bound (proj1 | ((L~ LA) \/ (L~ Emax))) is V11() real ext-real Element of REAL
(proj1 | ((L~ LA) \/ (L~ Emax))) .: the U1 of ((TOP-REAL 2) | ((L~ LA) \/ (L~ Emax))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | ((L~ LA) \/ (L~ Emax))) .: the U1 of ((TOP-REAL 2) | ((L~ LA) \/ (L~ Emax)))) is V11() real ext-real Element of REAL
W-most ((L~ LA) \/ (L~ Emax)) is functional Element of K6( the U1 of (TOP-REAL 2))
SW-corner ((L~ LA) \/ (L~ Emax)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-bound ((L~ LA) \/ (L~ Emax)) is V11() real ext-real Element of REAL
proj2 | ((L~ LA) \/ (L~ Emax)) is V19() V22( the U1 of ((TOP-REAL 2) | ((L~ LA) \/ (L~ Emax)))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | ((L~ LA) \/ (L~ Emax))), REAL ) V205((TOP-REAL 2) | ((L~ LA) \/ (L~ Emax))) Element of K6(K7( the U1 of ((TOP-REAL 2) | ((L~ LA) \/ (L~ Emax))),REAL))
lower_bound (proj2 | ((L~ LA) \/ (L~ Emax))) is V11() real ext-real Element of REAL
(proj2 | ((L~ LA) \/ (L~ Emax))) .: the U1 of ((TOP-REAL 2) | ((L~ LA) \/ (L~ Emax))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | ((L~ LA) \/ (L~ Emax))) .: the U1 of ((TOP-REAL 2) | ((L~ LA) \/ (L~ Emax)))) is V11() real ext-real Element of REAL
|[(W-bound ((L~ LA) \/ (L~ Emax))),(S-bound ((L~ LA) \/ (L~ Emax)))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NW-corner ((L~ LA) \/ (L~ Emax)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound ((L~ LA) \/ (L~ Emax)) is V11() real ext-real Element of REAL
upper_bound (proj2 | ((L~ LA) \/ (L~ Emax))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | ((L~ LA) \/ (L~ Emax))) .: the U1 of ((TOP-REAL 2) | ((L~ LA) \/ (L~ Emax)))) is V11() real ext-real Element of REAL
|[(W-bound ((L~ LA) \/ (L~ Emax))),(N-bound ((L~ LA) \/ (L~ Emax)))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner ((L~ LA) \/ (L~ Emax))),(NW-corner ((L~ LA) \/ (L~ Emax)))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SW-corner ((L~ LA) \/ (L~ Emax))),(NW-corner ((L~ LA) \/ (L~ Emax))))) /\ ((L~ LA) \/ (L~ Emax)) is functional Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (W-most ((L~ LA) \/ (L~ Emax))) is strict T_2 SubSpace of TOP-REAL 2
proj2 | (W-most ((L~ LA) \/ (L~ Emax))) is V19() V22( the U1 of ((TOP-REAL 2) | (W-most ((L~ LA) \/ (L~ Emax))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (W-most ((L~ LA) \/ (L~ Emax)))), REAL ) V205((TOP-REAL 2) | (W-most ((L~ LA) \/ (L~ Emax)))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (W-most ((L~ LA) \/ (L~ Emax)))),REAL))
the U1 of ((TOP-REAL 2) | (W-most ((L~ LA) \/ (L~ Emax)))) is set
K7( the U1 of ((TOP-REAL 2) | (W-most ((L~ LA) \/ (L~ Emax)))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (W-most ((L~ LA) \/ (L~ Emax)))),REAL)) is set
lower_bound (proj2 | (W-most ((L~ LA) \/ (L~ Emax)))) is V11() real ext-real Element of REAL
(proj2 | (W-most ((L~ LA) \/ (L~ Emax)))) .: the U1 of ((TOP-REAL 2) | (W-most ((L~ LA) \/ (L~ Emax)))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (W-most ((L~ LA) \/ (L~ Emax)))) .: the U1 of ((TOP-REAL 2) | (W-most ((L~ LA) \/ (L~ Emax))))) is V11() real ext-real Element of REAL
|[(W-bound ((L~ LA) \/ (L~ Emax))),(lower_bound (proj2 | (W-most ((L~ LA) \/ (L~ Emax)))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(W-min ((L~ LA) \/ (L~ Emax))) `1 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (k,i)) `1 is V11() real ext-real Element of REAL
W-bound (LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i)))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i)))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i)))) is V19() V22( the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i)))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i))))), REAL ) V205((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i))))),REAL))
the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i))))) is set
K7( the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i))))),REAL)) is set
lower_bound (proj1 | (LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i))))) is V11() real ext-real Element of REAL
(proj1 | (LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i))))) .: the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | (LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i))))) .: the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (j,i)))))) is V11() real ext-real Element of REAL
W-bound (L~ go) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ go) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ go) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ go))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ go)), REAL ) V205((TOP-REAL 2) | (L~ go)) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ go)),REAL))
the U1 of ((TOP-REAL 2) | (L~ go)) is set
K7( the U1 of ((TOP-REAL 2) | (L~ go)),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (L~ go)),REAL)) is set
lower_bound (proj1 | (L~ go)) is V11() real ext-real Element of REAL
(proj1 | (L~ go)) .: the U1 of ((TOP-REAL 2) | (L~ go)) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | (L~ go)) .: the U1 of ((TOP-REAL 2) | (L~ go))) is V11() real ext-real Element of REAL
((L~ LA) \/ (L~ Emax)) \/ (L~ go) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
W-min (((L~ LA) \/ (L~ Emax)) \/ (L~ go)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound (((L~ LA) \/ (L~ Emax)) \/ (L~ go)) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (((L~ LA) \/ (L~ Emax)) \/ (L~ go)) is strict T_2 SubSpace of TOP-REAL 2
proj1 | (((L~ LA) \/ (L~ Emax)) \/ (L~ go)) is V19() V22( the U1 of ((TOP-REAL 2) | (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))), REAL ) V205((TOP-REAL 2) | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))),REAL))
the U1 of ((TOP-REAL 2) | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))) is set
K7( the U1 of ((TOP-REAL 2) | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))),REAL)) is set
lower_bound (proj1 | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))) is V11() real ext-real Element of REAL
(proj1 | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))) .: the U1 of ((TOP-REAL 2) | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))) .: the U1 of ((TOP-REAL 2) | (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))) is V11() real ext-real Element of REAL
W-most (((L~ LA) \/ (L~ Emax)) \/ (L~ go)) is functional Element of K6( the U1 of (TOP-REAL 2))
SW-corner (((L~ LA) \/ (L~ Emax)) \/ (L~ go)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-bound (((L~ LA) \/ (L~ Emax)) \/ (L~ go)) is V11() real ext-real Element of REAL
proj2 | (((L~ LA) \/ (L~ Emax)) \/ (L~ go)) is V19() V22( the U1 of ((TOP-REAL 2) | (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))), REAL ) V205((TOP-REAL 2) | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))),REAL))
lower_bound (proj2 | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))) is V11() real ext-real Element of REAL
(proj2 | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))) .: the U1 of ((TOP-REAL 2) | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))) .: the U1 of ((TOP-REAL 2) | (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))) is V11() real ext-real Element of REAL
|[(W-bound (((L~ LA) \/ (L~ Emax)) \/ (L~ go))),(S-bound (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NW-corner (((L~ LA) \/ (L~ Emax)) \/ (L~ go)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound (((L~ LA) \/ (L~ Emax)) \/ (L~ go)) is V11() real ext-real Element of REAL
upper_bound (proj2 | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (((L~ LA) \/ (L~ Emax)) \/ (L~ go))) .: the U1 of ((TOP-REAL 2) | (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))) is V11() real ext-real Element of REAL
|[(W-bound (((L~ LA) \/ (L~ Emax)) \/ (L~ go))),(N-bound (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (((L~ LA) \/ (L~ Emax)) \/ (L~ go))),(NW-corner (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SW-corner (((L~ LA) \/ (L~ Emax)) \/ (L~ go))),(NW-corner (((L~ LA) \/ (L~ Emax)) \/ (L~ go))))) /\ (((L~ LA) \/ (L~ Emax)) \/ (L~ go)) is functional Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (W-most (((L~ LA) \/ (L~ Emax)) \/ (L~ go))) is strict T_2 SubSpace of TOP-REAL 2
proj2 | (W-most (((L~ LA) \/ (L~ Emax)) \/ (L~ go))) is V19() V22( the U1 of ((TOP-REAL 2) | (W-most (((L~ LA) \/ (L~ Emax)) \/ (L~ go))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (W-most (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))), REAL ) V205((TOP-REAL 2) | (W-most (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (W-most (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))),REAL))
the U1 of ((TOP-REAL 2) | (W-most (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))) is set
K7( the U1 of ((TOP-REAL 2) | (W-most (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (W-most (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))),REAL)) is set
lower_bound (proj2 | (W-most (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))) is V11() real ext-real Element of REAL
(proj2 | (W-most (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))) .: the U1 of ((TOP-REAL 2) | (W-most (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (W-most (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))) .: the U1 of ((TOP-REAL 2) | (W-most (((L~ LA) \/ (L~ Emax)) \/ (L~ go))))) is V11() real ext-real Element of REAL
|[(W-bound (((L~ LA) \/ (L~ Emax)) \/ (L~ go))),(lower_bound (proj2 | (W-most (((L~ LA) \/ (L~ Emax)) \/ (L~ go)))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-min (L~ W2) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound (L~ W2) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ W2) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ W2) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ W2))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ W2)), REAL ) V205((TOP-REAL 2) | (L~ W2)) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ W2)),REAL))
the U1 of ((TOP-REAL 2) | (L~ W2)) is set
K7( the U1 of ((TOP-REAL 2) | (L~ W2)),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (L~ W2)),REAL)) is set
lower_bound (proj1 | (L~ W2)) is V11() real ext-real Element of REAL
(proj1 | (L~ W2)) .: the U1 of ((TOP-REAL 2) | (L~ W2)) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | (L~ W2)) .: the U1 of ((TOP-REAL 2) | (L~ W2))) is V11() real ext-real Element of REAL
W-most (L~ W2) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SW-corner (L~ W2) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-bound (L~ W2) is V11() real ext-real Element of REAL
proj2 | (L~ W2) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ W2))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ W2)), REAL ) V205((TOP-REAL 2) | (L~ W2)) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ W2)),REAL))
lower_bound (proj2 | (L~ W2)) is V11() real ext-real Element of REAL
(proj2 | (L~ W2)) .: the U1 of ((TOP-REAL 2) | (L~ W2)) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (L~ W2)) .: the U1 of ((TOP-REAL 2) | (L~ W2))) is V11() real ext-real Element of REAL
|[(W-bound (L~ W2)),(S-bound (L~ W2))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NW-corner (L~ W2) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound (L~ W2) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ W2)) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (L~ W2)) .: the U1 of ((TOP-REAL 2) | (L~ W2))) is V11() real ext-real Element of REAL
|[(W-bound (L~ W2)),(N-bound (L~ W2))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ W2)),(NW-corner (L~ W2))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SW-corner (L~ W2)),(NW-corner (L~ W2)))) /\ (L~ W2) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (W-most (L~ W2)) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (W-most (L~ W2)) is V19() V22( the U1 of ((TOP-REAL 2) | (W-most (L~ W2)))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (W-most (L~ W2))), REAL ) V205((TOP-REAL 2) | (W-most (L~ W2))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (W-most (L~ W2))),REAL))
the U1 of ((TOP-REAL 2) | (W-most (L~ W2))) is set
K7( the U1 of ((TOP-REAL 2) | (W-most (L~ W2))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (W-most (L~ W2))),REAL)) is set
lower_bound (proj2 | (W-most (L~ W2))) is V11() real ext-real Element of REAL
(proj2 | (W-most (L~ W2))) .: the U1 of ((TOP-REAL 2) | (W-most (L~ W2))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (W-most (L~ W2))) .: the U1 of ((TOP-REAL 2) | (W-most (L~ W2)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ W2)),(lower_bound (proj2 | (W-most (L~ W2))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
rng W2 is non trivial functional Element of K6( the U1 of (TOP-REAL 2))
dom W2 is non trivial V168() V169() V170() V171() V172() V173() Element of K6(NAT)
(W2 /. 2) `1 is V11() real ext-real Element of REAL
(W-min (L~ W2)) `1 is V11() real ext-real Element of REAL
Rotate (W2,(W-min (L~ W2))) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard FinSequence of the U1 of (TOP-REAL 2)
(Rotate (W2,(W-min (L~ W2)))) /. 2 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Upper_Seq (C,n)) . (len (Upper_Seq (C,n))) is V19() Function-like set
(Upper_Seq (C,n)) /. (len (Upper_Seq (C,n))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
east_halfline (E-max C) is non empty functional connected V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
godo is set
godo is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(east_halfline (E-max C)) /\ (L~ (Cage (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
godo `1 is V11() real ext-real Element of REAL
pion1 is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
L~ pion1 is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
godo is set
godo is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
godo `2 is V11() real ext-real Element of REAL
(E-max C) `2 is V11() real ext-real Element of REAL
k + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(k + 1) - 1 is V11() real ext-real Element of REAL
(len (Gauge (C,n))) - 1 is V11() real ext-real Element of REAL
(len (Gauge (C,n))) -' 1 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * (((len (Gauge (C,n))) -' 1),1) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (((len (Gauge (C,n))) -' 1),1)) `1 is V11() real ext-real Element of REAL
godo `1 is V11() real ext-real Element of REAL
(E-max C) `1 is V11() real ext-real Element of REAL
godo is set
godo is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
Index (godo,Emax) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
LSeg (Emax,(Index (godo,Emax))) is functional Element of K6( the U1 of (TOP-REAL 2))
ff is ordinal natural ext-real non negative set
(Lower_Seq (C,n)) . ff is V19() Function-like set
Index (((Gauge (C,n)) * (k,i)),(Lower_Seq (C,n))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Index (((Gauge (C,n)) * (k,i)),(Lower_Seq (C,n)))) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
len (L_Cut ((Lower_Seq (C,n)),((Gauge (C,n)) * (k,i)))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(len (Lower_Seq (C,n))) - (Index (((Gauge (C,n)) * (k,i)),(Lower_Seq (C,n)))) is V11() real ext-real Element of REAL
(len (Lower_Seq (C,n))) -' (Index (((Gauge (C,n)) * (k,i)),(Lower_Seq (C,n)))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Index (godo,Emax)) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((len (Lower_Seq (C,n))) -' (Index (((Gauge (C,n)) * (k,i)),(Lower_Seq (C,n))))) - 1 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (k,i)) .. (Lower_Seq (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
mid ((Lower_Seq (C,n)),(((Gauge (C,n)) * (k,i)) .. (Lower_Seq (C,n))),(len (Lower_Seq (C,n)))) is V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
(east_halfline (E-max C)) /\ (L~ (Cage (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
godo `1 is V11() real ext-real Element of REAL
0 + (Index (((Gauge (C,n)) * (k,i)),(Lower_Seq (C,n)))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((len (Lower_Seq (C,n))) - (Index (((Gauge (C,n)) * (k,i)),(Lower_Seq (C,n))))) - 1 is V11() real ext-real Element of REAL
(len (Lower_Seq (C,n))) - (((Gauge (C,n)) * (k,i)) .. (Lower_Seq (C,n))) is V11() real ext-real Element of REAL
(len (Lower_Seq (C,n))) -' (((Gauge (C,n)) * (k,i)) .. (Lower_Seq (C,n))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((len (Lower_Seq (C,n))) -' (((Gauge (C,n)) * (k,i)) .. (Lower_Seq (C,n)))) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Index (godo,Emax)) + (((Gauge (C,n)) * (k,i)) .. (Lower_Seq (C,n))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((Index (godo,Emax)) + (((Gauge (C,n)) * (k,i)) .. (Lower_Seq (C,n)))) -' 1 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
right_cell ((Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))),1) is functional Element of K6( the U1 of (TOP-REAL 2))
GoB (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))) is V19() non empty-yielding V22( NAT ) V23(K295( the U1 of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K295( the U1 of (TOP-REAL 2))
L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
p is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * ((len (Gauge (C,n))),p) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
[(len (Gauge (C,n))),p] is set
{(len (Gauge (C,n))),p} is non empty V168() V169() V170() V171() V172() V173() set
{{(len (Gauge (C,n))),p},{(len (Gauge (C,n)))}} is non empty set
len (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))) -: (W-min (L~ (Cage (C,n)))) is V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like special unfolded FinSequence of the U1 of (TOP-REAL 2)
LSeg ((Lower_Seq (C,n)),1) is functional Element of K6( the U1 of (TOP-REAL 2))
LSeg ((Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))),1) is functional Element of K6( the U1 of (TOP-REAL 2))
(Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))) /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))) /. (1 + 1) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
t is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
tt is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
tt + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
[t,(tt + 1)] is set
{t,(tt + 1)} is non empty V168() V169() V170() V171() V172() V173() set
{t} is non empty V168() V169() V170() V171() V172() V173() set
{{t,(tt + 1)},{t}} is non empty set
[t,tt] is set
{t,tt} is non empty V168() V169() V170() V171() V172() V173() set
{{t,tt},{t}} is non empty set
(Gauge (C,n)) * (t,(tt + 1)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Gauge (C,n)) * (t,tt) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(tt + 1) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
E-max (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))), REAL ) V205((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),REAL))
the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) is set
K7( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),REAL)) is set
upper_bound (proj1 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) is V11() real ext-real Element of REAL
(proj1 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) is V168() V169() V170() Element of K6(REAL)
upper_bound ((proj1 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SE-corner (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is V11() real ext-real Element of REAL
proj2 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))), REAL ) V205((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),REAL))
lower_bound (proj2 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) is V11() real ext-real Element of REAL
(proj2 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),(S-bound (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NE-corner (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),(N-bound (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),(NE-corner (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SE-corner (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),(NE-corner (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))))) /\ (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) is V19() V22( the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))), REAL ) V205((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))),REAL))
the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) is set
K7( the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))),REAL)) is set
upper_bound (proj2 | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
(proj2 | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) .: the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) is V168() V169() V170() Element of K6(REAL)
upper_bound ((proj2 | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) .: the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),(upper_bound (proj2 | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
4 - 1 is V11() real ext-real Element of REAL
t - 1 is V11() real ext-real Element of REAL
t -' 1 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * ((len (Gauge (C,n))),tt) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * ((len (Gauge (C,n))),tt)) `1 is V11() real ext-real Element of REAL
t + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
cell ((Gauge (C,n)),(t -' 1),tt) is functional Element of K6( the U1 of (TOP-REAL 2))
(Gauge (C,n)) * ((len (Gauge (C,n))),(tt + 1)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * ((len (Gauge (C,n))),(tt + 1))) `1 is V11() real ext-real Element of REAL
(t -' 1) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * ((t -' 1),(tt + 1)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * ((t -' 1),(tt + 1))) `2 is V11() real ext-real Element of REAL
(Gauge (C,n)) * (1,(tt + 1)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (1,(tt + 1))) `2 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (t,(tt + 1))) `2 is V11() real ext-real Element of REAL
(E-max C) `2 is V11() real ext-real Element of REAL
godo `2 is V11() real ext-real Element of REAL
(Gauge (C,n)) * ((t -' 1),tt) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * ((t -' 1),tt)) `2 is V11() real ext-real Element of REAL
(Gauge (C,n)) * (1,tt) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (1,tt)) `2 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (t,tt)) `2 is V11() real ext-real Element of REAL
LSeg (((Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))) /. 1),((Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))) /. (1 + 1))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
LSeg ((mid ((Lower_Seq (C,n)),(((Gauge (C,n)) * (k,i)) .. (Lower_Seq (C,n))),(len (Lower_Seq (C,n))))),(Index (godo,Emax))) is functional Element of K6( the U1 of (TOP-REAL 2))
LSeg ((Lower_Seq (C,n)),(((Index (godo,Emax)) + (((Gauge (C,n)) * (k,i)) .. (Lower_Seq (C,n)))) -' 1)) is functional Element of K6( the U1 of (TOP-REAL 2))
(1 + 1) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((1 + 1) + 1) - 1 is V11() real ext-real Element of REAL
((Index (godo,Emax)) + (((Gauge (C,n)) * (k,i)) .. (Lower_Seq (C,n)))) - 1 is V11() real ext-real Element of REAL
(LSeg ((Lower_Seq (C,n)),1)) /\ (LSeg ((Lower_Seq (C,n)),(((Index (godo,Emax)) + (((Gauge (C,n)) * (k,i)) .. (Lower_Seq (C,n)))) -' 1))) is functional Element of K6( the U1 of (TOP-REAL 2))
(Lower_Seq (C,n)) /. 2 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
{((Lower_Seq (C,n)) /. 2)} is non empty functional set
godo .. (Lower_Seq (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * ((len (Gauge (C,n))),j) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * ((len (Gauge (C,n))),j)) `1 is V11() real ext-real Element of REAL
(L~ pion1) ` is non empty functional Element of K6( the U1 of (TOP-REAL 2))
godo is functional Element of K6( the U1 of (TOP-REAL 2))
UBD (L~ pion1) is non empty functional open connected Element of K6( the U1 of (TOP-REAL 2))
LeftComp pion1 is non empty functional Element of K6( the U1 of (TOP-REAL 2))
n is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
C is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
Gauge (C,n) is V19() non empty-yielding V22( NAT ) V23(K295( the U1 of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K295( the U1 of (TOP-REAL 2))
len (Gauge (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
width (Gauge (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Upper_Seq (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
L~ (Upper_Seq (C,n)) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
Lower_Seq (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
L~ (Lower_Seq (C,n)) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
Lower_Arc C is non empty functional Element of K6( the U1 of (TOP-REAL 2))
j is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
k is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
i is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * (j,i) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Gauge (C,n)) * (k,i) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
k is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
G is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * (k,i) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Gauge (C,n)) * (G,i) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (G,i))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (G,i)))) /\ (L~ (Upper_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
{((Gauge (C,n)) * (k,i))} is non empty functional set
(LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (G,i)))) /\ (L~ (Lower_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
{((Gauge (C,n)) * (G,i))} is non empty functional set
n is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
C is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
Gauge (C,n) is V19() non empty-yielding V22( NAT ) V23(K295( the U1 of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K295( the U1 of (TOP-REAL 2))
len (Gauge (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
width (Gauge (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Upper_Seq (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
L~ (Upper_Seq (C,n)) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
Lower_Seq (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
L~ (Lower_Seq (C,n)) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
Upper_Arc C is non empty functional Element of K6( the U1 of (TOP-REAL 2))
j is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
k is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
i is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * (j,i) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Gauge (C,n)) * (k,i) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
k is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
G is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * (k,i) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Gauge (C,n)) * (G,i) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (G,i))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (G,i)))) /\ (L~ (Upper_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
{((Gauge (C,n)) * (k,i))} is non empty functional set
(LSeg (((Gauge (C,n)) * (k,i)),((Gauge (C,n)) * (G,i)))) /\ (L~ (Lower_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
{((Gauge (C,n)) * (G,i))} is non empty functional set
n is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
C is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
Gauge (C,n) is V19() non empty-yielding V22( NAT ) V23(K295( the U1 of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K295( the U1 of (TOP-REAL 2))
len (Gauge (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
width (Gauge (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Cage (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
L~ (Cage (C,n)) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
Upper_Arc (L~ (Cage (C,n))) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
Lower_Arc (L~ (Cage (C,n))) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
Lower_Arc C is non empty functional Element of K6( the U1 of (TOP-REAL 2))
j is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
k is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
i is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * (j,i) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Gauge (C,n)) * (k,i) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
Lower_Seq (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
L~ (Lower_Seq (C,n)) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
Upper_Seq (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
L~ (Upper_Seq (C,n)) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
n is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
C is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
Gauge (C,n) is V19() non empty-yielding V22( NAT ) V23(K295( the U1 of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K295( the U1 of (TOP-REAL 2))
len (Gauge (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
width (Gauge (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Cage (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
L~ (Cage (C,n)) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
Upper_Arc (L~ (Cage (C,n))) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
Lower_Arc (L~ (Cage (C,n))) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
Upper_Arc C is non empty functional Element of K6( the U1 of (TOP-REAL 2))
j is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
k is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
i is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * (j,i) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Gauge (C,n)) * (k,i) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (C,n)) * (j,i)),((Gauge (C,n)) * (k,i))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
Lower_Seq (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
L~ (Lower_Seq (C,n)) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
Upper_Seq (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
L~ (Upper_Seq (C,n)) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
n is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
n + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
C is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
Gauge (C,(n + 1)) is V19() non empty-yielding V22( NAT ) V23(K295( the U1 of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K295( the U1 of (TOP-REAL 2))
len (Gauge (C,(n + 1))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Center (Gauge (C,(n + 1))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Cage (C,(n + 1)) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
L~ (Cage (C,(n + 1))) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
Upper_Arc (L~ (Cage (C,(n + 1)))) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
Lower_Arc (L~ (Cage (C,(n + 1)))) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
Lower_Arc C is non empty functional Element of K6( the U1 of (TOP-REAL 2))
i is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
j is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,(n + 1))) * (i,(Center (Gauge (C,(n + 1))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Gauge (C,(n + 1))) * (j,(Center (Gauge (C,(n + 1))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (C,(n + 1))) * (i,(Center (Gauge (C,(n + 1)))))),((Gauge (C,(n + 1))) * (j,(Center (Gauge (C,(n + 1))))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
width (Gauge (C,(n + 1))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
n is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
n + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
C is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
Gauge (C,(n + 1)) is V19() non empty-yielding V22( NAT ) V23(K295( the U1 of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K295( the U1 of (TOP-REAL 2))
len (Gauge (C,(n + 1))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Center (Gauge (C,(n + 1))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Cage (C,(n + 1)) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
L~ (Cage (C,(n + 1))) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
Upper_Arc (L~ (Cage (C,(n + 1)))) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
Lower_Arc (L~ (Cage (C,(n + 1)))) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
Upper_Arc C is non empty functional Element of K6( the U1 of (TOP-REAL 2))
i is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
j is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,(n + 1))) * (i,(Center (Gauge (C,(n + 1))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Gauge (C,(n + 1))) * (j,(Center (Gauge (C,(n + 1))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (C,(n + 1))) * (i,(Center (Gauge (C,(n + 1)))))),((Gauge (C,(n + 1))) * (j,(Center (Gauge (C,(n + 1))))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
width (Gauge (C,(n + 1))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
n is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
C is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
Gauge (C,n) is V19() non empty-yielding V22( NAT ) V23(K295( the U1 of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K295( the U1 of (TOP-REAL 2))
len (Gauge (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
width (Gauge (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Upper_Seq (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
L~ (Upper_Seq (C,n)) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
Lower_Seq (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
L~ (Lower_Seq (C,n)) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
Upper_Arc C is non empty functional Element of K6( the U1 of (TOP-REAL 2))
i is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
j is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
k is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
k is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * (i,k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Gauge (C,n)) * (i,k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(Gauge (C,n)) * (j,k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
((LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k))))) /\ (L~ (Upper_Seq (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
{((Gauge (C,n)) * (j,k))} is non empty functional set
((LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k))))) /\ (L~ (Lower_Seq (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
{((Gauge (C,n)) * (i,k))} is non empty functional set
[i,k] is set
{i,k} is non empty V168() V169() V170() V171() V172() V173() set
{i} is non empty V168() V169() V170() V171() V172() V173() set
{{i,k},{i}} is non empty set
Indices (Gauge (C,n)) is set
<*((Gauge (C,n)) * (j,k)),((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))*> is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() V39(3) FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
L~ <*((Gauge (C,n)) * (j,k)),((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))*> is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
[(len (Gauge (C,n))),k] is set
{(len (Gauge (C,n))),k} is non empty V168() V169() V170() V171() V172() V173() set
{(len (Gauge (C,n)))} is non empty V168() V169() V170() V171() V172() V173() set
{{(len (Gauge (C,n))),k},{(len (Gauge (C,n)))}} is non empty set
[1,k] is set
{1,k} is non empty V168() V169() V170() V171() V172() V173() set
{{1,k},{1}} is non empty set
[j,k] is set
{j,k} is non empty V168() V169() V170() V171() V172() V173() set
{j} is non empty V168() V169() V170() V171() V172() V173() set
{{j,k},{j}} is non empty set
((Gauge (C,n)) * (i,k)) `2 is V11() real ext-real Element of REAL
(Gauge (C,n)) * (1,k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (1,k)) `2 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (j,k)) `2 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (i,k)) `1 is V11() real ext-real Element of REAL
(Gauge (C,n)) * (i,1) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (i,1)) `1 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (i,k)) `1 is V11() real ext-real Element of REAL
|[(((Gauge (C,n)) * (i,k)) `1),(((Gauge (C,n)) * (j,k)) `2)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
[(len (Gauge (C,n))),k] is set
{(len (Gauge (C,n))),k} is non empty V168() V169() V170() V171() V172() V173() set
{{(len (Gauge (C,n))),k},{(len (Gauge (C,n)))}} is non empty set
Cage (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
L~ (Cage (C,n)) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
W-bound (L~ (Cage (C,n))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (C,n))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ (Cage (C,n))) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))), REAL ) V205((TOP-REAL 2) | (L~ (Cage (C,n)))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL))
the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))) is set
K7( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL)) is set
lower_bound (proj1 | (L~ (Cage (C,n)))) is V11() real ext-real Element of REAL
(proj1 | (L~ (Cage (C,n)))) .: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | (L~ (Cage (C,n)))) .: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n))))) is V11() real ext-real Element of REAL
W-min (L~ (Cage (C,n))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-most (L~ (Cage (C,n))) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SW-corner (L~ (Cage (C,n))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Cage (C,n))) is V11() real ext-real Element of REAL
proj2 | (L~ (Cage (C,n))) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))), REAL ) V205((TOP-REAL 2) | (L~ (Cage (C,n)))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL))
lower_bound (proj2 | (L~ (Cage (C,n)))) is V11() real ext-real Element of REAL
(proj2 | (L~ (Cage (C,n)))) .: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (L~ (Cage (C,n)))) .: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Cage (C,n)))),(S-bound (L~ (Cage (C,n))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NW-corner (L~ (Cage (C,n))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Cage (C,n))) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ (Cage (C,n)))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (L~ (Cage (C,n)))) .: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Cage (C,n)))),(N-bound (L~ (Cage (C,n))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (C,n)))),(NW-corner (L~ (Cage (C,n))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SW-corner (L~ (Cage (C,n)))),(NW-corner (L~ (Cage (C,n)))))) /\ (L~ (Cage (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (W-most (L~ (Cage (C,n)))) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Cage (C,n)))) is V19() V22( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n)))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))), REAL ) V205((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),REAL))
the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))) is set
K7( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),REAL)) is set
lower_bound (proj2 | (W-most (L~ (Cage (C,n))))) is V11() real ext-real Element of REAL
(proj2 | (W-most (L~ (Cage (C,n))))) .: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (W-most (L~ (Cage (C,n))))) .: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n)))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Cage (C,n)))),(lower_bound (proj2 | (W-most (L~ (Cage (C,n))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Cage (C,n))) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ (Cage (C,n)))) is V11() real ext-real Element of REAL
upper_bound ((proj1 | (L~ (Cage (C,n)))) .: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n))))) is V11() real ext-real Element of REAL
E-max (L~ (Cage (C,n))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-most (L~ (Cage (C,n))) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SE-corner (L~ (Cage (C,n))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
|[(E-bound (L~ (Cage (C,n)))),(S-bound (L~ (Cage (C,n))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NE-corner (L~ (Cage (C,n))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
|[(E-bound (L~ (Cage (C,n)))),(N-bound (L~ (Cage (C,n))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Cage (C,n)))),(NE-corner (L~ (Cage (C,n))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SE-corner (L~ (Cage (C,n)))),(NE-corner (L~ (Cage (C,n)))))) /\ (L~ (Cage (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (E-most (L~ (Cage (C,n)))) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Cage (C,n)))) is V19() V22( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n)))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))), REAL ) V205((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),REAL))
