:: JORDAN semantic presentation

REAL is non empty V42() V166() V167() V168() V172() V200() non bounded_below non bounded_above interval set
NAT is V166() V167() V168() V169() V170() V171() V172() V200() bounded_below Element of bool REAL
bool REAL is non empty set
I[01] is non empty strict TopSpace-like T_0 T_1 T_2 V82() normal T_3 T_4 connected compact locally_connected V211() V246() pathwise_connected pseudocompact SubSpace of R^1
R^1 is non empty strict TopSpace-like T_0 T_1 T_2 V211() TopStruct
the carrier of I[01] is non empty V166() V167() V168() set
[:I[01],I[01]:] is non empty strict TopSpace-like T_0 T_1 T_2 TopStruct
the carrier of [:I[01],I[01]:] is non empty set
COMPLEX is non empty V42() V166() V172() set
omega is V166() V167() V168() V169() V170() V171() V172() V200() bounded_below set
bool omega is non empty set
bool NAT is non empty set
1 is non empty ordinal natural complex ext-real positive non negative real V33() V119() V166() V167() V168() V169() V170() V171() left_end bounded_below Element of NAT
RAT is non empty V42() V166() V167() V168() V169() V172() set
[:1,1:] is Relation-like RAT -valued INT -valued non empty V156() V157() V158() V159() set
INT is non empty V42() V166() V167() V168() V169() V170() V172() set
bool [:1,1:] is non empty set
[:[:1,1:],1:] is Relation-like RAT -valued INT -valued non empty V156() V157() V158() V159() set
bool [:[:1,1:],1:] is non empty set
[:[:1,1:],REAL:] is Relation-like non empty V156() V157() V158() set
bool [:[:1,1:],REAL:] is non empty set
[:REAL,REAL:] is Relation-like non empty V156() V157() V158() set
[:[:REAL,REAL:],REAL:] is Relation-like non empty V156() V157() V158() set
bool [:[:REAL,REAL:],REAL:] is non empty set
2 is non empty ordinal natural complex ext-real positive non negative real V33() V119() V166() V167() V168() V169() V170() V171() left_end bounded_below Element of NAT
[:2,2:] is Relation-like RAT -valued INT -valued non empty V156() V157() V158() V159() set
[:[:2,2:],REAL:] is Relation-like non empty V156() V157() V158() set
bool [:[:2,2:],REAL:] is non empty set
bool [:REAL,REAL:] is non empty set
TOP-REAL 2 is non empty TopSpace-like T_0 T_1 T_2 connected V132() V178() V179() V180() V181() V182() V183() V184() strict add-continuous Mult-continuous pathwise_connected RLTopStruct
the carrier of (TOP-REAL 2) is functional non empty set
bool the carrier of (TOP-REAL 2) is non empty set
I[01] is non empty strict TopSpace-like T_0 T_1 T_2 V82() normal T_3 T_4 connected compact locally_connected V211() V246() pathwise_connected pseudocompact TopStruct
the carrier of I[01] is non empty V166() V167() V168() set
RealSpace is non empty strict Reflexive discerning symmetric triangle Discerning V211() MetrStruct
0 is Relation-like non-empty empty-yielding RAT -valued Function-like one-to-one constant functional empty ordinal natural complex ext-real non positive non negative real V33() V119() V156() V157() V158() V159() V166() V167() V168() V169() V170() V171() V172() bounded_below interval Element of NAT
the Relation-like non-empty empty-yielding RAT -valued Function-like one-to-one constant functional empty V156() V157() V158() V159() V166() V167() V168() V169() V170() V171() V172() bounded_below interval set is Relation-like non-empty empty-yielding RAT -valued Function-like one-to-one constant functional empty V156() V157() V158() V159() V166() V167() V168() V169() V170() V171() V172() bounded_below interval set
Closed-Interval-TSpace (0,1) is non empty strict TopSpace-like T_0 T_1 T_2 V211() SubSpace of R^1
the carrier of (Closed-Interval-TSpace (0,1)) is non empty V166() V167() V168() set
[:R^1,R^1:] is non empty strict TopSpace-like T_0 T_1 T_2 TopStruct
the carrier of [:R^1,R^1:] is non empty set
[: the carrier of [:R^1,R^1:], the carrier of (TOP-REAL 2):] is Relation-like non empty set
bool [: the carrier of [:R^1,R^1:], the carrier of (TOP-REAL 2):] is non empty set
{} is Relation-like non-empty empty-yielding RAT -valued Function-like one-to-one constant functional empty V156() V157() V158() V159() V166() V167() V168() V169() V170() V171() V172() bounded_below interval set
{{},1} is non empty set
K618() is non empty strict TopSpace-like T_0 T_1 T_2 V211() V271() SubSpace of R^1
the carrier of K618() is non empty V166() V167() V168() set
bool the carrier of K618() is non empty set
bool (bool the carrier of K618()) is non empty set
Tunit_circle 2 is non empty TopSpace-like T_0 T_1 T_2 V82() normal T_3 T_4 connected compact V246() being_simple_closed_curve pathwise_connected pseudocompact SubSpace of TOP-REAL 2
the carrier of (Tunit_circle 2) is non empty set
[: the carrier of K618(), the carrier of (Tunit_circle 2):] is Relation-like non empty set
bool [: the carrier of K618(), the carrier of (Tunit_circle 2):] is non empty set
CircleMap is Relation-like the carrier of K618() -defined the carrier of K618() -defined the carrier of (Tunit_circle 2) -valued the carrier of (Tunit_circle 2) -valued Function-like non empty total total quasi_total quasi_total onto continuous Element of bool [: the carrier of K618(), the carrier of (Tunit_circle 2):]
c[10] is Element of the carrier of (Tunit_circle 2)
Topen_unit_circle c[10] is non empty strict TopSpace-like T_0 T_1 T_2 V118( Tunit_circle 2) SubSpace of Tunit_circle 2
the carrier of (Topen_unit_circle c[10]) is non empty set
].0,1.[ is non empty V166() V167() V168() non left_end non right_end bounded_below bounded_above real-bounded interval Element of bool REAL
R^1 ].0,1.[ is non empty connected V166() V167() V168() interval Element of bool the carrier of K618()
K618() | (R^1 ].0,1.[) is non empty strict TopSpace-like T_0 T_1 T_2 V211() V271() SubSpace of K618()
the carrier of (K618() | (R^1 ].0,1.[)) is non empty V166() V167() V168() set
[: the carrier of (Topen_unit_circle c[10]), the carrier of (K618() | (R^1 ].0,1.[)):] is Relation-like non empty V156() V157() V158() set
bool [: the carrier of (Topen_unit_circle c[10]), the carrier of (K618() | (R^1 ].0,1.[)):] is non empty set
c[-10] is Element of the carrier of (Tunit_circle 2)
Topen_unit_circle c[-10] is non empty strict TopSpace-like T_0 T_1 T_2 V118( Tunit_circle 2) SubSpace of Tunit_circle 2
the carrier of (Topen_unit_circle c[-10]) is non empty set
1 / 2 is complex ext-real non negative real Element of REAL
3 is non empty ordinal natural complex ext-real positive non negative real V33() V119() V166() V167() V168() V169() V170() V171() left_end bounded_below Element of NAT
3 / 2 is complex ext-real non negative real Element of REAL
].(1 / 2),(3 / 2).[ is non empty V166() V167() V168() non left_end non right_end bounded_below bounded_above real-bounded interval Element of bool REAL
R^1 ].(1 / 2),(3 / 2).[ is non empty connected V166() V167() V168() interval Element of bool the carrier of K618()
K618() | (R^1 ].(1 / 2),(3 / 2).[) is non empty strict TopSpace-like T_0 T_1 T_2 V211() V271() SubSpace of K618()
the carrier of (K618() | (R^1 ].(1 / 2),(3 / 2).[)) is non empty V166() V167() V168() set
[: the carrier of (Topen_unit_circle c[-10]), the carrier of (K618() | (R^1 ].(1 / 2),(3 / 2).[)):] is Relation-like non empty V156() V157() V158() set
bool [: the carrier of (Topen_unit_circle c[-10]), the carrier of (K618() | (R^1 ].(1 / 2),(3 / 2).[)):] is non empty set
[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):] is Relation-like non empty set
bool [: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):] is non empty set
[: the carrier of I[01], the carrier of I[01]:] is Relation-like non empty V156() V157() V158() set
bool [: the carrier of I[01], the carrier of I[01]:] is non empty set
bool the carrier of [:I[01],I[01]:] is non empty set
[:COMPLEX,COMPLEX:] is Relation-like non empty V156() set
bool [:COMPLEX,COMPLEX:] is non empty set
[:COMPLEX,REAL:] is Relation-like non empty V156() V157() V158() set
bool [:COMPLEX,REAL:] is non empty set
[:[:COMPLEX,COMPLEX:],COMPLEX:] is Relation-like non empty V156() set
bool [:[:COMPLEX,COMPLEX:],COMPLEX:] is non empty set
[:RAT,RAT:] is Relation-like RAT -valued non empty V156() V157() V158() set
bool [:RAT,RAT:] is non empty set
[:[:RAT,RAT:],RAT:] is Relation-like RAT -valued non empty V156() V157() V158() set
bool [:[:RAT,RAT:],RAT:] is non empty set
[:INT,INT:] is Relation-like RAT -valued INT -valued non empty V156() V157() V158() set
bool [:INT,INT:] is non empty set
[:[:INT,INT:],INT:] is Relation-like RAT -valued INT -valued non empty V156() V157() V158() set
bool [:[:INT,INT:],INT:] is non empty set
[:NAT,NAT:] is Relation-like RAT -valued INT -valued V156() V157() V158() V159() set
[:[:NAT,NAT:],NAT:] is Relation-like RAT -valued INT -valued V156() V157() V158() V159() set
bool [:[:NAT,NAT:],NAT:] is non empty set
[: the carrier of (TOP-REAL 2),REAL:] is Relation-like non empty V156() V157() V158() set
bool [: the carrier of (TOP-REAL 2),REAL:] is non empty set
4 is non empty ordinal natural complex ext-real positive non negative real V33() V119() V166() V167() V168() V169() V170() V171() left_end bounded_below Element of NAT
sqrt 4 is non empty complex ext-real positive non negative real Element of REAL
the carrier of R^1 is non empty V166() V167() V168() set
R2Homeomorphism is Relation-like the carrier of [:R^1,R^1:] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of bool [: the carrier of [:R^1,R^1:], the carrier of (TOP-REAL 2):]
[.0,1.] is non empty V166() V167() V168() compact interval Element of bool REAL
0[01] is complex ext-real real Element of the carrier of I[01]
1[01] is complex ext-real real Element of the carrier of I[01]
proj2 is Relation-like the carrier of (TOP-REAL 2) -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of (TOP-REAL 2),REAL:]
proj1 is Relation-like the carrier of (TOP-REAL 2) -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of (TOP-REAL 2),REAL:]
- 1 is complex ext-real non positive real Element of REAL
|[(- 1),0]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
|[1,0]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
R^2-unit_square is functional non empty non trivial closed connected compact bounded being_special_polygon being_simple_closed_curve with_the_max_arc Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | R^2-unit_square is non empty strict TopSpace-like T_0 T_1 T_2 V82() normal T_3 T_4 compact V246() pseudocompact SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | R^2-unit_square) is non empty set
bool the carrier of R^1 is non empty set
Closed-Interval-TSpace ((- 1),1) is non empty strict TopSpace-like T_0 T_1 T_2 V211() SubSpace of R^1
the carrier of (Closed-Interval-TSpace ((- 1),1)) is non empty V166() V167() V168() set
(#) (0,1) is complex ext-real real Element of the carrier of (Closed-Interval-TSpace (0,1))
(0,1) (#) is complex ext-real real Element of the carrier of (Closed-Interval-TSpace (0,1))
{0} is functional non empty V166() V167() V168() V169() V170() V171() left_end bounded_below set
C0 is set
l1 is set
C1 is set
l0 is set
C0 \/ C1 is set
(C0 \/ C1) \/ l0 is set
C0 is set
h1 is set
C1 is set
l0 is set
l1 is set
C0 \/ C1 is set
(C0 \/ C1) \/ l0 is set
((C0 \/ C1) \/ l0) \/ l1 is set
C0 is set
h1 is set
C1 is set
l0 is set
l1 is set
C0 \/ C1 is set
(C0 \/ C1) \/ l0 is set
((C0 \/ C1) \/ l0) \/ l1 is set
C0 is Reflexive symmetric triangle MetrStruct
the carrier of C0 is set
C1 is Element of the carrier of C0
l0 is Element of the carrier of C0
dist (C1,l0) is complex ext-real real Element of REAL
C0 is ordinal natural complex ext-real non negative real V33() V119() V166() V167() V168() V169() V170() V171() bounded_below Element of NAT
TOP-REAL C0 is non empty TopSpace-like T_0 T_1 T_2 connected V132() V178() V179() V180() V181() V182() V183() V184() strict add-continuous Mult-continuous pathwise_connected RLTopStruct
the carrier of (TOP-REAL C0) is functional non empty set
C1 is Relation-like Function-like V49(C0) V50() V156() V157() V158() Element of the carrier of (TOP-REAL C0)
l0 is Relation-like Function-like V49(C0) V50() V156() V157() V158() Element of the carrier of (TOP-REAL C0)
dist (C1,l0) is complex ext-real real Element of REAL
Euclid C0 is non empty strict Reflexive discerning symmetric triangle Discerning MetrStruct
the carrier of (Euclid C0) is non empty set
l1 is Element of the carrier of (Euclid C0)
h1 is Element of the carrier of (Euclid C0)
dist (l1,h1) is complex ext-real non negative real Element of REAL
C0 is ordinal natural complex ext-real non negative real V33() V119() V166() V167() V168() V169() V170() V171() bounded_below Element of NAT
TOP-REAL C0 is non empty TopSpace-like T_0 T_1 T_2 connected V132() V178() V179() V180() V181() V182() V183() V184() strict add-continuous Mult-continuous pathwise_connected RLTopStruct
the carrier of (TOP-REAL C0) is functional non empty set
C1 is Relation-like Function-like V49(C0) V50() V156() V157() V158() Element of the carrier of (TOP-REAL C0)
l0 is Relation-like Function-like V49(C0) V50() V156() V157() V158() Element of the carrier of (TOP-REAL C0)
C1 + l0 is Relation-like Function-like V49(C0) V50() V156() V157() V158() Element of the carrier of (TOP-REAL C0)
the U7 of (TOP-REAL C0) is Relation-like [: the carrier of (TOP-REAL C0), the carrier of (TOP-REAL C0):] -defined the carrier of (TOP-REAL C0) -valued Function-like non empty total quasi_total Element of bool [:[: the carrier of (TOP-REAL C0), the carrier of (TOP-REAL C0):], the carrier of (TOP-REAL C0):]
[: the carrier of (TOP-REAL C0), the carrier of (TOP-REAL C0):] is Relation-like non empty set
[:[: the carrier of (TOP-REAL C0), the carrier of (TOP-REAL C0):], the carrier of (TOP-REAL C0):] is Relation-like non empty set
bool [:[: the carrier of (TOP-REAL C0), the carrier of (TOP-REAL C0):], the carrier of (TOP-REAL C0):] is non empty set
K224( the carrier of (TOP-REAL C0), the U7 of (TOP-REAL C0),C1,l0) is Relation-like Function-like V49(C0) V50() V156() V157() V158() Element of the carrier of (TOP-REAL C0)
(1 / 2) * (C1 + l0) is Relation-like Function-like V49(C0) V50() V156() V157() V158() Element of the carrier of (TOP-REAL C0)
(1 / 2) * C1 is Relation-like Function-like V49(C0) V50() V156() V157() V158() Element of the carrier of (TOP-REAL C0)
(1 / 2) * l0 is Relation-like Function-like V49(C0) V50() V156() V157() V158() Element of the carrier of (TOP-REAL C0)
((1 / 2) * C1) + ((1 / 2) * l0) is Relation-like Function-like V49(C0) V50() V156() V157() V158() Element of the carrier of (TOP-REAL C0)
K224( the carrier of (TOP-REAL C0), the U7 of (TOP-REAL C0),((1 / 2) * C1),((1 / 2) * l0)) is Relation-like Function-like V49(C0) V50() V156() V157() V158() Element of the carrier of (TOP-REAL C0)
0. (TOP-REAL C0) is Relation-like Function-like V49(C0) V50() zero V156() V157() V158() Element of the carrier of (TOP-REAL C0)
the ZeroF of (TOP-REAL C0) is Relation-like Function-like V49(C0) V50() V156() V157() V158() Element of the carrier of (TOP-REAL C0)
C1 - (((1 / 2) * C1) + ((1 / 2) * l0)) is Relation-like Function-like V49(C0) V50() V156() V157() V158() Element of the carrier of (TOP-REAL C0)
- (((1 / 2) * C1) + ((1 / 2) * l0)) is Relation-like Function-like V49(C0) V50() V156() V157() V158() Element of the carrier of (TOP-REAL C0)
K270((TOP-REAL C0),C1,(- (((1 / 2) * C1) + ((1 / 2) * l0)))) is Relation-like Function-like V49(C0) V50() V156() V157() V158() Element of the carrier of (TOP-REAL C0)
K224( the carrier of (TOP-REAL C0), the U7 of (TOP-REAL C0),C1,(- (((1 / 2) * C1) + ((1 / 2) * l0)))) is Relation-like Function-like V49(C0) V50() V156() V157() V158() Element of the carrier of (TOP-REAL C0)
C1 - ((1 / 2) * C1) is Relation-like Function-like V49(C0) V50() V156() V157() V158() Element of the carrier of (TOP-REAL C0)
- ((1 / 2) * C1) is Relation-like Function-like V49(C0) V50() V156() V157() V158() Element of the carrier of (TOP-REAL C0)
K270((TOP-REAL C0),C1,(- ((1 / 2) * C1))) is Relation-like Function-like V49(C0) V50() V156() V157() V158() Element of the carrier of (TOP-REAL C0)
K224( the carrier of (TOP-REAL C0), the U7 of (TOP-REAL C0),C1,(- ((1 / 2) * C1))) is Relation-like Function-like V49(C0) V50() V156() V157() V158() Element of the carrier of (TOP-REAL C0)
(C1 - ((1 / 2) * C1)) - ((1 / 2) * l0) is Relation-like Function-like V49(C0) V50() V156() V157() V158() Element of the carrier of (TOP-REAL C0)
- ((1 / 2) * l0) is Relation-like Function-like V49(C0) V50() V156() V157() V158() Element of the carrier of (TOP-REAL C0)
K270((TOP-REAL C0),(C1 - ((1 / 2) * C1)),(- ((1 / 2) * l0))) is Relation-like Function-like V49(C0) V50() V156() V157() V158() Element of the carrier of (TOP-REAL C0)
K224( the carrier of (TOP-REAL C0), the U7 of (TOP-REAL C0),(C1 - ((1 / 2) * C1)),(- ((1 / 2) * l0))) is Relation-like Function-like V49(C0) V50() V156() V157() V158() Element of the carrier of (TOP-REAL C0)
1 * C1 is Relation-like Function-like V49(C0) V50() V156() V157() V158() Element of the carrier of (TOP-REAL C0)
(1 * C1) - ((1 / 2) * C1) is Relation-like Function-like V49(C0) V50() V156() V157() V158() Element of the carrier of (TOP-REAL C0)
K270((TOP-REAL C0),(1 * C1),(- ((1 / 2) * C1))) is Relation-like Function-like V49(C0) V50() V156() V157() V158() Element of the carrier of (TOP-REAL C0)
K224( the carrier of (TOP-REAL C0), the U7 of (TOP-REAL C0),(1 * C1),(- ((1 / 2) * C1))) is Relation-like Function-like V49(C0) V50() V156() V157() V158() Element of the carrier of (TOP-REAL C0)
((1 * C1) - ((1 / 2) * C1)) - ((1 / 2) * l0) is Relation-like Function-like V49(C0) V50() V156() V157() V158() Element of the carrier of (TOP-REAL C0)
K270((TOP-REAL C0),((1 * C1) - ((1 / 2) * C1)),(- ((1 / 2) * l0))) is Relation-like Function-like V49(C0) V50() V156() V157() V158() Element of the carrier of (TOP-REAL C0)
K224( the carrier of (TOP-REAL C0), the U7 of (TOP-REAL C0),((1 * C1) - ((1 / 2) * C1)),(- ((1 / 2) * l0))) is Relation-like Function-like V49(C0) V50() V156() V157() V158() Element of the carrier of (TOP-REAL C0)
1 - (1 / 2) is complex ext-real real Element of REAL
(1 - (1 / 2)) * C1 is Relation-like Function-like V49(C0) V50() V156() V157() V158() Element of the carrier of (TOP-REAL C0)
((1 - (1 / 2)) * C1) - ((1 / 2) * l0) is Relation-like Function-like V49(C0) V50() V156() V157() V158() Element of the carrier of (TOP-REAL C0)
K270((TOP-REAL C0),((1 - (1 / 2)) * C1),(- ((1 / 2) * l0))) is Relation-like Function-like V49(C0) V50() V156() V157() V158() Element of the carrier of (TOP-REAL C0)
K224( the carrier of (TOP-REAL C0), the U7 of (TOP-REAL C0),((1 - (1 / 2)) * C1),(- ((1 / 2) * l0))) is Relation-like Function-like V49(C0) V50() V156() V157() V158() Element of the carrier of (TOP-REAL C0)
C1 - l0 is Relation-like Function-like V49(C0) V50() V156() V157() V158() Element of the carrier of (TOP-REAL C0)
- l0 is Relation-like Function-like V49(C0) V50() V156() V157() V158() Element of the carrier of (TOP-REAL C0)
K270((TOP-REAL C0),C1,(- l0)) is Relation-like Function-like V49(C0) V50() V156() V157() V158() Element of the carrier of (TOP-REAL C0)
K224( the carrier of (TOP-REAL C0), the U7 of (TOP-REAL C0),C1,(- l0)) is Relation-like Function-like V49(C0) V50() V156() V157() V158() Element of the carrier of (TOP-REAL C0)
(1 / 2) * (C1 - l0) is Relation-like Function-like V49(C0) V50() V156() V157() V158() Element of the carrier of (TOP-REAL C0)
C0 is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
C0 `2 is complex ext-real real Element of REAL
C1 is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
C1 `2 is complex ext-real real Element of REAL
C0 + C1 is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) is Relation-like [: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of bool [:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):]
[:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):] is Relation-like non empty set
bool [:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):] is non empty set
K224( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),C0,C1) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
(1 / 2) * (C0 + C1) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
((1 / 2) * (C0 + C1)) `2 is complex ext-real real Element of REAL
(C0 + C1) `2 is complex ext-real real Element of REAL
(1 / 2) * ((C0 + C1) `2) is complex ext-real real Element of REAL