the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))) is set
K7( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),REAL)) is set
upper_bound (proj2 | (E-most (L~ (Cage (C,n))))) is V11() real ext-real Element of REAL
(proj2 | (E-most (L~ (Cage (C,n))))) .: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))) is V168() V169() V170() Element of K6(REAL)
upper_bound ((proj2 | (E-most (L~ (Cage (C,n))))) .: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n)))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Cage (C,n)))),(upper_bound (proj2 | (E-most (L~ (Cage (C,n))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
1 + 2 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
len (Lower_Seq (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
dom (Lower_Seq (C,n)) is non trivial V168() V169() V170() V171() V172() V173() Element of K6(NAT)
(Lower_Seq (C,n)) . 1 is V19() Function-like set
(Lower_Seq (C,n)) /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Lower_Seq (C,n)) . (len (Lower_Seq (C,n))) is V19() Function-like set
(Lower_Seq (C,n)) /. (len (Lower_Seq (C,n))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
L_Cut ((Lower_Seq (C,n)),((Gauge (C,n)) * (i,k))) is V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
(W-min (L~ (Cage (C,n)))) `1 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (1,k)) `1 is V11() real ext-real Element of REAL
rng (Lower_Seq (C,n)) is functional Element of K6( the U1 of (TOP-REAL 2))
LA is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
(E-max (L~ (Cage (C,n)))) `1 is V11() real ext-real Element of REAL
(Gauge (C,n)) * ((len (Gauge (C,n))),k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * ((len (Gauge (C,n))),k)) `1 is V11() real ext-real Element of REAL
1 + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
len LA is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Emax is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one non constant V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq s.c.c. FinSequence of the U1 of (TOP-REAL 2)
L~ Emax is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
[1,k] is set
{1,k} is non empty V168() V169() V170() V171() V172() V173() set
{{1,k},{1}} is non empty set
(Gauge (C,n)) * (1,k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (1,k)) `1 is V11() real ext-real Element of REAL
R_Cut ((Upper_Seq (C,n)),((Gauge (C,n)) * (j,k))) is V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
len (Upper_Seq (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
dom (Upper_Seq (C,n)) is non trivial V168() V169() V170() V171() V172() V173() Element of K6(NAT)
(Upper_Seq (C,n)) . 1 is V19() Function-like set
(Upper_Seq (C,n)) /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
[i,k] is set
{i,k} is non empty V168() V169() V170() V171() V172() V173() set
{{i,k},{i}} is non empty set
do is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
dom <*((Gauge (C,n)) * (j,k)),((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))*> is non trivial V168() V169() V170() V171() V172() V173() Element of K6(NAT)
<*((Gauge (C,n)) * (j,k)),((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))*> /. do is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
rng (Upper_Seq (C,n)) is functional Element of K6( the U1 of (TOP-REAL 2))
do is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
len Emax is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
dom Emax is non trivial V168() V169() V170() V171() V172() V173() Element of K6(NAT)
Emax /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
Emax . 1 is V19() Function-like set
LSeg (Emax,1) is functional Element of K6( the U1 of (TOP-REAL 2))
Emax /. (1 + 1) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (C,n)) * (i,k)),(Emax /. (1 + 1))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (Emax,1)) /\ (L~ <*((Gauge (C,n)) * (j,k)),((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))*>) is functional Element of K6( the U1 of (TOP-REAL 2))
go is set
LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
LSeg (((Gauge (C,n)) * (j,k)),((Gauge (C,n)) * (i,k))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,n)) * (j,k)),((Gauge (C,n)) * (i,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
(L~ <*((Gauge (C,n)) * (j,k)),((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))*>) /\ (LSeg (Emax,1)) is functional Element of K6( the U1 of (TOP-REAL 2))
rng Emax is non trivial functional Element of K6( the U1 of (TOP-REAL 2))
len do is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
go is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one non constant V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq s.c.c. FinSequence of the U1 of (TOP-REAL 2)
L~ go is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
len go is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
dom go is non trivial V168() V169() V170() V171() V172() V173() Element of K6(NAT)
go /. (len go) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
go . (len go) is V19() Function-like set
(len go) - 1 is V11() real ext-real Element of REAL
m is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
m + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(len go) -' 1 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
LSeg (go,m) is functional Element of K6( the U1 of (TOP-REAL 2))
go /. m is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((go /. m),((Gauge (C,n)) * (j,k))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (go,m)) /\ (L~ <*((Gauge (C,n)) * (j,k)),((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))*>) is functional Element of K6( the U1 of (TOP-REAL 2))
W2 is set
LSeg (((Gauge (C,n)) * (j,k)),((Gauge (C,n)) * (i,k))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,n)) * (j,k)),((Gauge (C,n)) * (i,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
go /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(L~ go) /\ (L~ Emax) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
{(go /. 1)} is non empty functional set
W2 is set
(Gauge (C,n)) * ((len (Gauge (C,n))),k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * ((len (Gauge (C,n))),k)) `1 is V11() real ext-real Element of REAL
(L~ (Upper_Seq (C,n))) /\ (L~ (Lower_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
{(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n))))} is non empty functional set
go /. 2 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (j,k)) .. (Upper_Seq (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
mid ((Upper_Seq (C,n)),1,(((Gauge (C,n)) * (j,k)) .. (Upper_Seq (C,n)))) is V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
(Upper_Seq (C,n)) | (((Gauge (C,n)) * (j,k)) .. (Upper_Seq (C,n))) is V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. FinSequence of the U1 of (TOP-REAL 2)
(Upper_Seq (C,n)) /. 2 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
rng go is non trivial functional Element of K6( the U1 of (TOP-REAL 2))
Emax /. (len Emax) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
pion1 is set
((Gauge (C,n)) * (j,k)) `1 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (i,k)) `2 is V11() real ext-real Element of REAL
<*((Gauge (C,n)) * (j,k)),((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))*> /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
len <*((Gauge (C,n)) * (j,k)),((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))*> is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
<*((Gauge (C,n)) * (j,k)),((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))*> /. (len <*((Gauge (C,n)) * (j,k)),((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))*>) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
pion1 is V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
L~ pion1 is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
pion1 /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
len pion1 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
pion1 /. (len pion1) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
pion1 is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() 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 V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
len (go ^' pion1) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(go ^' pion1) /. (len (go ^' pion1)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
<*((Gauge (C,n)) * (j,k)),((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))*> /. 3 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
pion1 /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
L~ pion1 is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(L~ go) /\ (L~ pion1) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
{(pion1 /. 1)} is non empty functional set
godo is set
2 + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
len pion1 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
rng pion1 is functional Element of K6( the U1 of (TOP-REAL 2))
godo is set
pion1 /. (len pion1) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
{(pion1 /. (len pion1))} is non empty functional set
(L~ Emax) /\ (L~ pion1) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
godo is set
godo is set
L~ (go ^' pion1) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(L~ (go ^' pion1)) /\ (L~ Emax) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(L~ go) \/ (L~ pion1) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
((L~ go) \/ (L~ pion1)) /\ (L~ Emax) is functional Element of K6( the U1 of (TOP-REAL 2))
{(Emax /. 1)} is non empty functional set
{(go /. 1)} \/ {(Emax /. 1)} is non empty set
(go ^' pion1) /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
{((go ^' pion1) /. 1)} is non empty functional set
{((go ^' pion1) /. 1)} \/ {(Emax /. 1)} is non empty set
{((go ^' pion1) /. 1),(Emax /. 1)} is non empty functional set
W-min C is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound C is V11() real ext-real Element of REAL
(TOP-REAL 2) | C is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | C is V19() V22( the U1 of ((TOP-REAL 2) | C)) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | C), REAL ) V205((TOP-REAL 2) | C) Element of K6(K7( the U1 of ((TOP-REAL 2) | C),REAL))
the U1 of ((TOP-REAL 2) | C) is set
K7( the U1 of ((TOP-REAL 2) | C),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | C),REAL)) is set
lower_bound (proj1 | C) is V11() real ext-real Element of REAL
(proj1 | C) .: the U1 of ((TOP-REAL 2) | C) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | C) .: the U1 of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
W-most C is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SW-corner C is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-bound C is V11() real ext-real Element of REAL
proj2 | C is V19() V22( the U1 of ((TOP-REAL 2) | C)) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | C), REAL ) V205((TOP-REAL 2) | C) Element of K6(K7( the U1 of ((TOP-REAL 2) | C),REAL))
lower_bound (proj2 | C) is V11() real ext-real Element of REAL
(proj2 | C) .: the U1 of ((TOP-REAL 2) | C) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | C) .: the U1 of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
|[(W-bound C),(S-bound C)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NW-corner C is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound C is V11() real ext-real Element of REAL
upper_bound (proj2 | C) is V11() real ext-real Element of REAL
upper_bound ((proj2 | C) .: the U1 of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
|[(W-bound C),(N-bound C)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner C),(NW-corner C)) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SW-corner C),(NW-corner C))) /\ C is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (W-most C) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (W-most C) is V19() V22( the U1 of ((TOP-REAL 2) | (W-most C))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (W-most C)), REAL ) V205((TOP-REAL 2) | (W-most C)) Element of K6(K7( the U1 of ((TOP-REAL 2) | (W-most C)),REAL))
the U1 of ((TOP-REAL 2) | (W-most C)) is set
K7( the U1 of ((TOP-REAL 2) | (W-most C)),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (W-most C)),REAL)) is set
lower_bound (proj2 | (W-most C)) is V11() real ext-real Element of REAL
(proj2 | (W-most C)) .: the U1 of ((TOP-REAL 2) | (W-most C)) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (W-most C)) .: the U1 of ((TOP-REAL 2) | (W-most C))) is V11() real ext-real Element of REAL
|[(W-bound C),(lower_bound (proj2 | (W-most C)))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-max C is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-bound C is V11() real ext-real Element of REAL
upper_bound (proj1 | C) is V11() real ext-real Element of REAL
upper_bound ((proj1 | C) .: the U1 of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
E-most C is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SE-corner C is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
|[(E-bound C),(S-bound C)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NE-corner C is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
|[(E-bound C),(N-bound C)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner C),(NE-corner C)) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SE-corner C),(NE-corner C))) /\ C is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (E-most C) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (E-most C) is V19() V22( the U1 of ((TOP-REAL 2) | (E-most C))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (E-most C)), REAL ) V205((TOP-REAL 2) | (E-most C)) Element of K6(K7( the U1 of ((TOP-REAL 2) | (E-most C)),REAL))
the U1 of ((TOP-REAL 2) | (E-most C)) is set
K7( the U1 of ((TOP-REAL 2) | (E-most C)),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (E-most C)),REAL)) is set
upper_bound (proj2 | (E-most C)) is V11() real ext-real Element of REAL
(proj2 | (E-most C)) .: the U1 of ((TOP-REAL 2) | (E-most C)) is V168() V169() V170() Element of K6(REAL)
upper_bound ((proj2 | (E-most C)) .: the U1 of ((TOP-REAL 2) | (E-most C))) is V11() real ext-real Element of REAL
|[(E-bound C),(upper_bound (proj2 | (E-most C)))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(go ^' pion1) ^' Emax is non empty V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
(len pion1) - 1 is V11() real ext-real Element of REAL
(len pion1) -' 1 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
LSeg (pion1,((len pion1) -' 1)) is functional Element of K6( the U1 of (TOP-REAL 2))
(LSeg (pion1,((len pion1) -' 1))) /\ (LSeg (Emax,1)) is functional Element of K6( the U1 of (TOP-REAL 2))
godo is set
((len pion1) -' 1) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
pion1 /. (((len pion1) -' 1) + 1) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((len pion1) - 1) + 1 is V11() real ext-real Element of REAL
(len pion1) - 2 is V11() real ext-real Element of REAL
(len pion1) -' 2 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((len pion1) -' 2) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((len pion1) - 2) + 1 is V11() real ext-real Element of REAL
(len go) + ((len pion1) -' 2) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
LSeg ((go ^' pion1),((len go) + ((len pion1) -' 2))) is functional Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((go ^' pion1),((len go) + ((len pion1) -' 2)))) /\ (LSeg (Emax,1)) is functional Element of K6( the U1 of (TOP-REAL 2))
{((go ^' pion1) /. (len (go ^' pion1)))} is non empty functional set
(rng go) /\ (rng pion1) is functional Element of K6( the U1 of (TOP-REAL 2))
(len (go ^' pion1)) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((len (go ^' pion1)) + 1) - 1 is V11() real ext-real Element of REAL
(len go) + (len pion1) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((len go) + (len pion1)) - 1 is V11() real ext-real Element of REAL
(len (go ^' pion1)) - 1 is V11() real ext-real Element of REAL
(len go) + ((len pion1) - 2) is V11() real ext-real Element of REAL
(len (go ^' pion1)) -' 1 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(L~ (Upper_Seq (C,n))) \/ (L~ (Lower_Seq (C,n))) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
LSeg (pion1,1) is functional Element of K6( the U1 of (TOP-REAL 2))
(LSeg (go,m)) /\ (LSeg (pion1,1)) is functional Element of K6( the U1 of (TOP-REAL 2))
godo is set
LSeg (go,((len go) -' 1)) is functional Element of K6( the U1 of (TOP-REAL 2))
(LSeg (go,((len go) -' 1))) /\ (LSeg (pion1,1)) is functional Element of K6( the U1 of (TOP-REAL 2))
{(go /. (len go))} is non empty functional set
1 + 0 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
len (Cage (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
len ((go ^' pion1) ^' Emax) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
ff is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard FinSequence of the U1 of (TOP-REAL 2)
L~ ff is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
(L~ (go ^' pion1)) \/ (L~ Emax) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
((L~ go) \/ (L~ pion1)) \/ (L~ Emax) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
right_cell (ff,1,(Gauge (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
(right_cell (ff,1,(Gauge (C,n)))) \ (L~ ff) is functional Element of K6( the U1 of (TOP-REAL 2))
RightComp ff is non empty functional Element of K6( the U1 of (TOP-REAL 2))
dom ff is non trivial V168() V169() V170() V171() V172() V173() Element of K6(NAT)
ff /. 2 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
rng ff is non trivial functional Element of K6( the U1 of (TOP-REAL 2))
rng (Cage (C,n)) is non trivial functional Element of K6( the U1 of (TOP-REAL 2))
(Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
W-max (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))), REAL ) V205((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),REAL))
the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is set
K7( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),REAL)) is set
lower_bound (proj1 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is V11() real ext-real Element of REAL
(proj1 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SW-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V11() real ext-real Element of REAL
proj2 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))), REAL ) V205((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),REAL))
lower_bound (proj2 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is V11() real ext-real Element of REAL
(proj2 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),(S-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NW-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),(N-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),(NW-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SW-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),(NW-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))) /\ (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is V19() V22( the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))), REAL ) V205((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))),REAL))
the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is set
K7( the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))),REAL)) is set
upper_bound (proj2 | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
(proj2 | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) .: the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V168() V169() V170() Element of K6(REAL)
upper_bound ((proj2 | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) .: the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),(upper_bound (proj2 | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(W-max (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .. (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
N-min (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
NE-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is V11() real ext-real Element of REAL
upper_bound ((proj1 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),(N-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((NW-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),(NE-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((NW-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),(NE-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))) /\ (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is V19() V22( the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))), REAL ) V205((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))),REAL))
the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is set
K7( the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))),REAL)) is set
lower_bound (proj1 | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
(proj1 | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) .: the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) .: the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))),(N-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(N-min (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .. (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
N-max (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
upper_bound (proj1 | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
upper_bound ((proj1 | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) .: the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))) is V11() real ext-real Element of REAL
|[(upper_bound (proj1 | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))),(N-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(N-max (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .. (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(E-max (L~ (Cage (C,n)))) .. (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
W-bound (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))) is V19() V22( the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))))), REAL ) V205((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))))),REAL))
the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))))) is set
K7( the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))))),REAL)) is set
lower_bound (proj1 | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))))) is V11() real ext-real Element of REAL
(proj1 | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))))) .: the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))))) .: the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))))) is V11() real ext-real Element of REAL
(L~ go) \/ (L~ Emax) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
len (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
right_cell ((Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))),1) is functional Element of K6( the U1 of (TOP-REAL 2))
GoB (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) is V19() non empty-yielding V22( NAT ) V23(K295( the U1 of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K295( the U1 of (TOP-REAL 2))
right_cell ((Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))),1,(GoB (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is functional Element of K6( the U1 of (TOP-REAL 2))
GoB (Cage (C,n)) is V19() non empty-yielding V22( NAT ) V23(K295( the U1 of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K295( the U1 of (TOP-REAL 2))
right_cell ((Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))),1,(GoB (Cage (C,n)))) is functional Element of K6( the U1 of (TOP-REAL 2))
right_cell ((Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))),1,(Gauge (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
(Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) -: (E-max (L~ (Cage (C,n)))) is V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like special unfolded FinSequence of the U1 of (TOP-REAL 2)
right_cell (((Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) -: (E-max (L~ (Cage (C,n))))),1,(Gauge (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
right_cell ((Upper_Seq (C,n)),1,(Gauge (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
right_cell ((R_Cut ((Upper_Seq (C,n)),((Gauge (C,n)) * (j,k)))),1,(Gauge (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
right_cell ((go ^' pion1),1,(Gauge (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
ff /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) is V19() V22( the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k))))), REAL ) V205((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k))))),REAL))
the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k))))) is set
K7( the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k))))),REAL)) is set
lower_bound (proj1 | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k))))) is V11() real ext-real Element of REAL
(proj1 | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k))))) .: the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k))))) .: the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))))) is V11() real ext-real Element of REAL
W-bound ((LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))))) is strict T_2 SubSpace of TOP-REAL 2
proj1 | ((LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))))) is V19() V22( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))))), REAL ) V205((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))))),REAL))
the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))))) is set
K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))))),REAL)) is set
lower_bound (proj1 | ((LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))))) is V11() real ext-real Element of REAL
(proj1 | ((LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | ((LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))))))) is V11() real ext-real Element of REAL
min ((W-bound (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k))))),(W-bound (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))))) is ext-real set
W-bound (L~ pion1) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ pion1) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ pion1) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ pion1))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ pion1)), REAL ) V205((TOP-REAL 2) | (L~ pion1)) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ pion1)),REAL))
the U1 of ((TOP-REAL 2) | (L~ pion1)) is set
K7( the U1 of ((TOP-REAL 2) | (L~ pion1)),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (L~ pion1)),REAL)) is set
lower_bound (proj1 | (L~ pion1)) is V11() real ext-real Element of REAL
(proj1 | (L~ pion1)) .: the U1 of ((TOP-REAL 2) | (L~ pion1)) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | (L~ pion1)) .: the U1 of ((TOP-REAL 2) | (L~ pion1))) is V11() real ext-real Element of REAL
W-min ((L~ go) \/ (L~ Emax)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound ((L~ go) \/ (L~ Emax)) is V11() real ext-real Element of REAL
(TOP-REAL 2) | ((L~ go) \/ (L~ Emax)) is strict T_2 SubSpace of TOP-REAL 2
proj1 | ((L~ go) \/ (L~ Emax)) is V19() V22( the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ Emax)))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ Emax))), REAL ) V205((TOP-REAL 2) | ((L~ go) \/ (L~ Emax))) Element of K6(K7( the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ Emax))),REAL))
the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ Emax))) is set
K7( the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ Emax))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ Emax))),REAL)) is set
lower_bound (proj1 | ((L~ go) \/ (L~ Emax))) is V11() real ext-real Element of REAL
(proj1 | ((L~ go) \/ (L~ Emax))) .: the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ Emax))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | ((L~ go) \/ (L~ Emax))) .: the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ Emax)))) is V11() real ext-real Element of REAL
W-most ((L~ go) \/ (L~ Emax)) is functional Element of K6( the U1 of (TOP-REAL 2))
SW-corner ((L~ go) \/ (L~ Emax)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-bound ((L~ go) \/ (L~ Emax)) is V11() real ext-real Element of REAL
proj2 | ((L~ go) \/ (L~ Emax)) is V19() V22( the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ Emax)))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ Emax))), REAL ) V205((TOP-REAL 2) | ((L~ go) \/ (L~ Emax))) Element of K6(K7( the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ Emax))),REAL))
lower_bound (proj2 | ((L~ go) \/ (L~ Emax))) is V11() real ext-real Element of REAL
(proj2 | ((L~ go) \/ (L~ Emax))) .: the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ Emax))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | ((L~ go) \/ (L~ Emax))) .: the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ Emax)))) is V11() real ext-real Element of REAL
|[(W-bound ((L~ go) \/ (L~ Emax))),(S-bound ((L~ go) \/ (L~ Emax)))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NW-corner ((L~ go) \/ (L~ Emax)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound ((L~ go) \/ (L~ Emax)) is V11() real ext-real Element of REAL
upper_bound (proj2 | ((L~ go) \/ (L~ Emax))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | ((L~ go) \/ (L~ Emax))) .: the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ Emax)))) is V11() real ext-real Element of REAL
|[(W-bound ((L~ go) \/ (L~ Emax))),(N-bound ((L~ go) \/ (L~ Emax)))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner ((L~ go) \/ (L~ Emax))),(NW-corner ((L~ go) \/ (L~ Emax)))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SW-corner ((L~ go) \/ (L~ Emax))),(NW-corner ((L~ go) \/ (L~ Emax))))) /\ ((L~ go) \/ (L~ Emax)) is functional Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (W-most ((L~ go) \/ (L~ Emax))) is strict T_2 SubSpace of TOP-REAL 2
proj2 | (W-most ((L~ go) \/ (L~ Emax))) is V19() V22( the U1 of ((TOP-REAL 2) | (W-most ((L~ go) \/ (L~ Emax))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (W-most ((L~ go) \/ (L~ Emax)))), REAL ) V205((TOP-REAL 2) | (W-most ((L~ go) \/ (L~ Emax)))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (W-most ((L~ go) \/ (L~ Emax)))),REAL))
the U1 of ((TOP-REAL 2) | (W-most ((L~ go) \/ (L~ Emax)))) is set
K7( the U1 of ((TOP-REAL 2) | (W-most ((L~ go) \/ (L~ Emax)))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (W-most ((L~ go) \/ (L~ Emax)))),REAL)) is set
lower_bound (proj2 | (W-most ((L~ go) \/ (L~ Emax)))) is V11() real ext-real Element of REAL
(proj2 | (W-most ((L~ go) \/ (L~ Emax)))) .: the U1 of ((TOP-REAL 2) | (W-most ((L~ go) \/ (L~ Emax)))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (W-most ((L~ go) \/ (L~ Emax)))) .: the U1 of ((TOP-REAL 2) | (W-most ((L~ go) \/ (L~ Emax))))) is V11() real ext-real Element of REAL
|[(W-bound ((L~ go) \/ (L~ Emax))),(lower_bound (proj2 | (W-most ((L~ go) \/ (L~ Emax)))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(W-min ((L~ go) \/ (L~ Emax))) `1 is V11() real ext-real Element of REAL
((L~ go) \/ (L~ Emax)) \/ (L~ pion1) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
W-min (((L~ go) \/ (L~ Emax)) \/ (L~ pion1)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound (((L~ go) \/ (L~ Emax)) \/ (L~ pion1)) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (((L~ go) \/ (L~ Emax)) \/ (L~ pion1)) is strict T_2 SubSpace of TOP-REAL 2
proj1 | (((L~ go) \/ (L~ Emax)) \/ (L~ pion1)) is V19() V22( the U1 of ((TOP-REAL 2) | (((L~ go) \/ (L~ Emax)) \/ (L~ pion1)))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (((L~ go) \/ (L~ Emax)) \/ (L~ pion1))), REAL ) V205((TOP-REAL 2) | (((L~ go) \/ (L~ Emax)) \/ (L~ pion1))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (((L~ go) \/ (L~ Emax)) \/ (L~ pion1))),REAL))
the U1 of ((TOP-REAL 2) | (((L~ go) \/ (L~ Emax)) \/ (L~ pion1))) is set
K7( the U1 of ((TOP-REAL 2) | (((L~ go) \/ (L~ Emax)) \/ (L~ pion1))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (((L~ go) \/ (L~ Emax)) \/ (L~ pion1))),REAL)) is set
lower_bound (proj1 | (((L~ go) \/ (L~ Emax)) \/ (L~ pion1))) is V11() real ext-real Element of REAL
(proj1 | (((L~ go) \/ (L~ Emax)) \/ (L~ pion1))) .: the U1 of ((TOP-REAL 2) | (((L~ go) \/ (L~ Emax)) \/ (L~ pion1))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | (((L~ go) \/ (L~ Emax)) \/ (L~ pion1))) .: the U1 of ((TOP-REAL 2) | (((L~ go) \/ (L~ Emax)) \/ (L~ pion1)))) is V11() real ext-real Element of REAL
W-most (((L~ go) \/ (L~ Emax)) \/ (L~ pion1)) is functional Element of K6( the U1 of (TOP-REAL 2))
SW-corner (((L~ go) \/ (L~ Emax)) \/ (L~ pion1)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-bound (((L~ go) \/ (L~ Emax)) \/ (L~ pion1)) is V11() real ext-real Element of REAL
proj2 | (((L~ go) \/ (L~ Emax)) \/ (L~ pion1)) is V19() V22( the U1 of ((TOP-REAL 2) | (((L~ go) \/ (L~ Emax)) \/ (L~ pion1)))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (((L~ go) \/ (L~ Emax)) \/ (L~ pion1))), REAL ) V205((TOP-REAL 2) | (((L~ go) \/ (L~ Emax)) \/ (L~ pion1))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (((L~ go) \/ (L~ Emax)) \/ (L~ pion1))),REAL))
lower_bound (proj2 | (((L~ go) \/ (L~ Emax)) \/ (L~ pion1))) is V11() real ext-real Element of REAL
(proj2 | (((L~ go) \/ (L~ Emax)) \/ (L~ pion1))) .: the U1 of ((TOP-REAL 2) | (((L~ go) \/ (L~ Emax)) \/ (L~ pion1))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (((L~ go) \/ (L~ Emax)) \/ (L~ pion1))) .: the U1 of ((TOP-REAL 2) | (((L~ go) \/ (L~ Emax)) \/ (L~ pion1)))) is V11() real ext-real Element of REAL
|[(W-bound (((L~ go) \/ (L~ Emax)) \/ (L~ pion1))),(S-bound (((L~ go) \/ (L~ Emax)) \/ (L~ pion1)))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NW-corner (((L~ go) \/ (L~ Emax)) \/ (L~ pion1)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound (((L~ go) \/ (L~ Emax)) \/ (L~ pion1)) is V11() real ext-real Element of REAL
upper_bound (proj2 | (((L~ go) \/ (L~ Emax)) \/ (L~ pion1))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (((L~ go) \/ (L~ Emax)) \/ (L~ pion1))) .: the U1 of ((TOP-REAL 2) | (((L~ go) \/ (L~ Emax)) \/ (L~ pion1)))) is V11() real ext-real Element of REAL
|[(W-bound (((L~ go) \/ (L~ Emax)) \/ (L~ pion1))),(N-bound (((L~ go) \/ (L~ Emax)) \/ (L~ pion1)))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (((L~ go) \/ (L~ Emax)) \/ (L~ pion1))),(NW-corner (((L~ go) \/ (L~ Emax)) \/ (L~ pion1)))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SW-corner (((L~ go) \/ (L~ Emax)) \/ (L~ pion1))),(NW-corner (((L~ go) \/ (L~ Emax)) \/ (L~ pion1))))) /\ (((L~ go) \/ (L~ Emax)) \/ (L~ pion1)) is functional Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (W-most (((L~ go) \/ (L~ Emax)) \/ (L~ pion1))) is strict T_2 SubSpace of TOP-REAL 2
proj2 | (W-most (((L~ go) \/ (L~ Emax)) \/ (L~ pion1))) is V19() V22( the U1 of ((TOP-REAL 2) | (W-most (((L~ go) \/ (L~ Emax)) \/ (L~ pion1))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (W-most (((L~ go) \/ (L~ Emax)) \/ (L~ pion1)))), REAL ) V205((TOP-REAL 2) | (W-most (((L~ go) \/ (L~ Emax)) \/ (L~ pion1)))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (W-most (((L~ go) \/ (L~ Emax)) \/ (L~ pion1)))),REAL))
the U1 of ((TOP-REAL 2) | (W-most (((L~ go) \/ (L~ Emax)) \/ (L~ pion1)))) is set
K7( the U1 of ((TOP-REAL 2) | (W-most (((L~ go) \/ (L~ Emax)) \/ (L~ pion1)))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (W-most (((L~ go) \/ (L~ Emax)) \/ (L~ pion1)))),REAL)) is set
lower_bound (proj2 | (W-most (((L~ go) \/ (L~ Emax)) \/ (L~ pion1)))) is V11() real ext-real Element of REAL
(proj2 | (W-most (((L~ go) \/ (L~ Emax)) \/ (L~ pion1)))) .: the U1 of ((TOP-REAL 2) | (W-most (((L~ go) \/ (L~ Emax)) \/ (L~ pion1)))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (W-most (((L~ go) \/ (L~ Emax)) \/ (L~ pion1)))) .: the U1 of ((TOP-REAL 2) | (W-most (((L~ go) \/ (L~ Emax)) \/ (L~ pion1))))) is V11() real ext-real Element of REAL
|[(W-bound (((L~ go) \/ (L~ Emax)) \/ (L~ pion1))),(lower_bound (proj2 | (W-most (((L~ go) \/ (L~ Emax)) \/ (L~ pion1)))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-min (L~ ff) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound (L~ ff) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ ff) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ ff) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ ff))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ ff)), REAL ) V205((TOP-REAL 2) | (L~ ff)) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ ff)),REAL))
the U1 of ((TOP-REAL 2) | (L~ ff)) is set
K7( the U1 of ((TOP-REAL 2) | (L~ ff)),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (L~ ff)),REAL)) is set
lower_bound (proj1 | (L~ ff)) is V11() real ext-real Element of REAL
(proj1 | (L~ ff)) .: the U1 of ((TOP-REAL 2) | (L~ ff)) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | (L~ ff)) .: the U1 of ((TOP-REAL 2) | (L~ ff))) is V11() real ext-real Element of REAL
W-most (L~ ff) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SW-corner (L~ ff) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-bound (L~ ff) is V11() real ext-real Element of REAL
proj2 | (L~ ff) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ ff))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ ff)), REAL ) V205((TOP-REAL 2) | (L~ ff)) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ ff)),REAL))
lower_bound (proj2 | (L~ ff)) is V11() real ext-real Element of REAL
(proj2 | (L~ ff)) .: the U1 of ((TOP-REAL 2) | (L~ ff)) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (L~ ff)) .: the U1 of ((TOP-REAL 2) | (L~ ff))) is V11() real ext-real Element of REAL
|[(W-bound (L~ ff)),(S-bound (L~ ff))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NW-corner (L~ ff) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound (L~ ff) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ ff)) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (L~ ff)) .: the U1 of ((TOP-REAL 2) | (L~ ff))) is V11() real ext-real Element of REAL
|[(W-bound (L~ ff)),(N-bound (L~ ff))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ ff)),(NW-corner (L~ ff))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SW-corner (L~ ff)),(NW-corner (L~ ff)))) /\ (L~ ff) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (W-most (L~ ff)) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (W-most (L~ ff)) is V19() V22( the U1 of ((TOP-REAL 2) | (W-most (L~ ff)))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (W-most (L~ ff))), REAL ) V205((TOP-REAL 2) | (W-most (L~ ff))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (W-most (L~ ff))),REAL))
the U1 of ((TOP-REAL 2) | (W-most (L~ ff))) is set
K7( the U1 of ((TOP-REAL 2) | (W-most (L~ ff))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (W-most (L~ ff))),REAL)) is set
lower_bound (proj2 | (W-most (L~ ff))) is V11() real ext-real Element of REAL
(proj2 | (W-most (L~ ff))) .: the U1 of ((TOP-REAL 2) | (W-most (L~ ff))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (W-most (L~ ff))) .: the U1 of ((TOP-REAL 2) | (W-most (L~ ff)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ ff)),(lower_bound (proj2 | (W-most (L~ ff))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(go ^' pion1) /. 2 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Upper_Seq (C,n)) ^' (Lower_Seq (C,n)) is non empty V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
((Upper_Seq (C,n)) ^' (Lower_Seq (C,n))) /. 2 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) /. 2 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(ff /. 2) `1 is V11() real ext-real Element of REAL
(W-min (L~ ff)) `1 is V11() real ext-real Element of REAL
Rotate (ff,(W-min (L~ ff))) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard FinSequence of the U1 of (TOP-REAL 2)
(Rotate (ff,(W-min (L~ ff)))) /. 2 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Upper_Seq (C,n)) . (len (Upper_Seq (C,n))) is V19() Function-like set
(Upper_Seq (C,n)) /. (len (Upper_Seq (C,n))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
east_halfline (E-max C) is non empty functional connected V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
W is set
p is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(east_halfline (E-max C)) /\ (L~ (Cage (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
p `1 is V11() real ext-real Element of REAL
godo is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like non constant V32() 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 closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
W is set
p is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
p `2 is V11() real ext-real Element of REAL
(E-max C) `2 is V11() real ext-real Element of REAL
p `1 is V11() real ext-real Element of REAL
p `1 is V11() real ext-real Element of REAL
p `1 is V11() real ext-real Element of REAL
p `1 is V11() real ext-real Element of REAL
j + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(j + 1) - 1 is V11() real ext-real Element of REAL