(C0 `2) + (C1 `2) is complex ext-real real Element of REAL
(1 / 2) * ((C0 `2) + (C1 `2)) is complex ext-real real Element of REAL
((C0 `2) + (C1 `2)) / 2 is complex ext-real real Element of REAL
C0 is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
C0 `2 is complex ext-real real Element of REAL
C1 is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
C1 `2 is complex ext-real real Element of REAL
C0 + C1 is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) is Relation-like [: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of bool [:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):]
[:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):] is Relation-like non empty set
bool [:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):] is non empty set
K224( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),C0,C1) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
(1 / 2) * (C0 + C1) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
((1 / 2) * (C0 + C1)) `2 is complex ext-real real Element of REAL
(C0 + C1) `2 is complex ext-real real Element of REAL
(1 / 2) * ((C0 + C1) `2) is complex ext-real real Element of REAL
(C0 `2) + (C1 `2) is complex ext-real real Element of REAL
(1 / 2) * ((C0 `2) + (C1 `2)) is complex ext-real real Element of REAL
((C0 `2) + (C1 `2)) / 2 is complex ext-real real Element of REAL
C0 is functional Element of bool the carrier of (TOP-REAL 2)
C1 is functional vertical Element of bool the carrier of (TOP-REAL 2)
C1 /\ C0 is functional Element of bool the carrier of (TOP-REAL 2)
l0 is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
l1 is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
l0 `1 is complex ext-real real Element of REAL
l1 `1 is complex ext-real real Element of REAL
C0 is functional Element of bool the carrier of (TOP-REAL 2)
C1 is functional horizontal Element of bool the carrier of (TOP-REAL 2)
C1 /\ C0 is functional Element of bool the carrier of (TOP-REAL 2)
l0 is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
l1 is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
l0 `2 is complex ext-real real Element of REAL
l1 `2 is complex ext-real real Element of REAL
C0 is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
C1 is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
l0 is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
LSeg (C1,l0) is functional closed closed boundary nowhere_dense connected compact compact bounded bounded Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * C1) + (b₁ * l0)) where b₁ is complex ext-real real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
LSeg (C0,l0) is functional closed closed boundary nowhere_dense connected compact compact bounded bounded Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * C0) + (b₁ * l0)) where b₁ is complex ext-real real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
C1 `1 is complex ext-real real Element of REAL
l0 `1 is complex ext-real real Element of REAL
C0 `1 is complex ext-real real Element of REAL
C0 is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
C1 is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
l0 is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
LSeg (C1,l0) is functional closed closed boundary nowhere_dense connected compact compact bounded bounded Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * C1) + (b<sub>1</sub> * l0)) where b<sub>1</sub> is complex ext-real real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
LSeg (C0,l0) is functional closed closed boundary nowhere_dense connected compact compact bounded bounded Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * C0) + (b<sub>1</sub> * l0)) where b<sub>1</sub> is complex ext-real real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
C1 `2 is complex ext-real real Element of REAL
l0 `2 is complex ext-real real Element of REAL
C0 `2 is complex ext-real real Element of REAL
C0 is functional Element of bool the carrier of (TOP-REAL 2)
SW-corner C0 is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
W-bound C0 is complex ext-real real Element of REAL
(TOP-REAL 2) | C0 is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj1 | C0 is Relation-like C0 -defined the carrier of (TOP-REAL 2) -defined the carrier of ((TOP-REAL 2) | C0) -defined REAL -valued Function-like total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ((TOP-REAL 2) | C0),REAL:]
the carrier of ((TOP-REAL 2) | C0) is set
[: the carrier of ((TOP-REAL 2) | C0),REAL:] is Relation-like V156() V157() V158() set
bool [: the carrier of ((TOP-REAL 2) | C0),REAL:] is non empty set
lower_bound (proj1 | C0) is complex ext-real real Element of REAL
(proj1 | C0) .: the carrier of ((TOP-REAL 2) | C0) is V166() V167() V168() Element of bool REAL
K663(((proj1 | C0) .: the carrier of ((TOP-REAL 2) | C0))) is complex ext-real real Element of REAL
S-bound C0 is complex ext-real real Element of REAL
proj2 | C0 is Relation-like C0 -defined the carrier of (TOP-REAL 2) -defined the carrier of ((TOP-REAL 2) | C0) -defined REAL -valued Function-like total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ((TOP-REAL 2) | C0),REAL:]
lower_bound (proj2 | C0) is complex ext-real real Element of REAL
(proj2 | C0) .: the carrier of ((TOP-REAL 2) | C0) is V166() V167() V168() Element of bool REAL
K663(((proj2 | C0) .: the carrier of ((TOP-REAL 2) | C0))) is complex ext-real real Element of REAL
|[(W-bound C0),(S-bound C0)]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
SE-corner C0 is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
E-bound C0 is complex ext-real real Element of REAL
upper_bound (proj1 | C0) is complex ext-real real Element of REAL
K662(((proj1 | C0) .: the carrier of ((TOP-REAL 2) | C0))) is complex ext-real real Element of REAL
|[(E-bound C0),(S-bound C0)]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner C0),(SE-corner C0)) is functional closed closed boundary nowhere_dense connected compact compact bounded bounded Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SW-corner C0)) + (b₁ * (SE-corner C0))) where b₁ is complex ext-real real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(SW-corner C0) `2 is complex ext-real real Element of REAL
(SE-corner C0) `2 is complex ext-real real Element of REAL
NW-corner C0 is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
N-bound C0 is complex ext-real real Element of REAL
upper_bound (proj2 | C0) is complex ext-real real Element of REAL
K662(((proj2 | C0) .: the carrier of ((TOP-REAL 2) | C0))) is complex ext-real real Element of REAL
|[(W-bound C0),(N-bound C0)]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
LSeg ((NW-corner C0),(SW-corner C0)) is functional closed closed boundary nowhere_dense connected compact compact bounded bounded Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NW-corner C0)) + (b₁ * (SW-corner C0))) where b₁ is complex ext-real real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(NW-corner C0) `1 is complex ext-real real Element of REAL
(SW-corner C0) `1 is complex ext-real real Element of REAL
NE-corner C0 is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
|[(E-bound C0),(N-bound C0)]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
LSeg ((NE-corner C0),(SE-corner C0)) is functional closed closed boundary nowhere_dense connected compact compact bounded bounded Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (NE-corner C0)) + (b₁ * (SE-corner C0))) where b₁ is complex ext-real real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(NE-corner C0) `1 is complex ext-real real Element of REAL
(SE-corner C0) `1 is complex ext-real real Element of REAL
C0 is functional Element of bool the carrier of (TOP-REAL 2)
SE-corner C0 is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
E-bound C0 is complex ext-real real Element of REAL
(TOP-REAL 2) | C0 is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj1 | C0 is Relation-like C0 -defined the carrier of (TOP-REAL 2) -defined the carrier of ((TOP-REAL 2) | C0) -defined REAL -valued Function-like total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ((TOP-REAL 2) | C0),REAL:]
the carrier of ((TOP-REAL 2) | C0) is set
[: the carrier of ((TOP-REAL 2) | C0),REAL:] is Relation-like V156() V157() V158() set
bool [: the carrier of ((TOP-REAL 2) | C0),REAL:] is non empty set
upper_bound (proj1 | C0) is complex ext-real real Element of REAL
(proj1 | C0) .: the carrier of ((TOP-REAL 2) | C0) is V166() V167() V168() Element of bool REAL
K662(((proj1 | C0) .: the carrier of ((TOP-REAL 2) | C0))) is complex ext-real real Element of REAL
S-bound C0 is complex ext-real real Element of REAL
proj2 | C0 is Relation-like C0 -defined the carrier of (TOP-REAL 2) -defined the carrier of ((TOP-REAL 2) | C0) -defined REAL -valued Function-like total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ((TOP-REAL 2) | C0),REAL:]
lower_bound (proj2 | C0) is complex ext-real real Element of REAL
(proj2 | C0) .: the carrier of ((TOP-REAL 2) | C0) is V166() V167() V168() Element of bool REAL
K663(((proj2 | C0) .: the carrier of ((TOP-REAL 2) | C0))) is complex ext-real real Element of REAL
|[(E-bound C0),(S-bound C0)]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
SW-corner C0 is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
W-bound C0 is complex ext-real real Element of REAL
lower_bound (proj1 | C0) is complex ext-real real Element of REAL
K663(((proj1 | C0) .: the carrier of ((TOP-REAL 2) | C0))) is complex ext-real real Element of REAL
|[(W-bound C0),(S-bound C0)]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner C0),(SW-corner C0)) is functional closed closed boundary nowhere_dense connected compact compact bounded bounded horizontal Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SE-corner C0)) + (b₁ * (SW-corner C0))) where b₁ is complex ext-real real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
NW-corner C0 is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
N-bound C0 is complex ext-real real Element of REAL
upper_bound (proj2 | C0) is complex ext-real real Element of REAL
K662(((proj2 | C0) .: the carrier of ((TOP-REAL 2) | C0))) is complex ext-real real Element of REAL
|[(W-bound C0),(N-bound C0)]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner C0),(NW-corner C0)) is functional closed closed boundary nowhere_dense connected compact compact bounded bounded vertical Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SW-corner C0)) + (b₁ * (NW-corner C0))) where b₁ is complex ext-real real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
NE-corner C0 is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
|[(E-bound C0),(N-bound C0)]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner C0),(NE-corner C0)) is functional closed closed boundary nowhere_dense connected compact compact bounded bounded vertical Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SE-corner C0)) + (b₁ * (NE-corner C0))) where b₁ is complex ext-real real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
C0 is functional Element of bool the carrier of (TOP-REAL 2)
W-bound C0 is complex ext-real real Element of REAL
(TOP-REAL 2) | C0 is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj1 | C0 is Relation-like C0 -defined the carrier of (TOP-REAL 2) -defined the carrier of ((TOP-REAL 2) | C0) -defined REAL -valued Function-like total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ((TOP-REAL 2) | C0),REAL:]
the carrier of ((TOP-REAL 2) | C0) is set
[: the carrier of ((TOP-REAL 2) | C0),REAL:] is Relation-like V156() V157() V158() set
bool [: the carrier of ((TOP-REAL 2) | C0),REAL:] is non empty set
lower_bound (proj1 | C0) is complex ext-real real Element of REAL
(proj1 | C0) .: the carrier of ((TOP-REAL 2) | C0) is V166() V167() V168() Element of bool REAL
K663(((proj1 | C0) .: the carrier of ((TOP-REAL 2) | C0))) is complex ext-real real Element of REAL
E-bound C0 is complex ext-real real Element of REAL
upper_bound (proj1 | C0) is complex ext-real real Element of REAL
K662(((proj1 | C0) .: the carrier of ((TOP-REAL 2) | C0))) is complex ext-real real Element of REAL
E-min C0 is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
E-most C0 is functional Element of bool the carrier of (TOP-REAL 2)
SE-corner C0 is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
S-bound C0 is complex ext-real real Element of REAL
proj2 | C0 is Relation-like C0 -defined the carrier of (TOP-REAL 2) -defined the carrier of ((TOP-REAL 2) | C0) -defined REAL -valued Function-like total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ((TOP-REAL 2) | C0),REAL:]
lower_bound (proj2 | C0) is complex ext-real real Element of REAL
(proj2 | C0) .: the carrier of ((TOP-REAL 2) | C0) is V166() V167() V168() Element of bool REAL
K663(((proj2 | C0) .: the carrier of ((TOP-REAL 2) | C0))) is complex ext-real real Element of REAL
|[(E-bound C0),(S-bound C0)]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
NE-corner C0 is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
N-bound C0 is complex ext-real real Element of REAL
upper_bound (proj2 | C0) is complex ext-real real Element of REAL
K662(((proj2 | C0) .: the carrier of ((TOP-REAL 2) | C0))) is complex ext-real real Element of REAL
|[(E-bound C0),(N-bound C0)]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner C0),(NE-corner C0)) is functional closed closed boundary nowhere_dense connected compact compact bounded bounded vertical Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SE-corner C0)) + (b₁ * (NE-corner C0))) where b₁ is complex ext-real real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((SE-corner C0),(NE-corner C0))) /\ C0 is functional Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (E-most C0) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj2 | (E-most C0) is Relation-like E-most C0 -defined the carrier of (TOP-REAL 2) -defined the carrier of ((TOP-REAL 2) | (E-most C0)) -defined REAL -valued Function-like total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ((TOP-REAL 2) | (E-most C0)),REAL:]
the carrier of ((TOP-REAL 2) | (E-most C0)) is set
[: the carrier of ((TOP-REAL 2) | (E-most C0)),REAL:] is Relation-like V156() V157() V158() set
bool [: the carrier of ((TOP-REAL 2) | (E-most C0)),REAL:] is non empty set
lower_bound (proj2 | (E-most C0)) is complex ext-real real Element of REAL
(proj2 | (E-most C0)) .: the carrier of ((TOP-REAL 2) | (E-most C0)) is V166() V167() V168() Element of bool REAL
K663(((proj2 | (E-most C0)) .: the carrier of ((TOP-REAL 2) | (E-most C0)))) is complex ext-real real Element of REAL
|[(E-bound C0),(lower_bound (proj2 | (E-most C0)))]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
(E-min C0) `1 is complex ext-real real Element of REAL
(W-bound C0) + (E-bound C0) is complex ext-real real Element of REAL
((W-bound C0) + (E-bound C0)) / 2 is complex ext-real real Element of REAL
Vertical_Line (((W-bound C0) + (E-bound C0)) / 2) is functional Element of bool the carrier of (TOP-REAL 2)
C0 is complex ext-real real set
Vertical_Line C0 is functional Element of bool the carrier of (TOP-REAL 2)
C1 is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
C1 `1 is complex ext-real real Element of REAL
l0 is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
l0 `1 is complex ext-real real Element of REAL
LSeg (C1,l0) is functional closed closed boundary nowhere_dense connected compact compact bounded bounded Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * C1) + (b<sub>1</sub> * l0)) where b<sub>1</sub> is complex ext-real real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
C0 - (C1 `1) is complex ext-real real Element of REAL
(l0 `1) - (C1 `1) is complex ext-real real Element of REAL
(C0 - (C1 `1)) / ((l0 `1) - (C1 `1)) is complex ext-real real Element of REAL
1 - ((C0 - (C1 `1)) / ((l0 `1) - (C1 `1))) is complex ext-real real Element of REAL
(1 - ((C0 - (C1 `1)) / ((l0 `1) - (C1 `1)))) * C1 is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
((C0 - (C1 `1)) / ((l0 `1) - (C1 `1))) * l0 is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
((1 - ((C0 - (C1 `1)) / ((l0 `1) - (C1 `1)))) * C1) + (((C0 - (C1 `1)) / ((l0 `1) - (C1 `1))) * l0) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) is Relation-like [: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of bool [:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):]
[:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):] is Relation-like non empty set
bool [:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):] is non empty set
K224( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),((1 - ((C0 - (C1 `1)) / ((l0 `1) - (C1 `1)))) * C1),(((C0 - (C1 `1)) / ((l0 `1) - (C1 `1))) * l0)) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
(C1 `1) - (C1 `1) is complex ext-real real Element of REAL
(((1 - ((C0 - (C1 `1)) / ((l0 `1) - (C1 `1)))) * C1) + (((C0 - (C1 `1)) / ((l0 `1) - (C1 `1))) * l0)) `1 is complex ext-real real Element of REAL
(1 - ((C0 - (C1 `1)) / ((l0 `1) - (C1 `1)))) * (C1 `1) is complex ext-real real Element of REAL
((C0 - (C1 `1)) / ((l0 `1) - (C1 `1))) * (l0 `1) is complex ext-real real Element of REAL
((1 - ((C0 - (C1 `1)) / ((l0 `1) - (C1 `1)))) * (C1 `1)) + (((C0 - (C1 `1)) / ((l0 `1) - (C1 `1))) * (l0 `1)) is complex ext-real real Element of REAL
((C0 - (C1 `1)) / ((l0 `1) - (C1 `1))) * ((l0 `1) - (C1 `1)) is complex ext-real real Element of REAL
(C1 `1) + (((C0 - (C1 `1)) / ((l0 `1) - (C1 `1))) * ((l0 `1) - (C1 `1))) is complex ext-real real Element of REAL
(C1 `1) + (C0 - (C1 `1)) is complex ext-real real Element of REAL
C0 is complex ext-real real set
Horizontal_Line C0 is functional Element of bool the carrier of (TOP-REAL 2)
C1 is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
C1 `2 is complex ext-real real Element of REAL
l0 is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
l0 `2 is complex ext-real real Element of REAL
LSeg (C1,l0) is functional closed closed boundary nowhere_dense connected compact compact bounded bounded Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * C1) + (b₁ * l0)) where b₁ is complex ext-real real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
C0 - (C1 `2) is complex ext-real real Element of REAL
(l0 `2) - (C1 `2) is complex ext-real real Element of REAL
(C0 - (C1 `2)) / ((l0 `2) - (C1 `2)) is complex ext-real real Element of REAL
1 - ((C0 - (C1 `2)) / ((l0 `2) - (C1 `2))) is complex ext-real real Element of REAL
(1 - ((C0 - (C1 `2)) / ((l0 `2) - (C1 `2)))) * C1 is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
((C0 - (C1 `2)) / ((l0 `2) - (C1 `2))) * l0 is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
((1 - ((C0 - (C1 `2)) / ((l0 `2) - (C1 `2)))) * C1) + (((C0 - (C1 `2)) / ((l0 `2) - (C1 `2))) * l0) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) is Relation-like [: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of bool [:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):]
[:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):] is Relation-like non empty set
bool [:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):] is non empty set
K224( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),((1 - ((C0 - (C1 `2)) / ((l0 `2) - (C1 `2)))) * C1),(((C0 - (C1 `2)) / ((l0 `2) - (C1 `2))) * l0)) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
(C1 `2) - (C1 `2) is complex ext-real real Element of REAL
(((1 - ((C0 - (C1 `2)) / ((l0 `2) - (C1 `2)))) * C1) + (((C0 - (C1 `2)) / ((l0 `2) - (C1 `2))) * l0)) `2 is complex ext-real real Element of REAL
(1 - ((C0 - (C1 `2)) / ((l0 `2) - (C1 `2)))) * (C1 `2) is complex ext-real real Element of REAL
((C0 - (C1 `2)) / ((l0 `2) - (C1 `2))) * (l0 `2) is complex ext-real real Element of REAL
((1 - ((C0 - (C1 `2)) / ((l0 `2) - (C1 `2)))) * (C1 `2)) + (((C0 - (C1 `2)) / ((l0 `2) - (C1 `2))) * (l0 `2)) is complex ext-real real Element of REAL
((C0 - (C1 `2)) / ((l0 `2) - (C1 `2))) * ((l0 `2) - (C1 `2)) is complex ext-real real Element of REAL
(C1 `2) + (((C0 - (C1 `2)) / ((l0 `2) - (C1 `2))) * ((l0 `2) - (C1 `2))) is complex ext-real real Element of REAL
(C1 `2) + (C0 - (C1 `2)) is complex ext-real real Element of REAL
C0 is ordinal natural complex ext-real non negative real V33() V119() V166() V167() V168() V169() V170() V171() bounded_below Element of NAT