(len (Gauge (C,n))) - 1 is V11() real ext-real Element of REAL
(len (Gauge (C,n))) -' 1 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * (((len (Gauge (C,n))) -' 1),1) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (((len (Gauge (C,n))) -' 1),1)) `1 is V11() real ext-real Element of REAL
(E-max C) `1 is V11() real ext-real Element of REAL
W is set
p is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
Index (p,Emax) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
LSeg (Emax,(Index (p,Emax))) is functional Element of K6( the U1 of (TOP-REAL 2))
t is ordinal natural ext-real non negative set
(Lower_Seq (C,n)) . t is V19() Function-like set
Index (((Gauge (C,n)) * (i,k)),(Lower_Seq (C,n))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Index (((Gauge (C,n)) * (i,k)),(Lower_Seq (C,n)))) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
len (L_Cut ((Lower_Seq (C,n)),((Gauge (C,n)) * (i,k)))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(len (Lower_Seq (C,n))) - (Index (((Gauge (C,n)) * (i,k)),(Lower_Seq (C,n)))) is V11() real ext-real Element of REAL
(len (Lower_Seq (C,n))) -' (Index (((Gauge (C,n)) * (i,k)),(Lower_Seq (C,n)))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Index (p,Emax)) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((len (Lower_Seq (C,n))) -' (Index (((Gauge (C,n)) * (i,k)),(Lower_Seq (C,n))))) - 1 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (i,k)) .. (Lower_Seq (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
mid ((Lower_Seq (C,n)),(((Gauge (C,n)) * (i,k)) .. (Lower_Seq (C,n))),(len (Lower_Seq (C,n)))) is V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
(east_halfline (E-max C)) /\ (L~ (Cage (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
p `1 is V11() real ext-real Element of REAL
0 + (Index (((Gauge (C,n)) * (i,k)),(Lower_Seq (C,n)))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((len (Lower_Seq (C,n))) - (Index (((Gauge (C,n)) * (i,k)),(Lower_Seq (C,n))))) - 1 is V11() real ext-real Element of REAL
(len (Lower_Seq (C,n))) - (((Gauge (C,n)) * (i,k)) .. (Lower_Seq (C,n))) is V11() real ext-real Element of REAL
(len (Lower_Seq (C,n))) -' (((Gauge (C,n)) * (i,k)) .. (Lower_Seq (C,n))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((len (Lower_Seq (C,n))) -' (((Gauge (C,n)) * (i,k)) .. (Lower_Seq (C,n)))) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Index (p,Emax)) + (((Gauge (C,n)) * (i,k)) .. (Lower_Seq (C,n))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((Index (p,Emax)) + (((Gauge (C,n)) * (i,k)) .. (Lower_Seq (C,n)))) -' 1 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
right_cell ((Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))),1) is functional Element of K6( the U1 of (TOP-REAL 2))
GoB (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))) is V19() non empty-yielding V22( NAT ) V23(K295( the U1 of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K295( the U1 of (TOP-REAL 2))
L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
jj2 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * ((len (Gauge (C,n))),jj2) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
[(len (Gauge (C,n))),jj2] is set
{(len (Gauge (C,n))),jj2} is non empty V168() V169() V170() V171() V172() V173() set
{{(len (Gauge (C,n))),jj2},{(len (Gauge (C,n)))}} is non empty set
len (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))) -: (W-min (L~ (Cage (C,n)))) is V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like special unfolded FinSequence of the U1 of (TOP-REAL 2)
LSeg ((Lower_Seq (C,n)),1) is functional Element of K6( the U1 of (TOP-REAL 2))
LSeg ((Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))),1) is functional Element of K6( the U1 of (TOP-REAL 2))
(Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))) /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))) /. (1 + 1) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
ii is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
jj is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
jj + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
[ii,(jj + 1)] is set
{ii,(jj + 1)} is non empty V168() V169() V170() V171() V172() V173() set
{ii} is non empty V168() V169() V170() V171() V172() V173() set
{{ii,(jj + 1)},{ii}} is non empty set
[ii,jj] is set
{ii,jj} is non empty V168() V169() V170() V171() V172() V173() set
{{ii,jj},{ii}} is non empty set
(Gauge (C,n)) * (ii,(jj + 1)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Gauge (C,n)) * (ii,jj) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(jj + 1) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
E-max (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))), REAL ) V205((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),REAL))
the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) is set
K7( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),REAL)) is set
upper_bound (proj1 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) is V11() real ext-real Element of REAL
(proj1 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) is V168() V169() V170() Element of K6(REAL)
upper_bound ((proj1 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SE-corner (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is V11() real ext-real Element of REAL
proj2 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))), REAL ) V205((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),REAL))
lower_bound (proj2 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) is V11() real ext-real Element of REAL
(proj2 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),(S-bound (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NE-corner (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),(N-bound (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),(NE-corner (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SE-corner (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),(NE-corner (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))))) /\ (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) is V19() V22( the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))), REAL ) V205((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))),REAL))
the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) is set
K7( the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))),REAL)) is set
upper_bound (proj2 | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
(proj2 | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) .: the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) is V168() V169() V170() Element of K6(REAL)
upper_bound ((proj2 | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) .: the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),(upper_bound (proj2 | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
4 - 1 is V11() real ext-real Element of REAL
ii - 1 is V11() real ext-real Element of REAL
ii -' 1 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * ((len (Gauge (C,n))),jj) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * ((len (Gauge (C,n))),jj)) `1 is V11() real ext-real Element of REAL
ii + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
cell ((Gauge (C,n)),(ii -' 1),jj) is functional Element of K6( the U1 of (TOP-REAL 2))
(Gauge (C,n)) * ((len (Gauge (C,n))),(jj + 1)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * ((len (Gauge (C,n))),(jj + 1))) `1 is V11() real ext-real Element of REAL
(ii -' 1) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * ((ii -' 1),(jj + 1)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * ((ii -' 1),(jj + 1))) `2 is V11() real ext-real Element of REAL
(Gauge (C,n)) * (1,(jj + 1)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (1,(jj + 1))) `2 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (ii,(jj + 1))) `2 is V11() real ext-real Element of REAL
(E-max C) `2 is V11() real ext-real Element of REAL
p `2 is V11() real ext-real Element of REAL
(Gauge (C,n)) * ((ii -' 1),jj) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * ((ii -' 1),jj)) `2 is V11() real ext-real Element of REAL
(Gauge (C,n)) * (1,jj) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (1,jj)) `2 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (ii,jj)) `2 is V11() real ext-real Element of REAL
LSeg (((Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))) /. 1),((Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))) /. (1 + 1))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
LSeg ((mid ((Lower_Seq (C,n)),(((Gauge (C,n)) * (i,k)) .. (Lower_Seq (C,n))),(len (Lower_Seq (C,n))))),(Index (p,Emax))) is functional Element of K6( the U1 of (TOP-REAL 2))
LSeg ((Lower_Seq (C,n)),(((Index (p,Emax)) + (((Gauge (C,n)) * (i,k)) .. (Lower_Seq (C,n)))) -' 1)) is functional Element of K6( the U1 of (TOP-REAL 2))
(1 + 1) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((1 + 1) + 1) - 1 is V11() real ext-real Element of REAL
((Index (p,Emax)) + (((Gauge (C,n)) * (i,k)) .. (Lower_Seq (C,n)))) - 1 is V11() real ext-real Element of REAL
(LSeg ((Lower_Seq (C,n)),1)) /\ (LSeg ((Lower_Seq (C,n)),(((Index (p,Emax)) + (((Gauge (C,n)) * (i,k)) .. (Lower_Seq (C,n)))) -' 1))) is functional Element of K6( the U1 of (TOP-REAL 2))
(Lower_Seq (C,n)) /. 2 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
{((Lower_Seq (C,n)) /. 2)} is non empty functional set
p .. (Lower_Seq (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * ((len (Gauge (C,n))),k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * ((len (Gauge (C,n))),k)) `1 is V11() real ext-real Element of REAL
(L~ godo) ` is non empty functional Element of K6( the U1 of (TOP-REAL 2))
W is functional Element of K6( the U1 of (TOP-REAL 2))
UBD (L~ godo) is non empty functional open connected Element of K6( the U1 of (TOP-REAL 2))
LeftComp godo is non empty functional Element of K6( the U1 of (TOP-REAL 2))
((Gauge (C,n)) * (j,k)) `1 is V11() real ext-real Element of REAL
{((Gauge (C,n)) * (i,k))} is non empty functional set
((Gauge (C,n)) * (i,k)) `2 is V11() real ext-real Element of REAL
{((Gauge (C,n)) * (i,k))} is non empty functional set
((Gauge (C,n)) * (j,k)) `1 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (i,k)) `2 is V11() real ext-real Element of REAL
n is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
C is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
Gauge (C,n) is V19() non empty-yielding V22( NAT ) V23(K295( the U1 of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K295( the U1 of (TOP-REAL 2))
len (Gauge (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
width (Gauge (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Upper_Seq (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
L~ (Upper_Seq (C,n)) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
Lower_Seq (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
L~ (Lower_Seq (C,n)) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
Lower_Arc C is non empty functional Element of K6( the U1 of (TOP-REAL 2))
i is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
j is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
k is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
k is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * (i,k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Gauge (C,n)) * (i,k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(Gauge (C,n)) * (j,k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
((LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k))))) /\ (L~ (Upper_Seq (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
{((Gauge (C,n)) * (j,k))} is non empty functional set
((LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k))))) /\ (L~ (Lower_Seq (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
{((Gauge (C,n)) * (i,k))} is non empty functional set
[i,k] is set
{i,k} is non empty V168() V169() V170() V171() V172() V173() set
{i} is non empty V168() V169() V170() V171() V172() V173() set
{{i,k},{i}} is non empty set
Indices (Gauge (C,n)) is set
<*((Gauge (C,n)) * (j,k)),((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))*> is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() V39(3) FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
L~ <*((Gauge (C,n)) * (j,k)),((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))*> is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
[(len (Gauge (C,n))),k] is set
{(len (Gauge (C,n))),k} is non empty V168() V169() V170() V171() V172() V173() set
{(len (Gauge (C,n)))} is non empty V168() V169() V170() V171() V172() V173() set
{{(len (Gauge (C,n))),k},{(len (Gauge (C,n)))}} is non empty set
[1,k] is set
{1,k} is non empty V168() V169() V170() V171() V172() V173() set
{{1,k},{1}} is non empty set
[j,k] is set
{j,k} is non empty V168() V169() V170() V171() V172() V173() set
{j} is non empty V168() V169() V170() V171() V172() V173() set
{{j,k},{j}} is non empty set
((Gauge (C,n)) * (i,k)) `2 is V11() real ext-real Element of REAL
(Gauge (C,n)) * (1,k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (1,k)) `2 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (j,k)) `2 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (i,k)) `1 is V11() real ext-real Element of REAL
(Gauge (C,n)) * (i,1) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (i,1)) `1 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (i,k)) `1 is V11() real ext-real Element of REAL
|[(((Gauge (C,n)) * (i,k)) `1),(((Gauge (C,n)) * (j,k)) `2)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
[(len (Gauge (C,n))),k] is set
{(len (Gauge (C,n))),k} is non empty V168() V169() V170() V171() V172() V173() set
{{(len (Gauge (C,n))),k},{(len (Gauge (C,n)))}} is non empty set
Cage (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
L~ (Cage (C,n)) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
W-bound (L~ (Cage (C,n))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (C,n))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ (Cage (C,n))) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))), REAL ) V205((TOP-REAL 2) | (L~ (Cage (C,n)))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL))
the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))) is set
K7( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL)) is set
lower_bound (proj1 | (L~ (Cage (C,n)))) is V11() real ext-real Element of REAL
(proj1 | (L~ (Cage (C,n)))) .: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | (L~ (Cage (C,n)))) .: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n))))) is V11() real ext-real Element of REAL
W-min (L~ (Cage (C,n))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-most (L~ (Cage (C,n))) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SW-corner (L~ (Cage (C,n))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Cage (C,n))) is V11() real ext-real Element of REAL
proj2 | (L~ (Cage (C,n))) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))), REAL ) V205((TOP-REAL 2) | (L~ (Cage (C,n)))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL))
lower_bound (proj2 | (L~ (Cage (C,n)))) is V11() real ext-real Element of REAL
(proj2 | (L~ (Cage (C,n)))) .: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (L~ (Cage (C,n)))) .: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Cage (C,n)))),(S-bound (L~ (Cage (C,n))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NW-corner (L~ (Cage (C,n))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Cage (C,n))) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ (Cage (C,n)))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (L~ (Cage (C,n)))) .: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Cage (C,n)))),(N-bound (L~ (Cage (C,n))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (C,n)))),(NW-corner (L~ (Cage (C,n))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SW-corner (L~ (Cage (C,n)))),(NW-corner (L~ (Cage (C,n)))))) /\ (L~ (Cage (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (W-most (L~ (Cage (C,n)))) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Cage (C,n)))) is V19() V22( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n)))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))), REAL ) V205((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),REAL))
the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))) is set
K7( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),REAL)) is set
lower_bound (proj2 | (W-most (L~ (Cage (C,n))))) is V11() real ext-real Element of REAL
(proj2 | (W-most (L~ (Cage (C,n))))) .: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (W-most (L~ (Cage (C,n))))) .: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n)))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Cage (C,n)))),(lower_bound (proj2 | (W-most (L~ (Cage (C,n))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Cage (C,n))) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ (Cage (C,n)))) is V11() real ext-real Element of REAL
upper_bound ((proj1 | (L~ (Cage (C,n)))) .: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n))))) is V11() real ext-real Element of REAL
E-max (L~ (Cage (C,n))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-most (L~ (Cage (C,n))) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SE-corner (L~ (Cage (C,n))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
|[(E-bound (L~ (Cage (C,n)))),(S-bound (L~ (Cage (C,n))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NE-corner (L~ (Cage (C,n))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
|[(E-bound (L~ (Cage (C,n)))),(N-bound (L~ (Cage (C,n))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Cage (C,n)))),(NE-corner (L~ (Cage (C,n))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SE-corner (L~ (Cage (C,n)))),(NE-corner (L~ (Cage (C,n)))))) /\ (L~ (Cage (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (E-most (L~ (Cage (C,n)))) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Cage (C,n)))) is V19() V22( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n)))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))), REAL ) V205((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),REAL))
the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))) is set
K7( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),REAL)) is set
upper_bound (proj2 | (E-most (L~ (Cage (C,n))))) is V11() real ext-real Element of REAL
(proj2 | (E-most (L~ (Cage (C,n))))) .: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))) is V168() V169() V170() Element of K6(REAL)
upper_bound ((proj2 | (E-most (L~ (Cage (C,n))))) .: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n)))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Cage (C,n)))),(upper_bound (proj2 | (E-most (L~ (Cage (C,n))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
1 + 2 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
len (Lower_Seq (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
dom (Lower_Seq (C,n)) is non trivial V168() V169() V170() V171() V172() V173() Element of K6(NAT)
(Lower_Seq (C,n)) . 1 is V19() Function-like set
(Lower_Seq (C,n)) /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Lower_Seq (C,n)) . (len (Lower_Seq (C,n))) is V19() Function-like set
(Lower_Seq (C,n)) /. (len (Lower_Seq (C,n))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
L_Cut ((Lower_Seq (C,n)),((Gauge (C,n)) * (i,k))) is V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
(W-min (L~ (Cage (C,n)))) `1 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (1,k)) `1 is V11() real ext-real Element of REAL
rng (Lower_Seq (C,n)) is functional Element of K6( the U1 of (TOP-REAL 2))
LA is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
(E-max (L~ (Cage (C,n)))) `1 is V11() real ext-real Element of REAL
(Gauge (C,n)) * ((len (Gauge (C,n))),k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * ((len (Gauge (C,n))),k)) `1 is V11() real ext-real Element of REAL
1 + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
len LA is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Emax is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one non constant V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq s.c.c. FinSequence of the U1 of (TOP-REAL 2)
L~ Emax is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
[1,k] is set
{1,k} is non empty V168() V169() V170() V171() V172() V173() set
{{1,k},{1}} is non empty set
(Gauge (C,n)) * (1,k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (1,k)) `1 is V11() real ext-real Element of REAL
R_Cut ((Upper_Seq (C,n)),((Gauge (C,n)) * (j,k))) is V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
len (Upper_Seq (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
dom (Upper_Seq (C,n)) is non trivial V168() V169() V170() V171() V172() V173() Element of K6(NAT)
(Upper_Seq (C,n)) . 1 is V19() Function-like set
(Upper_Seq (C,n)) /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
[i,k] is set
{i,k} is non empty V168() V169() V170() V171() V172() V173() set
{{i,k},{i}} is non empty set
do is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
dom <*((Gauge (C,n)) * (j,k)),((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))*> is non trivial V168() V169() V170() V171() V172() V173() Element of K6(NAT)
<*((Gauge (C,n)) * (j,k)),((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))*> /. do is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
rng (Upper_Seq (C,n)) is functional Element of K6( the U1 of (TOP-REAL 2))
do is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
len Emax is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
dom Emax is non trivial V168() V169() V170() V171() V172() V173() Element of K6(NAT)
Emax /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
Emax . 1 is V19() Function-like set
LSeg (Emax,1) is functional Element of K6( the U1 of (TOP-REAL 2))
Emax /. (1 + 1) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (C,n)) * (i,k)),(Emax /. (1 + 1))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (Emax,1)) /\ (L~ <*((Gauge (C,n)) * (j,k)),((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))*>) is functional Element of K6( the U1 of (TOP-REAL 2))
go is set
LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
LSeg (((Gauge (C,n)) * (j,k)),((Gauge (C,n)) * (i,k))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,n)) * (j,k)),((Gauge (C,n)) * (i,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
(L~ <*((Gauge (C,n)) * (j,k)),((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))*>) /\ (LSeg (Emax,1)) is functional Element of K6( the U1 of (TOP-REAL 2))
rng Emax is non trivial functional Element of K6( the U1 of (TOP-REAL 2))
len do is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
go is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one non constant V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq s.c.c. FinSequence of the U1 of (TOP-REAL 2)
L~ go is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
len go is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
dom go is non trivial V168() V169() V170() V171() V172() V173() Element of K6(NAT)
go /. (len go) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
go . (len go) is V19() Function-like set
(len go) - 1 is V11() real ext-real Element of REAL
m is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
m + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(len go) -' 1 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
LSeg (go,m) is functional Element of K6( the U1 of (TOP-REAL 2))
go /. m is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((go /. m),((Gauge (C,n)) * (j,k))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (go,m)) /\ (L~ <*((Gauge (C,n)) * (j,k)),((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))*>) is functional Element of K6( the U1 of (TOP-REAL 2))
W2 is set
LSeg (((Gauge (C,n)) * (j,k)),((Gauge (C,n)) * (i,k))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,n)) * (j,k)),((Gauge (C,n)) * (i,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
go /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
rng go is non trivial functional Element of K6( the U1 of (TOP-REAL 2))
(L~ go) /\ (L~ Emax) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
{(go /. 1)} is non empty functional set
W2 is set
(Gauge (C,n)) * ((len (Gauge (C,n))),k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * ((len (Gauge (C,n))),k)) `1 is V11() real ext-real Element of REAL
(L~ (Upper_Seq (C,n))) /\ (L~ (Lower_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
{(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n))))} is non empty functional set
go /. 2 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (j,k)) .. (Upper_Seq (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
mid ((Upper_Seq (C,n)),1,(((Gauge (C,n)) * (j,k)) .. (Upper_Seq (C,n)))) is V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
(Upper_Seq (C,n)) | (((Gauge (C,n)) * (j,k)) .. (Upper_Seq (C,n))) is V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. FinSequence of the U1 of (TOP-REAL 2)
(Upper_Seq (C,n)) /. 2 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
Emax /. (len Emax) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
pion1 is set
((Gauge (C,n)) * (j,k)) `1 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (i,k)) `2 is V11() real ext-real Element of REAL
<*((Gauge (C,n)) * (j,k)),((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))*> /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
len <*((Gauge (C,n)) * (j,k)),((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))*> is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
<*((Gauge (C,n)) * (j,k)),((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))*> /. (len <*((Gauge (C,n)) * (j,k)),((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))*>) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
pion1 is V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
L~ pion1 is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
pion1 /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
len pion1 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
pion1 /. (len pion1) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
pion1 is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() 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 V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
len (go ^' pion1) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(go ^' pion1) /. (len (go ^' pion1)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
<*((Gauge (C,n)) * (j,k)),((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))*> /. 3 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
pion1 /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
L~ pion1 is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(L~ go) /\ (L~ pion1) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
{(pion1 /. 1)} is non empty functional set
godo is set
2 + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
len pion1 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
rng pion1 is functional Element of K6( the U1 of (TOP-REAL 2))
godo is set
pion1 /. (len pion1) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
{(pion1 /. (len pion1))} is non empty functional set
(L~ Emax) /\ (L~ pion1) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
godo is set
godo is set
L~ (go ^' pion1) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(L~ (go ^' pion1)) /\ (L~ Emax) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(L~ go) \/ (L~ pion1) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
((L~ go) \/ (L~ pion1)) /\ (L~ Emax) is functional Element of K6( the U1 of (TOP-REAL 2))
{(Emax /. 1)} is non empty functional set
{(go /. 1)} \/ {(Emax /. 1)} is non empty set
(go ^' pion1) /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
{((go ^' pion1) /. 1)} is non empty functional set
{((go ^' pion1) /. 1)} \/ {(Emax /. 1)} is non empty set
{((go ^' pion1) /. 1),(Emax /. 1)} is non empty functional set
E-max C is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-bound C is V11() real ext-real Element of REAL
(TOP-REAL 2) | C is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | C is V19() V22( the U1 of ((TOP-REAL 2) | C)) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | C), REAL ) V205((TOP-REAL 2) | C) Element of K6(K7( the U1 of ((TOP-REAL 2) | C),REAL))
the U1 of ((TOP-REAL 2) | C) is set
K7( the U1 of ((TOP-REAL 2) | C),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | C),REAL)) is set
upper_bound (proj1 | C) is V11() real ext-real Element of REAL
(proj1 | C) .: the U1 of ((TOP-REAL 2) | C) is V168() V169() V170() Element of K6(REAL)
upper_bound ((proj1 | C) .: the U1 of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
E-most C is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SE-corner C is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-bound C is V11() real ext-real Element of REAL
proj2 | C is V19() V22( the U1 of ((TOP-REAL 2) | C)) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | C), REAL ) V205((TOP-REAL 2) | C) Element of K6(K7( the U1 of ((TOP-REAL 2) | C),REAL))
lower_bound (proj2 | C) is V11() real ext-real Element of REAL
(proj2 | C) .: the U1 of ((TOP-REAL 2) | C) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | C) .: the U1 of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
|[(E-bound C),(S-bound C)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NE-corner C is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound C is V11() real ext-real Element of REAL
upper_bound (proj2 | C) is V11() real ext-real Element of REAL
upper_bound ((proj2 | C) .: the U1 of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
|[(E-bound C),(N-bound C)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner C),(NE-corner C)) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SE-corner C),(NE-corner C))) /\ C is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (E-most C) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (E-most C) is V19() V22( the U1 of ((TOP-REAL 2) | (E-most C))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (E-most C)), REAL ) V205((TOP-REAL 2) | (E-most C)) Element of K6(K7( the U1 of ((TOP-REAL 2) | (E-most C)),REAL))
the U1 of ((TOP-REAL 2) | (E-most C)) is set
K7( the U1 of ((TOP-REAL 2) | (E-most C)),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (E-most C)),REAL)) is set
upper_bound (proj2 | (E-most C)) is V11() real ext-real Element of REAL
(proj2 | (E-most C)) .: the U1 of ((TOP-REAL 2) | (E-most C)) is V168() V169() V170() Element of K6(REAL)
upper_bound ((proj2 | (E-most C)) .: the U1 of ((TOP-REAL 2) | (E-most C))) is V11() real ext-real Element of REAL
|[(E-bound C),(upper_bound (proj2 | (E-most C)))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-min C is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound C is V11() real ext-real Element of REAL
lower_bound (proj1 | C) is V11() real ext-real Element of REAL
lower_bound ((proj1 | C) .: the U1 of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
W-most C is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SW-corner C is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
|[(W-bound C),(S-bound C)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NW-corner C is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
|[(W-bound C),(N-bound C)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner C),(NW-corner C)) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SW-corner C),(NW-corner C))) /\ C is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (W-most C) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (W-most C) is V19() V22( the U1 of ((TOP-REAL 2) | (W-most C))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (W-most C)), REAL ) V205((TOP-REAL 2) | (W-most C)) Element of K6(K7( the U1 of ((TOP-REAL 2) | (W-most C)),REAL))
the U1 of ((TOP-REAL 2) | (W-most C)) is set
K7( the U1 of ((TOP-REAL 2) | (W-most C)),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (W-most C)),REAL)) is set
lower_bound (proj2 | (W-most C)) is V11() real ext-real Element of REAL
(proj2 | (W-most C)) .: the U1 of ((TOP-REAL 2) | (W-most C)) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (W-most C)) .: the U1 of ((TOP-REAL 2) | (W-most C))) is V11() real ext-real Element of REAL
|[(W-bound C),(lower_bound (proj2 | (W-most C)))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(go ^' pion1) ^' Emax is non empty V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
(len pion1) - 1 is V11() real ext-real Element of REAL
(len pion1) -' 1 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
LSeg (pion1,((len pion1) -' 1)) is functional Element of K6( the U1 of (TOP-REAL 2))
(LSeg (pion1,((len pion1) -' 1))) /\ (LSeg (Emax,1)) is functional Element of K6( the U1 of (TOP-REAL 2))
godo is set
((len pion1) -' 1) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
pion1 /. (((len pion1) -' 1) + 1) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((len pion1) - 1) + 1 is V11() real ext-real Element of REAL
(len pion1) - 2 is V11() real ext-real Element of REAL
(len pion1) -' 2 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((len pion1) -' 2) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((len pion1) - 2) + 1 is V11() real ext-real Element of REAL
(len go) + ((len pion1) -' 2) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
LSeg ((go ^' pion1),((len go) + ((len pion1) -' 2))) is functional Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((go ^' pion1),((len go) + ((len pion1) -' 2)))) /\ (LSeg (Emax,1)) is functional Element of K6( the U1 of (TOP-REAL 2))
{((go ^' pion1) /. (len (go ^' pion1)))} is non empty functional set
(rng go) /\ (rng pion1) is functional Element of K6( the U1 of (TOP-REAL 2))
(len (go ^' pion1)) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((len (go ^' pion1)) + 1) - 1 is V11() real ext-real Element of REAL
(len go) + (len pion1) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((len go) + (len pion1)) - 1 is V11() real ext-real Element of REAL
(len (go ^' pion1)) - 1 is V11() real ext-real Element of REAL
(len go) + ((len pion1) - 2) is V11() real ext-real Element of REAL
(len (go ^' pion1)) -' 1 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(L~ (Upper_Seq (C,n))) \/ (L~ (Lower_Seq (C,n))) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
LSeg (pion1,1) is functional Element of K6( the U1 of (TOP-REAL 2))
(LSeg (go,m)) /\ (LSeg (pion1,1)) is functional Element of K6( the U1 of (TOP-REAL 2))
godo is set
LSeg (go,((len go) -' 1)) is functional Element of K6( the U1 of (TOP-REAL 2))
(LSeg (go,((len go) -' 1))) /\ (LSeg (pion1,1)) is functional Element of K6( the U1 of (TOP-REAL 2))
{(go /. (len go))} is non empty functional set
1 + 0 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
len (Cage (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
len ((go ^' pion1) ^' Emax) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
ff is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard FinSequence of the U1 of (TOP-REAL 2)
L~ ff is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
(L~ (go ^' pion1)) \/ (L~ Emax) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
((L~ go) \/ (L~ pion1)) \/ (L~ Emax) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
right_cell (ff,1,(Gauge (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
(right_cell (ff,1,(Gauge (C,n)))) \ (L~ ff) is functional Element of K6( the U1 of (TOP-REAL 2))
RightComp ff is non empty functional Element of K6( the U1 of (TOP-REAL 2))
dom ff is non trivial V168() V169() V170() V171() V172() V173() Element of K6(NAT)
ff /. 2 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
rng ff is non trivial functional Element of K6( the U1 of (TOP-REAL 2))
rng (Cage (C,n)) is non trivial functional Element of K6( the U1 of (TOP-REAL 2))
(Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
W-max (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))), REAL ) V205((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),REAL))
the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is set
K7( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),REAL)) is set
lower_bound (proj1 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is V11() real ext-real Element of REAL
(proj1 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SW-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V11() real ext-real Element of REAL
proj2 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))), REAL ) V205((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),REAL))
lower_bound (proj2 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is V11() real ext-real Element of REAL
(proj2 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),(S-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NW-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),(N-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),(NW-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SW-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),(NW-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))) /\ (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is V19() V22( the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))), REAL ) V205((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))),REAL))
the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is set
K7( the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))),REAL)) is set
upper_bound (proj2 | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
(proj2 | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) .: the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V168() V169() V170() Element of K6(REAL)
upper_bound ((proj2 | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) .: the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),(upper_bound (proj2 | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(W-max (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .. (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
N-min (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
NE-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is V11() real ext-real Element of REAL
upper_bound ((proj1 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),(N-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((NW-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),(NE-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((NW-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),(NE-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))) /\ (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is V19() V22( the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))), REAL ) V205((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))),REAL))
the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is set
K7( the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))),REAL)) is set
lower_bound (proj1 | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
(proj1 | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) .: the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) .: the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))),(N-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(N-min (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .. (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
N-max (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
upper_bound (proj1 | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
upper_bound ((proj1 | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) .: the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))) is V11() real ext-real Element of REAL
|[(upper_bound (proj1 | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))),(N-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(N-max (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .. (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(E-max (L~ (Cage (C,n)))) .. (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
W-bound (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))) is V19() V22( the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))))), REAL ) V205((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))))),REAL))
the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))))) is set
K7( the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))))),REAL)) is set
lower_bound (proj1 | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))))) is V11() real ext-real Element of REAL
(proj1 | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))))) .: the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))))) .: the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))))) is V11() real ext-real Element of REAL
(L~ go) \/ (L~ Emax) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
len (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