TOP-REAL C0 is non empty TopSpace-like T_0 T_1 T_2 connected V132() V178() V179() V180() V181() V182() V183() V184() strict add-continuous Mult-continuous pathwise_connected RLTopStruct
the carrier of (TOP-REAL C0) is functional non empty set
bool the carrier of (TOP-REAL C0) is non empty set
C1 is functional Element of bool the carrier of (TOP-REAL C0)
C1 is functional Element of bool the carrier of (TOP-REAL C0)
C0 is non empty ordinal natural complex ext-real positive non negative real set
TOP-REAL C0 is non empty TopSpace-like T_0 T_1 T_2 V132() V178() V179() V180() V181() V182() V183() V184() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C0) is functional non empty set
bool the carrier of (TOP-REAL C0) is non empty set
[#] (TOP-REAL C0) is functional non empty non proper non proper open open closed closed dense dense non boundary non boundary connected convex Element of bool the carrier of (TOP-REAL C0)
C1 is ordinal natural complex ext-real non negative real V33() V119() V166() V167() V168() V169() V170() V171() bounded_below Element of NAT
TOP-REAL C1 is non empty TopSpace-like T_0 T_1 T_2 connected V132() V178() V179() V180() V181() V182() V183() V184() strict add-continuous Mult-continuous pathwise_connected RLTopStruct
[#] (TOP-REAL C1) is functional non empty non proper non proper open open closed closed dense dense non boundary non boundary connected a_component convex Element of bool the carrier of (TOP-REAL C1)
the carrier of (TOP-REAL C1) is functional non empty set
bool the carrier of (TOP-REAL C1) is non empty set
C0 is functional closed compact bounded Element of bool the carrier of (TOP-REAL 2)
UMP C0 is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
E-bound C0 is complex ext-real real Element of REAL
(TOP-REAL 2) | C0 is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj1 | C0 is Relation-like C0 -defined the carrier of (TOP-REAL 2) -defined the carrier of ((TOP-REAL 2) | C0) -defined REAL -valued Function-like total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ((TOP-REAL 2) | C0),REAL:]
the carrier of ((TOP-REAL 2) | C0) is set
[: the carrier of ((TOP-REAL 2) | C0),REAL:] is Relation-like V156() V157() V158() set
bool [: the carrier of ((TOP-REAL 2) | C0),REAL:] is non empty set
upper_bound (proj1 | C0) is complex ext-real real Element of REAL
(proj1 | C0) .: the carrier of ((TOP-REAL 2) | C0) is V166() V167() V168() Element of bool REAL
K662(((proj1 | C0) .: the carrier of ((TOP-REAL 2) | C0))) is complex ext-real real Element of REAL
W-bound C0 is complex ext-real real Element of REAL
lower_bound (proj1 | C0) is complex ext-real real Element of REAL
K663(((proj1 | C0) .: the carrier of ((TOP-REAL 2) | C0))) is complex ext-real real Element of REAL
(E-bound C0) + (W-bound C0) is complex ext-real real Element of REAL
((E-bound C0) + (W-bound C0)) / 2 is complex ext-real real Element of REAL
Vertical_Line (((E-bound C0) + (W-bound C0)) / 2) is functional Element of bool the carrier of (TOP-REAL 2)
C0 /\ (Vertical_Line (((E-bound C0) + (W-bound C0)) / 2)) is functional Element of bool the carrier of (TOP-REAL 2)
proj2 .: (C0 /\ (Vertical_Line (((E-bound C0) + (W-bound C0)) / 2))) is V166() V167() V168() Element of bool REAL
K662((proj2 .: (C0 /\ (Vertical_Line (((E-bound C0) + (W-bound C0)) / 2))))) is complex ext-real real Element of REAL
|[(((E-bound C0) + (W-bound C0)) / 2),K662((proj2 .: (C0 /\ (Vertical_Line (((E-bound C0) + (W-bound C0)) / 2)))))]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
north_halfline (UMP C0) is functional non empty connected convex Element of bool the carrier of (TOP-REAL 2)
{(UMP C0)} is functional non empty closed compact bounded Element of bool the carrier of (TOP-REAL 2)
(north_halfline (UMP C0)) \ {(UMP C0)} is functional Element of bool the carrier of (TOP-REAL 2)
(W-bound C0) + (E-bound C0) is complex ext-real real Element of REAL
((W-bound C0) + (E-bound C0)) / 2 is complex ext-real real Element of REAL
h1 is set
rp is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
rp `1 is complex ext-real real Element of REAL
(UMP C0) `1 is complex ext-real real Element of REAL
(UMP C0) `2 is complex ext-real real Element of REAL
rp `2 is complex ext-real real Element of REAL
Vertical_Line (((W-bound C0) + (E-bound C0)) / 2) is functional Element of bool the carrier of (TOP-REAL 2)
C0 /\ (Vertical_Line (((W-bound C0) + (E-bound C0)) / 2)) is functional Element of bool the carrier of (TOP-REAL 2)
C0 is functional closed compact bounded Element of bool the carrier of (TOP-REAL 2)
LMP C0 is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
E-bound C0 is complex ext-real real Element of REAL
(TOP-REAL 2) | C0 is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj1 | C0 is Relation-like C0 -defined the carrier of (TOP-REAL 2) -defined the carrier of ((TOP-REAL 2) | C0) -defined REAL -valued Function-like total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ((TOP-REAL 2) | C0),REAL:]
the carrier of ((TOP-REAL 2) | C0) is set
[: the carrier of ((TOP-REAL 2) | C0),REAL:] is Relation-like V156() V157() V158() set
bool [: the carrier of ((TOP-REAL 2) | C0),REAL:] is non empty set
upper_bound (proj1 | C0) is complex ext-real real Element of REAL
(proj1 | C0) .: the carrier of ((TOP-REAL 2) | C0) is V166() V167() V168() Element of bool REAL
K662(((proj1 | C0) .: the carrier of ((TOP-REAL 2) | C0))) is complex ext-real real Element of REAL
W-bound C0 is complex ext-real real Element of REAL
lower_bound (proj1 | C0) is complex ext-real real Element of REAL
K663(((proj1 | C0) .: the carrier of ((TOP-REAL 2) | C0))) is complex ext-real real Element of REAL
(E-bound C0) + (W-bound C0) is complex ext-real real Element of REAL
((E-bound C0) + (W-bound C0)) / 2 is complex ext-real real Element of REAL
Vertical_Line (((E-bound C0) + (W-bound C0)) / 2) is functional Element of bool the carrier of (TOP-REAL 2)
C0 /\ (Vertical_Line (((E-bound C0) + (W-bound C0)) / 2)) is functional Element of bool the carrier of (TOP-REAL 2)
proj2 .: (C0 /\ (Vertical_Line (((E-bound C0) + (W-bound C0)) / 2))) is V166() V167() V168() Element of bool REAL
K663((proj2 .: (C0 /\ (Vertical_Line (((E-bound C0) + (W-bound C0)) / 2))))) is complex ext-real real Element of REAL
|[(((E-bound C0) + (W-bound C0)) / 2),K663((proj2 .: (C0 /\ (Vertical_Line (((E-bound C0) + (W-bound C0)) / 2)))))]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
south_halfline (LMP C0) is functional non empty connected convex Element of bool the carrier of (TOP-REAL 2)
{(LMP C0)} is functional non empty closed compact bounded Element of bool the carrier of (TOP-REAL 2)
(south_halfline (LMP C0)) \ {(LMP C0)} is functional Element of bool the carrier of (TOP-REAL 2)
(W-bound C0) + (E-bound C0) is complex ext-real real Element of REAL
((W-bound C0) + (E-bound C0)) / 2 is complex ext-real real Element of REAL
h1 is set
rp is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
rp `1 is complex ext-real real Element of REAL
(LMP C0) `1 is complex ext-real real Element of REAL
rp `2 is complex ext-real real Element of REAL
(LMP C0) `2 is complex ext-real real Element of REAL
Vertical_Line (((W-bound C0) + (E-bound C0)) / 2) is functional Element of bool the carrier of (TOP-REAL 2)
C0 /\ (Vertical_Line (((W-bound C0) + (E-bound C0)) / 2)) is functional Element of bool the carrier of (TOP-REAL 2)
C0 is functional closed compact bounded Element of bool the carrier of (TOP-REAL 2)
UMP C0 is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
E-bound C0 is complex ext-real real Element of REAL
(TOP-REAL 2) | C0 is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj1 | C0 is Relation-like C0 -defined the carrier of (TOP-REAL 2) -defined the carrier of ((TOP-REAL 2) | C0) -defined REAL -valued Function-like total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ((TOP-REAL 2) | C0),REAL:]
the carrier of ((TOP-REAL 2) | C0) is set
[: the carrier of ((TOP-REAL 2) | C0),REAL:] is Relation-like V156() V157() V158() set
bool [: the carrier of ((TOP-REAL 2) | C0),REAL:] is non empty set
upper_bound (proj1 | C0) is complex ext-real real Element of REAL
(proj1 | C0) .: the carrier of ((TOP-REAL 2) | C0) is V166() V167() V168() Element of bool REAL
K662(((proj1 | C0) .: the carrier of ((TOP-REAL 2) | C0))) is complex ext-real real Element of REAL
W-bound C0 is complex ext-real real Element of REAL
lower_bound (proj1 | C0) is complex ext-real real Element of REAL
K663(((proj1 | C0) .: the carrier of ((TOP-REAL 2) | C0))) is complex ext-real real Element of REAL
(E-bound C0) + (W-bound C0) is complex ext-real real Element of REAL
((E-bound C0) + (W-bound C0)) / 2 is complex ext-real real Element of REAL
Vertical_Line (((E-bound C0) + (W-bound C0)) / 2) is functional Element of bool the carrier of (TOP-REAL 2)
C0 /\ (Vertical_Line (((E-bound C0) + (W-bound C0)) / 2)) is functional Element of bool the carrier of (TOP-REAL 2)
proj2 .: (C0 /\ (Vertical_Line (((E-bound C0) + (W-bound C0)) / 2))) is V166() V167() V168() Element of bool REAL
K662((proj2 .: (C0 /\ (Vertical_Line (((E-bound C0) + (W-bound C0)) / 2))))) is complex ext-real real Element of REAL
|[(((E-bound C0) + (W-bound C0)) / 2),K662((proj2 .: (C0 /\ (Vertical_Line (((E-bound C0) + (W-bound C0)) / 2)))))]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
north_halfline (UMP C0) is functional non empty connected convex Element of bool the carrier of (TOP-REAL 2)
{(UMP C0)} is functional non empty closed compact bounded Element of bool the carrier of (TOP-REAL 2)
(north_halfline (UMP C0)) \ {(UMP C0)} is functional Element of bool the carrier of (TOP-REAL 2)
UBD C0 is functional non empty open connected being_Region Element of bool the carrier of (TOP-REAL 2)
{ b<sub>1</sub> where b<sub>1</sub> is functional Element of bool the carrier of (TOP-REAL 2) : b<sub>1</sub> is_outside_component_of C0 } is set
union { b<sub>1</sub> where b<sub>1</sub> is functional Element of bool the carrier of (TOP-REAL 2) : b<sub>1</sub> is_outside_component_of C0 } is set
l0 is functional non empty non bounded Element of bool the carrier of (TOP-REAL 2)
C0 is functional closed compact bounded Element of bool the carrier of (TOP-REAL 2)
LMP C0 is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
E-bound C0 is complex ext-real real Element of REAL
(TOP-REAL 2) | C0 is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj1 | C0 is Relation-like C0 -defined the carrier of (TOP-REAL 2) -defined the carrier of ((TOP-REAL 2) | C0) -defined REAL -valued Function-like total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ((TOP-REAL 2) | C0),REAL:]
the carrier of ((TOP-REAL 2) | C0) is set
[: the carrier of ((TOP-REAL 2) | C0),REAL:] is Relation-like V156() V157() V158() set
bool [: the carrier of ((TOP-REAL 2) | C0),REAL:] is non empty set
upper_bound (proj1 | C0) is complex ext-real real Element of REAL
(proj1 | C0) .: the carrier of ((TOP-REAL 2) | C0) is V166() V167() V168() Element of bool REAL
K662(((proj1 | C0) .: the carrier of ((TOP-REAL 2) | C0))) is complex ext-real real Element of REAL
W-bound C0 is complex ext-real real Element of REAL
lower_bound (proj1 | C0) is complex ext-real real Element of REAL
K663(((proj1 | C0) .: the carrier of ((TOP-REAL 2) | C0))) is complex ext-real real Element of REAL
(E-bound C0) + (W-bound C0) is complex ext-real real Element of REAL
((E-bound C0) + (W-bound C0)) / 2 is complex ext-real real Element of REAL
Vertical_Line (((E-bound C0) + (W-bound C0)) / 2) is functional Element of bool the carrier of (TOP-REAL 2)
C0 /\ (Vertical_Line (((E-bound C0) + (W-bound C0)) / 2)) is functional Element of bool the carrier of (TOP-REAL 2)
proj2 .: (C0 /\ (Vertical_Line (((E-bound C0) + (W-bound C0)) / 2))) is V166() V167() V168() Element of bool REAL
K663((proj2 .: (C0 /\ (Vertical_Line (((E-bound C0) + (W-bound C0)) / 2))))) is complex ext-real real Element of REAL
|[(((E-bound C0) + (W-bound C0)) / 2),K663((proj2 .: (C0 /\ (Vertical_Line (((E-bound C0) + (W-bound C0)) / 2)))))]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
south_halfline (LMP C0) is functional non empty connected convex Element of bool the carrier of (TOP-REAL 2)
{(LMP C0)} is functional non empty closed compact bounded Element of bool the carrier of (TOP-REAL 2)
(south_halfline (LMP C0)) \ {(LMP C0)} is functional Element of bool the carrier of (TOP-REAL 2)
UBD C0 is functional non empty open connected being_Region Element of bool the carrier of (TOP-REAL 2)
{ b<sub>1</sub> where b<sub>1</sub> is functional Element of bool the carrier of (TOP-REAL 2) : b<sub>1</sub> is_outside_component_of C0 } is set
union { b<sub>1</sub> where b<sub>1</sub> is functional Element of bool the carrier of (TOP-REAL 2) : b<sub>1</sub> is_outside_component_of C0 } is set
l0 is functional non empty non bounded Element of bool the carrier of (TOP-REAL 2)
C0 is functional Element of bool the carrier of (TOP-REAL 2)
C1 is functional Element of bool the carrier of (TOP-REAL 2)
UBD C1 is functional Element of bool the carrier of (TOP-REAL 2)
{ b<sub>1</sub> where b<sub>1</sub> is functional Element of bool the carrier of (TOP-REAL 2) : b<sub>1</sub> is_outside_component_of C1 } is set
union { b<sub>1</sub> where b<sub>1</sub> is functional Element of bool the carrier of (TOP-REAL 2) : b<sub>1</sub> is_outside_component_of C1 } is set
BDD C1 is functional Element of bool the carrier of (TOP-REAL 2)
{ b<sub>1</sub> where b<sub>1</sub> is functional Element of bool the carrier of (TOP-REAL 2) : b<sub>1</sub> is_inside_component_of C1 } is set
union { b<sub>1</sub> where b<sub>1</sub> is functional Element of bool the carrier of (TOP-REAL 2) : b<sub>1</sub> is_inside_component_of C1 } is set
C0 is functional Element of bool the carrier of (TOP-REAL 2)
C1 is functional Element of bool the carrier of (TOP-REAL 2)
BDD C1 is functional Element of bool the carrier of (TOP-REAL 2)
{ b<sub>1</sub> where b<sub>1</sub> is functional Element of bool the carrier of (TOP-REAL 2) : b<sub>1</sub> is_inside_component_of C1 } is set
union { b<sub>1</sub> where b<sub>1</sub> is functional Element of bool the carrier of (TOP-REAL 2) : b<sub>1</sub> is_inside_component_of C1 } is set
UBD C1 is functional Element of bool the carrier of (TOP-REAL 2)
{ b<sub>1</sub> where b<sub>1</sub> is functional Element of bool the carrier of (TOP-REAL 2) : b<sub>1</sub> is_outside_component_of C1 } is set
union { b<sub>1</sub> where b<sub>1</sub> is functional Element of bool the carrier of (TOP-REAL 2) : b<sub>1</sub> is_outside_component_of C1 } is set
C0 is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
{C0} is functional non empty closed compact bounded Element of bool the carrier of (TOP-REAL 2)
C1 is functional non empty closed connected compact bounded being_simple_closed_curve with_the_max_arc Element of bool the carrier of (TOP-REAL 2)
C1 ` is functional open Element of bool the carrier of (TOP-REAL 2)
the carrier of (TOP-REAL 2) \ C1 is set
(TOP-REAL 2) | (C1 `) is strict TopSpace-like T_0 T_1 T_2 V118( TOP-REAL 2) SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | (C1 `)) is set
bool the carrier of ((TOP-REAL 2) | (C1 `)) is non empty set
l0 is Element of bool the carrier of ((TOP-REAL 2) | (C1 `))
(#) ((- 1),1) is complex ext-real real Element of the carrier of (Closed-Interval-TSpace ((- 1),1))
((- 1),1) (#) is complex ext-real real Element of the carrier of (Closed-Interval-TSpace ((- 1),1))
L[01] (((#) ((- 1),1)),(((- 1),1) (#))) is Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined the carrier of (Closed-Interval-TSpace ((- 1),1)) -valued Function-like non empty total quasi_total V156() V157() V158() Element of bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((- 1),1)):]
[: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((- 1),1)):] is Relation-like non empty V156() V157() V158() set
bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((- 1),1)):] is non empty set
[:(TOP-REAL 2),(TOP-REAL 2):] is non empty strict TopSpace-like T_0 T_1 T_2 TopStruct
the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] is non empty set
rp is non empty TopSpace-like TopStruct
the carrier of rp is non empty set
rl is complex ext-real real Element of REAL
the carrier of rp --> rl is Relation-like the carrier of rp -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() Element of bool [: the carrier of rp,REAL:]
[: the carrier of rp,REAL:] is Relation-like non empty V156() V157() V158() set
bool [: the carrier of rp,REAL:] is non empty set
dom ( the carrier of rp --> rl) is non empty Element of bool the carrier of rp
bool the carrier of rp is non empty set
rng ( the carrier of rp --> rl) is non empty V166() V167() V168() Element of bool REAL
{rl} is non empty V166() V167() V168() Element of bool REAL
a is V166() V167() V168() Element of bool REAL
( the carrier of rp --> rl) " a is Element of bool the carrier of rp
(rng ( the carrier of rp --> rl)) /\ a is V166() V167() V168() Element of bool REAL
( the carrier of rp --> rl) " ((rng ( the carrier of rp --> rl)) /\ a) is Element of bool the carrier of rp
( the carrier of rp --> rl) " (rng ( the carrier of rp --> rl)) is Element of bool the carrier of rp
[#] rp is non empty non proper open closed dense non boundary Element of bool the carrier of rp
(rng ( the carrier of rp --> rl)) /\ a is V166() V167() V168() Element of bool REAL
( the carrier of rp --> rl) " ((rng ( the carrier of rp --> rl)) /\ a) is Element of bool the carrier of rp
( the carrier of rp --> rl) " {} is Relation-like non-empty empty-yielding RAT -valued Function-like one-to-one constant functional empty proper open closed boundary nowhere_dense connected compact V156() V157() V158() V159() V166() V167() V168() V169() V170() V171() V172() bounded_below interval Element of bool the carrier of rp
{} rp is Relation-like non-empty empty-yielding RAT -valued Function-like one-to-one constant functional empty proper open closed boundary nowhere_dense connected compact V156() V157() V158() V159() V166() V167() V168() V169() V170() V171() V172() bounded_below interval Element of bool the carrier of rp
rp is ordinal natural complex ext-real non negative real V33() V119() V166() V167() V168() V169() V170() V171() bounded_below Element of NAT
TOP-REAL rp is non empty TopSpace-like T_0 T_1 T_2 connected V132() V178() V179() V180() V181() V182() V183() V184() strict add-continuous Mult-continuous pathwise_connected RLTopStruct
the carrier of (TOP-REAL rp) is functional non empty set
rl is non empty complex ext-real positive non negative real set
rg is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
Ball (rg,rl) is functional non empty open connected bounded convex Element of bool the carrier of (TOP-REAL rp)
bool the carrier of (TOP-REAL rp) is non empty set
rg - rg is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
- rg is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
K270((TOP-REAL rp),rg,(- rg)) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
the U7 of (TOP-REAL rp) is Relation-like [: the carrier of (TOP-REAL rp), the carrier of (TOP-REAL rp):] -defined the carrier of (TOP-REAL rp) -valued Function-like non empty total quasi_total Element of bool [:[: the carrier of (TOP-REAL rp), the carrier of (TOP-REAL rp):], the carrier of (TOP-REAL rp):]
[: the carrier of (TOP-REAL rp), the carrier of (TOP-REAL rp):] is Relation-like non empty set
[:[: the carrier of (TOP-REAL rp), the carrier of (TOP-REAL rp):], the carrier of (TOP-REAL rp):] is Relation-like non empty set
bool [:[: the carrier of (TOP-REAL rp), the carrier of (TOP-REAL rp):], the carrier of (TOP-REAL rp):] is non empty set
K224( the carrier of (TOP-REAL rp), the U7 of (TOP-REAL rp),rg,(- rg)) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
|.(rg - rg).| is complex ext-real non negative real Element of REAL
rp is ordinal natural complex ext-real non negative real V33() V119() V166() V167() V168() V169() V170() V171() bounded_below Element of NAT
TOP-REAL rp is non empty TopSpace-like T_0 T_1 T_2 connected V132() V178() V179() V180() V181() V182() V183() V184() strict add-continuous Mult-continuous pathwise_connected RLTopStruct
the carrier of (TOP-REAL rp) is functional non empty set
rl is complex ext-real non negative real set
rg is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
Tdisk (rg,rl) is non empty TopSpace-like T_0 T_1 T_2 V270(rp) SubSpace of TOP-REAL rp
the carrier of (Tdisk (rg,rl)) is non empty set
cl_Ball (rg,rl) is functional non empty closed connected bounded convex Element of bool the carrier of (TOP-REAL rp)
bool the carrier of (TOP-REAL rp) is non empty set
rg - rg is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
- rg is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
K270((TOP-REAL rp),rg,(- rg)) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
the U7 of (TOP-REAL rp) is Relation-like [: the carrier of (TOP-REAL rp), the carrier of (TOP-REAL rp):] -defined the carrier of (TOP-REAL rp) -valued Function-like non empty total quasi_total Element of bool [:[: the carrier of (TOP-REAL rp), the carrier of (TOP-REAL rp):], the carrier of (TOP-REAL rp):]
[: the carrier of (TOP-REAL rp), the carrier of (TOP-REAL rp):] is Relation-like non empty set
[:[: the carrier of (TOP-REAL rp), the carrier of (TOP-REAL rp):], the carrier of (TOP-REAL rp):] is Relation-like non empty set
bool [:[: the carrier of (TOP-REAL rp), the carrier of (TOP-REAL rp):], the carrier of (TOP-REAL rp):] is non empty set
K224( the carrier of (TOP-REAL rp), the U7 of (TOP-REAL rp),rg,(- rg)) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
|.(rg - rg).| is complex ext-real non negative real Element of REAL
rl is non empty ordinal natural complex ext-real positive non negative real V33() V119() V166() V167() V168() V169() V170() V171() left_end bounded_below Element of NAT
TOP-REAL rl is non empty TopSpace-like T_0 T_1 T_2 connected V132() V178() V179() V180() V181() V182() V183() V184() strict add-continuous Mult-continuous pathwise_connected RLTopStruct
the carrier of (TOP-REAL rl) is functional non empty set
rg is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
rp is non empty complex ext-real positive non negative real set
cl_Ball (rg,rp) is functional non empty closed connected bounded convex Element of bool the carrier of (TOP-REAL rl)
bool the carrier of (TOP-REAL rl) is non empty set
rd is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
{rd} is functional non empty closed compact bounded Element of bool the carrier of (TOP-REAL rl)
(cl_Ball (rg,rp)) \ {rd} is functional Element of bool the carrier of (TOP-REAL rl)
Tcircle (rg,rp) is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL rl
the carrier of (Tcircle (rg,rp)) is non empty set
Sphere (rg,rp) is functional non empty closed bounded Element of bool the carrier of (TOP-REAL rl)
Tdisk (rg,rp) is non empty TopSpace-like T_0 T_1 T_2 V270(rl) SubSpace of TOP-REAL rl
the carrier of (Tdisk (rg,rp)) is non empty set
the Element of the carrier of (Tcircle (rg,rp)) is Element of the carrier of (Tcircle (rg,rp))
rg - rg is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
- rg is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
K270((TOP-REAL rl),rg,(- rg)) is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
the U7 of (TOP-REAL rl) is Relation-like [: the carrier of (TOP-REAL rl), the carrier of (TOP-REAL rl):] -defined the carrier of (TOP-REAL rl) -valued Function-like non empty total quasi_total Element of bool [:[: the carrier of (TOP-REAL rl), the carrier of (TOP-REAL rl):], the carrier of (TOP-REAL rl):]
[: the carrier of (TOP-REAL rl), the carrier of (TOP-REAL rl):] is Relation-like non empty set
[:[: the carrier of (TOP-REAL rl), the carrier of (TOP-REAL rl):], the carrier of (TOP-REAL rl):] is Relation-like non empty set
bool [:[: the carrier of (TOP-REAL rl), the carrier of (TOP-REAL rl):], the carrier of (TOP-REAL rl):] is non empty set
K224( the carrier of (TOP-REAL rl), the U7 of (TOP-REAL rl),rg,(- rg)) is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
|.(rg - rg).| is complex ext-real non negative real Element of REAL
rp is complex ext-real real set
rl is complex ext-real real set
rg is ordinal natural complex ext-real non negative real V33() V119() V166() V167() V168() V169() V170() V171() bounded_below Element of NAT
TOP-REAL rg is non empty TopSpace-like T_0 T_1 T_2 connected V132() V178() V179() V180() V181() V182() V183() V184() strict add-continuous Mult-continuous pathwise_connected RLTopStruct
the carrier of (TOP-REAL rg) is functional non empty set
rd is Relation-like Function-like V49(rg) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rg)
Ball (rd,rp) is functional open connected bounded convex Element of bool the carrier of (TOP-REAL rg)
bool the carrier of (TOP-REAL rg) is non empty set
Ball (rd,rl) is functional open connected bounded convex Element of bool the carrier of (TOP-REAL rg)
Euclid rg is non empty strict Reflexive discerning symmetric triangle Discerning MetrStruct
the carrier of (Euclid rg) is non empty set
a is Element of the carrier of (Euclid rg)
Ball (a,rp) is Element of bool the carrier of (Euclid rg)
bool the carrier of (Euclid rg) is non empty set
Ball (a,rl) is Element of bool the carrier of (Euclid rg)
rp is complex ext-real real set
rl is ordinal natural complex ext-real non negative real V33() V119() V166() V167() V168() V169() V170() V171() bounded_below Element of NAT
TOP-REAL rl is non empty TopSpace-like T_0 T_1 T_2 connected V132() V178() V179() V180() V181() V182() V183() V184() strict add-continuous Mult-continuous pathwise_connected RLTopStruct
the carrier of (TOP-REAL rl) is functional non empty set
rg is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
cl_Ball (rg,rp) is functional closed connected bounded convex Element of bool the carrier of (TOP-REAL rl)
bool the carrier of (TOP-REAL rl) is non empty set
Ball (rg,rp) is functional open connected bounded convex Element of bool the carrier of (TOP-REAL rl)
(cl_Ball (rg,rp)) \ (Ball (rg,rp)) is functional Element of bool the carrier of (TOP-REAL rl)
Sphere (rg,rp) is functional closed bounded Element of bool the carrier of (TOP-REAL rl)
rd is set
a is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
a - rg is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
- rg is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
K270((TOP-REAL rl),a,(- rg)) is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
the U7 of (TOP-REAL rl) is Relation-like [: the carrier of (TOP-REAL rl), the carrier of (TOP-REAL rl):] -defined the carrier of (TOP-REAL rl) -valued Function-like non empty total quasi_total Element of bool [:[: the carrier of (TOP-REAL rl), the carrier of (TOP-REAL rl):], the carrier of (TOP-REAL rl):]
[: the carrier of (TOP-REAL rl), the carrier of (TOP-REAL rl):] is Relation-like non empty set
[:[: the carrier of (TOP-REAL rl), the carrier of (TOP-REAL rl):], the carrier of (TOP-REAL rl):] is Relation-like non empty set
bool [:[: the carrier of (TOP-REAL rl), the carrier of (TOP-REAL rl):], the carrier of (TOP-REAL rl):] is non empty set
K224( the carrier of (TOP-REAL rl), the U7 of (TOP-REAL rl),a,(- rg)) is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
|.(a - rg).| is complex ext-real non negative real Element of REAL
rd is set
a is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
a - rg is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
- rg is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
K270((TOP-REAL rl),a,(- rg)) is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
the U7 of (TOP-REAL rl) is Relation-like [: the carrier of (TOP-REAL rl), the carrier of (TOP-REAL rl):] -defined the carrier of (TOP-REAL rl) -valued Function-like non empty total quasi_total Element of bool [:[: the carrier of (TOP-REAL rl), the carrier of (TOP-REAL rl):], the carrier of (TOP-REAL rl):]
[: the carrier of (TOP-REAL rl), the carrier of (TOP-REAL rl):] is Relation-like non empty set
[:[: the carrier of (TOP-REAL rl), the carrier of (TOP-REAL rl):], the carrier of (TOP-REAL rl):] is Relation-like non empty set
bool [:[: the carrier of (TOP-REAL rl), the carrier of (TOP-REAL rl):], the carrier of (TOP-REAL rl):] is non empty set
K224( the carrier of (TOP-REAL rl), the U7 of (TOP-REAL rl),a,(- rg)) is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
|.(a - rg).| is complex ext-real non negative real Element of REAL
rp is complex ext-real real set
rl is ordinal natural complex ext-real non negative real V33() V119() V166() V167() V168() V169() V170() V171() bounded_below Element of NAT
TOP-REAL rl is non empty TopSpace-like T_0 T_1 T_2 connected V132() V178() V179() V180() V181() V182() V183() V184() strict add-continuous Mult-continuous pathwise_connected RLTopStruct
the carrier of (TOP-REAL rl) is functional non empty set
rg is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
rd is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
Sphere (rd,rp) is functional closed bounded Element of bool the carrier of (TOP-REAL rl)
bool the carrier of (TOP-REAL rl) is non empty set
LSeg (rd,rg) is functional closed compact bounded Element of bool the carrier of (TOP-REAL rl)
{ (((1 - b₁) * rd) + (b₁ * rg)) where b₁ is complex ext-real real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
{rd,rg} is functional non empty Element of bool the carrier of (TOP-REAL rl)
(LSeg (rd,rg)) \ {rd,rg} is functional Element of bool the carrier of (TOP-REAL rl)
Ball (rd,rp) is functional open connected bounded convex Element of bool the carrier of (TOP-REAL rl)
Euclid rl is non empty strict Reflexive discerning symmetric triangle Discerning MetrStruct
the carrier of (Euclid rl) is non empty set
a is Element of the carrier of (Euclid rl)
Sphere (a,rp) is Element of bool the carrier of (Euclid rl)
bool the carrier of (Euclid rl) is non empty set
{rd} is functional non empty closed compact bounded Element of bool the carrier of (TOP-REAL rl)
LSeg (rd,rd) is functional closed compact bounded Element of bool the carrier of (TOP-REAL rl)
{ (((1 - b₁) * rd) + (b₁ * rd)) where b₁ is complex ext-real real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
{rd,rd} is functional non empty Element of bool the carrier of (TOP-REAL rl)
{rd} \ {rd} is functional Element of bool the carrier of (TOP-REAL rl)
a is set
b is complex ext-real real Element of REAL
1 - b is complex ext-real real Element of REAL
(1 - b) * rd is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
b * rg is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
((1 - b) * rd) + (b * rg) is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
the U7 of (TOP-REAL rl) is Relation-like [: the carrier of (TOP-REAL rl), the carrier of (TOP-REAL rl):] -defined the carrier of (TOP-REAL rl) -valued Function-like non empty total quasi_total Element of bool [:[: the carrier of (TOP-REAL rl), the carrier of (TOP-REAL rl):], the carrier of (TOP-REAL rl):]
[: the carrier of (TOP-REAL rl), the carrier of (TOP-REAL rl):] is Relation-like non empty set
[:[: the carrier of (TOP-REAL rl), the carrier of (TOP-REAL rl):], the carrier of (TOP-REAL rl):] is Relation-like non empty set
bool [:[: the carrier of (TOP-REAL rl), the carrier of (TOP-REAL rl):], the carrier of (TOP-REAL rl):] is non empty set
K224( the carrier of (TOP-REAL rl), the U7 of (TOP-REAL rl),((1 - b) * rd),(b * rg)) is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
c is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
c - rd is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
- rd is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
K270((TOP-REAL rl),c,(- rd)) is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
K224( the carrier of (TOP-REAL rl), the U7 of (TOP-REAL rl),c,(- rd)) is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
((1 - b) * rd) - rd is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
K270((TOP-REAL rl),((1 - b) * rd),(- rd)) is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
K224( the carrier of (TOP-REAL rl), the U7 of (TOP-REAL rl),((1 - b) * rd),(- rd)) is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
(((1 - b) * rd) - rd) + (b * rg) is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
K224( the carrier of (TOP-REAL rl), the U7 of (TOP-REAL rl),(((1 - b) * rd) - rd),(b * rg)) is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
1 * rd is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
b * rd is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
(1 * rd) - (b * rd) is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
- (b * rd) is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
K270((TOP-REAL rl),(1 * rd),(- (b * rd))) is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
K224( the carrier of (TOP-REAL rl), the U7 of (TOP-REAL rl),(1 * rd),(- (b * rd))) is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
((1 * rd) - (b * rd)) - rd is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
K270((TOP-REAL rl),((1 * rd) - (b * rd)),(- rd)) is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
K224( the carrier of (TOP-REAL rl), the U7 of (TOP-REAL rl),((1 * rd) - (b * rd)),(- rd)) is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
(((1 * rd) - (b * rd)) - rd) + (b * rg) is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
K224( the carrier of (TOP-REAL rl), the U7 of (TOP-REAL rl),(((1 * rd) - (b * rd)) - rd),(b * rg)) is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
rd - (b * rd) is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
K270((TOP-REAL rl),rd,(- (b * rd))) is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
K224( the carrier of (TOP-REAL rl), the U7 of (TOP-REAL rl),rd,(- (b * rd))) is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
(rd - (b * rd)) - rd is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
K270((TOP-REAL rl),(rd - (b * rd)),(- rd)) is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
K224( the carrier of (TOP-REAL rl), the U7 of (TOP-REAL rl),(rd - (b * rd)),(- rd)) is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
((rd - (b * rd)) - rd) + (b * rg) is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
K224( the carrier of (TOP-REAL rl), the U7 of (TOP-REAL rl),((rd - (b * rd)) - rd),(b * rg)) is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
rd + (- (b * rd)) is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
(rd + (- (b * rd))) + (- rd) is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
K224( the carrier of (TOP-REAL rl), the U7 of (TOP-REAL rl),(rd + (- (b * rd))),(- rd)) is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
((rd + (- (b * rd))) + (- rd)) + (b * rg) is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
K224( the carrier of (TOP-REAL rl), the U7 of (TOP-REAL rl),((rd + (- (b * rd))) + (- rd)),(b * rg)) is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
rd + (- rd) is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
K224( the carrier of (TOP-REAL rl), the U7 of (TOP-REAL rl),rd,(- rd)) is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
(rd + (- rd)) + (- (b * rd)) is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
K224( the carrier of (TOP-REAL rl), the U7 of (TOP-REAL rl),(rd + (- rd)),(- (b * rd))) is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
((rd + (- rd)) + (- (b * rd))) + (b * rg) is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
K224( the carrier of (TOP-REAL rl), the U7 of (TOP-REAL rl),((rd + (- rd)) + (- (b * rd))),(b * rg)) is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
rd - rd is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
K270((TOP-REAL rl),rd,(- rd)) is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
(rd - rd) - (b * rd) is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
K270((TOP-REAL rl),(rd - rd),(- (b * rd))) is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
K224( the carrier of (TOP-REAL rl), the U7 of (TOP-REAL rl),(rd - rd),(- (b * rd))) is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
((rd - rd) - (b * rd)) + (b * rg) is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
K224( the carrier of (TOP-REAL rl), the U7 of (TOP-REAL rl),((rd - rd) - (b * rd)),(b * rg)) is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
0. (TOP-REAL rl) is Relation-like Function-like V49(rl) V50() zero V156() V157() V158() Element of the carrier of (TOP-REAL rl)
the ZeroF of (TOP-REAL rl) is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
(0. (TOP-REAL rl)) - (b * rd) is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
K270((TOP-REAL rl),(0. (TOP-REAL rl)),(- (b * rd))) is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
K224( the carrier of (TOP-REAL rl), the U7 of (TOP-REAL rl),(0. (TOP-REAL rl)),(- (b * rd))) is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
((0. (TOP-REAL rl)) - (b * rd)) + (b * rg) is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
K224( the carrier of (TOP-REAL rl), the U7 of (TOP-REAL rl),((0. (TOP-REAL rl)) - (b * rd)),(b * rg)) is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
(b * rg) - (b * rd) is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
K270((TOP-REAL rl),(b * rg),(- (b * rd))) is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
K224( the carrier of (TOP-REAL rl), the U7 of (TOP-REAL rl),(b * rg),(- (b * rd))) is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
rg - rd is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
K270((TOP-REAL rl),rg,(- rd)) is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
K224( the carrier of (TOP-REAL rl), the U7 of (TOP-REAL rl),rg,(- rd)) is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
b * (rg - rd) is Relation-like Function-like V49(rl) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rl)
|.(c - rd).| is complex ext-real non negative real Element of REAL
abs b is complex ext-real real Element of REAL
|.(rg - rd).| is complex ext-real non negative real Element of REAL
(abs b) * |.(rg - rd).| is complex ext-real real Element of REAL
b * |.(rg - rd).| is complex ext-real real Element of REAL
b * rp is complex ext-real real Element of REAL
1 * rp is complex ext-real real Element of REAL
rp is complex ext-real real set
rl is complex ext-real real set
rg is ordinal natural complex ext-real non negative real V33() V119() V166() V167() V168() V169() V170() V171() bounded_below Element of NAT
TOP-REAL rg is non empty TopSpace-like T_0 T_1 T_2 connected V132() V178() V179() V180() V181() V182() V183() V184() strict add-continuous Mult-continuous pathwise_connected RLTopStruct
the carrier of (TOP-REAL rg) is functional non empty set
rd is Relation-like Function-like V49(rg) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rg)
cl_Ball (rd,rp) is functional closed connected bounded convex Element of bool the carrier of (TOP-REAL rg)
bool the carrier of (TOP-REAL rg) is non empty set
Ball (rd,rl) is functional open connected bounded convex Element of bool the carrier of (TOP-REAL rg)
a is set
b is Relation-like Function-like V49(rg) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rg)
b - rd is Relation-like Function-like V49(rg) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rg)
- rd is Relation-like Function-like V49(rg) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rg)
K270((TOP-REAL rg),b,(- rd)) is Relation-like Function-like V49(rg) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rg)
the U7 of (TOP-REAL rg) is Relation-like [: the carrier of (TOP-REAL rg), the carrier of (TOP-REAL rg):] -defined the carrier of (TOP-REAL rg) -valued Function-like non empty total quasi_total Element of bool [:[: the carrier of (TOP-REAL rg), the carrier of (TOP-REAL rg):], the carrier of (TOP-REAL rg):]
[: the carrier of (TOP-REAL rg), the carrier of (TOP-REAL rg):] is Relation-like non empty set
[:[: the carrier of (TOP-REAL rg), the carrier of (TOP-REAL rg):], the carrier of (TOP-REAL rg):] is Relation-like non empty set
bool [:[: the carrier of (TOP-REAL rg), the carrier of (TOP-REAL rg):], the carrier of (TOP-REAL rg):] is non empty set
K224( the carrier of (TOP-REAL rg), the U7 of (TOP-REAL rg),b,(- rd)) is Relation-like Function-like V49(rg) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rg)
|.(b - rd).| is complex ext-real non negative real Element of REAL
rp is complex ext-real real set
rl is complex ext-real real set
rg is ordinal natural complex ext-real non negative real V33() V119() V166() V167() V168() V169() V170() V171() bounded_below Element of NAT