right_cell ((Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))),1) is functional Element of K6( the U1 of (TOP-REAL 2))
GoB (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) is V19() non empty-yielding V22( NAT ) V23(K295( the U1 of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K295( the U1 of (TOP-REAL 2))
right_cell ((Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))),1,(GoB (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is functional Element of K6( the U1 of (TOP-REAL 2))
GoB (Cage (C,n)) is V19() non empty-yielding V22( NAT ) V23(K295( the U1 of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K295( the U1 of (TOP-REAL 2))
right_cell ((Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))),1,(GoB (Cage (C,n)))) is functional Element of K6( the U1 of (TOP-REAL 2))
right_cell ((Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))),1,(Gauge (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
(Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) -: (E-max (L~ (Cage (C,n)))) is V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like special unfolded FinSequence of the U1 of (TOP-REAL 2)
right_cell (((Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) -: (E-max (L~ (Cage (C,n))))),1,(Gauge (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
right_cell ((Upper_Seq (C,n)),1,(Gauge (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
right_cell ((R_Cut ((Upper_Seq (C,n)),((Gauge (C,n)) * (j,k)))),1,(Gauge (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
right_cell ((go ^' pion1),1,(Gauge (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
ff /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) is V19() V22( the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k))))), REAL ) V205((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k))))),REAL))
the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k))))) is set
K7( the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k))))),REAL)) is set
lower_bound (proj1 | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k))))) is V11() real ext-real Element of REAL
(proj1 | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k))))) .: the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k))))) .: the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))))) is V11() real ext-real Element of REAL
W-bound ((LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))))) is strict T_2 SubSpace of TOP-REAL 2
proj1 | ((LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))))) is V19() V22( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))))), REAL ) V205((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))))),REAL))
the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))))) is set
K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))))),REAL)) is set
lower_bound (proj1 | ((LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))))) is V11() real ext-real Element of REAL
(proj1 | ((LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | ((LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))))))) is V11() real ext-real Element of REAL
min ((W-bound (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k))))),(W-bound (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))))) is ext-real set
W-bound (L~ pion1) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ pion1) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ pion1) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ pion1))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ pion1)), REAL ) V205((TOP-REAL 2) | (L~ pion1)) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ pion1)),REAL))
the U1 of ((TOP-REAL 2) | (L~ pion1)) is set
K7( the U1 of ((TOP-REAL 2) | (L~ pion1)),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (L~ pion1)),REAL)) is set
lower_bound (proj1 | (L~ pion1)) is V11() real ext-real Element of REAL
(proj1 | (L~ pion1)) .: the U1 of ((TOP-REAL 2) | (L~ pion1)) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | (L~ pion1)) .: the U1 of ((TOP-REAL 2) | (L~ pion1))) is V11() real ext-real Element of REAL
W-min ((L~ go) \/ (L~ Emax)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound ((L~ go) \/ (L~ Emax)) is V11() real ext-real Element of REAL
(TOP-REAL 2) | ((L~ go) \/ (L~ Emax)) is strict T_2 SubSpace of TOP-REAL 2
proj1 | ((L~ go) \/ (L~ Emax)) is V19() V22( the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ Emax)))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ Emax))), REAL ) V205((TOP-REAL 2) | ((L~ go) \/ (L~ Emax))) Element of K6(K7( the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ Emax))),REAL))
the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ Emax))) is set
K7( the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ Emax))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ Emax))),REAL)) is set
lower_bound (proj1 | ((L~ go) \/ (L~ Emax))) is V11() real ext-real Element of REAL
(proj1 | ((L~ go) \/ (L~ Emax))) .: the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ Emax))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | ((L~ go) \/ (L~ Emax))) .: the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ Emax)))) is V11() real ext-real Element of REAL
W-most ((L~ go) \/ (L~ Emax)) is functional Element of K6( the U1 of (TOP-REAL 2))
SW-corner ((L~ go) \/ (L~ Emax)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-bound ((L~ go) \/ (L~ Emax)) is V11() real ext-real Element of REAL
proj2 | ((L~ go) \/ (L~ Emax)) is V19() V22( the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ Emax)))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ Emax))), REAL ) V205((TOP-REAL 2) | ((L~ go) \/ (L~ Emax))) Element of K6(K7( the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ Emax))),REAL))
lower_bound (proj2 | ((L~ go) \/ (L~ Emax))) is V11() real ext-real Element of REAL
(proj2 | ((L~ go) \/ (L~ Emax))) .: the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ Emax))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | ((L~ go) \/ (L~ Emax))) .: the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ Emax)))) is V11() real ext-real Element of REAL
|[(W-bound ((L~ go) \/ (L~ Emax))),(S-bound ((L~ go) \/ (L~ Emax)))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NW-corner ((L~ go) \/ (L~ Emax)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound ((L~ go) \/ (L~ Emax)) is V11() real ext-real Element of REAL
upper_bound (proj2 | ((L~ go) \/ (L~ Emax))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | ((L~ go) \/ (L~ Emax))) .: the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ Emax)))) is V11() real ext-real Element of REAL
|[(W-bound ((L~ go) \/ (L~ Emax))),(N-bound ((L~ go) \/ (L~ Emax)))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner ((L~ go) \/ (L~ Emax))),(NW-corner ((L~ go) \/ (L~ Emax)))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SW-corner ((L~ go) \/ (L~ Emax))),(NW-corner ((L~ go) \/ (L~ Emax))))) /\ ((L~ go) \/ (L~ Emax)) is functional Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (W-most ((L~ go) \/ (L~ Emax))) is strict T_2 SubSpace of TOP-REAL 2
proj2 | (W-most ((L~ go) \/ (L~ Emax))) is V19() V22( the U1 of ((TOP-REAL 2) | (W-most ((L~ go) \/ (L~ Emax))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (W-most ((L~ go) \/ (L~ Emax)))), REAL ) V205((TOP-REAL 2) | (W-most ((L~ go) \/ (L~ Emax)))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (W-most ((L~ go) \/ (L~ Emax)))),REAL))
the U1 of ((TOP-REAL 2) | (W-most ((L~ go) \/ (L~ Emax)))) is set
K7( the U1 of ((TOP-REAL 2) | (W-most ((L~ go) \/ (L~ Emax)))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (W-most ((L~ go) \/ (L~ Emax)))),REAL)) is set
lower_bound (proj2 | (W-most ((L~ go) \/ (L~ Emax)))) is V11() real ext-real Element of REAL
(proj2 | (W-most ((L~ go) \/ (L~ Emax)))) .: the U1 of ((TOP-REAL 2) | (W-most ((L~ go) \/ (L~ Emax)))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (W-most ((L~ go) \/ (L~ Emax)))) .: the U1 of ((TOP-REAL 2) | (W-most ((L~ go) \/ (L~ Emax))))) is V11() real ext-real Element of REAL
|[(W-bound ((L~ go) \/ (L~ Emax))),(lower_bound (proj2 | (W-most ((L~ go) \/ (L~ Emax)))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(W-min ((L~ go) \/ (L~ Emax))) `1 is V11() real ext-real Element of REAL
((L~ go) \/ (L~ Emax)) \/ (L~ pion1) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
W-min (((L~ go) \/ (L~ Emax)) \/ (L~ pion1)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound (((L~ go) \/ (L~ Emax)) \/ (L~ pion1)) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (((L~ go) \/ (L~ Emax)) \/ (L~ pion1)) is strict T_2 SubSpace of TOP-REAL 2
proj1 | (((L~ go) \/ (L~ Emax)) \/ (L~ pion1)) is V19() V22( the U1 of ((TOP-REAL 2) | (((L~ go) \/ (L~ Emax)) \/ (L~ pion1)))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (((L~ go) \/ (L~ Emax)) \/ (L~ pion1))), REAL ) V205((TOP-REAL 2) | (((L~ go) \/ (L~ Emax)) \/ (L~ pion1))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (((L~ go) \/ (L~ Emax)) \/ (L~ pion1))),REAL))
the U1 of ((TOP-REAL 2) | (((L~ go) \/ (L~ Emax)) \/ (L~ pion1))) is set
K7( the U1 of ((TOP-REAL 2) | (((L~ go) \/ (L~ Emax)) \/ (L~ pion1))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (((L~ go) \/ (L~ Emax)) \/ (L~ pion1))),REAL)) is set
lower_bound (proj1 | (((L~ go) \/ (L~ Emax)) \/ (L~ pion1))) is V11() real ext-real Element of REAL
(proj1 | (((L~ go) \/ (L~ Emax)) \/ (L~ pion1))) .: the U1 of ((TOP-REAL 2) | (((L~ go) \/ (L~ Emax)) \/ (L~ pion1))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | (((L~ go) \/ (L~ Emax)) \/ (L~ pion1))) .: the U1 of ((TOP-REAL 2) | (((L~ go) \/ (L~ Emax)) \/ (L~ pion1)))) is V11() real ext-real Element of REAL
W-most (((L~ go) \/ (L~ Emax)) \/ (L~ pion1)) is functional Element of K6( the U1 of (TOP-REAL 2))
SW-corner (((L~ go) \/ (L~ Emax)) \/ (L~ pion1)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-bound (((L~ go) \/ (L~ Emax)) \/ (L~ pion1)) is V11() real ext-real Element of REAL
proj2 | (((L~ go) \/ (L~ Emax)) \/ (L~ pion1)) is V19() V22( the U1 of ((TOP-REAL 2) | (((L~ go) \/ (L~ Emax)) \/ (L~ pion1)))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (((L~ go) \/ (L~ Emax)) \/ (L~ pion1))), REAL ) V205((TOP-REAL 2) | (((L~ go) \/ (L~ Emax)) \/ (L~ pion1))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (((L~ go) \/ (L~ Emax)) \/ (L~ pion1))),REAL))
lower_bound (proj2 | (((L~ go) \/ (L~ Emax)) \/ (L~ pion1))) is V11() real ext-real Element of REAL
(proj2 | (((L~ go) \/ (L~ Emax)) \/ (L~ pion1))) .: the U1 of ((TOP-REAL 2) | (((L~ go) \/ (L~ Emax)) \/ (L~ pion1))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (((L~ go) \/ (L~ Emax)) \/ (L~ pion1))) .: the U1 of ((TOP-REAL 2) | (((L~ go) \/ (L~ Emax)) \/ (L~ pion1)))) is V11() real ext-real Element of REAL
|[(W-bound (((L~ go) \/ (L~ Emax)) \/ (L~ pion1))),(S-bound (((L~ go) \/ (L~ Emax)) \/ (L~ pion1)))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NW-corner (((L~ go) \/ (L~ Emax)) \/ (L~ pion1)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound (((L~ go) \/ (L~ Emax)) \/ (L~ pion1)) is V11() real ext-real Element of REAL
upper_bound (proj2 | (((L~ go) \/ (L~ Emax)) \/ (L~ pion1))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (((L~ go) \/ (L~ Emax)) \/ (L~ pion1))) .: the U1 of ((TOP-REAL 2) | (((L~ go) \/ (L~ Emax)) \/ (L~ pion1)))) is V11() real ext-real Element of REAL
|[(W-bound (((L~ go) \/ (L~ Emax)) \/ (L~ pion1))),(N-bound (((L~ go) \/ (L~ Emax)) \/ (L~ pion1)))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (((L~ go) \/ (L~ Emax)) \/ (L~ pion1))),(NW-corner (((L~ go) \/ (L~ Emax)) \/ (L~ pion1)))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SW-corner (((L~ go) \/ (L~ Emax)) \/ (L~ pion1))),(NW-corner (((L~ go) \/ (L~ Emax)) \/ (L~ pion1))))) /\ (((L~ go) \/ (L~ Emax)) \/ (L~ pion1)) is functional Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (W-most (((L~ go) \/ (L~ Emax)) \/ (L~ pion1))) is strict T_2 SubSpace of TOP-REAL 2
proj2 | (W-most (((L~ go) \/ (L~ Emax)) \/ (L~ pion1))) is V19() V22( the U1 of ((TOP-REAL 2) | (W-most (((L~ go) \/ (L~ Emax)) \/ (L~ pion1))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (W-most (((L~ go) \/ (L~ Emax)) \/ (L~ pion1)))), REAL ) V205((TOP-REAL 2) | (W-most (((L~ go) \/ (L~ Emax)) \/ (L~ pion1)))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (W-most (((L~ go) \/ (L~ Emax)) \/ (L~ pion1)))),REAL))
the U1 of ((TOP-REAL 2) | (W-most (((L~ go) \/ (L~ Emax)) \/ (L~ pion1)))) is set
K7( the U1 of ((TOP-REAL 2) | (W-most (((L~ go) \/ (L~ Emax)) \/ (L~ pion1)))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (W-most (((L~ go) \/ (L~ Emax)) \/ (L~ pion1)))),REAL)) is set
lower_bound (proj2 | (W-most (((L~ go) \/ (L~ Emax)) \/ (L~ pion1)))) is V11() real ext-real Element of REAL
(proj2 | (W-most (((L~ go) \/ (L~ Emax)) \/ (L~ pion1)))) .: the U1 of ((TOP-REAL 2) | (W-most (((L~ go) \/ (L~ Emax)) \/ (L~ pion1)))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (W-most (((L~ go) \/ (L~ Emax)) \/ (L~ pion1)))) .: the U1 of ((TOP-REAL 2) | (W-most (((L~ go) \/ (L~ Emax)) \/ (L~ pion1))))) is V11() real ext-real Element of REAL
|[(W-bound (((L~ go) \/ (L~ Emax)) \/ (L~ pion1))),(lower_bound (proj2 | (W-most (((L~ go) \/ (L~ Emax)) \/ (L~ pion1)))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-min (L~ ff) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound (L~ ff) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ ff) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ ff) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ ff))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ ff)), REAL ) V205((TOP-REAL 2) | (L~ ff)) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ ff)),REAL))
the U1 of ((TOP-REAL 2) | (L~ ff)) is set
K7( the U1 of ((TOP-REAL 2) | (L~ ff)),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (L~ ff)),REAL)) is set
lower_bound (proj1 | (L~ ff)) is V11() real ext-real Element of REAL
(proj1 | (L~ ff)) .: the U1 of ((TOP-REAL 2) | (L~ ff)) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | (L~ ff)) .: the U1 of ((TOP-REAL 2) | (L~ ff))) is V11() real ext-real Element of REAL
W-most (L~ ff) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SW-corner (L~ ff) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-bound (L~ ff) is V11() real ext-real Element of REAL
proj2 | (L~ ff) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ ff))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ ff)), REAL ) V205((TOP-REAL 2) | (L~ ff)) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ ff)),REAL))
lower_bound (proj2 | (L~ ff)) is V11() real ext-real Element of REAL
(proj2 | (L~ ff)) .: the U1 of ((TOP-REAL 2) | (L~ ff)) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (L~ ff)) .: the U1 of ((TOP-REAL 2) | (L~ ff))) is V11() real ext-real Element of REAL
|[(W-bound (L~ ff)),(S-bound (L~ ff))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NW-corner (L~ ff) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound (L~ ff) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ ff)) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (L~ ff)) .: the U1 of ((TOP-REAL 2) | (L~ ff))) is V11() real ext-real Element of REAL
|[(W-bound (L~ ff)),(N-bound (L~ ff))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ ff)),(NW-corner (L~ ff))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SW-corner (L~ ff)),(NW-corner (L~ ff)))) /\ (L~ ff) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (W-most (L~ ff)) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (W-most (L~ ff)) is V19() V22( the U1 of ((TOP-REAL 2) | (W-most (L~ ff)))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (W-most (L~ ff))), REAL ) V205((TOP-REAL 2) | (W-most (L~ ff))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (W-most (L~ ff))),REAL))
the U1 of ((TOP-REAL 2) | (W-most (L~ ff))) is set
K7( the U1 of ((TOP-REAL 2) | (W-most (L~ ff))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (W-most (L~ ff))),REAL)) is set
lower_bound (proj2 | (W-most (L~ ff))) is V11() real ext-real Element of REAL
(proj2 | (W-most (L~ ff))) .: the U1 of ((TOP-REAL 2) | (W-most (L~ ff))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (W-most (L~ ff))) .: the U1 of ((TOP-REAL 2) | (W-most (L~ ff)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ ff)),(lower_bound (proj2 | (W-most (L~ ff))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(go ^' pion1) /. 2 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Upper_Seq (C,n)) ^' (Lower_Seq (C,n)) is non empty V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
((Upper_Seq (C,n)) ^' (Lower_Seq (C,n))) /. 2 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) /. 2 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(ff /. 2) `1 is V11() real ext-real Element of REAL
(W-min (L~ ff)) `1 is V11() real ext-real Element of REAL
Rotate (ff,(W-min (L~ ff))) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard FinSequence of the U1 of (TOP-REAL 2)
(Rotate (ff,(W-min (L~ ff)))) /. 2 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Upper_Seq (C,n)) . (len (Upper_Seq (C,n))) is V19() Function-like set
(Upper_Seq (C,n)) /. (len (Upper_Seq (C,n))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
east_halfline (E-max C) is non empty functional connected V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
W is set
p is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(east_halfline (E-max C)) /\ (L~ (Cage (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
p `1 is V11() real ext-real Element of REAL
godo is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like non constant V32() 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 closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
W is set
p is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
p `2 is V11() real ext-real Element of REAL
(E-max C) `2 is V11() real ext-real Element of REAL
p `1 is V11() real ext-real Element of REAL
p `1 is V11() real ext-real Element of REAL
p `1 is V11() real ext-real Element of REAL
p `1 is V11() real ext-real Element of REAL
j + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(j + 1) - 1 is V11() real ext-real Element of REAL
(len (Gauge (C,n))) - 1 is V11() real ext-real Element of REAL
(len (Gauge (C,n))) -' 1 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * (((len (Gauge (C,n))) -' 1),1) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (((len (Gauge (C,n))) -' 1),1)) `1 is V11() real ext-real Element of REAL
(E-max C) `1 is V11() real ext-real Element of REAL
W is set
p is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
Index (p,Emax) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
LSeg (Emax,(Index (p,Emax))) is functional Element of K6( the U1 of (TOP-REAL 2))
t is ordinal natural ext-real non negative set
(Lower_Seq (C,n)) . t is V19() Function-like set
Index (((Gauge (C,n)) * (i,k)),(Lower_Seq (C,n))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Index (((Gauge (C,n)) * (i,k)),(Lower_Seq (C,n)))) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
len (L_Cut ((Lower_Seq (C,n)),((Gauge (C,n)) * (i,k)))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(len (Lower_Seq (C,n))) - (Index (((Gauge (C,n)) * (i,k)),(Lower_Seq (C,n)))) is V11() real ext-real Element of REAL
(len (Lower_Seq (C,n))) -' (Index (((Gauge (C,n)) * (i,k)),(Lower_Seq (C,n)))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Index (p,Emax)) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((len (Lower_Seq (C,n))) -' (Index (((Gauge (C,n)) * (i,k)),(Lower_Seq (C,n))))) - 1 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (i,k)) .. (Lower_Seq (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
mid ((Lower_Seq (C,n)),(((Gauge (C,n)) * (i,k)) .. (Lower_Seq (C,n))),(len (Lower_Seq (C,n)))) is V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
(east_halfline (E-max C)) /\ (L~ (Cage (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
p `1 is V11() real ext-real Element of REAL
0 + (Index (((Gauge (C,n)) * (i,k)),(Lower_Seq (C,n)))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((len (Lower_Seq (C,n))) - (Index (((Gauge (C,n)) * (i,k)),(Lower_Seq (C,n))))) - 1 is V11() real ext-real Element of REAL
(len (Lower_Seq (C,n))) - (((Gauge (C,n)) * (i,k)) .. (Lower_Seq (C,n))) is V11() real ext-real Element of REAL
(len (Lower_Seq (C,n))) -' (((Gauge (C,n)) * (i,k)) .. (Lower_Seq (C,n))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((len (Lower_Seq (C,n))) -' (((Gauge (C,n)) * (i,k)) .. (Lower_Seq (C,n)))) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Index (p,Emax)) + (((Gauge (C,n)) * (i,k)) .. (Lower_Seq (C,n))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((Index (p,Emax)) + (((Gauge (C,n)) * (i,k)) .. (Lower_Seq (C,n)))) -' 1 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
right_cell ((Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))),1) is functional Element of K6( the U1 of (TOP-REAL 2))
GoB (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))) is V19() non empty-yielding V22( NAT ) V23(K295( the U1 of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K295( the U1 of (TOP-REAL 2))
L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
jj2 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * ((len (Gauge (C,n))),jj2) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
[(len (Gauge (C,n))),jj2] is set
{(len (Gauge (C,n))),jj2} is non empty V168() V169() V170() V171() V172() V173() set
{{(len (Gauge (C,n))),jj2},{(len (Gauge (C,n)))}} is non empty set
len (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))) -: (W-min (L~ (Cage (C,n)))) is V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like special unfolded FinSequence of the U1 of (TOP-REAL 2)
LSeg ((Lower_Seq (C,n)),1) is functional Element of K6( the U1 of (TOP-REAL 2))
LSeg ((Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))),1) is functional Element of K6( the U1 of (TOP-REAL 2))
(Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))) /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))) /. (1 + 1) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
ii is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
jj is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
jj + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
[ii,(jj + 1)] is set
{ii,(jj + 1)} is non empty V168() V169() V170() V171() V172() V173() set
{ii} is non empty V168() V169() V170() V171() V172() V173() set
{{ii,(jj + 1)},{ii}} is non empty set
[ii,jj] is set
{ii,jj} is non empty V168() V169() V170() V171() V172() V173() set
{{ii,jj},{ii}} is non empty set
(Gauge (C,n)) * (ii,(jj + 1)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Gauge (C,n)) * (ii,jj) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(jj + 1) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
E-max (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))), REAL ) V205((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),REAL))
the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) is set
K7( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),REAL)) is set
upper_bound (proj1 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) is V11() real ext-real Element of REAL
(proj1 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) is V168() V169() V170() Element of K6(REAL)
upper_bound ((proj1 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SE-corner (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is V11() real ext-real Element of REAL
proj2 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))), REAL ) V205((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),REAL))
lower_bound (proj2 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) is V11() real ext-real Element of REAL
(proj2 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),(S-bound (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NE-corner (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),(N-bound (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),(NE-corner (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SE-corner (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),(NE-corner (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))))) /\ (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) is V19() V22( the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))), REAL ) V205((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))),REAL))
the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) is set
K7( the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))),REAL)) is set
upper_bound (proj2 | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
(proj2 | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) .: the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) is V168() V169() V170() Element of K6(REAL)
upper_bound ((proj2 | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) .: the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),(upper_bound (proj2 | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
4 - 1 is V11() real ext-real Element of REAL
ii - 1 is V11() real ext-real Element of REAL
ii -' 1 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * ((len (Gauge (C,n))),jj) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * ((len (Gauge (C,n))),jj)) `1 is V11() real ext-real Element of REAL
ii + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
cell ((Gauge (C,n)),(ii -' 1),jj) is functional Element of K6( the U1 of (TOP-REAL 2))
(Gauge (C,n)) * ((len (Gauge (C,n))),(jj + 1)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * ((len (Gauge (C,n))),(jj + 1))) `1 is V11() real ext-real Element of REAL
(ii -' 1) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * ((ii -' 1),(jj + 1)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * ((ii -' 1),(jj + 1))) `2 is V11() real ext-real Element of REAL
(Gauge (C,n)) * (1,(jj + 1)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (1,(jj + 1))) `2 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (ii,(jj + 1))) `2 is V11() real ext-real Element of REAL
(E-max C) `2 is V11() real ext-real Element of REAL
p `2 is V11() real ext-real Element of REAL
(Gauge (C,n)) * ((ii -' 1),jj) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * ((ii -' 1),jj)) `2 is V11() real ext-real Element of REAL
(Gauge (C,n)) * (1,jj) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (1,jj)) `2 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (ii,jj)) `2 is V11() real ext-real Element of REAL
LSeg (((Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))) /. 1),((Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))) /. (1 + 1))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
LSeg ((mid ((Lower_Seq (C,n)),(((Gauge (C,n)) * (i,k)) .. (Lower_Seq (C,n))),(len (Lower_Seq (C,n))))),(Index (p,Emax))) is functional Element of K6( the U1 of (TOP-REAL 2))
LSeg ((Lower_Seq (C,n)),(((Index (p,Emax)) + (((Gauge (C,n)) * (i,k)) .. (Lower_Seq (C,n)))) -' 1)) is functional Element of K6( the U1 of (TOP-REAL 2))
(1 + 1) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((1 + 1) + 1) - 1 is V11() real ext-real Element of REAL
((Index (p,Emax)) + (((Gauge (C,n)) * (i,k)) .. (Lower_Seq (C,n)))) - 1 is V11() real ext-real Element of REAL
(LSeg ((Lower_Seq (C,n)),1)) /\ (LSeg ((Lower_Seq (C,n)),(((Index (p,Emax)) + (((Gauge (C,n)) * (i,k)) .. (Lower_Seq (C,n)))) -' 1))) is functional Element of K6( the U1 of (TOP-REAL 2))
(Lower_Seq (C,n)) /. 2 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
{((Lower_Seq (C,n)) /. 2)} is non empty functional set
p .. (Lower_Seq (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * ((len (Gauge (C,n))),k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * ((len (Gauge (C,n))),k)) `1 is V11() real ext-real Element of REAL
(L~ godo) ` is non empty functional Element of K6( the U1 of (TOP-REAL 2))
W is functional Element of K6( the U1 of (TOP-REAL 2))
UBD (L~ godo) is non empty functional open connected Element of K6( the U1 of (TOP-REAL 2))
LeftComp godo is non empty functional Element of K6( the U1 of (TOP-REAL 2))
((Gauge (C,n)) * (j,k)) `1 is V11() real ext-real Element of REAL
{((Gauge (C,n)) * (i,k))} is non empty functional set
((Gauge (C,n)) * (i,k)) `2 is V11() real ext-real Element of REAL
{((Gauge (C,n)) * (i,k))} is non empty functional set
((Gauge (C,n)) * (j,k)) `1 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (i,k)) `2 is V11() real ext-real Element of REAL
n is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
C is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
Gauge (C,n) is V19() non empty-yielding V22( NAT ) V23(K295( the U1 of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K295( the U1 of (TOP-REAL 2))
len (Gauge (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
width (Gauge (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Upper_Seq (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
L~ (Upper_Seq (C,n)) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
Lower_Seq (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
L~ (Lower_Seq (C,n)) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
Upper_Arc C is non empty functional Element of K6( the U1 of (TOP-REAL 2))
j is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
i is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
k is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
k is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * (i,k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Gauge (C,n)) * (i,k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(Gauge (C,n)) * (j,k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
((LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k))))) /\ (L~ (Upper_Seq (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
{((Gauge (C,n)) * (j,k))} is non empty functional set
((LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k))))) /\ (L~ (Lower_Seq (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
{((Gauge (C,n)) * (i,k))} is non empty functional set
[j,k] is set
{j,k} is non empty V168() V169() V170() V171() V172() V173() set
{j} is non empty V168() V169() V170() V171() V172() V173() set
{{j,k},{j}} is non empty set
Indices (Gauge (C,n)) is set
Cage (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
L~ (Cage (C,n)) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
W-min (L~ (Cage (C,n))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound (L~ (Cage (C,n))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (C,n))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ (Cage (C,n))) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))), REAL ) V205((TOP-REAL 2) | (L~ (Cage (C,n)))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL))
the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))) is set
K7( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL)) is set
lower_bound (proj1 | (L~ (Cage (C,n)))) is V11() real ext-real Element of REAL
(proj1 | (L~ (Cage (C,n)))) .: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | (L~ (Cage (C,n)))) .: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n))))) is V11() real ext-real Element of REAL
W-most (L~ (Cage (C,n))) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SW-corner (L~ (Cage (C,n))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Cage (C,n))) is V11() real ext-real Element of REAL
proj2 | (L~ (Cage (C,n))) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))), REAL ) V205((TOP-REAL 2) | (L~ (Cage (C,n)))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL))
lower_bound (proj2 | (L~ (Cage (C,n)))) is V11() real ext-real Element of REAL
(proj2 | (L~ (Cage (C,n)))) .: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (L~ (Cage (C,n)))) .: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Cage (C,n)))),(S-bound (L~ (Cage (C,n))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NW-corner (L~ (Cage (C,n))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Cage (C,n))) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ (Cage (C,n)))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (L~ (Cage (C,n)))) .: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Cage (C,n)))),(N-bound (L~ (Cage (C,n))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (C,n)))),(NW-corner (L~ (Cage (C,n))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SW-corner (L~ (Cage (C,n)))),(NW-corner (L~ (Cage (C,n)))))) /\ (L~ (Cage (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (W-most (L~ (Cage (C,n)))) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Cage (C,n)))) is V19() V22( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n)))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))), REAL ) V205((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),REAL))
the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))) is set
K7( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),REAL)) is set
lower_bound (proj2 | (W-most (L~ (Cage (C,n))))) is V11() real ext-real Element of REAL
(proj2 | (W-most (L~ (Cage (C,n))))) .: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (W-most (L~ (Cage (C,n))))) .: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n)))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Cage (C,n)))),(lower_bound (proj2 | (W-most (L~ (Cage (C,n))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
R_Cut ((Upper_Seq (C,n)),((Gauge (C,n)) * (j,k))) is V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
len (Upper_Seq (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
dom (Upper_Seq (C,n)) is non trivial V168() V169() V170() V171() V172() V173() Element of K6(NAT)
(Upper_Seq (C,n)) . 1 is V19() Function-like set
(Upper_Seq (C,n)) /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
L_Cut ((Lower_Seq (C,n)),((Gauge (C,n)) * (i,k))) is V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (i,k)) `2 is V11() real ext-real Element of REAL
(Gauge (C,n)) * (1,k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (1,k)) `2 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (j,k)) `2 is V11() real ext-real Element of REAL
[i,k] is set
{i,k} is non empty V168() V169() V170() V171() V172() V173() set
{i} is non empty V168() V169() V170() V171() V172() V173() set
{{i,k},{i}} is non empty set
[(len (Gauge (C,n))),k] is set
{(len (Gauge (C,n))),k} is non empty V168() V169() V170() V171() V172() V173() set
{(len (Gauge (C,n)))} is non empty V168() V169() V170() V171() V172() V173() set
{{(len (Gauge (C,n))),k},{(len (Gauge (C,n)))}} is non empty set
[1,k] is set
{1,k} is non empty V168() V169() V170() V171() V172() V173() set
{{1,k},{1}} is non empty set
((Gauge (C,n)) * (j,k)) `1 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (1,k)) `1 is V11() real ext-real Element of REAL
<*((Gauge (C,n)) * (j,k)),((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))*> is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() V39(3) FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
[i,k] is set
{i,k} is non empty V168() V169() V170() V171() V172() V173() set
{{i,k},{i}} is non empty set
Emax is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
dom <*((Gauge (C,n)) * (j,k)),((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))*> is non trivial V168() V169() V170() V171() V172() V173() Element of K6(NAT)
<*((Gauge (C,n)) * (j,k)),((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))*> /. Emax is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-max (L~ (Cage (C,n))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Cage (C,n))) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ (Cage (C,n)))) is V11() real ext-real Element of REAL
upper_bound ((proj1 | (L~ (Cage (C,n)))) .: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n))))) is V11() real ext-real Element of REAL
E-most (L~ (Cage (C,n))) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SE-corner (L~ (Cage (C,n))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
|[(E-bound (L~ (Cage (C,n)))),(S-bound (L~ (Cage (C,n))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NE-corner (L~ (Cage (C,n))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
|[(E-bound (L~ (Cage (C,n)))),(N-bound (L~ (Cage (C,n))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Cage (C,n)))),(NE-corner (L~ (Cage (C,n))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SE-corner (L~ (Cage (C,n)))),(NE-corner (L~ (Cage (C,n)))))) /\ (L~ (Cage (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (E-most (L~ (Cage (C,n)))) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Cage (C,n)))) is V19() V22( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n)))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))), REAL ) V205((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),REAL))
the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))) is set
K7( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),REAL)) is set
upper_bound (proj2 | (E-most (L~ (Cage (C,n))))) is V11() real ext-real Element of REAL
(proj2 | (E-most (L~ (Cage (C,n))))) .: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))) is V168() V169() V170() Element of K6(REAL)
upper_bound ((proj2 | (E-most (L~ (Cage (C,n))))) .: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n)))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Cage (C,n)))),(upper_bound (proj2 | (E-most (L~ (Cage (C,n))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
1 + 2 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
len (Lower_Seq (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
dom (Lower_Seq (C,n)) is non trivial V168() V169() V170() V171() V172() V173() Element of K6(NAT)
(Lower_Seq (C,n)) . 1 is V19() Function-like set
(Lower_Seq (C,n)) /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Lower_Seq (C,n)) . (len (Lower_Seq (C,n))) is V19() Function-like set
(Lower_Seq (C,n)) /. (len (Lower_Seq (C,n))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
L~ <*((Gauge (C,n)) * (j,k)),((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))*> is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
(W-min (L~ (Cage (C,n)))) `1 is V11() real ext-real Element of REAL
rng (Upper_Seq (C,n)) is functional Element of K6( the U1 of (TOP-REAL 2))
go is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (i,k)) `1 is V11() real ext-real Element of REAL
(Gauge (C,n)) * (i,1) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (i,1)) `1 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (i,k)) `1 is V11() real ext-real Element of REAL
|[(((Gauge (C,n)) * (i,k)) `1),(((Gauge (C,n)) * (j,k)) `2)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
[(len (Gauge (C,n))),k] is set
{(len (Gauge (C,n))),k} is non empty V168() V169() V170() V171() V172() V173() set
{{(len (Gauge (C,n))),k},{(len (Gauge (C,n)))}} is non empty set
1 + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
len go is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
rng (Lower_Seq (C,n)) is functional Element of K6( the U1 of (TOP-REAL 2))
do is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
(E-max (L~ (Cage (C,n)))) `1 is V11() real ext-real Element of REAL
(Gauge (C,n)) * ((len (Gauge (C,n))),k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * ((len (Gauge (C,n))),k)) `1 is V11() real ext-real Element of REAL
len do is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
do is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one non constant V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq s.c.c. FinSequence of the U1 of (TOP-REAL 2)
L~ do is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
len do is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
dom do is non trivial V168() V169() V170() V171() V172() V173() Element of K6(NAT)
do /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
do . 1 is V19() Function-like set
LSeg (do,1) is functional Element of K6( the U1 of (TOP-REAL 2))
do /. (1 + 1) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (C,n)) * (i,k)),(do /. (1 + 1))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (do,1)) /\ (L~ <*((Gauge (C,n)) * (j,k)),((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))*>) is functional Element of K6( the U1 of (TOP-REAL 2))
go is set
LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
LSeg (((Gauge (C,n)) * (j,k)),((Gauge (C,n)) * (i,k))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,n)) * (j,k)),((Gauge (C,n)) * (i,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
(L~ <*((Gauge (C,n)) * (j,k)),((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))*>) /\ (LSeg (do,1)) is functional Element of K6( the U1 of (TOP-REAL 2))
rng do is non trivial functional Element of K6( the U1 of (TOP-REAL 2))
go is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one non constant V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq s.c.c. FinSequence of the U1 of (TOP-REAL 2)
L~ go is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
len go is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
dom go is non trivial V168() V169() V170() V171() V172() V173() Element of K6(NAT)
go /. (len go) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
go . (len go) is V19() Function-like set
(len go) - 1 is V11() real ext-real Element of REAL
m is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
m + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(len go) -' 1 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
LSeg (go,m) is functional Element of K6( the U1 of (TOP-REAL 2))
go /. m is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((go /. m),((Gauge (C,n)) * (j,k))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (go,m)) /\ (L~ <*((Gauge (C,n)) * (j,k)),((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))*>) is functional Element of K6( the U1 of (TOP-REAL 2))
W2 is set
LSeg (((Gauge (C,n)) * (j,k)),((Gauge (C,n)) * (i,k))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,n)) * (j,k)),((Gauge (C,n)) * (i,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
go /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
rng go is non trivial functional Element of K6( the U1 of (TOP-REAL 2))
(L~ go) /\ (L~ do) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
{(go /. 1)} is non empty functional set
W2 is set
(Gauge (C,n)) * ((len (Gauge (C,n))),k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * ((len (Gauge (C,n))),k)) `1 is V11() real ext-real Element of REAL
(L~ (Upper_Seq (C,n))) /\ (L~ (Lower_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
{(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n))))} is non empty functional set
go /. 2 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (j,k)) .. (Upper_Seq (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
mid ((Upper_Seq (C,n)),1,(((Gauge (C,n)) * (j,k)) .. (Upper_Seq (C,n)))) is V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
(Upper_Seq (C,n)) | (((Gauge (C,n)) * (j,k)) .. (Upper_Seq (C,n))) is V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. FinSequence of the U1 of (TOP-REAL 2)
(Upper_Seq (C,n)) /. 2 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
do /. (len do) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
pion1 is set
((Gauge (C,n)) * (i,k)) `2 is V11() real ext-real Element of REAL
<*((Gauge (C,n)) * (j,k)),((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))*> /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
len <*((Gauge (C,n)) * (j,k)),((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))*> is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
<*((Gauge (C,n)) * (j,k)),((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))*> /. (len <*((Gauge (C,n)) * (j,k)),((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))*>) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
pion1 is V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
L~ pion1 is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
pion1 /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
len pion1 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
pion1 /. (len pion1) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
pion1 is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() 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 V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
len (go ^' pion1) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(go ^' pion1) /. (len (go ^' pion1)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
<*((Gauge (C,n)) * (j,k)),((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))*> /. 3 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
pion1 /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
L~ pion1 is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(L~ go) /\ (L~ pion1) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
{(pion1 /. 1)} is non empty functional set
godo is set
2 + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
len pion1 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
rng pion1 is functional Element of K6( the U1 of (TOP-REAL 2))
godo is set
LSeg (pion1,1) is functional Element of K6( the U1 of (TOP-REAL 2))
(LSeg (go,m)) /\ (LSeg (pion1,1)) is functional Element of K6( the U1 of (TOP-REAL 2))
godo is set
LSeg (go,((len go) -' 1)) is functional Element of K6( the U1 of (TOP-REAL 2))
(LSeg (go,((len go) -' 1))) /\ (LSeg (pion1,1)) is functional Element of K6( the U1 of (TOP-REAL 2))
{(go /. (len go))} is non empty functional set
1 + 0 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
pion1 /. (len pion1) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
{(pion1 /. (len pion1))} is non empty functional set
(L~ do) /\ (L~ pion1) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
godo is set
godo is set
L~ (go ^' pion1) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(L~ (go ^' pion1)) /\ (L~ do) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(L~ go) \/ (L~ pion1) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
((L~ go) \/ (L~ pion1)) /\ (L~ do) is functional Element of K6( the U1 of (TOP-REAL 2))
{(do /. 1)} is non empty functional set
{(go /. 1)} \/ {(do /. 1)} is non empty set
(go ^' pion1) /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
{((go ^' pion1) /. 1)} is non empty functional set
{((go ^' pion1) /. 1)} \/ {(do /. 1)} is non empty set
{((go ^' pion1) /. 1),(do /. 1)} is non empty functional set
W-min C is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound C is V11() real ext-real Element of REAL
(TOP-REAL 2) | C is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | C is V19() V22( the U1 of ((TOP-REAL 2) | C)) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | C), REAL ) V205((TOP-REAL 2) | C) Element of K6(K7( the U1 of ((TOP-REAL 2) | C),REAL))
the U1 of ((TOP-REAL 2) | C) is set
K7( the U1 of ((TOP-REAL 2) | C),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | C),REAL)) is set
lower_bound (proj1 | C) is V11() real ext-real Element of REAL
(proj1 | C) .: the U1 of ((TOP-REAL 2) | C) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | C) .: the U1 of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
W-most C is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SW-corner C is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-bound C is V11() real ext-real Element of REAL
proj2 | C is V19() V22( the U1 of ((TOP-REAL 2) | C)) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | C), REAL ) V205((TOP-REAL 2) | C) Element of K6(K7( the U1 of ((TOP-REAL 2) | C),REAL))
lower_bound (proj2 | C) is V11() real ext-real Element of REAL
(proj2 | C) .: the U1 of ((TOP-REAL 2) | C) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | C) .: the U1 of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
|[(W-bound C),(S-bound C)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NW-corner C is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound C is V11() real ext-real Element of REAL
upper_bound (proj2 | C) is V11() real ext-real Element of REAL
upper_bound ((proj2 | C) .: the U1 of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
|[(W-bound C),(N-bound C)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner C),(NW-corner C)) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SW-corner C),(NW-corner C))) /\ C is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (W-most C) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (W-most C) is V19() V22( the U1 of ((TOP-REAL 2) | (W-most C))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (W-most C)), REAL ) V205((TOP-REAL 2) | (W-most C)) Element of K6(K7( the U1 of ((TOP-REAL 2) | (W-most C)),REAL))
the U1 of ((TOP-REAL 2) | (W-most C)) is set
K7( the U1 of ((TOP-REAL 2) | (W-most C)),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (W-most C)),REAL)) is set
lower_bound (proj2 | (W-most C)) is V11() real ext-real Element of REAL
(proj2 | (W-most C)) .: the U1 of ((TOP-REAL 2) | (W-most C)) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (W-most C)) .: the U1 of ((TOP-REAL 2) | (W-most C))) is V11() real ext-real Element of REAL
|[(W-bound C),(lower_bound (proj2 | (W-most C)))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-max C is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-bound C is V11() real ext-real Element of REAL
upper_bound (proj1 | C) is V11() real ext-real Element of REAL
upper_bound ((proj1 | C) .: the U1 of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
E-most C is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SE-corner C is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
|[(E-bound C),(S-bound C)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NE-corner C is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
|[(E-bound C),(N-bound C)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner C),(NE-corner C)) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SE-corner C),(NE-corner C))) /\ C is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (E-most C) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (E-most C) is V19() V22( the U1 of ((TOP-REAL 2) | (E-most C))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (E-most C)), REAL ) V205((TOP-REAL 2) | (E-most C)) Element of K6(K7( the U1 of ((TOP-REAL 2) | (E-most C)),REAL))
the U1 of ((TOP-REAL 2) | (E-most C)) is set
K7( the U1 of ((TOP-REAL 2) | (E-most C)),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (E-most C)),REAL)) is set
upper_bound (proj2 | (E-most C)) is V11() real ext-real Element of REAL
(proj2 | (E-most C)) .: the U1 of ((TOP-REAL 2) | (E-most C)) is V168() V169() V170() Element of K6(REAL)
upper_bound ((proj2 | (E-most C)) .: the U1 of ((TOP-REAL 2) | (E-most C))) is V11() real ext-real Element of REAL
|[(E-bound C),(upper_bound (proj2 | (E-most C)))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(go ^' pion1) ^' do is non empty V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
(len pion1) - 1 is V11() real ext-real Element of REAL
(len pion1) -' 1 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
LSeg (pion1,((len pion1) -' 1)) is functional Element of K6( the U1 of (TOP-REAL 2))
(LSeg (pion1,((len pion1) -' 1))) /\ (LSeg (do,1)) is functional Element of K6( the U1 of (TOP-REAL 2))
godo is set
((len pion1) -' 1) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
pion1 /. (((len pion1) -' 1) + 1) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((len pion1) - 1) + 1 is V11() real ext-real Element of REAL
(len pion1) - 2 is V11() real ext-real Element of REAL
(len pion1) -' 2 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((len pion1) -' 2) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((len pion1) - 2) + 1 is V11() real ext-real Element of REAL
(len go) + ((len pion1) -' 2) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
LSeg ((go ^' pion1),((len go) + ((len pion1) -' 2))) is functional Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((go ^' pion1),((len go) + ((len pion1) -' 2)))) /\ (LSeg (do,1)) is functional Element of K6( the U1 of (TOP-REAL 2))
{((go ^' pion1) /. (len (go ^' pion1)))} is non empty functional set
(rng go) /\ (rng pion1) is functional Element of K6( the U1 of (TOP-REAL 2))
(len (go ^' pion1)) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((len (go ^' pion1)) + 1) - 1 is V11() real ext-real Element of REAL
(len go) + (len pion1) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((len go) + (len pion1)) - 1 is V11() real ext-real Element of REAL
(len (go ^' pion1)) - 1 is V11() real ext-real Element of REAL
(len go) + ((len pion1) - 2) is V11() real ext-real Element of REAL
(len (go ^' pion1)) -' 1 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(L~ (Upper_Seq (C,n))) \/ (L~ (Lower_Seq (C,n))) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
len ((go ^' pion1) ^' do) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
godo is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard FinSequence of the U1 of (TOP-REAL 2)
L~ godo is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
(L~ (go ^' pion1)) \/ (L~ do) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
((L~ go) \/ (L~ pion1)) \/ (L~ do) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
W-bound (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) is V19() V22( the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k))))), REAL ) V205((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k))))),REAL))
the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k))))) is set
K7( the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k))))),REAL)) is set
lower_bound (proj1 | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k))))) is V11() real ext-real Element of REAL
(proj1 | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k))))) .: the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k))))) .: the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))))) is V11() real ext-real Element of REAL
W-bound (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))) is V19() V22( the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))))), REAL ) V205((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))))),REAL))
the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))))) is set
K7( the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))))),REAL)) is set
lower_bound (proj1 | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))))) is V11() real ext-real Element of REAL
(proj1 | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))))) .: the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))))) .: the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))))) is V11() real ext-real Element of REAL
W-bound ((LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))))) is strict T_2 SubSpace of TOP-REAL 2
proj1 | ((LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))))) is V19() V22( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))))), REAL ) V205((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))))),REAL))
the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))))) is set
K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))))),REAL)) is set
lower_bound (proj1 | ((LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))))) is V11() real ext-real Element of REAL
(proj1 | ((LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | ((LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))))))) is V11() real ext-real Element of REAL
min ((W-bound (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k))))),(W-bound (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))))) is ext-real set
W-bound (L~ pion1) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ pion1) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ pion1) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ pion1))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ pion1)), REAL ) V205((TOP-REAL 2) | (L~ pion1)) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ pion1)),REAL))
the U1 of ((TOP-REAL 2) | (L~ pion1)) is set
K7( the U1 of ((TOP-REAL 2) | (L~ pion1)),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (L~ pion1)),REAL)) is set
lower_bound (proj1 | (L~ pion1)) is V11() real ext-real Element of REAL
(proj1 | (L~ pion1)) .: the U1 of ((TOP-REAL 2) | (L~ pion1)) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | (L~ pion1)) .: the U1 of ((TOP-REAL 2) | (L~ pion1))) is V11() real ext-real Element of REAL
(L~ go) \/ (L~ do) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
right_cell (godo,1,(Gauge (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
(right_cell (godo,1,(Gauge (C,n)))) \ (L~ godo) is functional Element of K6( the U1 of (TOP-REAL 2))
RightComp godo is non empty functional Element of K6( the U1 of (TOP-REAL 2))
dom godo is non trivial V168() V169() V170() V171() V172() V173() Element of K6(NAT)
godo /. 2 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
rng godo is non trivial functional Element of K6( the U1 of (TOP-REAL 2))
godo /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
len (Cage (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
rng (Cage (C,n)) is non trivial functional Element of K6( the U1 of (TOP-REAL 2))
(Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
W-max (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))), REAL ) V205((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),REAL))
the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is set
K7( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),REAL)) is set
lower_bound (proj1 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is V11() real ext-real Element of REAL
(proj1 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SW-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V11() real ext-real Element of REAL
proj2 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))), REAL ) V205((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),REAL))
lower_bound (proj2 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is V11() real ext-real Element of REAL
(proj2 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),(S-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NW-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),(N-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),(NW-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SW-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),(NW-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))) /\ (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is V19() V22( the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))), REAL ) V205((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))),REAL))
the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is set
K7( the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))),REAL)) is set
upper_bound (proj2 | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
(proj2 | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) .: the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V168() V169() V170() Element of K6(REAL)
upper_bound ((proj2 | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) .: the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),(upper_bound (proj2 | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(W-max (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .. (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
N-min (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
NE-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is V11() real ext-real Element of REAL
upper_bound ((proj1 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),(N-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((NW-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),(NE-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((NW-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),(NE-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))) /\ (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is V19() V22( the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))), REAL ) V205((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))),REAL))
the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is set
K7( the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))),REAL)) is set
lower_bound (proj1 | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
(proj1 | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) .: the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) .: the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))),(N-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(N-min (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .. (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
N-max (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
upper_bound (proj1 | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
upper_bound ((proj1 | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) .: the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))) is V11() real ext-real Element of REAL
|[(upper_bound (proj1 | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))),(N-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(N-max (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .. (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(E-max (L~ (Cage (C,n)))) .. (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
len (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
right_cell ((Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))),1) is functional Element of K6( the U1 of (TOP-REAL 2))
GoB (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) is V19() non empty-yielding V22( NAT ) V23(K295( the U1 of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K295( the U1 of (TOP-REAL 2))
right_cell ((Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))),1,(GoB (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is functional Element of K6( the U1 of (TOP-REAL 2))
GoB (Cage (C,n)) is V19() non empty-yielding V22( NAT ) V23(K295( the U1 of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K295( the U1 of (TOP-REAL 2))
right_cell ((Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))),1,(GoB (Cage (C,n)))) is functional Element of K6( the U1 of (TOP-REAL 2))
right_cell ((Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))),1,(Gauge (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
(Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) -: (E-max (L~ (Cage (C,n)))) is V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like special unfolded FinSequence of the U1 of (TOP-REAL 2)
right_cell (((Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) -: (E-max (L~ (Cage (C,n))))),1,(Gauge (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
right_cell ((Upper_Seq (C,n)),1,(Gauge (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
right_cell ((R_Cut ((Upper_Seq (C,n)),((Gauge (C,n)) * (j,k)))),1,(Gauge (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
right_cell ((go ^' pion1),1,(Gauge (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
W-min ((L~ go) \/ (L~ do)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound ((L~ go) \/ (L~ do)) is V11() real ext-real Element of REAL
(TOP-REAL 2) | ((L~ go) \/ (L~ do)) is strict T_2 SubSpace of TOP-REAL 2
proj1 | ((L~ go) \/ (L~ do)) is V19() V22( the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ do)))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ do))), REAL ) V205((TOP-REAL 2) | ((L~ go) \/ (L~ do))) Element of K6(K7( the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ do))),REAL))
the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ do))) is set
K7( the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ do))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ do))),REAL)) is set
lower_bound (proj1 | ((L~ go) \/ (L~ do))) is V11() real ext-real Element of REAL
(proj1 | ((L~ go) \/ (L~ do))) .: the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ do))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | ((L~ go) \/ (L~ do))) .: the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ do)))) is V11() real ext-real Element of REAL
W-most ((L~ go) \/ (L~ do)) is functional Element of K6( the U1 of (TOP-REAL 2))
SW-corner ((L~ go) \/ (L~ do)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-bound ((L~ go) \/ (L~ do)) is V11() real ext-real Element of REAL
proj2 | ((L~ go) \/ (L~ do)) is V19() V22( the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ do)))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ do))), REAL ) V205((TOP-REAL 2) | ((L~ go) \/ (L~ do))) Element of K6(K7( the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ do))),REAL))
lower_bound (proj2 | ((L~ go) \/ (L~ do))) is V11() real ext-real Element of REAL
(proj2 | ((L~ go) \/ (L~ do))) .: the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ do))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | ((L~ go) \/ (L~ do))) .: the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ do)))) is V11() real ext-real Element of REAL
|[(W-bound ((L~ go) \/ (L~ do))),(S-bound ((L~ go) \/ (L~ do)))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NW-corner ((L~ go) \/ (L~ do)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound ((L~ go) \/ (L~ do)) is V11() real ext-real Element of REAL
upper_bound (proj2 | ((L~ go) \/ (L~ do))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | ((L~ go) \/ (L~ do))) .: the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ do)))) is V11() real ext-real Element of REAL
|[(W-bound ((L~ go) \/ (L~ do))),(N-bound ((L~ go) \/ (L~ do)))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner ((L~ go) \/ (L~ do))),(NW-corner ((L~ go) \/ (L~ do)))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( 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 K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (W-most ((L~ go) \/ (L~ do))) is strict T_2 SubSpace of TOP-REAL 2
proj2 | (W-most ((L~ go) \/ (L~ do))) is V19() V22( the U1 of ((TOP-REAL 2) | (W-most ((L~ go) \/ (L~ do))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (W-most ((L~ go) \/ (L~ do)))), REAL ) V205((TOP-REAL 2) | (W-most ((L~ go) \/ (L~ do)))) Element of K6(K7( 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
K7( the U1 of ((TOP-REAL 2) | (W-most ((L~ go) \/ (L~ do)))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (W-most ((L~ go) \/ (L~ do)))),REAL)) is set
lower_bound (proj2 | (W-most ((L~ go) \/ (L~ do)))) is V11() real ext-real Element of REAL
(proj2 | (W-most ((L~ go) \/ (L~ do)))) .: the U1 of ((TOP-REAL 2) | (W-most ((L~ go) \/ (L~ do)))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (W-most ((L~ go) \/ (L~ do)))) .: the U1 of ((TOP-REAL 2) | (W-most ((L~ go) \/ (L~ do))))) is V11() real ext-real Element of REAL
|[(W-bound ((L~ go) \/ (L~ do))),(lower_bound (proj2 | (W-most ((L~ go) \/ (L~ do)))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(W-min ((L~ go) \/ (L~ do))) `1 is V11() real ext-real Element of REAL
((L~ go) \/ (L~ do)) \/ (L~ pion1) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
W-min (((L~ go) \/ (L~ do)) \/ (L~ pion1)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound (((L~ go) \/ (L~ do)) \/ (L~ pion1)) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (((L~ go) \/ (L~ do)) \/ (L~ pion1)) is strict T_2 SubSpace of TOP-REAL 2
proj1 | (((L~ go) \/ (L~ do)) \/ (L~ pion1)) is V19() V22( the U1 of ((TOP-REAL 2) | (((L~ go) \/ (L~ do)) \/ (L~ pion1)))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (((L~ go) \/ (L~ do)) \/ (L~ pion1))), REAL ) V205((TOP-REAL 2) | (((L~ go) \/ (L~ do)) \/ (L~ pion1))) Element of K6(K7( 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 set
K7( the U1 of ((TOP-REAL 2) | (((L~ go) \/ (L~ do)) \/ (L~ pion1))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (((L~ go) \/ (L~ do)) \/ (L~ pion1))),REAL)) is set
lower_bound (proj1 | (((L~ go) \/ (L~ do)) \/ (L~ pion1))) is V11() real ext-real Element of REAL
(proj1 | (((L~ go) \/ (L~ do)) \/ (L~ pion1))) .: the U1 of ((TOP-REAL 2) | (((L~ go) \/ (L~ do)) \/ (L~ pion1))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | (((L~ go) \/ (L~ do)) \/ (L~ pion1))) .: the U1 of ((TOP-REAL 2) | (((L~ go) \/ (L~ do)) \/ (L~ pion1)))) is V11() real ext-real Element of REAL
W-most (((L~ go) \/ (L~ do)) \/ (L~ pion1)) is functional Element of K6( the U1 of (TOP-REAL 2))
SW-corner (((L~ go) \/ (L~ do)) \/ (L~ pion1)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-bound (((L~ go) \/ (L~ do)) \/ (L~ pion1)) is V11() real ext-real Element of REAL
proj2 | (((L~ go) \/ (L~ do)) \/ (L~ pion1)) is V19() V22( the U1 of ((TOP-REAL 2) | (((L~ go) \/ (L~ do)) \/ (L~ pion1)))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (((L~ go) \/ (L~ do)) \/ (L~ pion1))), REAL ) V205((TOP-REAL 2) | (((L~ go) \/ (L~ do)) \/ (L~ pion1))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (((L~ go) \/ (L~ do)) \/ (L~ pion1))),REAL))
lower_bound (proj2 | (((L~ go) \/ (L~ do)) \/ (L~ pion1))) is V11() real ext-real Element of REAL
(proj2 | (((L~ go) \/ (L~ do)) \/ (L~ pion1))) .: the U1 of ((TOP-REAL 2) | (((L~ go) \/ (L~ do)) \/ (L~ pion1))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (((L~ go) \/ (L~ do)) \/ (L~ pion1))) .: the U1 of ((TOP-REAL 2) | (((L~ go) \/ (L~ do)) \/ (L~ pion1)))) is V11() real ext-real Element of REAL
|[(W-bound (((L~ go) \/ (L~ do)) \/ (L~ pion1))),(S-bound (((L~ go) \/ (L~ do)) \/ (L~ pion1)))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NW-corner (((L~ go) \/ (L~ do)) \/ (L~ pion1)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound (((L~ go) \/ (L~ do)) \/ (L~ pion1)) is V11() real ext-real Element of REAL
upper_bound (proj2 | (((L~ go) \/ (L~ do)) \/ (L~ pion1))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (((L~ go) \/ (L~ do)) \/ (L~ pion1))) .: the U1 of ((TOP-REAL 2) | (((L~ go) \/ (L~ do)) \/ (L~ pion1)))) is V11() real ext-real Element of REAL
|[(W-bound (((L~ go) \/ (L~ do)) \/ (L~ pion1))),(N-bound (((L~ go) \/ (L~ do)) \/ (L~ pion1)))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() 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 non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( 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 K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (W-most (((L~ go) \/ (L~ do)) \/ (L~ pion1))) is strict T_2 SubSpace of TOP-REAL 2
proj2 | (W-most (((L~ go) \/ (L~ do)) \/ (L~ pion1))) is V19() V22( the U1 of ((TOP-REAL 2) | (W-most (((L~ go) \/ (L~ do)) \/ (L~ pion1))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (W-most (((L~ go) \/ (L~ do)) \/ (L~ pion1)))), REAL ) V205((TOP-REAL 2) | (W-most (((L~ go) \/ (L~ do)) \/ (L~ pion1)))) Element of K6(K7( 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
K7( the U1 of ((TOP-REAL 2) | (W-most (((L~ go) \/ (L~ do)) \/ (L~ pion1)))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (W-most (((L~ go) \/ (L~ do)) \/ (L~ pion1)))),REAL)) is set
lower_bound (proj2 | (W-most (((L~ go) \/ (L~ do)) \/ (L~ pion1)))) is V11() real ext-real Element of REAL
(proj2 | (W-most (((L~ go) \/ (L~ do)) \/ (L~ pion1)))) .: the U1 of ((TOP-REAL 2) | (W-most (((L~ go) \/ (L~ do)) \/ (L~ pion1)))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (W-most (((L~ go) \/ (L~ do)) \/ (L~ pion1)))) .: the U1 of ((TOP-REAL 2) | (W-most (((L~ go) \/ (L~ do)) \/ (L~ pion1))))) is V11() real ext-real Element of REAL
|[(W-bound (((L~ go) \/ (L~ do)) \/ (L~ pion1))),(lower_bound (proj2 | (W-most (((L~ go) \/ (L~ do)) \/ (L~ pion1)))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-min (L~ godo) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound (L~ godo) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ godo) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ godo) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ godo))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ godo)), REAL ) V205((TOP-REAL 2) | (L~ godo)) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ godo)),REAL))
the U1 of ((TOP-REAL 2) | (L~ godo)) is set
K7( the U1 of ((TOP-REAL 2) | (L~ godo)),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (L~ godo)),REAL)) is set
lower_bound (proj1 | (L~ godo)) is V11() real ext-real Element of REAL
(proj1 | (L~ godo)) .: the U1 of ((TOP-REAL 2) | (L~ godo)) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | (L~ godo)) .: the U1 of ((TOP-REAL 2) | (L~ godo))) is V11() real ext-real Element of REAL
W-most (L~ godo) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SW-corner (L~ godo) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-bound (L~ godo) is V11() real ext-real Element of REAL
proj2 | (L~ godo) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ godo))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ godo)), REAL ) V205((TOP-REAL 2) | (L~ godo)) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ godo)),REAL))
lower_bound (proj2 | (L~ godo)) is V11() real ext-real Element of REAL
(proj2 | (L~ godo)) .: the U1 of ((TOP-REAL 2) | (L~ godo)) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (L~ godo)) .: the U1 of ((TOP-REAL 2) | (L~ godo))) is V11() real ext-real Element of REAL
|[(W-bound (L~ godo)),(S-bound (L~ godo))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NW-corner (L~ godo) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound (L~ godo) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ godo)) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (L~ godo)) .: the U1 of ((TOP-REAL 2) | (L~ godo))) is V11() real ext-real Element of REAL
|[(W-bound (L~ godo)),(N-bound (L~ godo))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ godo)),(NW-corner (L~ godo))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SW-corner (L~ godo)),(NW-corner (L~ godo)))) /\ (L~ godo) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (W-most (L~ godo)) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (W-most (L~ godo)) is V19() V22( the U1 of ((TOP-REAL 2) | (W-most (L~ godo)))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (W-most (L~ godo))), REAL ) V205((TOP-REAL 2) | (W-most (L~ godo))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (W-most (L~ godo))),REAL))
the U1 of ((TOP-REAL 2) | (W-most (L~ godo))) is set
K7( the U1 of ((TOP-REAL 2) | (W-most (L~ godo))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (W-most (L~ godo))),REAL)) is set
lower_bound (proj2 | (W-most (L~ godo))) is V11() real ext-real Element of REAL
(proj2 | (W-most (L~ godo))) .: the U1 of ((TOP-REAL 2) | (W-most (L~ godo))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (W-most (L~ godo))) .: the U1 of ((TOP-REAL 2) | (W-most (L~ godo)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ godo)),(lower_bound (proj2 | (W-most (L~ godo))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(go ^' pion1) /. 2 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Upper_Seq (C,n)) ^' (Lower_Seq (C,n)) is non empty V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
((Upper_Seq (C,n)) ^' (Lower_Seq (C,n))) /. 2 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) /. 2 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(godo /. 2) `1 is V11() real ext-real Element of REAL
(W-min (L~ godo)) `1 is V11() real ext-real Element of REAL
Rotate (godo,(W-min (L~ godo))) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like non constant V32() 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 V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Upper_Seq (C,n)) . (len (Upper_Seq (C,n))) is V19() Function-like set
(Upper_Seq (C,n)) /. (len (Upper_Seq (C,n))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
east_halfline (E-max C) is non empty functional connected V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
W is set
p is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(east_halfline (E-max C)) /\ (L~ (Cage (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
p `1 is V11() real ext-real Element of REAL
godo is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like non constant V32() 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 closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
W is set
p is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
p `2 is V11() real ext-real Element of REAL
(E-max C) `2 is V11() real ext-real Element of REAL
p `1 is V11() real ext-real Element of REAL
p `1 is V11() real ext-real Element of REAL
p `1 is V11() real ext-real Element of REAL
p `1 is V11() real ext-real Element of REAL
i + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(i + 1) - 1 is V11() real ext-real Element of REAL
(len (Gauge (C,n))) - 1 is V11() real ext-real Element of REAL
(len (Gauge (C,n))) -' 1 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * (((len (Gauge (C,n))) -' 1),1) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (((len (Gauge (C,n))) -' 1),1)) `1 is V11() real ext-real Element of REAL
(E-max C) `1 is V11() real ext-real Element of REAL
W is set
p is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
Index (p,do) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
LSeg (do,(Index (p,do))) is functional Element of K6( the U1 of (TOP-REAL 2))
t is ordinal natural ext-real non negative set
(Lower_Seq (C,n)) . t is V19() Function-like set
Index (((Gauge (C,n)) * (i,k)),(Lower_Seq (C,n))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Index (((Gauge (C,n)) * (i,k)),(Lower_Seq (C,n)))) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
len (L_Cut ((Lower_Seq (C,n)),((Gauge (C,n)) * (i,k)))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(len (Lower_Seq (C,n))) - (Index (((Gauge (C,n)) * (i,k)),(Lower_Seq (C,n)))) is V11() real ext-real Element of REAL
(len (Lower_Seq (C,n))) -' (Index (((Gauge (C,n)) * (i,k)),(Lower_Seq (C,n)))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Index (p,do)) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((len (Lower_Seq (C,n))) -' (Index (((Gauge (C,n)) * (i,k)),(Lower_Seq (C,n))))) - 1 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (i,k)) .. (Lower_Seq (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
mid ((Lower_Seq (C,n)),(((Gauge (C,n)) * (i,k)) .. (Lower_Seq (C,n))),(len (Lower_Seq (C,n)))) is V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
(east_halfline (E-max C)) /\ (L~ (Cage (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
p `1 is V11() real ext-real Element of REAL
0 + (Index (((Gauge (C,n)) * (i,k)),(Lower_Seq (C,n)))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((len (Lower_Seq (C,n))) - (Index (((Gauge (C,n)) * (i,k)),(Lower_Seq (C,n))))) - 1 is V11() real ext-real Element of REAL
(len (Lower_Seq (C,n))) - (((Gauge (C,n)) * (i,k)) .. (Lower_Seq (C,n))) is V11() real ext-real Element of REAL
(len (Lower_Seq (C,n))) -' (((Gauge (C,n)) * (i,k)) .. (Lower_Seq (C,n))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((len (Lower_Seq (C,n))) -' (((Gauge (C,n)) * (i,k)) .. (Lower_Seq (C,n)))) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Index (p,do)) + (((Gauge (C,n)) * (i,k)) .. (Lower_Seq (C,n))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((Index (p,do)) + (((Gauge (C,n)) * (i,k)) .. (Lower_Seq (C,n)))) -' 1 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
right_cell ((Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))),1) is functional Element of K6( the U1 of (TOP-REAL 2))
GoB (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))) is V19() non empty-yielding V22( NAT ) V23(K295( the U1 of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K295( the U1 of (TOP-REAL 2))
L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
jj2 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * ((len (Gauge (C,n))),jj2) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
[(len (Gauge (C,n))),jj2] is set
{(len (Gauge (C,n))),jj2} is non empty V168() V169() V170() V171() V172() V173() set
{{(len (Gauge (C,n))),jj2},{(len (Gauge (C,n)))}} is non empty set
len (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))) -: (W-min (L~ (Cage (C,n)))) is V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like special unfolded FinSequence of the U1 of (TOP-REAL 2)
LSeg ((Lower_Seq (C,n)),1) is functional Element of K6( the U1 of (TOP-REAL 2))
LSeg ((Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))),1) is functional Element of K6( the U1 of (TOP-REAL 2))
(Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))) /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))) /. (1 + 1) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
ii is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
jj is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
jj + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
[ii,(jj + 1)] is set
{ii,(jj + 1)} is non empty V168() V169() V170() V171() V172() V173() set
{ii} is non empty V168() V169() V170() V171() V172() V173() set
{{ii,(jj + 1)},{ii}} is non empty set
[ii,jj] is set
{ii,jj} is non empty V168() V169() V170() V171() V172() V173() set
{{ii,jj},{ii}} is non empty set
(Gauge (C,n)) * (ii,(jj + 1)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Gauge (C,n)) * (ii,jj) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(jj + 1) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
E-max (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))), REAL ) V205((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),REAL))
the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) is set
K7( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),REAL)) is set
upper_bound (proj1 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) is V11() real ext-real Element of REAL
(proj1 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) is V168() V169() V170() Element of K6(REAL)
upper_bound ((proj1 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SE-corner (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is V11() real ext-real Element of REAL
proj2 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))), REAL ) V205((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),REAL))