TOP-REAL rg is non empty TopSpace-like T_0 T_1 T_2 connected V132() V178() V179() V180() V181() V182() V183() V184() strict add-continuous Mult-continuous pathwise_connected RLTopStruct
the carrier of (TOP-REAL rg) is functional non empty set
rd is Relation-like Function-like V49(rg) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rg)
Sphere (rd,rp) is functional closed bounded Element of bool the carrier of (TOP-REAL rg)
bool the carrier of (TOP-REAL rg) is non empty set
Ball (rd,rl) is functional open connected bounded convex Element of bool the carrier of (TOP-REAL rg)
cl_Ball (rd,rp) is functional closed connected bounded convex Element of bool the carrier of (TOP-REAL rg)
rp is ordinal natural complex ext-real non negative real V33() V119() V166() V167() V168() V169() V170() V171() bounded_below Element of NAT
TOP-REAL rp is non empty TopSpace-like T_0 T_1 T_2 connected V132() V178() V179() V180() V181() V182() V183() V184() strict add-continuous Mult-continuous pathwise_connected RLTopStruct
the carrier of (TOP-REAL rp) is functional non empty set
rl is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
rg is non empty complex ext-real real set
Ball (rl,rg) is functional open connected bounded convex Element of bool the carrier of (TOP-REAL rp)
bool the carrier of (TOP-REAL rp) is non empty set
Cl (Ball (rl,rg)) is functional closed Element of bool the carrier of (TOP-REAL rp)
cl_Ball (rl,rg) is functional closed connected bounded convex Element of bool the carrier of (TOP-REAL rp)
rd is set
Euclid rp is non empty strict Reflexive discerning symmetric triangle Discerning MetrStruct
the carrier of (Euclid rp) is non empty set
a is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
b is Element of the carrier of (Euclid rp)
c is complex ext-real real set
Ball (b,c) is Element of bool the carrier of (Euclid rp)
bool the carrier of (Euclid rp) is non empty set
Sphere (rl,rg) is functional closed bounded Element of bool the carrier of (TOP-REAL rp)
(Ball (rl,rg)) \/ (Sphere (rl,rg)) is functional Element of bool the carrier of (TOP-REAL rp)
a - a is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
- a is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
K270((TOP-REAL rp),a,(- a)) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
the U7 of (TOP-REAL rp) is Relation-like [: the carrier of (TOP-REAL rp), the carrier of (TOP-REAL rp):] -defined the carrier of (TOP-REAL rp) -valued Function-like non empty total quasi_total Element of bool [:[: the carrier of (TOP-REAL rp), the carrier of (TOP-REAL rp):], the carrier of (TOP-REAL rp):]
[: the carrier of (TOP-REAL rp), the carrier of (TOP-REAL rp):] is Relation-like non empty set
[:[: the carrier of (TOP-REAL rp), the carrier of (TOP-REAL rp):], the carrier of (TOP-REAL rp):] is Relation-like non empty set
bool [:[: the carrier of (TOP-REAL rp), the carrier of (TOP-REAL rp):], the carrier of (TOP-REAL rp):] is non empty set
K224( the carrier of (TOP-REAL rp), the U7 of (TOP-REAL rp),a,(- a)) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
|.(a - a).| is complex ext-real non negative real Element of REAL
Ball (a,c) is functional open connected bounded convex Element of bool the carrier of (TOP-REAL rp)
a - rl is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
- rl is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
K270((TOP-REAL rp),a,(- rl)) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
the U7 of (TOP-REAL rp) is Relation-like [: the carrier of (TOP-REAL rp), the carrier of (TOP-REAL rp):] -defined the carrier of (TOP-REAL rp) -valued Function-like non empty total quasi_total Element of bool [:[: the carrier of (TOP-REAL rp), the carrier of (TOP-REAL rp):], the carrier of (TOP-REAL rp):]
[: the carrier of (TOP-REAL rp), the carrier of (TOP-REAL rp):] is Relation-like non empty set
[:[: the carrier of (TOP-REAL rp), the carrier of (TOP-REAL rp):], the carrier of (TOP-REAL rp):] is Relation-like non empty set
bool [:[: the carrier of (TOP-REAL rp), the carrier of (TOP-REAL rp):], the carrier of (TOP-REAL rp):] is non empty set
K224( the carrier of (TOP-REAL rp), the U7 of (TOP-REAL rp),a,(- rl)) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
|.(a - rl).| is complex ext-real non negative real Element of REAL
rl - rl is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
K270((TOP-REAL rp),rl,(- rl)) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
K224( the carrier of (TOP-REAL rp), the U7 of (TOP-REAL rp),rl,(- rl)) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
|.(rl - rl).| is complex ext-real non negative real Element of REAL
2 * rg is complex ext-real real Element of REAL
c / (2 * rg) is complex ext-real real Element of REAL
1 - (c / (2 * rg)) is complex ext-real real Element of REAL
(1 - (c / (2 * rg))) * a is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
(c / (2 * rg)) * rl is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
((1 - (c / (2 * rg))) * a) + ((c / (2 * rg)) * rl) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
K224( the carrier of (TOP-REAL rp), the U7 of (TOP-REAL rp),((1 - (c / (2 * rg))) * a),((c / (2 * rg)) * rl)) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
1 * rg is complex ext-real real Element of REAL
LSeg (a,rl) is functional closed compact bounded Element of bool the carrier of (TOP-REAL rp)
{ (((1 - b₁) * a) + (b₁ * rl)) where b₁ is complex ext-real real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
{a,rl} is functional non empty Element of bool the carrier of (TOP-REAL rp)
(LSeg (a,rl)) \ {a,rl} is functional Element of bool the carrier of (TOP-REAL rp)
(((1 - (c / (2 * rg))) * a) + ((c / (2 * rg)) * rl)) - a is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
- a is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
K270((TOP-REAL rp),(((1 - (c / (2 * rg))) * a) + ((c / (2 * rg)) * rl)),(- a)) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
K224( the carrier of (TOP-REAL rp), the U7 of (TOP-REAL rp),(((1 - (c / (2 * rg))) * a) + ((c / (2 * rg)) * rl)),(- a)) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
((1 - (c / (2 * rg))) * a) - a is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
K270((TOP-REAL rp),((1 - (c / (2 * rg))) * a),(- a)) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
K224( the carrier of (TOP-REAL rp), the U7 of (TOP-REAL rp),((1 - (c / (2 * rg))) * a),(- a)) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
(((1 - (c / (2 * rg))) * a) - a) + ((c / (2 * rg)) * rl) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
K224( the carrier of (TOP-REAL rp), the U7 of (TOP-REAL rp),(((1 - (c / (2 * rg))) * a) - a),((c / (2 * rg)) * rl)) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
1 * a is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
(c / (2 * rg)) * a is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
(1 * a) - ((c / (2 * rg)) * a) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
- ((c / (2 * rg)) * a) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
K270((TOP-REAL rp),(1 * a),(- ((c / (2 * rg)) * a))) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
K224( the carrier of (TOP-REAL rp), the U7 of (TOP-REAL rp),(1 * a),(- ((c / (2 * rg)) * a))) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
((1 * a) - ((c / (2 * rg)) * a)) - a is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
K270((TOP-REAL rp),((1 * a) - ((c / (2 * rg)) * a)),(- a)) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
K224( the carrier of (TOP-REAL rp), the U7 of (TOP-REAL rp),((1 * a) - ((c / (2 * rg)) * a)),(- a)) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
(((1 * a) - ((c / (2 * rg)) * a)) - a) + ((c / (2 * rg)) * rl) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
K224( the carrier of (TOP-REAL rp), the U7 of (TOP-REAL rp),(((1 * a) - ((c / (2 * rg)) * a)) - a),((c / (2 * rg)) * rl)) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
a - ((c / (2 * rg)) * a) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
K270((TOP-REAL rp),a,(- ((c / (2 * rg)) * a))) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
K224( the carrier of (TOP-REAL rp), the U7 of (TOP-REAL rp),a,(- ((c / (2 * rg)) * a))) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
(a - ((c / (2 * rg)) * a)) - a is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
K270((TOP-REAL rp),(a - ((c / (2 * rg)) * a)),(- a)) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
K224( the carrier of (TOP-REAL rp), the U7 of (TOP-REAL rp),(a - ((c / (2 * rg)) * a)),(- a)) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
((a - ((c / (2 * rg)) * a)) - a) + ((c / (2 * rg)) * rl) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
K224( the carrier of (TOP-REAL rp), the U7 of (TOP-REAL rp),((a - ((c / (2 * rg)) * a)) - a),((c / (2 * rg)) * rl)) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
a + (- ((c / (2 * rg)) * a)) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
(a + (- ((c / (2 * rg)) * a))) + (- a) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
K224( the carrier of (TOP-REAL rp), the U7 of (TOP-REAL rp),(a + (- ((c / (2 * rg)) * a))),(- a)) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
((a + (- ((c / (2 * rg)) * a))) + (- a)) + ((c / (2 * rg)) * rl) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
K224( the carrier of (TOP-REAL rp), the U7 of (TOP-REAL rp),((a + (- ((c / (2 * rg)) * a))) + (- a)),((c / (2 * rg)) * rl)) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
a + (- a) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
K224( the carrier of (TOP-REAL rp), the U7 of (TOP-REAL rp),a,(- a)) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
(a + (- a)) + (- ((c / (2 * rg)) * a)) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
K224( the carrier of (TOP-REAL rp), the U7 of (TOP-REAL rp),(a + (- a)),(- ((c / (2 * rg)) * a))) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
((a + (- a)) + (- ((c / (2 * rg)) * a))) + ((c / (2 * rg)) * rl) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
K224( the carrier of (TOP-REAL rp), the U7 of (TOP-REAL rp),((a + (- a)) + (- ((c / (2 * rg)) * a))),((c / (2 * rg)) * rl)) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
a - a is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
K270((TOP-REAL rp),a,(- a)) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
(a - a) - ((c / (2 * rg)) * a) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
K270((TOP-REAL rp),(a - a),(- ((c / (2 * rg)) * a))) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
K224( the carrier of (TOP-REAL rp), the U7 of (TOP-REAL rp),(a - a),(- ((c / (2 * rg)) * a))) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
((a - a) - ((c / (2 * rg)) * a)) + ((c / (2 * rg)) * rl) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
K224( the carrier of (TOP-REAL rp), the U7 of (TOP-REAL rp),((a - a) - ((c / (2 * rg)) * a)),((c / (2 * rg)) * rl)) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
0. (TOP-REAL rp) is Relation-like Function-like V49(rp) V50() zero V156() V157() V158() Element of the carrier of (TOP-REAL rp)
the ZeroF of (TOP-REAL rp) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
(0. (TOP-REAL rp)) - ((c / (2 * rg)) * a) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
K270((TOP-REAL rp),(0. (TOP-REAL rp)),(- ((c / (2 * rg)) * a))) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
K224( the carrier of (TOP-REAL rp), the U7 of (TOP-REAL rp),(0. (TOP-REAL rp)),(- ((c / (2 * rg)) * a))) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
((0. (TOP-REAL rp)) - ((c / (2 * rg)) * a)) + ((c / (2 * rg)) * rl) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
K224( the carrier of (TOP-REAL rp), the U7 of (TOP-REAL rp),((0. (TOP-REAL rp)) - ((c / (2 * rg)) * a)),((c / (2 * rg)) * rl)) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
((c / (2 * rg)) * rl) - ((c / (2 * rg)) * a) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
K270((TOP-REAL rp),((c / (2 * rg)) * rl),(- ((c / (2 * rg)) * a))) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
K224( the carrier of (TOP-REAL rp), the U7 of (TOP-REAL rp),((c / (2 * rg)) * rl),(- ((c / (2 * rg)) * a))) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
rl - a is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
K270((TOP-REAL rp),rl,(- a)) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
K224( the carrier of (TOP-REAL rp), the U7 of (TOP-REAL rp),rl,(- a)) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
(c / (2 * rg)) * (rl - a) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
|.((((1 - (c / (2 * rg))) * a) + ((c / (2 * rg)) * rl)) - a).| is complex ext-real non negative real Element of REAL
abs (c / (2 * rg)) is complex ext-real real Element of REAL
|.(rl - a).| is complex ext-real non negative real Element of REAL
(abs (c / (2 * rg))) * |.(rl - a).| is complex ext-real real Element of REAL
(c / (2 * rg)) * |.(rl - a).| is complex ext-real real Element of REAL
(c / (2 * rg)) * |.(a - rl).| is complex ext-real real Element of REAL
c / 2 is complex ext-real real Element of REAL
Sphere (a,(c / 2)) is functional closed bounded Element of bool the carrier of (TOP-REAL rp)
c / 1 is complex ext-real real Element of REAL
Ball (a,c) is functional open connected bounded convex Element of bool the carrier of (TOP-REAL rp)
Ball (a,c) is functional open connected bounded convex Element of bool the carrier of (TOP-REAL rp)
Ball (a,c) is functional open connected bounded convex Element of bool the carrier of (TOP-REAL rp)
rp is ordinal natural complex ext-real non negative real V33() V119() V166() V167() V168() V169() V170() V171() bounded_below Element of NAT
TOP-REAL rp is non empty TopSpace-like T_0 T_1 T_2 connected V132() V178() V179() V180() V181() V182() V183() V184() strict add-continuous Mult-continuous pathwise_connected RLTopStruct
the carrier of (TOP-REAL rp) is functional non empty set
rl is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
rg is non empty complex ext-real real set
Ball (rl,rg) is functional open connected bounded convex Element of bool the carrier of (TOP-REAL rp)
bool the carrier of (TOP-REAL rp) is non empty set
Fr (Ball (rl,rg)) is functional closed boundary nowhere_dense Element of bool the carrier of (TOP-REAL rp)
Cl (Ball (rl,rg)) is functional closed Element of bool the carrier of (TOP-REAL rp)
(Ball (rl,rg)) ` is functional closed Element of bool the carrier of (TOP-REAL rp)
the carrier of (TOP-REAL rp) \ (Ball (rl,rg)) is set
Cl ((Ball (rl,rg)) `) is functional closed Element of bool the carrier of (TOP-REAL rp)
(Cl (Ball (rl,rg))) /\ (Cl ((Ball (rl,rg)) `)) is functional closed Element of bool the carrier of (TOP-REAL rp)
Sphere (rl,rg) is functional closed bounded Element of bool the carrier of (TOP-REAL rp)
(Cl (Ball (rl,rg))) \ (Ball (rl,rg)) is functional Element of bool the carrier of (TOP-REAL rp)
cl_Ball (rl,rg) is functional closed connected bounded convex Element of bool the carrier of (TOP-REAL rp)
(cl_Ball (rl,rg)) \ (Ball (rl,rg)) is functional Element of bool the carrier of (TOP-REAL rp)
rp is non empty ordinal natural complex ext-real positive non negative real V33() V119() V166() V167() V168() V169() V170() V171() left_end bounded_below Element of NAT
TOP-REAL rp is non empty TopSpace-like T_0 T_1 T_2 connected V132() V178() V179() V180() V181() V182() V183() V184() strict add-continuous Mult-continuous pathwise_connected RLTopStruct
the carrier of (TOP-REAL rp) is functional non empty set
bool the carrier of (TOP-REAL rp) is non empty set
[#] (TOP-REAL rp) is functional non empty non proper non proper open open closed closed dense dense non boundary non boundary connected a_component convex Element of bool the carrier of (TOP-REAL rp)
rl is functional Element of bool the carrier of (TOP-REAL rp)
rp is ordinal natural complex ext-real non negative real V33() V119() V166() V167() V168() V169() V170() V171() bounded_below Element of NAT
TOP-REAL rp is non empty TopSpace-like T_0 T_1 T_2 connected V132() V178() V179() V180() V181() V182() V183() V184() strict add-continuous Mult-continuous pathwise_connected RLTopStruct
the carrier of (TOP-REAL rp) is functional non empty set
bool the carrier of (TOP-REAL rp) is non empty set
0. (TOP-REAL rp) is Relation-like Function-like V49(rp) V50() zero V156() V157() V158() Element of the carrier of (TOP-REAL rp)
the ZeroF of (TOP-REAL rp) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
cl_Ball ((0. (TOP-REAL rp)),1) is functional non empty closed connected bounded convex Element of bool the carrier of (TOP-REAL rp)
0. (TOP-REAL rp) is Relation-like Function-like V49(rp) V50() zero V156() V157() V158() Element of the carrier of (TOP-REAL rp)
the ZeroF of (TOP-REAL rp) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
Ball ((0. (TOP-REAL rp)),1) is functional non empty open connected bounded convex Element of bool the carrier of (TOP-REAL rp)
rp is ordinal natural complex ext-real non negative real V33() V119() V166() V167() V168() V169() V170() V171() bounded_below Element of NAT
TOP-REAL rp is non empty TopSpace-like T_0 T_1 T_2 connected V132() V178() V179() V180() V181() V182() V183() V184() strict add-continuous Mult-continuous pathwise_connected RLTopStruct
the carrier of (TOP-REAL rp) is functional non empty set
bool the carrier of (TOP-REAL rp) is non empty set
rl is functional bounded Element of bool the carrier of (TOP-REAL rp)
Cl rl is functional closed Element of bool the carrier of (TOP-REAL rp)
rp is ordinal natural complex ext-real non negative real V33() V119() V166() V167() V168() V169() V170() V171() bounded_below Element of NAT
TOP-REAL rp is non empty TopSpace-like T_0 T_1 T_2 connected V132() V178() V179() V180() V181() V182() V183() V184() strict add-continuous Mult-continuous pathwise_connected RLTopStruct
the carrier of (TOP-REAL rp) is functional non empty set
bool the carrier of (TOP-REAL rp) is non empty set
rl is functional bounded Element of bool the carrier of (TOP-REAL rp)
Fr rl is functional closed Element of bool the carrier of (TOP-REAL rp)
Cl rl is functional closed closed bounded Element of bool the carrier of (TOP-REAL rp)
rl ` is functional Element of bool the carrier of (TOP-REAL rp)
the carrier of (TOP-REAL rp) \ rl is set
Cl (rl `) is functional closed Element of bool the carrier of (TOP-REAL rp)
(Cl rl) /\ (Cl (rl `)) is functional closed Element of bool the carrier of (TOP-REAL rp)
rp is ordinal natural complex ext-real non negative real V33() V119() V166() V167() V168() V169() V170() V171() bounded_below Element of NAT
TOP-REAL rp is non empty TopSpace-like T_0 T_1 T_2 connected V132() V178() V179() V180() V181() V182() V183() V184() strict add-continuous Mult-continuous pathwise_connected RLTopStruct
the carrier of (TOP-REAL rp) is functional non empty set
bool the carrier of (TOP-REAL rp) is non empty set
rl is functional closed Element of bool the carrier of (TOP-REAL rp)
rg is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
rl ` is functional open Element of bool the carrier of (TOP-REAL rp)
the carrier of (TOP-REAL rp) \ rl is set
Euclid rp is non empty strict Reflexive discerning symmetric triangle Discerning MetrStruct
the carrier of (Euclid rp) is non empty set
the topology of (TOP-REAL rp) is non empty open Element of bool (bool the carrier of (TOP-REAL rp))
bool (bool the carrier of (TOP-REAL rp)) is non empty set
TopStruct(# the carrier of (TOP-REAL rp), the topology of (TOP-REAL rp) #) is non empty strict TopSpace-like TopStruct
TopSpaceMetr (Euclid rp) is TopStruct
the carrier of (TopSpaceMetr (Euclid rp)) is set
bool the carrier of (TopSpaceMetr (Euclid rp)) is non empty set
a is Element of bool the carrier of (TopSpaceMetr (Euclid rp))
rd is Element of the carrier of (Euclid rp)
b is complex ext-real real set
Ball (rd,b) is Element of bool the carrier of (Euclid rp)
bool the carrier of (Euclid rp) is non empty set
c is non empty complex ext-real positive non negative real set
Ball (rg,c) is functional non empty open connected bounded convex Element of bool the carrier of (TOP-REAL rp)
Ball (rd,c) is Element of bool the carrier of (Euclid rp)
rp is ordinal natural complex ext-real non negative real V33() V119() V166() V167() V168() V169() V170() V171() bounded_below Element of NAT
TOP-REAL rp is non empty TopSpace-like T_0 T_1 T_2 connected V132() V178() V179() V180() V181() V182() V183() V184() strict add-continuous Mult-continuous pathwise_connected RLTopStruct
the carrier of (TOP-REAL rp) is functional non empty set
bool the carrier of (TOP-REAL rp) is non empty set
rl is functional bounded Element of bool the carrier of (TOP-REAL rp)
rg is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
Euclid rp is non empty strict Reflexive discerning symmetric triangle Discerning MetrStruct
the carrier of (Euclid rp) is non empty set
bool the carrier of (Euclid rp) is non empty set
rd is bounded Element of bool the carrier of (Euclid rp)
a is complex ext-real real Element of REAL
b is Element of the carrier of (Euclid rp)
Ball (b,a) is Element of bool the carrier of (Euclid rp)
c is non empty complex ext-real positive non negative real set
d is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
d - rg is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
- rg is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
K270((TOP-REAL rp),d,(- rg)) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
the U7 of (TOP-REAL rp) is Relation-like [: the carrier of (TOP-REAL rp), the carrier of (TOP-REAL rp):] -defined the carrier of (TOP-REAL rp) -valued Function-like non empty total quasi_total Element of bool [:[: the carrier of (TOP-REAL rp), the carrier of (TOP-REAL rp):], the carrier of (TOP-REAL rp):]
[: the carrier of (TOP-REAL rp), the carrier of (TOP-REAL rp):] is Relation-like non empty set
[:[: the carrier of (TOP-REAL rp), the carrier of (TOP-REAL rp):], the carrier of (TOP-REAL rp):] is Relation-like non empty set
bool [:[: the carrier of (TOP-REAL rp), the carrier of (TOP-REAL rp):], the carrier of (TOP-REAL rp):] is non empty set
K224( the carrier of (TOP-REAL rp), the U7 of (TOP-REAL rp),d,(- rg)) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
|.(d - rg).| is complex ext-real non negative real Element of REAL
c + |.(d - rg).| is non empty complex ext-real positive non negative real Element of REAL
lg is non empty complex ext-real positive non negative real Element of REAL
Ball (rg,lg) is functional non empty open connected bounded convex Element of bool the carrier of (TOP-REAL rp)
pg is set
ld is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
pd is Element of the carrier of (Euclid rp)
dist (pd,b) is complex ext-real non negative real Element of REAL
ld - d is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
- d is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
K270((TOP-REAL rp),ld,(- d)) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
K224( the carrier of (TOP-REAL rp), the U7 of (TOP-REAL rp),ld,(- d)) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
|.(ld - d).| is complex ext-real non negative real Element of REAL
ld - rg is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
K270((TOP-REAL rp),ld,(- rg)) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
K224( the carrier of (TOP-REAL rp), the U7 of (TOP-REAL rp),ld,(- rg)) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
|.(ld - rg).| is complex ext-real non negative real Element of REAL
|.(ld - d).| + |.(d - rg).| is complex ext-real non negative real Element of REAL
rp is TopStruct
the carrier of rp is set
rl is TopStruct
the carrier of rl is set
[: the carrier of rp, the carrier of rl:] is Relation-like set
bool [: the carrier of rp, the carrier of rl:] is non empty set
rg is Relation-like the carrier of rp -defined the carrier of rl -valued Function-like quasi_total Element of bool [: the carrier of rp, the carrier of rl:]
rp is non empty TopSpace-like T_0 T_1 T_2 TopStruct
rl is non empty TopSpace-like T_0 T_1 T_2 SubSpace of rp
rp is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
rl is complex ext-real real set
Tdisk (rp,rl) is TopSpace-like T_0 T_1 T_2 V270(2) SubSpace of TOP-REAL 2
rg is functional Element of bool the carrier of (TOP-REAL 2)
the carrier of (Tdisk (rp,rl)) is set
cl_Ball (rp,rl) is functional proper closed connected bounded convex Element of bool the carrier of (TOP-REAL 2)
rp is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
rl is complex ext-real real set
Tdisk (rp,rl) is TopSpace-like T_0 T_1 T_2 closed V270(2) SubSpace of TOP-REAL 2
[#] (Tdisk (rp,rl)) is non proper open closed dense Element of bool the carrier of (Tdisk (rp,rl))
the carrier of (Tdisk (rp,rl)) is set
bool the carrier of (Tdisk (rp,rl)) is non empty set
cl_Ball (rp,rl) is functional proper closed connected bounded convex Element of bool the carrier of (TOP-REAL 2)
rd is functional Element of bool the carrier of (TOP-REAL 2)
rp is non empty TopSpace-like TopStruct
the carrier of rp is non empty set
rl is Element of the carrier of rp
rg is Element of the carrier of rp
rd is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total Path of rl,rg
rng rd is non empty Element of bool the carrier of rp
bool the carrier of rp is non empty set
dom rd is non empty V166() V167() V168() Element of bool the carrier of I[01]
bool the carrier of I[01] is non empty set
a is connected V166() V167() V168() interval Element of bool the carrier of R^1
b is V166() V167() V168() Element of bool the carrier of I[01]
rd .: b is Element of bool the carrier of rp
rp is non empty TopSpace-like TopStruct
the carrier of rp is non empty set
rl is non empty TopSpace-like SubSpace of rp
the carrier of rl is non empty set
rg is Element of the carrier of rp
rd is Element of the carrier of rp
a is Element of the carrier of rl
b is Element of the carrier of rl
c is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total Path of rg,rd
rng c is non empty Element of bool the carrier of rp
bool the carrier of rp is non empty set
[: the carrier of I[01], the carrier of rl:] is Relation-like non empty set
bool [: the carrier of I[01], the carrier of rl:] is non empty set
c . 0 is set
c . 1 is set
d is Relation-like the carrier of I[01] -defined the carrier of rl -valued Function-like non empty total quasi_total Element of bool [: the carrier of I[01], the carrier of rl:]
d . 0 is set
d . 1 is set
rp is non empty TopSpace-like connected pathwise_connected TopStruct
the carrier of rp is non empty set
rl is non empty TopSpace-like SubSpace of rp
the carrier of rl is non empty set
rg is Element of the carrier of rp
rd is Element of the carrier of rp
a is Element of the carrier of rl
b is Element of the carrier of rl
c is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total continuous Path of rg,rd
rng c is non empty Element of bool the carrier of rp
bool the carrier of rp is non empty set
rp is non empty TopSpace-like TopStruct
the carrier of rp is non empty set
rl is Element of the carrier of rp
rg is Element of the carrier of rp
rd is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total Path of rl,rg
rng rd is non empty Element of bool the carrier of rp
bool the carrier of rp is non empty set
- rd is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total Path of rg,rl
rng (- rd) is non empty Element of bool the carrier of rp
a is set
dom rd is non empty V166() V167() V168() Element of bool the carrier of I[01]
bool the carrier of I[01] is non empty set
b is set
rd . b is set
dom (- rd) is non empty V166() V167() V168() Element of bool the carrier of I[01]
c is complex ext-real real Element of the carrier of I[01]
1 - c is complex ext-real real Element of REAL
(- rd) . (1 - c) is set
1 - (1 - c) is complex ext-real real Element of REAL
rd . (1 - (1 - c)) is set
rp is non empty TopSpace-like TopStruct
the carrier of rp is non empty set
rl is Element of the carrier of rp
rg is Element of the carrier of rp
rd is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total Path of rl,rg
rng rd is non empty Element of bool the carrier of rp
bool the carrier of rp is non empty set
- rd is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total Path of rg,rl
rng (- rd) is non empty Element of bool the carrier of rp
- (- rd) is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total Path of rl,rg
rp is non empty TopSpace-like connected pathwise_connected TopStruct
the carrier of rp is non empty set
rl is Element of the carrier of rp
rg is Element of the carrier of rp
rd is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total continuous Path of rl,rg
rng rd is non empty Element of bool the carrier of rp
bool the carrier of rp is non empty set
- rd is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total continuous Path of rg,rl
rng (- rd) is non empty Element of bool the carrier of rp
rp is non empty TopSpace-like TopStruct
the carrier of rp is non empty set
rl is Element of the carrier of rp
rg is Element of the carrier of rp
rd is Element of the carrier of rp
a is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total Path of rl,rg
rng a is non empty Element of bool the carrier of rp
bool the carrier of rp is non empty set
b is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total Path of rg,rd
a + b is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total Path of rl,rd
rng (a + b) is non empty Element of bool the carrier of rp
c is set
dom a is non empty V166() V167() V168() Element of bool the carrier of I[01]
bool the carrier of I[01] is non empty set
d is set
a . d is set
dom (a + b) is non empty V166() V167() V168() Element of bool the carrier of I[01]
lg is complex ext-real real Element of the carrier of I[01]
(1 / 2) * lg is complex ext-real real Element of REAL
lg / 2 is complex ext-real real Element of REAL
(a + b) . (lg / 2) is set
2 * (lg / 2) is complex ext-real real Element of REAL
a . (2 * (lg / 2)) is set
rp is non empty TopSpace-like connected pathwise_connected TopStruct
the carrier of rp is non empty set
rl is Element of the carrier of rp
rg is Element of the carrier of rp
rd is Element of the carrier of rp
a is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total continuous Path of rl,rg
rng a is non empty Element of bool the carrier of rp
bool the carrier of rp is non empty set
b is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total continuous Path of rg,rd
a + b is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total continuous Path of rl,rd
rng (a + b) is non empty Element of bool the carrier of rp
rp is non empty TopSpace-like TopStruct
the carrier of rp is non empty set
rg is Element of the carrier of rp
rd is Element of the carrier of rp
rl is Element of the carrier of rp
a is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total Path of rg,rd
rng a is non empty Element of bool the carrier of rp
bool the carrier of rp is non empty set
b is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total Path of rl,rg
b + a is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total Path of rl,rd
rng (b + a) is non empty Element of bool the carrier of rp
c is set
dom a is non empty V166() V167() V168() Element of bool the carrier of I[01]
bool the carrier of I[01] is non empty set
d is set
a . d is set
dom (b + a) is non empty V166() V167() V168() Element of bool the carrier of I[01]
lg is complex ext-real real Element of the carrier of I[01]
0 + (1 / 2) is complex ext-real non negative real Element of REAL
lg / 2 is complex ext-real real Element of REAL
(lg / 2) + (1 / 2) is complex ext-real real Element of REAL
lg + 1 is complex ext-real real Element of REAL
1 + 1 is non empty ordinal natural complex ext-real positive non negative real Element of REAL
(lg + 1) / 2 is complex ext-real real Element of REAL
2 / 2 is complex ext-real non negative real Element of REAL
(b + a) . ((lg / 2) + (1 / 2)) is set
2 * ((lg / 2) + (1 / 2)) is complex ext-real real Element of REAL
(2 * ((lg / 2) + (1 / 2))) - 1 is complex ext-real real Element of REAL
a . ((2 * ((lg / 2) + (1 / 2))) - 1) is set
rp is non empty TopSpace-like connected pathwise_connected TopStruct
the carrier of rp is non empty set
rg is Element of the carrier of rp
rd is Element of the carrier of rp
rl is Element of the carrier of rp
a is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total continuous Path of rg,rd
rng a is non empty Element of bool the carrier of rp
bool the carrier of rp is non empty set
b is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total continuous Path of rl,rg
b + a is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total continuous Path of rl,rd
rng (b + a) is non empty Element of bool the carrier of rp
rp is non empty TopSpace-like TopStruct
the carrier of rp is non empty set
rl is Element of the carrier of rp
rg is Element of the carrier of rp
rd is Element of the carrier of rp
a is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total Path of rl,rg
rng a is non empty Element of bool the carrier of rp
bool the carrier of rp is non empty set
b is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total Path of rg,rd
a + b is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total Path of rl,rd
rng (a + b) is non empty Element of bool the carrier of rp
rng b is non empty Element of bool the carrier of rp
(rng a) \/ (rng b) is non empty Element of bool the carrier of rp
c is set
dom (a + b) is non empty V166() V167() V168() Element of bool the carrier of I[01]
bool the carrier of I[01] is non empty set
d is set
(a + b) . d is set
lg is complex ext-real real Element of the carrier of I[01]
(a + b) . lg is Element of the carrier of rp
2 * lg is complex ext-real real Element of REAL
a . (2 * lg) is set
dom a is non empty V166() V167() V168() Element of bool the carrier of I[01]
lg is complex ext-real real Element of the carrier of I[01]
(a + b) . lg is Element of the carrier of rp
2 * lg is complex ext-real real Element of REAL
(2 * lg) - 1 is complex ext-real real Element of REAL
b . ((2 * lg) - 1) is set
dom b is non empty V166() V167() V168() Element of bool the carrier of I[01]
lg is complex ext-real real Element of the carrier of I[01]
rp is non empty TopSpace-like connected pathwise_connected TopStruct
the carrier of rp is non empty set
rl is Element of the carrier of rp
rg is Element of the carrier of rp
rd is Element of the carrier of rp
a is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total continuous Path of rl,rg
rng a is non empty Element of bool the carrier of rp
bool the carrier of rp is non empty set
b is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total continuous Path of rg,rd
a + b is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total continuous Path of rl,rd
rng (a + b) is non empty Element of bool the carrier of rp
rng b is non empty Element of bool the carrier of rp
(rng a) \/ (rng b) is non empty Element of bool the carrier of rp
rp is non empty TopSpace-like TopStruct
the carrier of rp is non empty set
rl is Element of the carrier of rp
rg is Element of the carrier of rp
rd is Element of the carrier of rp
a is Element of the carrier of rp
b is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total Path of rl,rg
rng b is non empty Element of bool the carrier of rp
bool the carrier of rp is non empty set
c is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total Path of rg,rd
b + c is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total Path of rl,rd
rng c is non empty Element of bool the carrier of rp
(rng b) \/ (rng c) is non empty Element of bool the carrier of rp
d is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total Path of rd,a
(b + c) + d is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total Path of rl,a
rng ((b + c) + d) is non empty Element of bool the carrier of rp
rng d is non empty Element of bool the carrier of rp
((rng b) \/ (rng c)) \/ (rng d) is non empty Element of bool the carrier of rp
rng (b + c) is non empty Element of bool the carrier of rp
(rng (b + c)) \/ (rng d) is non empty Element of bool the carrier of rp
rp is non empty TopSpace-like connected pathwise_connected TopStruct
the carrier of rp is non empty set
rl is Element of the carrier of rp
rg is Element of the carrier of rp
rd is Element of the carrier of rp
a is Element of the carrier of rp
b is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total continuous Path of rl,rg
rng b is non empty Element of bool the carrier of rp
bool the carrier of rp is non empty set
c is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total continuous Path of rg,rd
b + c is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total continuous Path of rl,rd
rng c is non empty Element of bool the carrier of rp
(rng b) \/ (rng c) is non empty Element of bool the carrier of rp
d is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total continuous Path of rd,a
(b + c) + d is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total continuous Path of rl,a
rng ((b + c) + d) is non empty Element of bool the carrier of rp
rng d is non empty Element of bool the carrier of rp
((rng b) \/ (rng c)) \/ (rng d) is non empty Element of bool the carrier of rp
rp is non empty TopSpace-like TopStruct
the carrier of rp is non empty set
rl is Element of the carrier of rp
rg is Element of the carrier of rp
rd is Element of the carrier of rp
a is Element of the carrier of rp
b is Element of the carrier of rp
c is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total Path of rl,rg
rng c is non empty Element of bool the carrier of rp
bool the carrier of rp is non empty set
d is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total Path of rg,rd
c + d is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total Path of rl,rd
rng d is non empty Element of bool the carrier of rp
(rng c) \/ (rng d) is non empty Element of bool the carrier of rp
lg is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total Path of rd,a
(c + d) + lg is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total Path of rl,a
rng lg is non empty Element of bool the carrier of rp
((rng c) \/ (rng d)) \/ (rng lg) is non empty Element of bool the carrier of rp
pg is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total Path of a,b
((c + d) + lg) + pg is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total Path of rl,b
rng (((c + d) + lg) + pg) is non empty Element of bool the carrier of rp
rng pg is non empty Element of bool the carrier of rp
(((rng c) \/ (rng d)) \/ (rng lg)) \/ (rng pg) is non empty Element of bool the carrier of rp
rng ((c + d) + lg) is non empty Element of bool the carrier of rp
(rng ((c + d) + lg)) \/ (rng pg) is non empty Element of bool the carrier of rp
rp is non empty TopSpace-like connected pathwise_connected TopStruct
the carrier of rp is non empty set
rl is Element of the carrier of rp
rg is Element of the carrier of rp
rd is Element of the carrier of rp
a is Element of the carrier of rp
b is Element of the carrier of rp
c is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total continuous Path of rl,rg
rng c is non empty Element of bool the carrier of rp
bool the carrier of rp is non empty set
d is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total continuous Path of rg,rd
c + d is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total continuous Path of rl,rd
rng d is non empty Element of bool the carrier of rp
(rng c) \/ (rng d) is non empty Element of bool the carrier of rp
lg is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total continuous Path of rd,a
(c + d) + lg is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total continuous Path of rl,a
rng lg is non empty Element of bool the carrier of rp
((rng c) \/ (rng d)) \/ (rng lg) is non empty Element of bool the carrier of rp
pg is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total continuous Path of a,b
((c + d) + lg) + pg is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total continuous Path of rl,b
rng (((c + d) + lg) + pg) is non empty Element of bool the carrier of rp
rng pg is non empty Element of bool the carrier of rp
(((rng c) \/ (rng d)) \/ (rng lg)) \/ (rng pg) is non empty Element of bool the carrier of rp
rp is non empty TopSpace-like TopStruct
the carrier of rp is non empty set
rl is Element of the carrier of rp
rg is Element of the carrier of rp
rd is Element of the carrier of rp
a is Element of the carrier of rp
b is Element of the carrier of rp
c is Element of the carrier of rp