lower_bound (proj2 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) is V11() real ext-real Element of REAL
(proj2 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),(S-bound (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NE-corner (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),(N-bound (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),(NE-corner (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SE-corner (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),(NE-corner (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))))) /\ (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) is V19() V22( the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))), REAL ) V205((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))),REAL))
the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) is set
K7( the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))),REAL)) is set
upper_bound (proj2 | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
(proj2 | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) .: the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) is V168() V169() V170() Element of K6(REAL)
upper_bound ((proj2 | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) .: the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),(upper_bound (proj2 | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
4 - 1 is V11() real ext-real Element of REAL
ii - 1 is V11() real ext-real Element of REAL
ii -' 1 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * ((len (Gauge (C,n))),jj) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * ((len (Gauge (C,n))),jj)) `1 is V11() real ext-real Element of REAL
ii + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
cell ((Gauge (C,n)),(ii -' 1),jj) is functional Element of K6( the U1 of (TOP-REAL 2))
(Gauge (C,n)) * ((len (Gauge (C,n))),(jj + 1)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * ((len (Gauge (C,n))),(jj + 1))) `1 is V11() real ext-real Element of REAL
(ii -' 1) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * ((ii -' 1),(jj + 1)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * ((ii -' 1),(jj + 1))) `2 is V11() real ext-real Element of REAL
(Gauge (C,n)) * (1,(jj + 1)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (1,(jj + 1))) `2 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (ii,(jj + 1))) `2 is V11() real ext-real Element of REAL
(E-max C) `2 is V11() real ext-real Element of REAL
p `2 is V11() real ext-real Element of REAL
(Gauge (C,n)) * ((ii -' 1),jj) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * ((ii -' 1),jj)) `2 is V11() real ext-real Element of REAL
(Gauge (C,n)) * (1,jj) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (1,jj)) `2 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (ii,jj)) `2 is V11() real ext-real Element of REAL
LSeg (((Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))) /. 1),((Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))) /. (1 + 1))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
LSeg ((mid ((Lower_Seq (C,n)),(((Gauge (C,n)) * (i,k)) .. (Lower_Seq (C,n))),(len (Lower_Seq (C,n))))),(Index (p,do))) is functional Element of K6( the U1 of (TOP-REAL 2))
LSeg ((Lower_Seq (C,n)),(((Index (p,do)) + (((Gauge (C,n)) * (i,k)) .. (Lower_Seq (C,n)))) -' 1)) is functional Element of K6( the U1 of (TOP-REAL 2))
(1 + 1) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((1 + 1) + 1) - 1 is V11() real ext-real Element of REAL
((Index (p,do)) + (((Gauge (C,n)) * (i,k)) .. (Lower_Seq (C,n)))) - 1 is V11() real ext-real Element of REAL
(LSeg ((Lower_Seq (C,n)),1)) /\ (LSeg ((Lower_Seq (C,n)),(((Index (p,do)) + (((Gauge (C,n)) * (i,k)) .. (Lower_Seq (C,n)))) -' 1))) is functional Element of K6( the U1 of (TOP-REAL 2))
(Lower_Seq (C,n)) /. 2 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
{((Lower_Seq (C,n)) /. 2)} is non empty functional set
p .. (Lower_Seq (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * ((len (Gauge (C,n))),k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * ((len (Gauge (C,n))),k)) `1 is V11() real ext-real Element of REAL
(L~ godo) ` is non empty functional Element of K6( the U1 of (TOP-REAL 2))
W is functional Element of K6( the U1 of (TOP-REAL 2))
UBD (L~ godo) is non empty functional open connected Element of K6( the U1 of (TOP-REAL 2))
LeftComp godo is non empty functional Element of K6( the U1 of (TOP-REAL 2))
{((Gauge (C,n)) * (i,k))} is non empty functional set
((Gauge (C,n)) * (i,k)) `2 is V11() real ext-real Element of REAL
{((Gauge (C,n)) * (i,k))} is non empty functional set
((Gauge (C,n)) * (i,k)) `2 is V11() real ext-real Element of REAL
n is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
C is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
Gauge (C,n) is V19() non empty-yielding V22( NAT ) V23(K295( the U1 of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K295( the U1 of (TOP-REAL 2))
len (Gauge (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
width (Gauge (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Upper_Seq (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
L~ (Upper_Seq (C,n)) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
Lower_Seq (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
L~ (Lower_Seq (C,n)) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
Lower_Arc C is non empty functional Element of K6( the U1 of (TOP-REAL 2))
j is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
i is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
k is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
k is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * (i,k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Gauge (C,n)) * (i,k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(Gauge (C,n)) * (j,k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
((LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k))))) /\ (L~ (Upper_Seq (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
{((Gauge (C,n)) * (j,k))} is non empty functional set
((LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k))))) /\ (L~ (Lower_Seq (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
{((Gauge (C,n)) * (i,k))} is non empty functional set
[j,k] is set
{j,k} is non empty V168() V169() V170() V171() V172() V173() set
{j} is non empty V168() V169() V170() V171() V172() V173() set
{{j,k},{j}} is non empty set
Indices (Gauge (C,n)) is set
Cage (C,n) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
L~ (Cage (C,n)) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
W-min (L~ (Cage (C,n))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound (L~ (Cage (C,n))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (Cage (C,n))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ (Cage (C,n))) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))), REAL ) V205((TOP-REAL 2) | (L~ (Cage (C,n)))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL))
the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))) is set
K7( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL)) is set
lower_bound (proj1 | (L~ (Cage (C,n)))) is V11() real ext-real Element of REAL
(proj1 | (L~ (Cage (C,n)))) .: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | (L~ (Cage (C,n)))) .: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n))))) is V11() real ext-real Element of REAL
W-most (L~ (Cage (C,n))) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SW-corner (L~ (Cage (C,n))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Cage (C,n))) is V11() real ext-real Element of REAL
proj2 | (L~ (Cage (C,n))) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))), REAL ) V205((TOP-REAL 2) | (L~ (Cage (C,n)))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))),REAL))
lower_bound (proj2 | (L~ (Cage (C,n)))) is V11() real ext-real Element of REAL
(proj2 | (L~ (Cage (C,n)))) .: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n)))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (L~ (Cage (C,n)))) .: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Cage (C,n)))),(S-bound (L~ (Cage (C,n))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NW-corner (L~ (Cage (C,n))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Cage (C,n))) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ (Cage (C,n)))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (L~ (Cage (C,n)))) .: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Cage (C,n)))),(N-bound (L~ (Cage (C,n))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Cage (C,n)))),(NW-corner (L~ (Cage (C,n))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SW-corner (L~ (Cage (C,n)))),(NW-corner (L~ (Cage (C,n)))))) /\ (L~ (Cage (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (W-most (L~ (Cage (C,n)))) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Cage (C,n)))) is V19() V22( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n)))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))), REAL ) V205((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),REAL))
the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))) is set
K7( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))),REAL)) is set
lower_bound (proj2 | (W-most (L~ (Cage (C,n))))) is V11() real ext-real Element of REAL
(proj2 | (W-most (L~ (Cage (C,n))))) .: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (W-most (L~ (Cage (C,n))))) .: the U1 of ((TOP-REAL 2) | (W-most (L~ (Cage (C,n)))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Cage (C,n)))),(lower_bound (proj2 | (W-most (L~ (Cage (C,n))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
R_Cut ((Upper_Seq (C,n)),((Gauge (C,n)) * (j,k))) is V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
len (Upper_Seq (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
dom (Upper_Seq (C,n)) is non trivial V168() V169() V170() V171() V172() V173() Element of K6(NAT)
(Upper_Seq (C,n)) . 1 is V19() Function-like set
(Upper_Seq (C,n)) /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
L_Cut ((Lower_Seq (C,n)),((Gauge (C,n)) * (i,k))) is V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (i,k)) `2 is V11() real ext-real Element of REAL
(Gauge (C,n)) * (1,k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (1,k)) `2 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (j,k)) `2 is V11() real ext-real Element of REAL
[i,k] is set
{i,k} is non empty V168() V169() V170() V171() V172() V173() set
{i} is non empty V168() V169() V170() V171() V172() V173() set
{{i,k},{i}} is non empty set
[(len (Gauge (C,n))),k] is set
{(len (Gauge (C,n))),k} is non empty V168() V169() V170() V171() V172() V173() set
{(len (Gauge (C,n)))} is non empty V168() V169() V170() V171() V172() V173() set
{{(len (Gauge (C,n))),k},{(len (Gauge (C,n)))}} is non empty set
[1,k] is set
{1,k} is non empty V168() V169() V170() V171() V172() V173() set
{{1,k},{1}} is non empty set
((Gauge (C,n)) * (j,k)) `1 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (1,k)) `1 is V11() real ext-real Element of REAL
<*((Gauge (C,n)) * (j,k)),((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))*> is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() V39(3) FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
[i,k] is set
{i,k} is non empty V168() V169() V170() V171() V172() V173() set
{{i,k},{i}} is non empty set
Emax is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
dom <*((Gauge (C,n)) * (j,k)),((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))*> is non trivial V168() V169() V170() V171() V172() V173() Element of K6(NAT)
<*((Gauge (C,n)) * (j,k)),((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))*> /. Emax is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-max (L~ (Cage (C,n))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Cage (C,n))) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ (Cage (C,n)))) is V11() real ext-real Element of REAL
upper_bound ((proj1 | (L~ (Cage (C,n)))) .: the U1 of ((TOP-REAL 2) | (L~ (Cage (C,n))))) is V11() real ext-real Element of REAL
E-most (L~ (Cage (C,n))) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SE-corner (L~ (Cage (C,n))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
|[(E-bound (L~ (Cage (C,n)))),(S-bound (L~ (Cage (C,n))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NE-corner (L~ (Cage (C,n))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
|[(E-bound (L~ (Cage (C,n)))),(N-bound (L~ (Cage (C,n))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Cage (C,n)))),(NE-corner (L~ (Cage (C,n))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SE-corner (L~ (Cage (C,n)))),(NE-corner (L~ (Cage (C,n)))))) /\ (L~ (Cage (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (E-most (L~ (Cage (C,n)))) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Cage (C,n)))) is V19() V22( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n)))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))), REAL ) V205((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),REAL))
the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))) is set
K7( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))),REAL)) is set
upper_bound (proj2 | (E-most (L~ (Cage (C,n))))) is V11() real ext-real Element of REAL
(proj2 | (E-most (L~ (Cage (C,n))))) .: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n))))) is V168() V169() V170() Element of K6(REAL)
upper_bound ((proj2 | (E-most (L~ (Cage (C,n))))) .: the U1 of ((TOP-REAL 2) | (E-most (L~ (Cage (C,n)))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Cage (C,n)))),(upper_bound (proj2 | (E-most (L~ (Cage (C,n))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
1 + 2 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
len (Lower_Seq (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
dom (Lower_Seq (C,n)) is non trivial V168() V169() V170() V171() V172() V173() Element of K6(NAT)
(Lower_Seq (C,n)) . 1 is V19() Function-like set
(Lower_Seq (C,n)) /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Lower_Seq (C,n)) . (len (Lower_Seq (C,n))) is V19() Function-like set
(Lower_Seq (C,n)) /. (len (Lower_Seq (C,n))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
L~ <*((Gauge (C,n)) * (j,k)),((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))*> is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
(W-min (L~ (Cage (C,n)))) `1 is V11() real ext-real Element of REAL
rng (Upper_Seq (C,n)) is functional Element of K6( the U1 of (TOP-REAL 2))
go is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (i,k)) `1 is V11() real ext-real Element of REAL
(Gauge (C,n)) * (i,1) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (i,1)) `1 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (i,k)) `1 is V11() real ext-real Element of REAL
|[(((Gauge (C,n)) * (i,k)) `1),(((Gauge (C,n)) * (j,k)) `2)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
[(len (Gauge (C,n))),k] is set
{(len (Gauge (C,n))),k} is non empty V168() V169() V170() V171() V172() V173() set
{{(len (Gauge (C,n))),k},{(len (Gauge (C,n)))}} is non empty set
1 + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
len go is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
rng (Lower_Seq (C,n)) is functional Element of K6( the U1 of (TOP-REAL 2))
do is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
(E-max (L~ (Cage (C,n)))) `1 is V11() real ext-real Element of REAL
(Gauge (C,n)) * ((len (Gauge (C,n))),k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * ((len (Gauge (C,n))),k)) `1 is V11() real ext-real Element of REAL
len do is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
do is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one non constant V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq s.c.c. FinSequence of the U1 of (TOP-REAL 2)
L~ do is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
len do is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
dom do is non trivial V168() V169() V170() V171() V172() V173() Element of K6(NAT)
do /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
do . 1 is V19() Function-like set
LSeg (do,1) is functional Element of K6( the U1 of (TOP-REAL 2))
do /. (1 + 1) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (C,n)) * (i,k)),(do /. (1 + 1))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (do,1)) /\ (L~ <*((Gauge (C,n)) * (j,k)),((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))*>) is functional Element of K6( the U1 of (TOP-REAL 2))
go is set
LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
LSeg (((Gauge (C,n)) * (j,k)),((Gauge (C,n)) * (i,k))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,n)) * (j,k)),((Gauge (C,n)) * (i,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
(L~ <*((Gauge (C,n)) * (j,k)),((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))*>) /\ (LSeg (do,1)) is functional Element of K6( the U1 of (TOP-REAL 2))
rng do is non trivial functional Element of K6( the U1 of (TOP-REAL 2))
go is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one non constant V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq s.c.c. FinSequence of the U1 of (TOP-REAL 2)
L~ go is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
len go is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
dom go is non trivial V168() V169() V170() V171() V172() V173() Element of K6(NAT)
go /. (len go) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
go . (len go) is V19() Function-like set
(len go) - 1 is V11() real ext-real Element of REAL
m is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
m + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(len go) -' 1 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
LSeg (go,m) is functional Element of K6( the U1 of (TOP-REAL 2))
go /. m is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((go /. m),((Gauge (C,n)) * (j,k))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (go,m)) /\ (L~ <*((Gauge (C,n)) * (j,k)),((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))*>) is functional Element of K6( the U1 of (TOP-REAL 2))
W2 is set
LSeg (((Gauge (C,n)) * (j,k)),((Gauge (C,n)) * (i,k))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,n)) * (j,k)),((Gauge (C,n)) * (i,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
go /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
rng go is non trivial functional Element of K6( the U1 of (TOP-REAL 2))
(L~ go) /\ (L~ do) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
{(go /. 1)} is non empty functional set
W2 is set
(Gauge (C,n)) * ((len (Gauge (C,n))),k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * ((len (Gauge (C,n))),k)) `1 is V11() real ext-real Element of REAL
(L~ (Upper_Seq (C,n))) /\ (L~ (Lower_Seq (C,n))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
{(W-min (L~ (Cage (C,n)))),(E-max (L~ (Cage (C,n))))} is non empty functional set
go /. 2 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (j,k)) .. (Upper_Seq (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
mid ((Upper_Seq (C,n)),1,(((Gauge (C,n)) * (j,k)) .. (Upper_Seq (C,n)))) is V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
(Upper_Seq (C,n)) | (((Gauge (C,n)) * (j,k)) .. (Upper_Seq (C,n))) is V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. FinSequence of the U1 of (TOP-REAL 2)
(Upper_Seq (C,n)) /. 2 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
do /. (len do) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
pion1 is set
((Gauge (C,n)) * (i,k)) `2 is V11() real ext-real Element of REAL
<*((Gauge (C,n)) * (j,k)),((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))*> /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
len <*((Gauge (C,n)) * (j,k)),((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))*> is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
<*((Gauge (C,n)) * (j,k)),((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))*> /. (len <*((Gauge (C,n)) * (j,k)),((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))*>) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
pion1 is V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
L~ pion1 is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
pion1 /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
len pion1 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
pion1 /. (len pion1) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
pion1 is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() 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 V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
len (go ^' pion1) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(go ^' pion1) /. (len (go ^' pion1)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
<*((Gauge (C,n)) * (j,k)),((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))*> /. 3 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
pion1 /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
L~ pion1 is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(L~ go) /\ (L~ pion1) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
{(pion1 /. 1)} is non empty functional set
godo is set
2 + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
len pion1 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
rng pion1 is functional Element of K6( the U1 of (TOP-REAL 2))
godo is set
LSeg (pion1,1) is functional Element of K6( the U1 of (TOP-REAL 2))
(LSeg (go,m)) /\ (LSeg (pion1,1)) is functional Element of K6( the U1 of (TOP-REAL 2))
godo is set
LSeg (go,((len go) -' 1)) is functional Element of K6( the U1 of (TOP-REAL 2))
(LSeg (go,((len go) -' 1))) /\ (LSeg (pion1,1)) is functional Element of K6( the U1 of (TOP-REAL 2))
{(go /. (len go))} is non empty functional set
1 + 0 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
pion1 /. (len pion1) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
{(pion1 /. (len pion1))} is non empty functional set
(L~ do) /\ (L~ pion1) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
godo is set
godo is set
L~ (go ^' pion1) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(L~ (go ^' pion1)) /\ (L~ do) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(L~ go) \/ (L~ pion1) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
((L~ go) \/ (L~ pion1)) /\ (L~ do) is functional Element of K6( the U1 of (TOP-REAL 2))
{(do /. 1)} is non empty functional set
{(go /. 1)} \/ {(do /. 1)} is non empty set
(go ^' pion1) /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
{((go ^' pion1) /. 1)} is non empty functional set
{((go ^' pion1) /. 1)} \/ {(do /. 1)} is non empty set
{((go ^' pion1) /. 1),(do /. 1)} is non empty functional set
E-max C is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-bound C is V11() real ext-real Element of REAL
(TOP-REAL 2) | C is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | C is V19() V22( the U1 of ((TOP-REAL 2) | C)) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | C), REAL ) V205((TOP-REAL 2) | C) Element of K6(K7( the U1 of ((TOP-REAL 2) | C),REAL))
the U1 of ((TOP-REAL 2) | C) is set
K7( the U1 of ((TOP-REAL 2) | C),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | C),REAL)) is set
upper_bound (proj1 | C) is V11() real ext-real Element of REAL
(proj1 | C) .: the U1 of ((TOP-REAL 2) | C) is V168() V169() V170() Element of K6(REAL)
upper_bound ((proj1 | C) .: the U1 of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
E-most C is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SE-corner C is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-bound C is V11() real ext-real Element of REAL
proj2 | C is V19() V22( the U1 of ((TOP-REAL 2) | C)) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | C), REAL ) V205((TOP-REAL 2) | C) Element of K6(K7( the U1 of ((TOP-REAL 2) | C),REAL))
lower_bound (proj2 | C) is V11() real ext-real Element of REAL
(proj2 | C) .: the U1 of ((TOP-REAL 2) | C) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | C) .: the U1 of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
|[(E-bound C),(S-bound C)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NE-corner C is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound C is V11() real ext-real Element of REAL
upper_bound (proj2 | C) is V11() real ext-real Element of REAL
upper_bound ((proj2 | C) .: the U1 of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
|[(E-bound C),(N-bound C)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner C),(NE-corner C)) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SE-corner C),(NE-corner C))) /\ C is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (E-most C) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (E-most C) is V19() V22( the U1 of ((TOP-REAL 2) | (E-most C))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (E-most C)), REAL ) V205((TOP-REAL 2) | (E-most C)) Element of K6(K7( the U1 of ((TOP-REAL 2) | (E-most C)),REAL))
the U1 of ((TOP-REAL 2) | (E-most C)) is set
K7( the U1 of ((TOP-REAL 2) | (E-most C)),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (E-most C)),REAL)) is set
upper_bound (proj2 | (E-most C)) is V11() real ext-real Element of REAL
(proj2 | (E-most C)) .: the U1 of ((TOP-REAL 2) | (E-most C)) is V168() V169() V170() Element of K6(REAL)
upper_bound ((proj2 | (E-most C)) .: the U1 of ((TOP-REAL 2) | (E-most C))) is V11() real ext-real Element of REAL
|[(E-bound C),(upper_bound (proj2 | (E-most C)))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-min C is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound C is V11() real ext-real Element of REAL
lower_bound (proj1 | C) is V11() real ext-real Element of REAL
lower_bound ((proj1 | C) .: the U1 of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
W-most C is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SW-corner C is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
|[(W-bound C),(S-bound C)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NW-corner C is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
|[(W-bound C),(N-bound C)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner C),(NW-corner C)) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SW-corner C),(NW-corner C))) /\ C is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (W-most C) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (W-most C) is V19() V22( the U1 of ((TOP-REAL 2) | (W-most C))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (W-most C)), REAL ) V205((TOP-REAL 2) | (W-most C)) Element of K6(K7( the U1 of ((TOP-REAL 2) | (W-most C)),REAL))
the U1 of ((TOP-REAL 2) | (W-most C)) is set
K7( the U1 of ((TOP-REAL 2) | (W-most C)),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (W-most C)),REAL)) is set
lower_bound (proj2 | (W-most C)) is V11() real ext-real Element of REAL
(proj2 | (W-most C)) .: the U1 of ((TOP-REAL 2) | (W-most C)) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (W-most C)) .: the U1 of ((TOP-REAL 2) | (W-most C))) is V11() real ext-real Element of REAL
|[(W-bound C),(lower_bound (proj2 | (W-most C)))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(go ^' pion1) ^' do is non empty V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
(len pion1) - 1 is V11() real ext-real Element of REAL
(len pion1) -' 1 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
LSeg (pion1,((len pion1) -' 1)) is functional Element of K6( the U1 of (TOP-REAL 2))
(LSeg (pion1,((len pion1) -' 1))) /\ (LSeg (do,1)) is functional Element of K6( the U1 of (TOP-REAL 2))
godo is set
((len pion1) -' 1) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
pion1 /. (((len pion1) -' 1) + 1) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((len pion1) - 1) + 1 is V11() real ext-real Element of REAL
(len pion1) - 2 is V11() real ext-real Element of REAL
(len pion1) -' 2 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((len pion1) -' 2) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((len pion1) - 2) + 1 is V11() real ext-real Element of REAL
(len go) + ((len pion1) -' 2) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
LSeg ((go ^' pion1),((len go) + ((len pion1) -' 2))) is functional Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((go ^' pion1),((len go) + ((len pion1) -' 2)))) /\ (LSeg (do,1)) is functional Element of K6( the U1 of (TOP-REAL 2))
{((go ^' pion1) /. (len (go ^' pion1)))} is non empty functional set
(rng go) /\ (rng pion1) is functional Element of K6( the U1 of (TOP-REAL 2))
(len (go ^' pion1)) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((len (go ^' pion1)) + 1) - 1 is V11() real ext-real Element of REAL
(len go) + (len pion1) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((len go) + (len pion1)) - 1 is V11() real ext-real Element of REAL
(len (go ^' pion1)) - 1 is V11() real ext-real Element of REAL
(len go) + ((len pion1) - 2) is V11() real ext-real Element of REAL
(len (go ^' pion1)) -' 1 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(L~ (Upper_Seq (C,n))) \/ (L~ (Lower_Seq (C,n))) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
len ((go ^' pion1) ^' do) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
godo is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard FinSequence of the U1 of (TOP-REAL 2)
L~ godo is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
(L~ (go ^' pion1)) \/ (L~ do) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
((L~ go) \/ (L~ pion1)) \/ (L~ do) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
W-bound (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) is V19() V22( the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k))))), REAL ) V205((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k))))),REAL))
the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k))))) is set
K7( the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k))))),REAL)) is set
lower_bound (proj1 | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k))))) is V11() real ext-real Element of REAL
(proj1 | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k))))) .: the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k))))) .: the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))))) is V11() real ext-real Element of REAL
W-bound (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))) is V19() V22( the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))))), REAL ) V205((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))))),REAL))
the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))))) is set
K7( the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))))),REAL)) is set
lower_bound (proj1 | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))))) is V11() real ext-real Element of REAL
(proj1 | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))))) .: the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))))) .: the U1 of ((TOP-REAL 2) | (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))))) is V11() real ext-real Element of REAL
W-bound ((LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))))) is strict T_2 SubSpace of TOP-REAL 2
proj1 | ((LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))))) is V19() V22( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))))), REAL ) V205((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))))),REAL))
the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))))) is set
K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))))),REAL)) is set
lower_bound (proj1 | ((LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))))) is V11() real ext-real Element of REAL
(proj1 | ((LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | ((LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k)))) \/ (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k))))))) is V11() real ext-real Element of REAL
min ((W-bound (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (j,k))))),(W-bound (LSeg (((Gauge (C,n)) * (i,k)),((Gauge (C,n)) * (i,k)))))) is ext-real set
W-bound (L~ pion1) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ pion1) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ pion1) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ pion1))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ pion1)), REAL ) V205((TOP-REAL 2) | (L~ pion1)) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ pion1)),REAL))
the U1 of ((TOP-REAL 2) | (L~ pion1)) is set
K7( the U1 of ((TOP-REAL 2) | (L~ pion1)),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (L~ pion1)),REAL)) is set
lower_bound (proj1 | (L~ pion1)) is V11() real ext-real Element of REAL
(proj1 | (L~ pion1)) .: the U1 of ((TOP-REAL 2) | (L~ pion1)) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | (L~ pion1)) .: the U1 of ((TOP-REAL 2) | (L~ pion1))) is V11() real ext-real Element of REAL
(L~ go) \/ (L~ do) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
right_cell (godo,1,(Gauge (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
(right_cell (godo,1,(Gauge (C,n)))) \ (L~ godo) is functional Element of K6( the U1 of (TOP-REAL 2))
RightComp godo is non empty functional Element of K6( the U1 of (TOP-REAL 2))
dom godo is non trivial V168() V169() V170() V171() V172() V173() Element of K6(NAT)
godo /. 2 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
rng godo is non trivial functional Element of K6( the U1 of (TOP-REAL 2))
godo /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
len (Cage (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
rng (Cage (C,n)) is non trivial functional Element of K6( the U1 of (TOP-REAL 2))
(Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
W-max (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))), REAL ) V205((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),REAL))
the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is set
K7( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),REAL)) is set
lower_bound (proj1 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is V11() real ext-real Element of REAL
(proj1 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SW-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V11() real ext-real Element of REAL
proj2 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))), REAL ) V205((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),REAL))
lower_bound (proj2 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is V11() real ext-real Element of REAL
(proj2 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),(S-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NW-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),(N-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),(NW-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SW-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),(NW-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))) /\ (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is V19() V22( the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))), REAL ) V205((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))),REAL))
the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is set
K7( the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))),REAL)) is set
upper_bound (proj2 | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
(proj2 | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) .: the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V168() V169() V170() Element of K6(REAL)
upper_bound ((proj2 | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) .: the U1 of ((TOP-REAL 2) | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),(upper_bound (proj2 | (W-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(W-max (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .. (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
N-min (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
NE-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is V11() real ext-real Element of REAL
upper_bound ((proj1 | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),(N-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((NW-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),(NE-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((NW-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))),(NE-corner (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))) /\ (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is V19() V22( the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))), REAL ) V205((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))),REAL))
the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is set
K7( the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))),REAL)) is set
lower_bound (proj1 | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
(proj1 | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) .: the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) .: the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))),(N-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(N-min (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .. (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
N-max (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
upper_bound (proj1 | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
upper_bound ((proj1 | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))) .: the U1 of ((TOP-REAL 2) | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))) is V11() real ext-real Element of REAL
|[(upper_bound (proj1 | (N-most (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))))),(N-bound (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(N-max (L~ (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) .. (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(E-max (L~ (Cage (C,n)))) .. (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
len (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
right_cell ((Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))),1) is functional Element of K6( the U1 of (TOP-REAL 2))
GoB (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) is V19() non empty-yielding V22( NAT ) V23(K295( the U1 of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K295( the U1 of (TOP-REAL 2))
right_cell ((Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))),1,(GoB (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))))) is functional Element of K6( the U1 of (TOP-REAL 2))
GoB (Cage (C,n)) is V19() non empty-yielding V22( NAT ) V23(K295( the U1 of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K295( the U1 of (TOP-REAL 2))
right_cell ((Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))),1,(GoB (Cage (C,n)))) is functional Element of K6( the U1 of (TOP-REAL 2))
right_cell ((Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))),1,(Gauge (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
(Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) -: (E-max (L~ (Cage (C,n)))) is V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like special unfolded FinSequence of the U1 of (TOP-REAL 2)
right_cell (((Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) -: (E-max (L~ (Cage (C,n))))),1,(Gauge (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
right_cell ((Upper_Seq (C,n)),1,(Gauge (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
right_cell ((R_Cut ((Upper_Seq (C,n)),((Gauge (C,n)) * (j,k)))),1,(Gauge (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
right_cell ((go ^' pion1),1,(Gauge (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
W-min ((L~ go) \/ (L~ do)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound ((L~ go) \/ (L~ do)) is V11() real ext-real Element of REAL
(TOP-REAL 2) | ((L~ go) \/ (L~ do)) is strict T_2 SubSpace of TOP-REAL 2
proj1 | ((L~ go) \/ (L~ do)) is V19() V22( the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ do)))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ do))), REAL ) V205((TOP-REAL 2) | ((L~ go) \/ (L~ do))) Element of K6(K7( the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ do))),REAL))
the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ do))) is set
K7( the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ do))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ do))),REAL)) is set
lower_bound (proj1 | ((L~ go) \/ (L~ do))) is V11() real ext-real Element of REAL
(proj1 | ((L~ go) \/ (L~ do))) .: the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ do))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | ((L~ go) \/ (L~ do))) .: the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ do)))) is V11() real ext-real Element of REAL
W-most ((L~ go) \/ (L~ do)) is functional Element of K6( the U1 of (TOP-REAL 2))
SW-corner ((L~ go) \/ (L~ do)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-bound ((L~ go) \/ (L~ do)) is V11() real ext-real Element of REAL
proj2 | ((L~ go) \/ (L~ do)) is V19() V22( the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ do)))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ do))), REAL ) V205((TOP-REAL 2) | ((L~ go) \/ (L~ do))) Element of K6(K7( the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ do))),REAL))
lower_bound (proj2 | ((L~ go) \/ (L~ do))) is V11() real ext-real Element of REAL
(proj2 | ((L~ go) \/ (L~ do))) .: the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ do))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | ((L~ go) \/ (L~ do))) .: the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ do)))) is V11() real ext-real Element of REAL
|[(W-bound ((L~ go) \/ (L~ do))),(S-bound ((L~ go) \/ (L~ do)))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NW-corner ((L~ go) \/ (L~ do)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound ((L~ go) \/ (L~ do)) is V11() real ext-real Element of REAL
upper_bound (proj2 | ((L~ go) \/ (L~ do))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | ((L~ go) \/ (L~ do))) .: the U1 of ((TOP-REAL 2) | ((L~ go) \/ (L~ do)))) is V11() real ext-real Element of REAL
|[(W-bound ((L~ go) \/ (L~ do))),(N-bound ((L~ go) \/ (L~ do)))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner ((L~ go) \/ (L~ do))),(NW-corner ((L~ go) \/ (L~ do)))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( 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 K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (W-most ((L~ go) \/ (L~ do))) is strict T_2 SubSpace of TOP-REAL 2
proj2 | (W-most ((L~ go) \/ (L~ do))) is V19() V22( the U1 of ((TOP-REAL 2) | (W-most ((L~ go) \/ (L~ do))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (W-most ((L~ go) \/ (L~ do)))), REAL ) V205((TOP-REAL 2) | (W-most ((L~ go) \/ (L~ do)))) Element of K6(K7( 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
K7( the U1 of ((TOP-REAL 2) | (W-most ((L~ go) \/ (L~ do)))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (W-most ((L~ go) \/ (L~ do)))),REAL)) is set
lower_bound (proj2 | (W-most ((L~ go) \/ (L~ do)))) is V11() real ext-real Element of REAL
(proj2 | (W-most ((L~ go) \/ (L~ do)))) .: the U1 of ((TOP-REAL 2) | (W-most ((L~ go) \/ (L~ do)))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (W-most ((L~ go) \/ (L~ do)))) .: the U1 of ((TOP-REAL 2) | (W-most ((L~ go) \/ (L~ do))))) is V11() real ext-real Element of REAL
|[(W-bound ((L~ go) \/ (L~ do))),(lower_bound (proj2 | (W-most ((L~ go) \/ (L~ do)))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(W-min ((L~ go) \/ (L~ do))) `1 is V11() real ext-real Element of REAL
((L~ go) \/ (L~ do)) \/ (L~ pion1) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
W-min (((L~ go) \/ (L~ do)) \/ (L~ pion1)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound (((L~ go) \/ (L~ do)) \/ (L~ pion1)) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (((L~ go) \/ (L~ do)) \/ (L~ pion1)) is strict T_2 SubSpace of TOP-REAL 2
proj1 | (((L~ go) \/ (L~ do)) \/ (L~ pion1)) is V19() V22( the U1 of ((TOP-REAL 2) | (((L~ go) \/ (L~ do)) \/ (L~ pion1)))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (((L~ go) \/ (L~ do)) \/ (L~ pion1))), REAL ) V205((TOP-REAL 2) | (((L~ go) \/ (L~ do)) \/ (L~ pion1))) Element of K6(K7( 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 set
K7( the U1 of ((TOP-REAL 2) | (((L~ go) \/ (L~ do)) \/ (L~ pion1))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (((L~ go) \/ (L~ do)) \/ (L~ pion1))),REAL)) is set
lower_bound (proj1 | (((L~ go) \/ (L~ do)) \/ (L~ pion1))) is V11() real ext-real Element of REAL
(proj1 | (((L~ go) \/ (L~ do)) \/ (L~ pion1))) .: the U1 of ((TOP-REAL 2) | (((L~ go) \/ (L~ do)) \/ (L~ pion1))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | (((L~ go) \/ (L~ do)) \/ (L~ pion1))) .: the U1 of ((TOP-REAL 2) | (((L~ go) \/ (L~ do)) \/ (L~ pion1)))) is V11() real ext-real Element of REAL
W-most (((L~ go) \/ (L~ do)) \/ (L~ pion1)) is functional Element of K6( the U1 of (TOP-REAL 2))
SW-corner (((L~ go) \/ (L~ do)) \/ (L~ pion1)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-bound (((L~ go) \/ (L~ do)) \/ (L~ pion1)) is V11() real ext-real Element of REAL
proj2 | (((L~ go) \/ (L~ do)) \/ (L~ pion1)) is V19() V22( the U1 of ((TOP-REAL 2) | (((L~ go) \/ (L~ do)) \/ (L~ pion1)))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (((L~ go) \/ (L~ do)) \/ (L~ pion1))), REAL ) V205((TOP-REAL 2) | (((L~ go) \/ (L~ do)) \/ (L~ pion1))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (((L~ go) \/ (L~ do)) \/ (L~ pion1))),REAL))
lower_bound (proj2 | (((L~ go) \/ (L~ do)) \/ (L~ pion1))) is V11() real ext-real Element of REAL
(proj2 | (((L~ go) \/ (L~ do)) \/ (L~ pion1))) .: the U1 of ((TOP-REAL 2) | (((L~ go) \/ (L~ do)) \/ (L~ pion1))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (((L~ go) \/ (L~ do)) \/ (L~ pion1))) .: the U1 of ((TOP-REAL 2) | (((L~ go) \/ (L~ do)) \/ (L~ pion1)))) is V11() real ext-real Element of REAL
|[(W-bound (((L~ go) \/ (L~ do)) \/ (L~ pion1))),(S-bound (((L~ go) \/ (L~ do)) \/ (L~ pion1)))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NW-corner (((L~ go) \/ (L~ do)) \/ (L~ pion1)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound (((L~ go) \/ (L~ do)) \/ (L~ pion1)) is V11() real ext-real Element of REAL
upper_bound (proj2 | (((L~ go) \/ (L~ do)) \/ (L~ pion1))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (((L~ go) \/ (L~ do)) \/ (L~ pion1))) .: the U1 of ((TOP-REAL 2) | (((L~ go) \/ (L~ do)) \/ (L~ pion1)))) is V11() real ext-real Element of REAL
|[(W-bound (((L~ go) \/ (L~ do)) \/ (L~ pion1))),(N-bound (((L~ go) \/ (L~ do)) \/ (L~ pion1)))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() 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 non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( 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 K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (W-most (((L~ go) \/ (L~ do)) \/ (L~ pion1))) is strict T_2 SubSpace of TOP-REAL 2
proj2 | (W-most (((L~ go) \/ (L~ do)) \/ (L~ pion1))) is V19() V22( the U1 of ((TOP-REAL 2) | (W-most (((L~ go) \/ (L~ do)) \/ (L~ pion1))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (W-most (((L~ go) \/ (L~ do)) \/ (L~ pion1)))), REAL ) V205((TOP-REAL 2) | (W-most (((L~ go) \/ (L~ do)) \/ (L~ pion1)))) Element of K6(K7( 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
K7( the U1 of ((TOP-REAL 2) | (W-most (((L~ go) \/ (L~ do)) \/ (L~ pion1)))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (W-most (((L~ go) \/ (L~ do)) \/ (L~ pion1)))),REAL)) is set
lower_bound (proj2 | (W-most (((L~ go) \/ (L~ do)) \/ (L~ pion1)))) is V11() real ext-real Element of REAL
(proj2 | (W-most (((L~ go) \/ (L~ do)) \/ (L~ pion1)))) .: the U1 of ((TOP-REAL 2) | (W-most (((L~ go) \/ (L~ do)) \/ (L~ pion1)))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (W-most (((L~ go) \/ (L~ do)) \/ (L~ pion1)))) .: the U1 of ((TOP-REAL 2) | (W-most (((L~ go) \/ (L~ do)) \/ (L~ pion1))))) is V11() real ext-real Element of REAL
|[(W-bound (((L~ go) \/ (L~ do)) \/ (L~ pion1))),(lower_bound (proj2 | (W-most (((L~ go) \/ (L~ do)) \/ (L~ pion1)))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-min (L~ godo) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound (L~ godo) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ godo) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ godo) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ godo))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ godo)), REAL ) V205((TOP-REAL 2) | (L~ godo)) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ godo)),REAL))
the U1 of ((TOP-REAL 2) | (L~ godo)) is set
K7( the U1 of ((TOP-REAL 2) | (L~ godo)),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (L~ godo)),REAL)) is set
lower_bound (proj1 | (L~ godo)) is V11() real ext-real Element of REAL
(proj1 | (L~ godo)) .: the U1 of ((TOP-REAL 2) | (L~ godo)) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | (L~ godo)) .: the U1 of ((TOP-REAL 2) | (L~ godo))) is V11() real ext-real Element of REAL
W-most (L~ godo) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SW-corner (L~ godo) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-bound (L~ godo) is V11() real ext-real Element of REAL
proj2 | (L~ godo) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ godo))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ godo)), REAL ) V205((TOP-REAL 2) | (L~ godo)) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ godo)),REAL))
lower_bound (proj2 | (L~ godo)) is V11() real ext-real Element of REAL
(proj2 | (L~ godo)) .: the U1 of ((TOP-REAL 2) | (L~ godo)) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (L~ godo)) .: the U1 of ((TOP-REAL 2) | (L~ godo))) is V11() real ext-real Element of REAL
|[(W-bound (L~ godo)),(S-bound (L~ godo))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NW-corner (L~ godo) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound (L~ godo) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ godo)) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (L~ godo)) .: the U1 of ((TOP-REAL 2) | (L~ godo))) is V11() real ext-real Element of REAL
|[(W-bound (L~ godo)),(N-bound (L~ godo))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner (L~ godo)),(NW-corner (L~ godo))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SW-corner (L~ godo)),(NW-corner (L~ godo)))) /\ (L~ godo) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (W-most (L~ godo)) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (W-most (L~ godo)) is V19() V22( the U1 of ((TOP-REAL 2) | (W-most (L~ godo)))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (W-most (L~ godo))), REAL ) V205((TOP-REAL 2) | (W-most (L~ godo))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (W-most (L~ godo))),REAL))
the U1 of ((TOP-REAL 2) | (W-most (L~ godo))) is set
K7( the U1 of ((TOP-REAL 2) | (W-most (L~ godo))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (W-most (L~ godo))),REAL)) is set
lower_bound (proj2 | (W-most (L~ godo))) is V11() real ext-real Element of REAL
(proj2 | (W-most (L~ godo))) .: the U1 of ((TOP-REAL 2) | (W-most (L~ godo))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (W-most (L~ godo))) .: the U1 of ((TOP-REAL 2) | (W-most (L~ godo)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ godo)),(lower_bound (proj2 | (W-most (L~ godo))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(go ^' pion1) /. 2 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Upper_Seq (C,n)) ^' (Lower_Seq (C,n)) is non empty V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
((Upper_Seq (C,n)) ^' (Lower_Seq (C,n))) /. 2 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) /. 2 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(godo /. 2) `1 is V11() real ext-real Element of REAL
(W-min (L~ godo)) `1 is V11() real ext-real Element of REAL
Rotate (godo,(W-min (L~ godo))) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like non constant V32() 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 V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Upper_Seq (C,n)) . (len (Upper_Seq (C,n))) is V19() Function-like set
(Upper_Seq (C,n)) /. (len (Upper_Seq (C,n))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
east_halfline (E-max C) is non empty functional connected V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
W is set
p is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(east_halfline (E-max C)) /\ (L~ (Cage (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
p `1 is V11() real ext-real Element of REAL
godo is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like non constant V32() 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 closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
W is set
p is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
p `2 is V11() real ext-real Element of REAL
(E-max C) `2 is V11() real ext-real Element of REAL
p `1 is V11() real ext-real Element of REAL
p `1 is V11() real ext-real Element of REAL
p `1 is V11() real ext-real Element of REAL
p `1 is V11() real ext-real Element of REAL
i + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(i + 1) - 1 is V11() real ext-real Element of REAL
(len (Gauge (C,n))) - 1 is V11() real ext-real Element of REAL
(len (Gauge (C,n))) -' 1 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * (((len (Gauge (C,n))) -' 1),1) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (((len (Gauge (C,n))) -' 1),1)) `1 is V11() real ext-real Element of REAL
(E-max C) `1 is V11() real ext-real Element of REAL
W is set
p is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
Index (p,do) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
LSeg (do,(Index (p,do))) is functional Element of K6( the U1 of (TOP-REAL 2))
t is ordinal natural ext-real non negative set
(Lower_Seq (C,n)) . t is V19() Function-like set
Index (((Gauge (C,n)) * (i,k)),(Lower_Seq (C,n))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Index (((Gauge (C,n)) * (i,k)),(Lower_Seq (C,n)))) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
len (L_Cut ((Lower_Seq (C,n)),((Gauge (C,n)) * (i,k)))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(len (Lower_Seq (C,n))) - (Index (((Gauge (C,n)) * (i,k)),(Lower_Seq (C,n)))) is V11() real ext-real Element of REAL
(len (Lower_Seq (C,n))) -' (Index (((Gauge (C,n)) * (i,k)),(Lower_Seq (C,n)))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Index (p,do)) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((len (Lower_Seq (C,n))) -' (Index (((Gauge (C,n)) * (i,k)),(Lower_Seq (C,n))))) - 1 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (i,k)) .. (Lower_Seq (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
mid ((Lower_Seq (C,n)),(((Gauge (C,n)) * (i,k)) .. (Lower_Seq (C,n))),(len (Lower_Seq (C,n)))) is V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the U1 of (TOP-REAL 2)
(east_halfline (E-max C)) /\ (L~ (Cage (C,n))) is functional Element of K6( the U1 of (TOP-REAL 2))
p `1 is V11() real ext-real Element of REAL
0 + (Index (((Gauge (C,n)) * (i,k)),(Lower_Seq (C,n)))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((len (Lower_Seq (C,n))) - (Index (((Gauge (C,n)) * (i,k)),(Lower_Seq (C,n))))) - 1 is V11() real ext-real Element of REAL
(len (Lower_Seq (C,n))) - (((Gauge (C,n)) * (i,k)) .. (Lower_Seq (C,n))) is V11() real ext-real Element of REAL
(len (Lower_Seq (C,n))) -' (((Gauge (C,n)) * (i,k)) .. (Lower_Seq (C,n))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((len (Lower_Seq (C,n))) -' (((Gauge (C,n)) * (i,k)) .. (Lower_Seq (C,n)))) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Index (p,do)) + (((Gauge (C,n)) * (i,k)) .. (Lower_Seq (C,n))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((Index (p,do)) + (((Gauge (C,n)) * (i,k)) .. (Lower_Seq (C,n)))) -' 1 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
right_cell ((Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))),1) is functional Element of K6( the U1 of (TOP-REAL 2))
GoB (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))) is V19() non empty-yielding V22( NAT ) V23(K295( the U1 of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K295( the U1 of (TOP-REAL 2))
L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
jj2 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * ((len (Gauge (C,n))),jj2) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
[(len (Gauge (C,n))),jj2] is set
{(len (Gauge (C,n))),jj2} is non empty V168() V169() V170() V171() V172() V173() set
{{(len (Gauge (C,n))),jj2},{(len (Gauge (C,n)))}} is non empty set
len (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))) -: (W-min (L~ (Cage (C,n)))) is V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like special unfolded FinSequence of the U1 of (TOP-REAL 2)
LSeg ((Lower_Seq (C,n)),1) is functional Element of K6( the U1 of (TOP-REAL 2))
LSeg ((Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))),1) is functional Element of K6( the U1 of (TOP-REAL 2))
(Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))) /. 1 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))) /. (1 + 1) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
ii is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
jj is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
jj + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
[ii,(jj + 1)] is set
{ii,(jj + 1)} is non empty V168() V169() V170() V171() V172() V173() set
{ii} is non empty V168() V169() V170() V171() V172() V173() set
{{ii,(jj + 1)},{ii}} is non empty set
[ii,jj] is set
{ii,jj} is non empty V168() V169() V170() V171() V172() V173() set
{{ii,jj},{ii}} is non empty set
(Gauge (C,n)) * (ii,(jj + 1)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Gauge (C,n)) * (ii,jj) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(jj + 1) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
E-max (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-bound (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))), REAL ) V205((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),REAL))
the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) is set
K7( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),REAL)) is set
upper_bound (proj1 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) is V11() real ext-real Element of REAL
(proj1 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) is V168() V169() V170() Element of K6(REAL)
upper_bound ((proj1 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SE-corner (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-bound (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is V11() real ext-real Element of REAL
proj2 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is V19() V22( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))), REAL ) V205((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),REAL))
lower_bound (proj2 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) is V11() real ext-real Element of REAL
(proj2 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),(S-bound (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NE-corner (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is V11() real ext-real Element of REAL
upper_bound (proj2 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) .: the U1 of ((TOP-REAL 2) | (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),(N-bound (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),(NE-corner (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SE-corner (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),(NE-corner (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))))) /\ (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) is strict T_2 compact SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))) is V19() V22( the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))), REAL ) V205((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))),REAL))
the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) is set
K7( the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))),REAL)) is set
upper_bound (proj2 | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) is V11() real ext-real Element of REAL
(proj2 | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) .: the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) is V168() V169() V170() Element of K6(REAL)
upper_bound ((proj2 | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))) .: the U1 of ((TOP-REAL 2) | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))))),(upper_bound (proj2 | (E-most (L~ (Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n))))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
4 - 1 is V11() real ext-real Element of REAL
ii - 1 is V11() real ext-real Element of REAL
ii -' 1 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * ((len (Gauge (C,n))),jj) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * ((len (Gauge (C,n))),jj)) `1 is V11() real ext-real Element of REAL
ii + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
cell ((Gauge (C,n)),(ii -' 1),jj) is functional Element of K6( the U1 of (TOP-REAL 2))
(Gauge (C,n)) * ((len (Gauge (C,n))),(jj + 1)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * ((len (Gauge (C,n))),(jj + 1))) `1 is V11() real ext-real Element of REAL
(ii -' 1) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * ((ii -' 1),(jj + 1)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * ((ii -' 1),(jj + 1))) `2 is V11() real ext-real Element of REAL
(Gauge (C,n)) * (1,(jj + 1)) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (1,(jj + 1))) `2 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (ii,(jj + 1))) `2 is V11() real ext-real Element of REAL
(E-max C) `2 is V11() real ext-real Element of REAL
p `2 is V11() real ext-real Element of REAL
(Gauge (C,n)) * ((ii -' 1),jj) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * ((ii -' 1),jj)) `2 is V11() real ext-real Element of REAL
(Gauge (C,n)) * (1,jj) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * (1,jj)) `2 is V11() real ext-real Element of REAL
((Gauge (C,n)) * (ii,jj)) `2 is V11() real ext-real Element of REAL
LSeg (((Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))) /. 1),((Rotate ((Cage (C,n)),(E-max (L~ (Cage (C,n)))))) /. (1 + 1))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
LSeg ((mid ((Lower_Seq (C,n)),(((Gauge (C,n)) * (i,k)) .. (Lower_Seq (C,n))),(len (Lower_Seq (C,n))))),(Index (p,do))) is functional Element of K6( the U1 of (TOP-REAL 2))
LSeg ((Lower_Seq (C,n)),(((Index (p,do)) + (((Gauge (C,n)) * (i,k)) .. (Lower_Seq (C,n)))) -' 1)) is functional Element of K6( the U1 of (TOP-REAL 2))
(1 + 1) + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
((1 + 1) + 1) - 1 is V11() real ext-real Element of REAL
((Index (p,do)) + (((Gauge (C,n)) * (i,k)) .. (Lower_Seq (C,n)))) - 1 is V11() real ext-real Element of REAL
(LSeg ((Lower_Seq (C,n)),1)) /\ (LSeg ((Lower_Seq (C,n)),(((Index (p,do)) + (((Gauge (C,n)) * (i,k)) .. (Lower_Seq (C,n)))) -' 1))) is functional Element of K6( the U1 of (TOP-REAL 2))
(Lower_Seq (C,n)) /. 2 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
{((Lower_Seq (C,n)) /. 2)} is non empty functional set
p .. (Lower_Seq (C,n)) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,n)) * ((len (Gauge (C,n))),k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,n)) * ((len (Gauge (C,n))),k)) `1 is V11() real ext-real Element of REAL
(L~ godo) ` is non empty functional Element of K6( the U1 of (TOP-REAL 2))
W is functional Element of K6( the U1 of (TOP-REAL 2))
UBD (L~ godo) is non empty functional open connected Element of K6( the U1 of (TOP-REAL 2))
LeftComp godo is non empty functional Element of K6( the U1 of (TOP-REAL 2))
{((Gauge (C,n)) * (i,k))} is non empty functional set
((Gauge (C,n)) * (i,k)) `2 is V11() real ext-real Element of REAL
{((Gauge (C,n)) * (i,k))} is non empty functional set
((Gauge (C,n)) * (i,k)) `2 is V11() real ext-real Element of REAL
n is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
n + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
C is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
Gauge (C,(n + 1)) is V19() non empty-yielding V22( NAT ) V23(K295( the U1 of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K295( the U1 of (TOP-REAL 2))
len (Gauge (C,(n + 1))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
width (Gauge (C,(n + 1))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Cage (C,(n + 1)) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
L~ (Cage (C,(n + 1))) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
Upper_Arc (L~ (Cage (C,(n + 1)))) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
Lower_Arc (L~ (Cage (C,(n + 1)))) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
Upper_Arc C is non empty functional Element of K6( the U1 of (TOP-REAL 2))
i is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
j is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
k is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
k is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,(n + 1))) * (i,k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Gauge (C,(n + 1))) * (j,k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Gauge (C,(n + 1))) * (j,k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) \/ (LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
[j,k] is set
{j,k} is non empty V168() V169() V170() V171() V172() V173() set
{j} is non empty V168() V169() V170() V171() V172() V173() set
{{j,k},{j}} is non empty set
Indices (Gauge (C,(n + 1))) is set
[i,k] is set
{i,k} is non empty V168() V169() V170() V171() V172() V173() set
{i} is non empty V168() V169() V170() V171() V172() V173() set
{{i,k},{i}} is non empty set
((Gauge (C,(n + 1))) * (j,k)) `2 is V11() real ext-real Element of REAL
(Gauge (C,(n + 1))) * (1,k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,(n + 1))) * (1,k)) `2 is V11() real ext-real Element of REAL
((Gauge (C,(n + 1))) * (i,k)) `2 is V11() real ext-real Element of REAL
Lower_Seq (C,(n + 1)) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
L~ (Lower_Seq (C,(n + 1))) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
[j,k] is set
{j,k} is non empty V168() V169() V170() V171() V172() V173() set
{{j,k},{j}} is non empty set
((Gauge (C,(n + 1))) * (j,k)) `1 is V11() real ext-real Element of REAL
(Gauge (C,(n + 1))) * (j,1) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,(n + 1))) * (j,1)) `1 is V11() real ext-real Element of REAL
((Gauge (C,(n + 1))) * (j,k)) `1 is V11() real ext-real Element of REAL
Upper_Seq (C,(n + 1)) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
L~ (Upper_Seq (C,(n + 1))) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
x is set
i3 is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
S-most i3 is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SW-corner i3 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound i3 is V11() real ext-real Element of REAL
(TOP-REAL 2) | i3 is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | i3 is V19() V22( the U1 of ((TOP-REAL 2) | i3)) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | i3), REAL ) V205((TOP-REAL 2) | i3) Element of K6(K7( the U1 of ((TOP-REAL 2) | i3),REAL))
the U1 of ((TOP-REAL 2) | i3) is set
K7( the U1 of ((TOP-REAL 2) | i3),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | i3),REAL)) is set
lower_bound (proj1 | i3) is V11() real ext-real Element of REAL
(proj1 | i3) .: the U1 of ((TOP-REAL 2) | i3) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | i3) .: the U1 of ((TOP-REAL 2) | i3)) is V11() real ext-real Element of REAL
S-bound i3 is V11() real ext-real Element of REAL
proj2 | i3 is V19() V22( the U1 of ((TOP-REAL 2) | i3)) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | i3), REAL ) V205((TOP-REAL 2) | i3) Element of K6(K7( the U1 of ((TOP-REAL 2) | i3),REAL))
lower_bound (proj2 | i3) is V11() real ext-real Element of REAL
(proj2 | i3) .: the U1 of ((TOP-REAL 2) | i3) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | i3) .: the U1 of ((TOP-REAL 2) | i3)) is V11() real ext-real Element of REAL
|[(W-bound i3),(S-bound i3)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
SE-corner i3 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-bound i3 is V11() real ext-real Element of REAL
upper_bound (proj1 | i3) is V11() real ext-real Element of REAL
upper_bound ((proj1 | i3) .: the U1 of ((TOP-REAL 2) | i3)) is V11() real ext-real Element of REAL
|[(E-bound i3),(S-bound i3)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner i3),(SE-corner i3)) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SW-corner i3),(SE-corner i3))) /\ i3 is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
x is set
pp is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
proj2 .: ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1))))) is V168() V169() V170() Element of K6(REAL)
lower_bound (proj2 .: ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))))) is V11() real ext-real Element of REAL
m is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,(n + 1))) * (j,m) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,(n + 1))) * (j,m)) `2 is V11() real ext-real Element of REAL
((Gauge (C,(n + 1))) * (j,m)) `1 is V11() real ext-real Element of REAL
|[(((Gauge (C,(n + 1))) * (j,1)) `1),(lower_bound (proj2 .: ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
|[(((Gauge (C,(n + 1))) * (j,1)) `1),(lower_bound (proj2 .: ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))))))]| `1 is V11() real ext-real Element of REAL
pp `1 is V11() real ext-real Element of REAL
|[(((Gauge (C,(n + 1))) * (j,1)) `1),(lower_bound (proj2 .: ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))))))]| `2 is V11() real ext-real Element of REAL
S-bound ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1))))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1))))) is strict T_2 SubSpace of TOP-REAL 2
proj2 | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1))))) is V19() V22( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))))), REAL ) V205((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))))),REAL))
the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))))) is set
K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))))),REAL)) is set
lower_bound (proj2 | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))))) is V11() real ext-real Element of REAL
(proj2 | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1))))))) is V11() real ext-real Element of REAL
S-min ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-most ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1))))) is functional Element of K6( the U1 of (TOP-REAL 2))
SW-corner ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1))))) is V11() real ext-real Element of REAL
proj1 | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1))))) is V19() V22( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))))), REAL ) V205((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))))),REAL))
lower_bound (proj1 | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))))) is V11() real ext-real Element of REAL
(proj1 | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1))))))) is V11() real ext-real Element of REAL
|[(W-bound ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))))),(S-bound ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
SE-corner ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-bound ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1))))) is V11() real ext-real Element of REAL
upper_bound (proj1 | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))))) is V11() real ext-real Element of REAL
upper_bound ((proj1 | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1))))))) is V11() real ext-real Element of REAL
|[(E-bound ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))))),(S-bound ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))))),(SE-corner ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1))))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SW-corner ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))))),(SE-corner ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))))))) /\ ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1))))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (S-most ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))))) is strict T_2 SubSpace of TOP-REAL 2
proj1 | (S-most ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))))) is V19() V22( the U1 of ((TOP-REAL 2) | (S-most ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (S-most ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1))))))), REAL ) V205((TOP-REAL 2) | (S-most ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1))))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (S-most ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1))))))),REAL))
the U1 of ((TOP-REAL 2) | (S-most ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1))))))) is set
K7( the U1 of ((TOP-REAL 2) | (S-most ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1))))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (S-most ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1))))))),REAL)) is set
lower_bound (proj1 | (S-most ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1))))))) is V11() real ext-real Element of REAL
(proj1 | (S-most ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1))))))) .: the U1 of ((TOP-REAL 2) | (S-most ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1))))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | (S-most ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1))))))) .: the U1 of ((TOP-REAL 2) | (S-most ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))))))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (S-most ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))))))),(S-bound ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(S-min ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))))) `2 is V11() real ext-real Element of REAL
pp `2 is V11() real ext-real Element of REAL
LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,m))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
x is set
i3 is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
E-most i3 is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SE-corner i3 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-bound i3 is V11() real ext-real Element of REAL
(TOP-REAL 2) | i3 is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | i3 is V19() V22( the U1 of ((TOP-REAL 2) | i3)) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | i3), REAL ) V205((TOP-REAL 2) | i3) Element of K6(K7( the U1 of ((TOP-REAL 2) | i3),REAL))
the U1 of ((TOP-REAL 2) | i3) is set
K7( the U1 of ((TOP-REAL 2) | i3),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | i3),REAL)) is set
upper_bound (proj1 | i3) is V11() real ext-real Element of REAL
(proj1 | i3) .: the U1 of ((TOP-REAL 2) | i3) is V168() V169() V170() Element of K6(REAL)
upper_bound ((proj1 | i3) .: the U1 of ((TOP-REAL 2) | i3)) is V11() real ext-real Element of REAL
S-bound i3 is V11() real ext-real Element of REAL
proj2 | i3 is V19() V22( the U1 of ((TOP-REAL 2) | i3)) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | i3), REAL ) V205((TOP-REAL 2) | i3) Element of K6(K7( the U1 of ((TOP-REAL 2) | i3),REAL))
lower_bound (proj2 | i3) is V11() real ext-real Element of REAL
(proj2 | i3) .: the U1 of ((TOP-REAL 2) | i3) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | i3) .: the U1 of ((TOP-REAL 2) | i3)) is V11() real ext-real Element of REAL
|[(E-bound i3),(S-bound i3)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NE-corner i3 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound i3 is V11() real ext-real Element of REAL
upper_bound (proj2 | i3) is V11() real ext-real Element of REAL
upper_bound ((proj2 | i3) .: the U1 of ((TOP-REAL 2) | i3)) is V11() real ext-real Element of REAL
|[(E-bound i3),(N-bound i3)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner i3),(NE-corner i3)) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SE-corner i3),(NE-corner i3))) /\ i3 is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
x is set
pp is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
proj1 .: ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))) is V168() V169() V170() Element of K6(REAL)
upper_bound (proj1 .: ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))) is V11() real ext-real Element of REAL
m is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,(n + 1))) * (m,k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,(n + 1))) * (m,k)) `1 is V11() real ext-real Element of REAL
((Gauge (C,(n + 1))) * (m,k)) `2 is V11() real ext-real Element of REAL
|[(upper_bound (proj1 .: ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))),(((Gauge (C,(n + 1))) * (1,k)) `2)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
|[(upper_bound (proj1 .: ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))),(((Gauge (C,(n + 1))) * (1,k)) `2)]| `2 is V11() real ext-real Element of REAL
pp `2 is V11() real ext-real Element of REAL
|[(upper_bound (proj1 .: ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))),(((Gauge (C,(n + 1))) * (1,k)) `2)]| `1 is V11() real ext-real Element of REAL
E-bound ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))) is strict T_2 SubSpace of TOP-REAL 2
proj1 | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))) is V19() V22( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))), REAL ) V205((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))),REAL))
the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))) is set
K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))),REAL)) is set
upper_bound (proj1 | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))) is V11() real ext-real Element of REAL
(proj1 | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))) is V168() V169() V170() Element of K6(REAL)
upper_bound ((proj1 | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))) is V11() real ext-real Element of REAL
E-min ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-most ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))) is functional Element of K6( the U1 of (TOP-REAL 2))
SE-corner ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-bound ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))) is V11() real ext-real Element of REAL
proj2 | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))) is V19() V22( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))), REAL ) V205((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))),REAL))
lower_bound (proj2 | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))) is V11() real ext-real Element of REAL
(proj2 | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))) is V11() real ext-real Element of REAL
|[(E-bound ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))),(S-bound ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NE-corner ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))) is V11() real ext-real Element of REAL
upper_bound (proj2 | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))) is V11() real ext-real Element of REAL
|[(E-bound ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))),(N-bound ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))),(NE-corner ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SE-corner ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))),(NE-corner ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))))) /\ ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (E-most ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))) is strict T_2 SubSpace of TOP-REAL 2
proj2 | (E-most ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))) is V19() V22( the U1 of ((TOP-REAL 2) | (E-most ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (E-most ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))), REAL ) V205((TOP-REAL 2) | (E-most ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (E-most ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))),REAL))
the U1 of ((TOP-REAL 2) | (E-most ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))) is set
K7( the U1 of ((TOP-REAL 2) | (E-most ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (E-most ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))),REAL)) is set
lower_bound (proj2 | (E-most ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))) is V11() real ext-real Element of REAL
(proj2 | (E-most ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))) .: the U1 of ((TOP-REAL 2) | (E-most ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (E-most ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))) .: the U1 of ((TOP-REAL 2) | (E-most ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))))) is V11() real ext-real Element of REAL
|[(E-bound ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))),(lower_bound (proj2 | (E-most ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(E-min ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))) `1 is V11() real ext-real Element of REAL
pp `1 is V11() real ext-real Element of REAL
LSeg (((Gauge (C,(n + 1))) * (m,k)),((Gauge (C,(n + 1))) * (i,k))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
x is set
i3 is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
W-most i3 is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SW-corner i3 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound i3 is V11() real ext-real Element of REAL
(TOP-REAL 2) | i3 is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | i3 is V19() V22( the U1 of ((TOP-REAL 2) | i3)) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | i3), REAL ) V205((TOP-REAL 2) | i3) Element of K6(K7( the U1 of ((TOP-REAL 2) | i3),REAL))
the U1 of ((TOP-REAL 2) | i3) is set
K7( the U1 of ((TOP-REAL 2) | i3),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | i3),REAL)) is set
lower_bound (proj1 | i3) is V11() real ext-real Element of REAL