d is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total Path of rl,rg
rng d is non empty Element of bool the carrier of rp
bool the carrier of rp is non empty set
lg is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total Path of rg,rd
d + lg is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total Path of rl,rd
rng lg is non empty Element of bool the carrier of rp
(rng d) \/ (rng lg) is non empty Element of bool the carrier of rp
pg is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total Path of rd,a
(d + lg) + pg is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total Path of rl,a
rng pg is non empty Element of bool the carrier of rp
((rng d) \/ (rng lg)) \/ (rng pg) is non empty Element of bool the carrier of rp
ld is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total Path of a,b
((d + lg) + pg) + ld is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total Path of rl,b
rng ld is non empty Element of bool the carrier of rp
(((rng d) \/ (rng lg)) \/ (rng pg)) \/ (rng ld) is non empty Element of bool the carrier of rp
pd is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total Path of b,c
(((d + lg) + pg) + ld) + pd is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total Path of rl,c
rng ((((d + lg) + pg) + ld) + pd) is non empty Element of bool the carrier of rp
rng pd is non empty Element of bool the carrier of rp
((((rng d) \/ (rng lg)) \/ (rng pg)) \/ (rng ld)) \/ (rng pd) is non empty Element of bool the carrier of rp
rng (((d + lg) + pg) + ld) is non empty Element of bool the carrier of rp
(rng (((d + lg) + pg) + ld)) \/ (rng pd) is non empty Element of bool the carrier of rp
rp is non empty TopSpace-like connected pathwise_connected TopStruct
the carrier of rp is non empty set
rl is Element of the carrier of rp
rg is Element of the carrier of rp
rd is Element of the carrier of rp
a is Element of the carrier of rp
b is Element of the carrier of rp
c is Element of the carrier of rp
d is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total continuous Path of rl,rg
rng d is non empty Element of bool the carrier of rp
bool the carrier of rp is non empty set
lg is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total continuous Path of rg,rd
d + lg is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total continuous Path of rl,rd
rng lg is non empty Element of bool the carrier of rp
(rng d) \/ (rng lg) is non empty Element of bool the carrier of rp
pg is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total continuous Path of rd,a
(d + lg) + pg is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total continuous Path of rl,a
rng pg is non empty Element of bool the carrier of rp
((rng d) \/ (rng lg)) \/ (rng pg) is non empty Element of bool the carrier of rp
ld is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total continuous Path of a,b
((d + lg) + pg) + ld is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total continuous Path of rl,b
rng ld is non empty Element of bool the carrier of rp
(((rng d) \/ (rng lg)) \/ (rng pg)) \/ (rng ld) is non empty Element of bool the carrier of rp
pd is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total continuous Path of b,c
(((d + lg) + pg) + ld) + pd is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total continuous Path of rl,c
rng ((((d + lg) + pg) + ld) + pd) is non empty Element of bool the carrier of rp
rng pd is non empty Element of bool the carrier of rp
((((rng d) \/ (rng lg)) \/ (rng pg)) \/ (rng ld)) \/ (rng pd) is non empty Element of bool the carrier of rp
rp is non empty TopSpace-like TopStruct
the carrier of rp is non empty set
rl is Element of the carrier of rp
I[01] --> rl is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total continuous Element of bool [: the carrier of I[01], the carrier of rp:]
[: the carrier of I[01], the carrier of rp:] is Relation-like non empty set
bool [: the carrier of I[01], the carrier of rp:] is non empty set
the carrier of I[01] --> rl is Relation-like the carrier of I[01] -defined the carrier of rp -valued Function-like non empty total quasi_total Element of bool [: the carrier of I[01], the carrier of rp:]
(I[01] --> rl) . 0 is set
(I[01] --> rl) . 1 is set
rp is ordinal natural complex ext-real non negative real V33() V119() V166() V167() V168() V169() V170() V171() bounded_below Element of NAT
TOP-REAL rp is non empty TopSpace-like T_0 T_1 T_2 connected V132() V178() V179() V180() V181() V182() V183() V184() strict add-continuous Mult-continuous pathwise_connected RLTopStruct
the carrier of (TOP-REAL rp) is functional non empty set
bool the carrier of (TOP-REAL rp) is non empty set
rl is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
rg is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
rd is functional Element of bool the carrier of (TOP-REAL rp)
(TOP-REAL rp) | rd is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL rp
the carrier of ((TOP-REAL rp) | rd) is set
[: the carrier of I[01], the carrier of ((TOP-REAL rp) | rd):] is Relation-like set
bool [: the carrier of I[01], the carrier of ((TOP-REAL rp) | rd):] is non empty set
b is Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL rp) | rd) -valued Function-like quasi_total Element of bool [: the carrier of I[01], the carrier of ((TOP-REAL rp) | rd):]
b . 0 is set
b . 1 is set
a is functional non empty Element of bool the carrier of (TOP-REAL rp)
(TOP-REAL rp) | a is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL rp
the carrier of ((TOP-REAL rp) | a) is non empty set
[: the carrier of I[01], the carrier of ((TOP-REAL rp) | a):] is Relation-like non empty set
bool [: the carrier of I[01], the carrier of ((TOP-REAL rp) | a):] is non empty set
[: the carrier of I[01], the carrier of (TOP-REAL rp):] is Relation-like non empty set
bool [: the carrier of I[01], the carrier of (TOP-REAL rp):] is non empty set
c is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL rp) -valued Function-like non empty total quasi_total Element of bool [: the carrier of I[01], the carrier of (TOP-REAL rp):]
d is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL rp) -valued Function-like non empty total quasi_total continuous Path of rl,rg
rng b is Element of bool the carrier of ((TOP-REAL rp) | rd)
bool the carrier of ((TOP-REAL rp) | rd) is non empty set
[#] ((TOP-REAL rp) | rd) is non proper open closed dense Element of bool the carrier of ((TOP-REAL rp) | rd)
rp is ordinal natural complex ext-real non negative real V33() V119() V166() V167() V168() V169() V170() V171() bounded_below Element of NAT
TOP-REAL rp is non empty TopSpace-like T_0 T_1 T_2 connected V132() V178() V179() V180() V181() V182() V183() V184() strict add-continuous Mult-continuous pathwise_connected RLTopStruct
the carrier of (TOP-REAL rp) is functional non empty set
rl is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
rg is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
LSeg (rl,rg) is functional closed compact bounded Element of bool the carrier of (TOP-REAL rp)
bool the carrier of (TOP-REAL rp) is non empty set
{ (((1 - b₁) * rl) + (b₁ * rg)) where b₁ is complex ext-real real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(TOP-REAL rp) | (LSeg (rl,rg)) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL rp
the carrier of ((TOP-REAL rp) | (LSeg (rl,rg))) is set
[: the carrier of I[01], the carrier of ((TOP-REAL rp) | (LSeg (rl,rg))):] is Relation-like set
bool [: the carrier of I[01], the carrier of ((TOP-REAL rp) | (LSeg (rl,rg))):] is non empty set
I[01] --> rl is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL rp) -valued Function-like non empty total quasi_total continuous Element of bool [: the carrier of I[01], the carrier of (TOP-REAL rp):]
[: the carrier of I[01], the carrier of (TOP-REAL rp):] is Relation-like non empty set
bool [: the carrier of I[01], the carrier of (TOP-REAL rp):] is non empty set
the carrier of I[01] --> rl is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL rp) -valued Function-like non empty total quasi_total Element of bool [: the carrier of I[01], the carrier of (TOP-REAL rp):]
rd is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL rp) -valued Function-like non empty total quasi_total continuous Path of rl,rg
{rl} is functional non empty closed compact bounded Element of bool the carrier of (TOP-REAL rp)
rng rd is functional non empty Element of bool the carrier of (TOP-REAL rp)
a is Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL rp) | (LSeg (rl,rg))) -valued Function-like quasi_total Element of bool [: the carrier of I[01], the carrier of ((TOP-REAL rp) | (LSeg (rl,rg))):]
rng a is Element of bool the carrier of ((TOP-REAL rp) | (LSeg (rl,rg)))
bool the carrier of ((TOP-REAL rp) | (LSeg (rl,rg))) is non empty set
rp is functional Element of bool the carrier of (TOP-REAL 2)
rl is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
rg is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
rd is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
a is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
{rl,rg} is functional non empty Element of bool the carrier of (TOP-REAL 2)
I[01] --> rd is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total continuous Element of bool [: the carrier of I[01], the carrier of (TOP-REAL 2):]
[: the carrier of I[01], the carrier of (TOP-REAL 2):] is Relation-like non empty set
bool [: the carrier of I[01], the carrier of (TOP-REAL 2):] is non empty set
the carrier of I[01] --> rd is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of bool [: the carrier of I[01], the carrier of (TOP-REAL 2):]
b is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total continuous Path of rd,a
rng b is functional non empty Element of bool the carrier of (TOP-REAL 2)
{rd} is functional non empty proper closed compact bounded Element of bool the carrier of (TOP-REAL 2)
c is set
b is functional non empty Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | b is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | b) is non empty set
[: the carrier of I[01], the carrier of ((TOP-REAL 2) | b):] is Relation-like non empty set
bool [: the carrier of I[01], the carrier of ((TOP-REAL 2) | b):] is non empty set
d is Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL 2) | b) -valued Function-like non empty total quasi_total Element of bool [: the carrier of I[01], the carrier of ((TOP-REAL 2) | b):]
rng d is non empty Element of bool the carrier of ((TOP-REAL 2) | b)
bool the carrier of ((TOP-REAL 2) | b) is non empty set
c is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total continuous Path of rd,a
[: the carrier of I[01], the carrier of (TOP-REAL 2):] is Relation-like non empty set
bool [: the carrier of I[01], the carrier of (TOP-REAL 2):] is non empty set
pg is Element of the carrier of ((TOP-REAL 2) | b)
ld is Element of the carrier of ((TOP-REAL 2) | b)
d . 0 is set
d . 1 is set
d . 0 is set
d . 1 is set
lg is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of bool [: the carrier of I[01], the carrier of (TOP-REAL 2):]
pd is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total continuous Path of rd,a
rng pd is functional non empty Element of bool the carrier of (TOP-REAL 2)
rp is complex ext-real real set
rl is complex ext-real real set
rg is complex ext-real real set
rd is complex ext-real real set
rectangle (rp,rl,rg,rd) is functional non empty proper closed compact bounded Element of bool the carrier of (TOP-REAL 2)
closed_inside_of_rectangle (rp,rl,rg,rd) is functional connected convex Element of bool the carrier of (TOP-REAL 2)
{ b₁ where b₁ is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2) : ( rp <= b₁ `1 & b<sub>1</sub> `1 <= rl & rg <= b₁ `2 & b<sub>1</sub> `2 <= rd ) } is set
a is set
{ b₁ where b₁ is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2) : ( ( b₁ `1 = rp & b<sub>1</sub> `2 <= rd & rg <= b₁ `2 ) or ( b<sub>1</sub> `1 <= rl & rp <= b₁ `1 & b<sub>1</sub> `2 = rd ) or ( b₁ `1 <= rl & rp <= b<sub>1</sub> `1 & b₁ `2 = rg ) or ( b<sub>1</sub> `1 = rl & b₁ `2 <= rd & rg <= b<sub>1</sub> `2 ) ) } is set
b is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
b `1 is complex ext-real real Element of REAL
b `2 is complex ext-real real Element of REAL
rp is complex ext-real real set
rl is complex ext-real real set
rg is complex ext-real real set
rd is complex ext-real real set
inside_of_rectangle (rp,rl,rg,rd) is functional Element of bool the carrier of (TOP-REAL 2)
{ b₁ where b₁ is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2) : ( not b₁ `1 <= rp & not rl <= b<sub>1</sub> `1 & not b₁ `2 <= rg & not rd <= b<sub>1</sub> `2 ) } is set
closed_inside_of_rectangle (rp,rl,rg,rd) is functional connected convex Element of bool the carrier of (TOP-REAL 2)
{ b₁ where b₁ is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2) : ( rp <= b₁ `1 & b<sub>1</sub> `1 <= rl & rg <= b₁ `2 & b<sub>1</sub> `2 <= rd ) } is set
a is set
b is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
b `1 is complex ext-real real Element of REAL
b `2 is complex ext-real real Element of REAL
rp is complex ext-real real set
rl is complex ext-real real set
rg is complex ext-real real set
rd is complex ext-real real set
closed_inside_of_rectangle (rp,rl,rg,rd) is functional connected convex Element of bool the carrier of (TOP-REAL 2)
{ b₁ where b₁ is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2) : ( rp <= b₁ `1 & b<sub>1</sub> `1 <= rl & rg <= b₁ `2 & b<sub>1</sub> `2 <= rd ) } is set
outside_of_rectangle (rp,rl,rg,rd) is functional Element of bool the carrier of (TOP-REAL 2)
{ b₁ where b₁ is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2) : ( not rp <= b₁ `1 or not b<sub>1</sub> `1 <= rl or not rg <= b₁ `2 or not b<sub>1</sub> `2 <= rd ) } is set
(outside_of_rectangle (rp,rl,rg,rd)) ` is functional Element of bool the carrier of (TOP-REAL 2)
the carrier of (TOP-REAL 2) \ (outside_of_rectangle (rp,rl,rg,rd)) is set
c is set
d is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
d `1 is complex ext-real real Element of REAL
d `2 is complex ext-real real Element of REAL
lg is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
lg `1 is complex ext-real real Element of REAL
lg `2 is complex ext-real real Element of REAL
c is set
d is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
d `1 is complex ext-real real Element of REAL
d `2 is complex ext-real real Element of REAL
rp is complex ext-real real set
rl is complex ext-real real set
rg is complex ext-real real set
rd is complex ext-real real set
closed_inside_of_rectangle (rp,rl,rg,rd) is functional connected convex Element of bool the carrier of (TOP-REAL 2)
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2) : ( rp <= b<sub>1</sub> `1 & b₁ `1 <= rl & rg <= b<sub>1</sub> `2 & b₁ `2 <= rd ) } is set
outside_of_rectangle (rp,rl,rg,rd) is functional Element of bool the carrier of (TOP-REAL 2)
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2) : ( not rp <= b<sub>1</sub> `1 or not b₁ `1 <= rl or not rg <= b<sub>1</sub> `2 or not b₁ `2 <= rd ) } is set
b is functional open Element of bool the carrier of (TOP-REAL 2)
b ` is functional closed Element of bool the carrier of (TOP-REAL 2)
the carrier of (TOP-REAL 2) \ b is set
rp is complex ext-real real set
rl is complex ext-real real set
rg is complex ext-real real set
rd is complex ext-real real set
closed_inside_of_rectangle (rp,rl,rg,rd) is functional closed connected convex Element of bool the carrier of (TOP-REAL 2)
{ b₁ where b₁ is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2) : ( rp <= b₁ `1 & b<sub>1</sub> `1 <= rl & rg <= b₁ `2 & b<sub>1</sub> `2 <= rd ) } is set
outside_of_rectangle (rp,rl,rg,rd) is functional Element of bool the carrier of (TOP-REAL 2)
{ b₁ where b₁ is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2) : ( not rp <= b₁ `1 or not b<sub>1</sub> `1 <= rl or not rg <= b₁ `2 or not b<sub>1</sub> `2 <= rd ) } is set
c is set
d is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
d `1 is complex ext-real real Element of REAL
d `2 is complex ext-real real Element of REAL
lg is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
lg `1 is complex ext-real real Element of REAL
lg `2 is complex ext-real real Element of REAL
rp is complex ext-real real set
rl is complex ext-real real set
rg is complex ext-real real set
rd is complex ext-real real set
closed_inside_of_rectangle (rp,rl,rg,rd) is functional closed connected convex Element of bool the carrier of (TOP-REAL 2)
{ b₁ where b₁ is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2) : ( rp <= b₁ `1 & b<sub>1</sub> `1 <= rl & rg <= b₁ `2 & b<sub>1</sub> `2 <= rd ) } is set
inside_of_rectangle (rp,rl,rg,rd) is functional Element of bool the carrier of (TOP-REAL 2)
{ b₁ where b₁ is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2) : ( not b₁ `1 <= rp & not rl <= b<sub>1</sub> `1 & not b₁ `2 <= rg & not rd <= b<sub>1</sub> `2 ) } is set
(closed_inside_of_rectangle (rp,rl,rg,rd)) /\ (inside_of_rectangle (rp,rl,rg,rd)) is functional Element of bool the carrier of (TOP-REAL 2)
(inside_of_rectangle (rp,rl,rg,rd)) /\ (inside_of_rectangle (rp,rl,rg,rd)) is functional Element of bool the carrier of (TOP-REAL 2)
(inside_of_rectangle (rp,rl,rg,rd)) /\ (closed_inside_of_rectangle (rp,rl,rg,rd)) is functional Element of bool the carrier of (TOP-REAL 2)
rp is complex ext-real real set
rl is complex ext-real real set
rg is complex ext-real real set
rd is complex ext-real real set
closed_inside_of_rectangle (rp,rl,rg,rd) is functional closed connected convex Element of bool the carrier of (TOP-REAL 2)
{ b₁ where b₁ is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2) : ( rp <= b₁ `1 & b<sub>1</sub> `1 <= rl & rg <= b₁ `2 & b<sub>1</sub> `2 <= rd ) } is set
Int (closed_inside_of_rectangle (rp,rl,rg,rd)) is functional open Element of bool the carrier of (TOP-REAL 2)
(closed_inside_of_rectangle (rp,rl,rg,rd)) ` is functional open Element of bool the carrier of (TOP-REAL 2)
the carrier of (TOP-REAL 2) \ (closed_inside_of_rectangle (rp,rl,rg,rd)) is set
Cl ((closed_inside_of_rectangle (rp,rl,rg,rd)) `) is functional closed Element of bool the carrier of (TOP-REAL 2)
(Cl ((closed_inside_of_rectangle (rp,rl,rg,rd)) `)) ` is functional open Element of bool the carrier of (TOP-REAL 2)
the carrier of (TOP-REAL 2) \ (Cl ((closed_inside_of_rectangle (rp,rl,rg,rd)) `)) is set
inside_of_rectangle (rp,rl,rg,rd) is functional Element of bool the carrier of (TOP-REAL 2)
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2) : ( not b<sub>1</sub> `1 <= rp & not rl <= b₁ `1 & not b<sub>1</sub> `2 <= rg & not rd <= b₁ `2 ) } is set
rectangle (rp,rl,rg,rd) is functional non empty proper closed compact bounded Element of bool the carrier of (TOP-REAL 2)
outside_of_rectangle (rp,rl,rg,rd) is functional Element of bool the carrier of (TOP-REAL 2)
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2) : ( not rp <= b<sub>1</sub> `1 or not b₁ `1 <= rl or not rg <= b<sub>1</sub> `2 or not b₁ `2 <= rd ) } is set
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2) : ( ( b<sub>1</sub> `1 = rp & b₁ `2 <= rd & rg <= b<sub>1</sub> `2 ) or ( b₁ `1 <= rl & rp <= b<sub>1</sub> `1 & b₁ `2 = rd ) or ( b<sub>1</sub> `1 <= rl & rp <= b₁ `1 & b<sub>1</sub> `2 = rg ) or ( b₁ `1 = rl & b<sub>1</sub> `2 <= rd & rg <= b₁ `2 ) ) } is set
(outside_of_rectangle (rp,rl,rg,rd)) ` is functional Element of bool the carrier of (TOP-REAL 2)
the carrier of (TOP-REAL 2) \ (outside_of_rectangle (rp,rl,rg,rd)) is set
((outside_of_rectangle (rp,rl,rg,rd)) `) ` is functional Element of bool the carrier of (TOP-REAL 2)
the carrier of (TOP-REAL 2) \ ((outside_of_rectangle (rp,rl,rg,rd)) `) is set
Cl (((outside_of_rectangle (rp,rl,rg,rd)) `) `) is functional closed Element of bool the carrier of (TOP-REAL 2)
(Cl (((outside_of_rectangle (rp,rl,rg,rd)) `) `)) ` is functional open Element of bool the carrier of (TOP-REAL 2)
the carrier of (TOP-REAL 2) \ (Cl (((outside_of_rectangle (rp,rl,rg,rd)) `) `)) is set
(outside_of_rectangle (rp,rl,rg,rd)) \/ (rectangle (rp,rl,rg,rd)) is functional non empty Element of bool the carrier of (TOP-REAL 2)
((outside_of_rectangle (rp,rl,rg,rd)) \/ (rectangle (rp,rl,rg,rd))) ` is functional Element of bool the carrier of (TOP-REAL 2)