(proj1 | i3) .: the U1 of ((TOP-REAL 2) | i3) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | i3) .: the U1 of ((TOP-REAL 2) | i3)) is V11() real ext-real Element of REAL
S-bound i3 is V11() real ext-real Element of REAL
proj2 | i3 is V19() V22( the U1 of ((TOP-REAL 2) | i3)) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | i3), REAL ) V205((TOP-REAL 2) | i3) Element of K6(K7( the U1 of ((TOP-REAL 2) | i3),REAL))
lower_bound (proj2 | i3) is V11() real ext-real Element of REAL
(proj2 | i3) .: the U1 of ((TOP-REAL 2) | i3) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | i3) .: the U1 of ((TOP-REAL 2) | i3)) is V11() real ext-real Element of REAL
|[(W-bound i3),(S-bound i3)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NW-corner i3 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound i3 is V11() real ext-real Element of REAL
upper_bound (proj2 | i3) is V11() real ext-real Element of REAL
upper_bound ((proj2 | i3) .: the U1 of ((TOP-REAL 2) | i3)) is V11() real ext-real Element of REAL
|[(W-bound i3),(N-bound i3)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner i3),(NW-corner i3)) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SW-corner i3),(NW-corner i3))) /\ i3 is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
x is set
pp is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
proj1 .: ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))) is V168() V169() V170() Element of K6(REAL)
lower_bound (proj1 .: ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))) is V11() real ext-real Element of REAL
m is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,(n + 1))) * (m,k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,(n + 1))) * (m,k)) `1 is V11() real ext-real Element of REAL
((Gauge (C,(n + 1))) * (m,k)) `2 is V11() real ext-real Element of REAL
|[(lower_bound (proj1 .: ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))),(((Gauge (C,(n + 1))) * (1,k)) `2)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
|[(lower_bound (proj1 .: ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))),(((Gauge (C,(n + 1))) * (1,k)) `2)]| `2 is V11() real ext-real Element of REAL
pp `2 is V11() real ext-real Element of REAL
|[(lower_bound (proj1 .: ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))),(((Gauge (C,(n + 1))) * (1,k)) `2)]| `1 is V11() real ext-real Element of REAL
W-bound ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))) is strict T_2 SubSpace of TOP-REAL 2
proj1 | ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))) is V19() V22( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))), REAL ) V205((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))),REAL))
the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))) is set
K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))),REAL)) is set
lower_bound (proj1 | ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))) is V11() real ext-real Element of REAL
(proj1 | ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))) is V11() real ext-real Element of REAL
W-min ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-most ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))) is functional Element of K6( the U1 of (TOP-REAL 2))
SW-corner ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-bound ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))) is V11() real ext-real Element of REAL
proj2 | ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))) is V19() V22( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))), REAL ) V205((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))),REAL))
lower_bound (proj2 | ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))) is V11() real ext-real Element of REAL
(proj2 | ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))) is V11() real ext-real Element of REAL
|[(W-bound ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))),(S-bound ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NW-corner ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))) is V11() real ext-real Element of REAL
upper_bound (proj2 | ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))) is V11() real ext-real Element of REAL
|[(W-bound ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))),(N-bound ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))),(NW-corner ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SW-corner ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))),(NW-corner ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))))) /\ ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (W-most ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))) is strict T_2 SubSpace of TOP-REAL 2
proj2 | (W-most ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))) is V19() V22( the U1 of ((TOP-REAL 2) | (W-most ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (W-most ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))), REAL ) V205((TOP-REAL 2) | (W-most ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (W-most ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))),REAL))
the U1 of ((TOP-REAL 2) | (W-most ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))) is set
K7( the U1 of ((TOP-REAL 2) | (W-most ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (W-most ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))),REAL)) is set
lower_bound (proj2 | (W-most ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))) is V11() real ext-real Element of REAL
(proj2 | (W-most ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))) .: the U1 of ((TOP-REAL 2) | (W-most ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (W-most ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))) .: the U1 of ((TOP-REAL 2) | (W-most ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))))) is V11() real ext-real Element of REAL
|[(W-bound ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))),(lower_bound (proj2 | (W-most ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(W-min ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))) `1 is V11() real ext-real Element of REAL
pp `1 is V11() real ext-real Element of REAL
LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (m,k))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
j1 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,(n + 1))) * (j,j1) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (C,(n + 1))) * (j,j1)),((Gauge (C,(n + 1))) * (j,k))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,(n + 1))) * (j,j1)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
{((Gauge (C,(n + 1))) * (j,j1))} is non empty functional set
i3 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,(n + 1))) * (i3,k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i3,k))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i3,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
{((Gauge (C,(n + 1))) * (i3,k))} is non empty functional set
(LSeg (((Gauge (C,(n + 1))) * (j,j1)),((Gauge (C,(n + 1))) * (j,k)))) \/ (LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i3,k)))) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
((LSeg (((Gauge (C,(n + 1))) * (j,j1)),((Gauge (C,(n + 1))) * (j,k)))) \/ (LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i3,k))))) /\ (L~ (Upper_Seq (C,(n + 1)))) is functional Element of K6( the U1 of (TOP-REAL 2))
x is set
x is set
((LSeg (((Gauge (C,(n + 1))) * (j,j1)),((Gauge (C,(n + 1))) * (j,k)))) \/ (LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i3,k))))) /\ (L~ (Lower_Seq (C,(n + 1)))) is functional Element of K6( the U1 of (TOP-REAL 2))
x is set
x is set
i3 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,(n + 1))) * (i3,k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (C,(n + 1))) * (i3,k)),((Gauge (C,(n + 1))) * (j,k))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,(n + 1))) * (i3,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
{((Gauge (C,(n + 1))) * (i3,k))} is non empty functional set
LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i3,k))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,(n + 1))) * (j,j1)),((Gauge (C,(n + 1))) * (j,k)))) \/ (LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i3,k)))) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i3,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
((LSeg (((Gauge (C,(n + 1))) * (j,j1)),((Gauge (C,(n + 1))) * (j,k)))) \/ (LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i3,k))))) /\ (L~ (Upper_Seq (C,(n + 1)))) is functional Element of K6( the U1 of (TOP-REAL 2))
x is set
x is set
((LSeg (((Gauge (C,(n + 1))) * (j,j1)),((Gauge (C,(n + 1))) * (j,k)))) \/ (LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i3,k))))) /\ (L~ (Lower_Seq (C,(n + 1)))) is functional Element of K6( the U1 of (TOP-REAL 2))
x is set
x is set
n is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
n + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
C is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
Gauge (C,(n + 1)) is V19() non empty-yielding V22( NAT ) V23(K295( the U1 of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K295( the U1 of (TOP-REAL 2))
len (Gauge (C,(n + 1))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
width (Gauge (C,(n + 1))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Cage (C,(n + 1)) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
L~ (Cage (C,(n + 1))) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
Upper_Arc (L~ (Cage (C,(n + 1)))) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
Lower_Arc (L~ (Cage (C,(n + 1)))) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
Lower_Arc C is non empty functional Element of K6( the U1 of (TOP-REAL 2))
i is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
j is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
k is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
k is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,(n + 1))) * (i,k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Gauge (C,(n + 1))) * (j,k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Gauge (C,(n + 1))) * (j,k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) \/ (LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
[j,k] is set
{j,k} is non empty V168() V169() V170() V171() V172() V173() set
{j} is non empty V168() V169() V170() V171() V172() V173() set
{{j,k},{j}} is non empty set
Indices (Gauge (C,(n + 1))) is set
[i,k] is set
{i,k} is non empty V168() V169() V170() V171() V172() V173() set
{i} is non empty V168() V169() V170() V171() V172() V173() set
{{i,k},{i}} is non empty set
((Gauge (C,(n + 1))) * (j,k)) `2 is V11() real ext-real Element of REAL
(Gauge (C,(n + 1))) * (1,k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,(n + 1))) * (1,k)) `2 is V11() real ext-real Element of REAL
((Gauge (C,(n + 1))) * (i,k)) `2 is V11() real ext-real Element of REAL
Lower_Seq (C,(n + 1)) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
L~ (Lower_Seq (C,(n + 1))) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
[j,k] is set
{j,k} is non empty V168() V169() V170() V171() V172() V173() set
{{j,k},{j}} is non empty set
((Gauge (C,(n + 1))) * (j,k)) `1 is V11() real ext-real Element of REAL
(Gauge (C,(n + 1))) * (j,1) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,(n + 1))) * (j,1)) `1 is V11() real ext-real Element of REAL
((Gauge (C,(n + 1))) * (j,k)) `1 is V11() real ext-real Element of REAL
Upper_Seq (C,(n + 1)) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the U1 of (TOP-REAL 2)
L~ (Upper_Seq (C,(n + 1))) is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
x is set
i3 is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
S-most i3 is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SW-corner i3 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound i3 is V11() real ext-real Element of REAL
(TOP-REAL 2) | i3 is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | i3 is V19() V22( the U1 of ((TOP-REAL 2) | i3)) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | i3), REAL ) V205((TOP-REAL 2) | i3) Element of K6(K7( the U1 of ((TOP-REAL 2) | i3),REAL))
the U1 of ((TOP-REAL 2) | i3) is set
K7( the U1 of ((TOP-REAL 2) | i3),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | i3),REAL)) is set
lower_bound (proj1 | i3) is V11() real ext-real Element of REAL
(proj1 | i3) .: the U1 of ((TOP-REAL 2) | i3) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | i3) .: the U1 of ((TOP-REAL 2) | i3)) is V11() real ext-real Element of REAL
S-bound i3 is V11() real ext-real Element of REAL
proj2 | i3 is V19() V22( the U1 of ((TOP-REAL 2) | i3)) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | i3), REAL ) V205((TOP-REAL 2) | i3) Element of K6(K7( the U1 of ((TOP-REAL 2) | i3),REAL))
lower_bound (proj2 | i3) is V11() real ext-real Element of REAL
(proj2 | i3) .: the U1 of ((TOP-REAL 2) | i3) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | i3) .: the U1 of ((TOP-REAL 2) | i3)) is V11() real ext-real Element of REAL
|[(W-bound i3),(S-bound i3)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
SE-corner i3 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-bound i3 is V11() real ext-real Element of REAL
upper_bound (proj1 | i3) is V11() real ext-real Element of REAL
upper_bound ((proj1 | i3) .: the U1 of ((TOP-REAL 2) | i3)) is V11() real ext-real Element of REAL
|[(E-bound i3),(S-bound i3)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner i3),(SE-corner i3)) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SW-corner i3),(SE-corner i3))) /\ i3 is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
x is set
pp is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
proj2 .: ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1))))) is V168() V169() V170() Element of K6(REAL)
lower_bound (proj2 .: ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))))) is V11() real ext-real Element of REAL
m is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,(n + 1))) * (j,m) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,(n + 1))) * (j,m)) `2 is V11() real ext-real Element of REAL
((Gauge (C,(n + 1))) * (j,m)) `1 is V11() real ext-real Element of REAL
|[(((Gauge (C,(n + 1))) * (j,1)) `1),(lower_bound (proj2 .: ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
|[(((Gauge (C,(n + 1))) * (j,1)) `1),(lower_bound (proj2 .: ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))))))]| `1 is V11() real ext-real Element of REAL
pp `1 is V11() real ext-real Element of REAL
|[(((Gauge (C,(n + 1))) * (j,1)) `1),(lower_bound (proj2 .: ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))))))]| `2 is V11() real ext-real Element of REAL
S-bound ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1))))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1))))) is strict T_2 SubSpace of TOP-REAL 2
proj2 | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1))))) is V19() V22( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))))), REAL ) V205((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))))),REAL))
the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))))) is set
K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))))),REAL)) is set
lower_bound (proj2 | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))))) is V11() real ext-real Element of REAL
(proj2 | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1))))))) is V11() real ext-real Element of REAL
S-min ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-most ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1))))) is functional Element of K6( the U1 of (TOP-REAL 2))
SW-corner ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1))))) is V11() real ext-real Element of REAL
proj1 | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1))))) is V19() V22( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))))), REAL ) V205((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))))),REAL))
lower_bound (proj1 | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))))) is V11() real ext-real Element of REAL
(proj1 | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1))))))) is V11() real ext-real Element of REAL
|[(W-bound ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))))),(S-bound ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
SE-corner ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-bound ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1))))) is V11() real ext-real Element of REAL
upper_bound (proj1 | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))))) is V11() real ext-real Element of REAL
upper_bound ((proj1 | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1))))))) is V11() real ext-real Element of REAL
|[(E-bound ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))))),(S-bound ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))))),(SE-corner ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1))))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SW-corner ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))))),(SE-corner ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))))))) /\ ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1))))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (S-most ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))))) is strict T_2 SubSpace of TOP-REAL 2
proj1 | (S-most ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))))) is V19() V22( the U1 of ((TOP-REAL 2) | (S-most ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (S-most ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1))))))), REAL ) V205((TOP-REAL 2) | (S-most ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1))))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (S-most ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1))))))),REAL))
the U1 of ((TOP-REAL 2) | (S-most ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1))))))) is set
K7( the U1 of ((TOP-REAL 2) | (S-most ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1))))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (S-most ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1))))))),REAL)) is set
lower_bound (proj1 | (S-most ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1))))))) is V11() real ext-real Element of REAL
(proj1 | (S-most ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1))))))) .: the U1 of ((TOP-REAL 2) | (S-most ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1))))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | (S-most ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1))))))) .: the U1 of ((TOP-REAL 2) | (S-most ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))))))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (S-most ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))))))),(S-bound ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(S-min ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))))) `2 is V11() real ext-real Element of REAL
pp `2 is V11() real ext-real Element of REAL
LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (j,m))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
x is set
i3 is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
E-most i3 is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SE-corner i3 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-bound i3 is V11() real ext-real Element of REAL
(TOP-REAL 2) | i3 is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | i3 is V19() V22( the U1 of ((TOP-REAL 2) | i3)) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | i3), REAL ) V205((TOP-REAL 2) | i3) Element of K6(K7( the U1 of ((TOP-REAL 2) | i3),REAL))
the U1 of ((TOP-REAL 2) | i3) is set
K7( the U1 of ((TOP-REAL 2) | i3),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | i3),REAL)) is set
upper_bound (proj1 | i3) is V11() real ext-real Element of REAL
(proj1 | i3) .: the U1 of ((TOP-REAL 2) | i3) is V168() V169() V170() Element of K6(REAL)
upper_bound ((proj1 | i3) .: the U1 of ((TOP-REAL 2) | i3)) is V11() real ext-real Element of REAL
S-bound i3 is V11() real ext-real Element of REAL
proj2 | i3 is V19() V22( the U1 of ((TOP-REAL 2) | i3)) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | i3), REAL ) V205((TOP-REAL 2) | i3) Element of K6(K7( the U1 of ((TOP-REAL 2) | i3),REAL))
lower_bound (proj2 | i3) is V11() real ext-real Element of REAL
(proj2 | i3) .: the U1 of ((TOP-REAL 2) | i3) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | i3) .: the U1 of ((TOP-REAL 2) | i3)) is V11() real ext-real Element of REAL
|[(E-bound i3),(S-bound i3)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NE-corner i3 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound i3 is V11() real ext-real Element of REAL
upper_bound (proj2 | i3) is V11() real ext-real Element of REAL
upper_bound ((proj2 | i3) .: the U1 of ((TOP-REAL 2) | i3)) is V11() real ext-real Element of REAL
|[(E-bound i3),(N-bound i3)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner i3),(NE-corner i3)) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SE-corner i3),(NE-corner i3))) /\ i3 is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
x is set
pp is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
proj1 .: ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))) is V168() V169() V170() Element of K6(REAL)
upper_bound (proj1 .: ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))) is V11() real ext-real Element of REAL
m is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,(n + 1))) * (m,k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,(n + 1))) * (m,k)) `1 is V11() real ext-real Element of REAL
((Gauge (C,(n + 1))) * (m,k)) `2 is V11() real ext-real Element of REAL
|[(upper_bound (proj1 .: ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))),(((Gauge (C,(n + 1))) * (1,k)) `2)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
|[(upper_bound (proj1 .: ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))),(((Gauge (C,(n + 1))) * (1,k)) `2)]| `2 is V11() real ext-real Element of REAL
pp `2 is V11() real ext-real Element of REAL
|[(upper_bound (proj1 .: ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))),(((Gauge (C,(n + 1))) * (1,k)) `2)]| `1 is V11() real ext-real Element of REAL
E-bound ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))) is strict T_2 SubSpace of TOP-REAL 2
proj1 | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))) is V19() V22( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))), REAL ) V205((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))),REAL))
the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))) is set
K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))),REAL)) is set
upper_bound (proj1 | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))) is V11() real ext-real Element of REAL
(proj1 | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))) is V168() V169() V170() Element of K6(REAL)
upper_bound ((proj1 | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))) is V11() real ext-real Element of REAL
E-min ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
E-most ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))) is functional Element of K6( the U1 of (TOP-REAL 2))
SE-corner ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-bound ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))) is V11() real ext-real Element of REAL
proj2 | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))) is V19() V22( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))), REAL ) V205((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))),REAL))
lower_bound (proj2 | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))) is V11() real ext-real Element of REAL
(proj2 | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))) is V11() real ext-real Element of REAL
|[(E-bound ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))),(S-bound ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NE-corner ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))) is V11() real ext-real Element of REAL
upper_bound (proj2 | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))) is V11() real ext-real Element of REAL
|[(E-bound ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))),(N-bound ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SE-corner ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))),(NE-corner ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SE-corner ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))),(NE-corner ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))))) /\ ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (E-most ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))) is strict T_2 SubSpace of TOP-REAL 2
proj2 | (E-most ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))) is V19() V22( the U1 of ((TOP-REAL 2) | (E-most ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (E-most ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))), REAL ) V205((TOP-REAL 2) | (E-most ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (E-most ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))),REAL))
the U1 of ((TOP-REAL 2) | (E-most ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))) is set
K7( the U1 of ((TOP-REAL 2) | (E-most ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (E-most ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))),REAL)) is set
lower_bound (proj2 | (E-most ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))) is V11() real ext-real Element of REAL
(proj2 | (E-most ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))) .: the U1 of ((TOP-REAL 2) | (E-most ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (E-most ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))) .: the U1 of ((TOP-REAL 2) | (E-most ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))))) is V11() real ext-real Element of REAL
|[(E-bound ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))),(lower_bound (proj2 | (E-most ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(E-min ((LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))) `1 is V11() real ext-real Element of REAL
pp `1 is V11() real ext-real Element of REAL
LSeg (((Gauge (C,(n + 1))) * (m,k)),((Gauge (C,(n + 1))) * (i,k))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
x is set
i3 is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
W-most i3 is non empty functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
SW-corner i3 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-bound i3 is V11() real ext-real Element of REAL
(TOP-REAL 2) | i3 is strict T_2 compact SubSpace of TOP-REAL 2
proj1 | i3 is V19() V22( the U1 of ((TOP-REAL 2) | i3)) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | i3), REAL ) V205((TOP-REAL 2) | i3) Element of K6(K7( the U1 of ((TOP-REAL 2) | i3),REAL))
the U1 of ((TOP-REAL 2) | i3) is set
K7( the U1 of ((TOP-REAL 2) | i3),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | i3),REAL)) is set
lower_bound (proj1 | i3) is V11() real ext-real Element of REAL
(proj1 | i3) .: the U1 of ((TOP-REAL 2) | i3) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | i3) .: the U1 of ((TOP-REAL 2) | i3)) is V11() real ext-real Element of REAL
S-bound i3 is V11() real ext-real Element of REAL
proj2 | i3 is V19() V22( the U1 of ((TOP-REAL 2) | i3)) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | i3), REAL ) V205((TOP-REAL 2) | i3) Element of K6(K7( the U1 of ((TOP-REAL 2) | i3),REAL))
lower_bound (proj2 | i3) is V11() real ext-real Element of REAL
(proj2 | i3) .: the U1 of ((TOP-REAL 2) | i3) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | i3) .: the U1 of ((TOP-REAL 2) | i3)) is V11() real ext-real Element of REAL
|[(W-bound i3),(S-bound i3)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NW-corner i3 is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound i3 is V11() real ext-real Element of REAL
upper_bound (proj2 | i3) is V11() real ext-real Element of REAL
upper_bound ((proj2 | i3) .: the U1 of ((TOP-REAL 2) | i3)) is V11() real ext-real Element of REAL
|[(W-bound i3),(N-bound i3)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner i3),(NW-corner i3)) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SW-corner i3),(NW-corner i3))) /\ i3 is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
x is set
pp is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
proj1 .: ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))) is V168() V169() V170() Element of K6(REAL)
lower_bound (proj1 .: ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))) is V11() real ext-real Element of REAL
m is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,(n + 1))) * (m,k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
((Gauge (C,(n + 1))) * (m,k)) `1 is V11() real ext-real Element of REAL
((Gauge (C,(n + 1))) * (m,k)) `2 is V11() real ext-real Element of REAL
|[(lower_bound (proj1 .: ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))),(((Gauge (C,(n + 1))) * (1,k)) `2)]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
|[(lower_bound (proj1 .: ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))),(((Gauge (C,(n + 1))) * (1,k)) `2)]| `2 is V11() real ext-real Element of REAL
pp `2 is V11() real ext-real Element of REAL
|[(lower_bound (proj1 .: ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))),(((Gauge (C,(n + 1))) * (1,k)) `2)]| `1 is V11() real ext-real Element of REAL
W-bound ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))) is strict T_2 SubSpace of TOP-REAL 2
proj1 | ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))) is V19() V22( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))), REAL ) V205((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))),REAL))
the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))) is set
K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))),REAL)) is set
lower_bound (proj1 | ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))) is V11() real ext-real Element of REAL
(proj1 | ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj1 | ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))) is V11() real ext-real Element of REAL
W-min ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
W-most ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))) is functional Element of K6( the U1 of (TOP-REAL 2))
SW-corner ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
S-bound ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))) is V11() real ext-real Element of REAL
proj2 | ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))) is V19() V22( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))), REAL ) V205((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))),REAL))
lower_bound (proj2 | ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))) is V11() real ext-real Element of REAL
(proj2 | ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))) is V11() real ext-real Element of REAL
|[(W-bound ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))),(S-bound ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
NW-corner ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
N-bound ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))) is V11() real ext-real Element of REAL
upper_bound (proj2 | ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))) .: the U1 of ((TOP-REAL 2) | ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))) is V11() real ext-real Element of REAL
|[(W-bound ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))),(N-bound ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg ((SW-corner ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))),(NW-corner ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg ((SW-corner ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))),(NW-corner ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))))) /\ ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
(TOP-REAL 2) | (W-most ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))) is strict T_2 SubSpace of TOP-REAL 2
proj2 | (W-most ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))) is V19() V22( the U1 of ((TOP-REAL 2) | (W-most ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))))) V23( REAL ) Function-like V46( the U1 of ((TOP-REAL 2) | (W-most ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))), REAL ) V205((TOP-REAL 2) | (W-most ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))) Element of K6(K7( the U1 of ((TOP-REAL 2) | (W-most ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))),REAL))
the U1 of ((TOP-REAL 2) | (W-most ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))) is set
K7( the U1 of ((TOP-REAL 2) | (W-most ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))),REAL) is set
K6(K7( the U1 of ((TOP-REAL 2) | (W-most ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))),REAL)) is set
lower_bound (proj2 | (W-most ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))) is V11() real ext-real Element of REAL
(proj2 | (W-most ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))) .: the U1 of ((TOP-REAL 2) | (W-most ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))) is V168() V169() V170() Element of K6(REAL)
lower_bound ((proj2 | (W-most ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))) .: the U1 of ((TOP-REAL 2) | (W-most ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))))) is V11() real ext-real Element of REAL
|[(W-bound ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))),(lower_bound (proj2 | (W-most ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1))))))))]| is non empty V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(W-min ((LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))))) `1 is V11() real ext-real Element of REAL
pp `1 is V11() real ext-real Element of REAL
LSeg (((Gauge (C,(n + 1))) * (i,k)),((Gauge (C,(n + 1))) * (m,k))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
j1 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,(n + 1))) * (j,j1) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (C,(n + 1))) * (j,j1)),((Gauge (C,(n + 1))) * (j,k))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,(n + 1))) * (j,j1)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Lower_Seq (C,(n + 1)))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
{((Gauge (C,(n + 1))) * (j,j1))} is non empty functional set
i3 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,(n + 1))) * (i3,k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i3,k))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i3,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
{((Gauge (C,(n + 1))) * (i3,k))} is non empty functional set
(LSeg (((Gauge (C,(n + 1))) * (j,j1)),((Gauge (C,(n + 1))) * (j,k)))) \/ (LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i3,k)))) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
((LSeg (((Gauge (C,(n + 1))) * (j,j1)),((Gauge (C,(n + 1))) * (j,k)))) \/ (LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i3,k))))) /\ (L~ (Upper_Seq (C,(n + 1)))) is functional Element of K6( the U1 of (TOP-REAL 2))
x is set
x is set
((LSeg (((Gauge (C,(n + 1))) * (j,j1)),((Gauge (C,(n + 1))) * (j,k)))) \/ (LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i3,k))))) /\ (L~ (Lower_Seq (C,(n + 1)))) is functional Element of K6( the U1 of (TOP-REAL 2))
x is set
x is set
i3 is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,(n + 1))) * (i3,k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (C,(n + 1))) * (i3,k)),((Gauge (C,(n + 1))) * (j,k))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,(n + 1))) * (i3,k)),((Gauge (C,(n + 1))) * (j,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
{((Gauge (C,(n + 1))) * (i3,k))} is non empty functional set
LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i3,k))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,(n + 1))) * (j,j1)),((Gauge (C,(n + 1))) * (j,k)))) \/ (LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i3,k)))) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i3,k)))) /\ (L~ (Upper_Seq (C,(n + 1)))) is functional closed bounded compact Element of K6( the U1 of (TOP-REAL 2))
((LSeg (((Gauge (C,(n + 1))) * (j,j1)),((Gauge (C,(n + 1))) * (j,k)))) \/ (LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i3,k))))) /\ (L~ (Upper_Seq (C,(n + 1)))) is functional Element of K6( the U1 of (TOP-REAL 2))
x is set
x is set
((LSeg (((Gauge (C,(n + 1))) * (j,j1)),((Gauge (C,(n + 1))) * (j,k)))) \/ (LSeg (((Gauge (C,(n + 1))) * (j,k)),((Gauge (C,(n + 1))) * (i3,k))))) /\ (L~ (Lower_Seq (C,(n + 1)))) is functional Element of K6( the U1 of (TOP-REAL 2))
x is set
x is set
n is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
n + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
C is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
Gauge (C,(n + 1)) is V19() non empty-yielding V22( NAT ) V23(K295( the U1 of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K295( the U1 of (TOP-REAL 2))
len (Gauge (C,(n + 1))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
width (Gauge (C,(n + 1))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Cage (C,(n + 1)) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
L~ (Cage (C,(n + 1))) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
Upper_Arc (L~ (Cage (C,(n + 1)))) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
Center (Gauge (C,(n + 1))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Lower_Arc (L~ (Cage (C,(n + 1)))) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
Upper_Arc C is non empty functional Element of K6( the U1 of (TOP-REAL 2))
i is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
j is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
k is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,(n + 1))) * (i,k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Gauge (C,(n + 1))) * ((Center (Gauge (C,(n + 1)))),j) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Gauge (C,(n + 1))) * ((Center (Gauge (C,(n + 1)))),k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (C,(n + 1))) * ((Center (Gauge (C,(n + 1)))),j)),((Gauge (C,(n + 1))) * ((Center (Gauge (C,(n + 1)))),k))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
LSeg (((Gauge (C,(n + 1))) * ((Center (Gauge (C,(n + 1)))),k)),((Gauge (C,(n + 1))) * (i,k))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,(n + 1))) * ((Center (Gauge (C,(n + 1)))),j)),((Gauge (C,(n + 1))) * ((Center (Gauge (C,(n + 1)))),k)))) \/ (LSeg (((Gauge (C,(n + 1))) * ((Center (Gauge (C,(n + 1)))),k)),((Gauge (C,(n + 1))) * (i,k)))) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
n is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
n + 1 is non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
C is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
Gauge (C,(n + 1)) is V19() non empty-yielding V22( NAT ) V23(K295( the U1 of (TOP-REAL 2))) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of K295( the U1 of (TOP-REAL 2))
len (Gauge (C,(n + 1))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
width (Gauge (C,(n + 1))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Cage (C,(n + 1)) is non empty non trivial V19() V22( NAT ) V23( the U1 of (TOP-REAL 2)) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented FinSequence of the U1 of (TOP-REAL 2)
L~ (Cage (C,(n + 1))) is non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical Element of K6( the U1 of (TOP-REAL 2))
Upper_Arc (L~ (Cage (C,(n + 1)))) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
Center (Gauge (C,(n + 1))) is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
Lower_Arc (L~ (Cage (C,(n + 1)))) is non empty functional Element of K6( the U1 of (TOP-REAL 2))
Lower_Arc C is non empty functional Element of K6( the U1 of (TOP-REAL 2))
i is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
j is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
k is ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() Element of NAT
(Gauge (C,(n + 1))) * (i,k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Gauge (C,(n + 1))) * ((Center (Gauge (C,(n + 1)))),j) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
(Gauge (C,(n + 1))) * ((Center (Gauge (C,(n + 1)))),k) is V19() V22( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V160() Element of the U1 of (TOP-REAL 2)
LSeg (((Gauge (C,(n + 1))) * ((Center (Gauge (C,(n + 1)))),j)),((Gauge (C,(n + 1))) * ((Center (Gauge (C,(n + 1)))),k))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
LSeg (((Gauge (C,(n + 1))) * ((Center (Gauge (C,(n + 1)))),k)),((Gauge (C,(n + 1))) * (i,k))) is non empty functional closed closed connected bounded bounded compact compact V264( TOP-REAL 2) Element of K6( the U1 of (TOP-REAL 2))
(LSeg (((Gauge (C,(n + 1))) * ((Center (Gauge (C,(n + 1)))),j)),((Gauge (C,(n + 1))) * ((Center (Gauge (C,(n + 1)))),k)))) \/ (LSeg (((Gauge (C,(n + 1))) * ((Center (Gauge (C,(n + 1)))),k)),((Gauge (C,(n + 1))) * (i,k)))) is non empty functional Element of K6( the U1 of (TOP-REAL 2))