the carrier of (TOP-REAL 2) \ ((outside_of_rectangle (rp,rl,rg,rd)) \/ (rectangle (rp,rl,rg,rd))) is set
(rectangle (rp,rl,rg,rd)) ` is functional non empty open Element of bool the carrier of (TOP-REAL 2)
the carrier of (TOP-REAL 2) \ (rectangle (rp,rl,rg,rd)) is set
((outside_of_rectangle (rp,rl,rg,rd)) `) /\ ((rectangle (rp,rl,rg,rd)) `) is functional Element of bool the carrier of (TOP-REAL 2)
(closed_inside_of_rectangle (rp,rl,rg,rd)) /\ ((rectangle (rp,rl,rg,rd)) `) is functional Element of bool the carrier of (TOP-REAL 2)
(inside_of_rectangle (rp,rl,rg,rd)) \/ (outside_of_rectangle (rp,rl,rg,rd)) is functional Element of bool the carrier of (TOP-REAL 2)
(closed_inside_of_rectangle (rp,rl,rg,rd)) /\ ((inside_of_rectangle (rp,rl,rg,rd)) \/ (outside_of_rectangle (rp,rl,rg,rd))) is functional Element of bool the carrier of (TOP-REAL 2)
(closed_inside_of_rectangle (rp,rl,rg,rd)) /\ (inside_of_rectangle (rp,rl,rg,rd)) is functional Element of bool the carrier of (TOP-REAL 2)
(closed_inside_of_rectangle (rp,rl,rg,rd)) /\ (outside_of_rectangle (rp,rl,rg,rd)) is functional Element of bool the carrier of (TOP-REAL 2)
((closed_inside_of_rectangle (rp,rl,rg,rd)) /\ (inside_of_rectangle (rp,rl,rg,rd))) \/ ((closed_inside_of_rectangle (rp,rl,rg,rd)) /\ (outside_of_rectangle (rp,rl,rg,rd))) is functional Element of bool the carrier of (TOP-REAL 2)
((closed_inside_of_rectangle (rp,rl,rg,rd)) /\ (inside_of_rectangle (rp,rl,rg,rd))) \/ {} is set
rp is complex ext-real real set
rl is complex ext-real real set
rg is complex ext-real real set
rd is complex ext-real real set
closed_inside_of_rectangle (rp,rl,rg,rd) is functional closed connected convex Element of bool the carrier of (TOP-REAL 2)
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2) : ( rp <= b<sub>1</sub> `1 & b₁ `1 <= rl & rg <= b<sub>1</sub> `2 & b₁ `2 <= rd ) } is set
inside_of_rectangle (rp,rl,rg,rd) is functional Element of bool the carrier of (TOP-REAL 2)
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2) : ( not b<sub>1</sub> `1 <= rp & not rl <= b₁ `1 & not b<sub>1</sub> `2 <= rg & not rd <= b₁ `2 ) } is set
(closed_inside_of_rectangle (rp,rl,rg,rd)) \ (inside_of_rectangle (rp,rl,rg,rd)) is functional Element of bool the carrier of (TOP-REAL 2)
rectangle (rp,rl,rg,rd) is functional non empty proper closed compact bounded Element of bool the carrier of (TOP-REAL 2)
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2) : ( ( b<sub>1</sub> `1 = rp & b₁ `2 <= rd & rg <= b<sub>1</sub> `2 ) or ( b₁ `1 <= rl & rp <= b<sub>1</sub> `1 & b₁ `2 = rd ) or ( b<sub>1</sub> `1 <= rl & rp <= b₁ `1 & b<sub>1</sub> `2 = rg ) or ( b₁ `1 = rl & b<sub>1</sub> `2 <= rd & rg <= b₁ `2 ) ) } is set
d is set
lg is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
lg `1 is complex ext-real real Element of REAL
lg `2 is complex ext-real real Element of REAL
d is set
lg is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
lg `1 is complex ext-real real Element of REAL
lg `2 is complex ext-real real Element of REAL
pg is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
pg `1 is complex ext-real real Element of REAL
pg `2 is complex ext-real real Element of REAL
rp is complex ext-real real set
rl is complex ext-real real set
rg is complex ext-real real set
rd is complex ext-real real set
closed_inside_of_rectangle (rp,rl,rg,rd) is functional closed connected convex Element of bool the carrier of (TOP-REAL 2)
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2) : ( rp <= b<sub>1</sub> `1 & b₁ `1 <= rl & rg <= b<sub>1</sub> `2 & b₁ `2 <= rd ) } is set
Fr (closed_inside_of_rectangle (rp,rl,rg,rd)) is functional closed boundary nowhere_dense Element of bool the carrier of (TOP-REAL 2)
Cl (closed_inside_of_rectangle (rp,rl,rg,rd)) is functional closed Element of bool the carrier of (TOP-REAL 2)
(closed_inside_of_rectangle (rp,rl,rg,rd)) ` is functional open Element of bool the carrier of (TOP-REAL 2)
the carrier of (TOP-REAL 2) \ (closed_inside_of_rectangle (rp,rl,rg,rd)) is set
Cl ((closed_inside_of_rectangle (rp,rl,rg,rd)) `) is functional closed Element of bool the carrier of (TOP-REAL 2)
(Cl (closed_inside_of_rectangle (rp,rl,rg,rd))) /\ (Cl ((closed_inside_of_rectangle (rp,rl,rg,rd)) `)) is functional closed Element of bool the carrier of (TOP-REAL 2)
rectangle (rp,rl,rg,rd) is functional non empty proper closed compact bounded Element of bool the carrier of (TOP-REAL 2)
Int (closed_inside_of_rectangle (rp,rl,rg,rd)) is functional open Element of bool the carrier of (TOP-REAL 2)
(Cl ((closed_inside_of_rectangle (rp,rl,rg,rd)) `)) ` is functional open Element of bool the carrier of (TOP-REAL 2)
the carrier of (TOP-REAL 2) \ (Cl ((closed_inside_of_rectangle (rp,rl,rg,rd)) `)) is set
(closed_inside_of_rectangle (rp,rl,rg,rd)) \ (Int (closed_inside_of_rectangle (rp,rl,rg,rd))) is functional Element of bool the carrier of (TOP-REAL 2)
inside_of_rectangle (rp,rl,rg,rd) is functional Element of bool the carrier of (TOP-REAL 2)
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2) : ( not b<sub>1</sub> `1 <= rp & not rl <= b₁ `1 & not b<sub>1</sub> `2 <= rg & not rd <= b₁ `2 ) } is set
(closed_inside_of_rectangle (rp,rl,rg,rd)) \ (inside_of_rectangle (rp,rl,rg,rd)) is functional Element of bool the carrier of (TOP-REAL 2)
rp is complex ext-real real set
rl is complex ext-real real set
rg is complex ext-real real set
rd is complex ext-real real set
closed_inside_of_rectangle (rp,rl,rg,rd) is functional closed connected convex Element of bool the carrier of (TOP-REAL 2)
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2) : ( rp <= b<sub>1</sub> `1 & b₁ `1 <= rl & rg <= b<sub>1</sub> `2 & b₁ `2 <= rd ) } is set
W-bound (closed_inside_of_rectangle (rp,rl,rg,rd)) is complex ext-real real Element of REAL
(TOP-REAL 2) | (closed_inside_of_rectangle (rp,rl,rg,rd)) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj1 | (closed_inside_of_rectangle (rp,rl,rg,rd)) is Relation-like closed_inside_of_rectangle (rp,rl,rg,rd) -defined the carrier of (TOP-REAL 2) -defined the carrier of ((TOP-REAL 2) | (closed_inside_of_rectangle (rp,rl,rg,rd))) -defined REAL -valued Function-like total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ((TOP-REAL 2) | (closed_inside_of_rectangle (rp,rl,rg,rd))),REAL:]
the carrier of ((TOP-REAL 2) | (closed_inside_of_rectangle (rp,rl,rg,rd))) is set
[: the carrier of ((TOP-REAL 2) | (closed_inside_of_rectangle (rp,rl,rg,rd))),REAL:] is Relation-like V156() V157() V158() set
bool [: the carrier of ((TOP-REAL 2) | (closed_inside_of_rectangle (rp,rl,rg,rd))),REAL:] is non empty set
lower_bound (proj1 | (closed_inside_of_rectangle (rp,rl,rg,rd))) is complex ext-real real Element of REAL
(proj1 | (closed_inside_of_rectangle (rp,rl,rg,rd))) .: the carrier of ((TOP-REAL 2) | (closed_inside_of_rectangle (rp,rl,rg,rd))) is V166() V167() V168() Element of bool REAL
K663(((proj1 | (closed_inside_of_rectangle (rp,rl,rg,rd))) .: the carrier of ((TOP-REAL 2) | (closed_inside_of_rectangle (rp,rl,rg,rd))))) is complex ext-real real Element of REAL
|[rp,rg]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
b is V166() V167() V168() Element of bool REAL
c is complex ext-real real set
d is set
(proj1 | (closed_inside_of_rectangle (rp,rl,rg,rd))) . d is complex ext-real real set
lg is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
lg `1 is complex ext-real real Element of REAL
lg `2 is complex ext-real real Element of REAL
c is complex ext-real real set
|[rp,rg]| `1 is complex ext-real real Element of REAL
(proj1 | (closed_inside_of_rectangle (rp,rl,rg,rd))) . |[rp,rg]| is complex ext-real real set
rp is complex ext-real real set
rl is complex ext-real real set
rg is complex ext-real real set
rd is complex ext-real real set
closed_inside_of_rectangle (rp,rl,rg,rd) is functional closed connected convex Element of bool the carrier of (TOP-REAL 2)
{ b₁ where b₁ is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2) : ( rp <= b₁ `1 & b<sub>1</sub> `1 <= rl & rg <= b₁ `2 & b<sub>1</sub> `2 <= rd ) } is set
S-bound (closed_inside_of_rectangle (rp,rl,rg,rd)) is complex ext-real real Element of REAL
(TOP-REAL 2) | (closed_inside_of_rectangle (rp,rl,rg,rd)) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj2 | (closed_inside_of_rectangle (rp,rl,rg,rd)) is Relation-like closed_inside_of_rectangle (rp,rl,rg,rd) -defined the carrier of (TOP-REAL 2) -defined the carrier of ((TOP-REAL 2) | (closed_inside_of_rectangle (rp,rl,rg,rd))) -defined REAL -valued Function-like total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ((TOP-REAL 2) | (closed_inside_of_rectangle (rp,rl,rg,rd))),REAL:]
the carrier of ((TOP-REAL 2) | (closed_inside_of_rectangle (rp,rl,rg,rd))) is set
[: the carrier of ((TOP-REAL 2) | (closed_inside_of_rectangle (rp,rl,rg,rd))),REAL:] is Relation-like V156() V157() V158() set
bool [: the carrier of ((TOP-REAL 2) | (closed_inside_of_rectangle (rp,rl,rg,rd))),REAL:] is non empty set
lower_bound (proj2 | (closed_inside_of_rectangle (rp,rl,rg,rd))) is complex ext-real real Element of REAL
(proj2 | (closed_inside_of_rectangle (rp,rl,rg,rd))) .: the carrier of ((TOP-REAL 2) | (closed_inside_of_rectangle (rp,rl,rg,rd))) is V166() V167() V168() Element of bool REAL
K663(((proj2 | (closed_inside_of_rectangle (rp,rl,rg,rd))) .: the carrier of ((TOP-REAL 2) | (closed_inside_of_rectangle (rp,rl,rg,rd))))) is complex ext-real real Element of REAL
|[rp,rg]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
b is V166() V167() V168() Element of bool REAL
c is complex ext-real real set
d is set
(proj2 | (closed_inside_of_rectangle (rp,rl,rg,rd))) . d is complex ext-real real set
lg is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
lg `1 is complex ext-real real Element of REAL
lg `2 is complex ext-real real Element of REAL
c is complex ext-real real set
|[rp,rg]| `2 is complex ext-real real Element of REAL
(proj2 | (closed_inside_of_rectangle (rp,rl,rg,rd))) . |[rp,rg]| is complex ext-real real set
rp is complex ext-real real set
rl is complex ext-real real set
rg is complex ext-real real set
rd is complex ext-real real set
closed_inside_of_rectangle (rp,rl,rg,rd) is functional closed connected convex Element of bool the carrier of (TOP-REAL 2)
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2) : ( rp <= b<sub>1</sub> `1 & b₁ `1 <= rl & rg <= b<sub>1</sub> `2 & b₁ `2 <= rd ) } is set
E-bound (closed_inside_of_rectangle (rp,rl,rg,rd)) is complex ext-real real Element of REAL
(TOP-REAL 2) | (closed_inside_of_rectangle (rp,rl,rg,rd)) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj1 | (closed_inside_of_rectangle (rp,rl,rg,rd)) is Relation-like closed_inside_of_rectangle (rp,rl,rg,rd) -defined the carrier of (TOP-REAL 2) -defined the carrier of ((TOP-REAL 2) | (closed_inside_of_rectangle (rp,rl,rg,rd))) -defined REAL -valued Function-like total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ((TOP-REAL 2) | (closed_inside_of_rectangle (rp,rl,rg,rd))),REAL:]
the carrier of ((TOP-REAL 2) | (closed_inside_of_rectangle (rp,rl,rg,rd))) is set
[: the carrier of ((TOP-REAL 2) | (closed_inside_of_rectangle (rp,rl,rg,rd))),REAL:] is Relation-like V156() V157() V158() set
bool [: the carrier of ((TOP-REAL 2) | (closed_inside_of_rectangle (rp,rl,rg,rd))),REAL:] is non empty set
upper_bound (proj1 | (closed_inside_of_rectangle (rp,rl,rg,rd))) is complex ext-real real Element of REAL
(proj1 | (closed_inside_of_rectangle (rp,rl,rg,rd))) .: the carrier of ((TOP-REAL 2) | (closed_inside_of_rectangle (rp,rl,rg,rd))) is V166() V167() V168() Element of bool REAL
K662(((proj1 | (closed_inside_of_rectangle (rp,rl,rg,rd))) .: the carrier of ((TOP-REAL 2) | (closed_inside_of_rectangle (rp,rl,rg,rd))))) is complex ext-real real Element of REAL
b is V166() V167() V168() Element of bool REAL
c is complex ext-real real set
d is set
(proj1 | (closed_inside_of_rectangle (rp,rl,rg,rd))) . d is complex ext-real real set
lg is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
lg `1 is complex ext-real real Element of REAL
lg `2 is complex ext-real real Element of REAL
c is complex ext-real real set
|[rl,rd]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
|[rl,rd]| `1 is complex ext-real real Element of REAL
|[rl,rd]| `2 is complex ext-real real Element of REAL
(proj1 | (closed_inside_of_rectangle (rp,rl,rg,rd))) . |[rl,rd]| is complex ext-real real set
|[rp,rg]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
rp is complex ext-real real set
rl is complex ext-real real set
rg is complex ext-real real set
rd is complex ext-real real set
closed_inside_of_rectangle (rp,rl,rg,rd) is functional closed connected convex Element of bool the carrier of (TOP-REAL 2)
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2) : ( rp <= b<sub>1</sub> `1 & b₁ `1 <= rl & rg <= b<sub>1</sub> `2 & b₁ `2 <= rd ) } is set
N-bound (closed_inside_of_rectangle (rp,rl,rg,rd)) is complex ext-real real Element of REAL
(TOP-REAL 2) | (closed_inside_of_rectangle (rp,rl,rg,rd)) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj2 | (closed_inside_of_rectangle (rp,rl,rg,rd)) is Relation-like closed_inside_of_rectangle (rp,rl,rg,rd) -defined the carrier of (TOP-REAL 2) -defined the carrier of ((TOP-REAL 2) | (closed_inside_of_rectangle (rp,rl,rg,rd))) -defined REAL -valued Function-like total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ((TOP-REAL 2) | (closed_inside_of_rectangle (rp,rl,rg,rd))),REAL:]
the carrier of ((TOP-REAL 2) | (closed_inside_of_rectangle (rp,rl,rg,rd))) is set
[: the carrier of ((TOP-REAL 2) | (closed_inside_of_rectangle (rp,rl,rg,rd))),REAL:] is Relation-like V156() V157() V158() set
bool [: the carrier of ((TOP-REAL 2) | (closed_inside_of_rectangle (rp,rl,rg,rd))),REAL:] is non empty set
upper_bound (proj2 | (closed_inside_of_rectangle (rp,rl,rg,rd))) is complex ext-real real Element of REAL
(proj2 | (closed_inside_of_rectangle (rp,rl,rg,rd))) .: the carrier of ((TOP-REAL 2) | (closed_inside_of_rectangle (rp,rl,rg,rd))) is V166() V167() V168() Element of bool REAL
K662(((proj2 | (closed_inside_of_rectangle (rp,rl,rg,rd))) .: the carrier of ((TOP-REAL 2) | (closed_inside_of_rectangle (rp,rl,rg,rd))))) is complex ext-real real Element of REAL
b is V166() V167() V168() Element of bool REAL
c is complex ext-real real set
d is set
(proj2 | (closed_inside_of_rectangle (rp,rl,rg,rd))) . d is complex ext-real real set
lg is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
lg `1 is complex ext-real real Element of REAL
lg `2 is complex ext-real real Element of REAL
c is complex ext-real real set
|[rl,rd]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
|[rl,rd]| `1 is complex ext-real real Element of REAL
|[rl,rd]| `2 is complex ext-real real Element of REAL
(proj2 | (closed_inside_of_rectangle (rp,rl,rg,rd))) . |[rl,rd]| is complex ext-real real set
|[rp,rg]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
rp is complex ext-real real set
rl is complex ext-real real set
rg is complex ext-real real set
rd is complex ext-real real set
closed_inside_of_rectangle (rp,rl,rg,rd) is functional closed connected convex Element of bool the carrier of (TOP-REAL 2)
{ b<sub>1</sub> where b<sub>1</sub> is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2) : ( rp <= b<sub>1</sub> `1 & b₁ `1 <= rl & rg <= b<sub>1</sub> `2 & b₁ `2 <= rd ) } is set
rectangle (rp,rl,rg,rd) is functional non empty proper closed compact bounded Element of bool the carrier of (TOP-REAL 2)
a is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
b is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
c is functional Element of bool the carrier of (TOP-REAL 2)
First_Point (c,a,b,(rectangle (rp,rl,rg,rd))) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
Segment (c,a,b,a,(First_Point (c,a,b,(rectangle (rp,rl,rg,rd))))) is functional Element of bool the carrier of (TOP-REAL 2)
ld is set
Fr (closed_inside_of_rectangle (rp,rl,rg,rd)) is functional closed boundary nowhere_dense Element of bool the carrier of (TOP-REAL 2)
Cl (closed_inside_of_rectangle (rp,rl,rg,rd)) is functional closed Element of bool the carrier of (TOP-REAL 2)
(closed_inside_of_rectangle (rp,rl,rg,rd)) ` is functional open Element of bool the carrier of (TOP-REAL 2)
the carrier of (TOP-REAL 2) \ (closed_inside_of_rectangle (rp,rl,rg,rd)) is set
Cl ((closed_inside_of_rectangle (rp,rl,rg,rd)) `) is functional closed Element of bool the carrier of (TOP-REAL 2)
(Cl (closed_inside_of_rectangle (rp,rl,rg,rd))) /\ (Cl ((closed_inside_of_rectangle (rp,rl,rg,rd)) `)) is functional closed Element of bool the carrier of (TOP-REAL 2)
c \ (closed_inside_of_rectangle (rp,rl,rg,rd)) is functional Element of bool the carrier of (TOP-REAL 2)
{} (TOP-REAL 2) is Relation-like non-empty empty-yielding RAT -valued Function-like one-to-one constant functional empty proper open closed boundary nowhere_dense connected compact V156() V157() V158() V159() V166() V167() V168() V169() V170() V171() V172() bounded being_Region horizontal vertical bounded_below interval Element of bool the carrier of (TOP-REAL 2)
c /\ (rectangle (rp,rl,rg,rd)) is functional Element of bool the carrier of (TOP-REAL 2)
pd is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
pd is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
R is functional non empty Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | R is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | R) is non empty set
[: the carrier of I[01], the carrier of ((TOP-REAL 2) | R):] is Relation-like non empty set
bool [: the carrier of I[01], the carrier of ((TOP-REAL 2) | R):] is non empty set
dR is Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL 2) | R) -valued Function-like non empty total quasi_total Element of bool [: the carrier of I[01], the carrier of ((TOP-REAL 2) | R):]
dR . 0 is set
dR . 1 is set
rng dR is non empty Element of bool the carrier of ((TOP-REAL 2) | R)
bool the carrier of ((TOP-REAL 2) | R) is non empty set
[#] ((TOP-REAL 2) | R) is non empty non proper open closed dense non boundary Element of bool the carrier of ((TOP-REAL 2) | R)
dom dR is non empty V166() V167() V168() Element of bool the carrier of I[01]
bool the carrier of I[01] is non empty set
TR is set
dR . TR is set
C is complex ext-real real Element of REAL
Segment (R,a,b,a,(First_Point (c,a,b,(rectangle (rp,rl,rg,rd))))) is functional Element of bool the carrier of (TOP-REAL 2)
P is set
dR . P is set
U is complex ext-real real Element of REAL
Segment (R,a,b,a,pd) is functional Element of bool the carrier of (TOP-REAL 2)
(Segment (R,a,b,a,pd)) \ (closed_inside_of_rectangle (rp,rl,rg,rd)) is functional Element of bool the carrier of (TOP-REAL 2)
l is set
{ b₁ where b₁ is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2) : ( LE a,b₁,R,a,b & LE b₁,pd,R,a,b ) } is set
LJ is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
k is set
dR . k is set
x is complex ext-real real Element of REAL
A1 is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
{ b₁ where b₁ is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2) : ( LE a,b₁,R,a,b & LE b₁, First_Point (c,a,b,(rectangle (rp,rl,rg,rd))),R,a,b ) } is set
A1 is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
pd is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
rp is non empty TopSpace-like TopStruct
rl is non empty TopSpace-like TopStruct
[:rp,rl:] is non empty strict TopSpace-like TopStruct
the carrier of [:rp,rl:] is non empty set
rg is Element of the carrier of [:rp,rl:]
rg `1 is set
the carrier of rp is non empty set
the carrier of rl is non empty set
[: the carrier of rp, the carrier of rl:] is Relation-like non empty set
rg `2 is set
the carrier of rl is non empty set
[: the carrier of rp, the carrier of rl:] is Relation-like non empty set
[: the carrier of [:(TOP-REAL 2),(TOP-REAL 2):],REAL:] is Relation-like non empty V156() V157() V158() set
bool [: the carrier of [:(TOP-REAL 2),(TOP-REAL 2):],REAL:] is non empty set
rp is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
rp `1 is complex ext-real real Element of REAL
rl is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() Element of bool [: the carrier of [:(TOP-REAL 2),(TOP-REAL 2):],REAL:]
rg is Element of the carrier of [:(TOP-REAL 2),(TOP-REAL 2):]
rl . rg is complex ext-real real Element of REAL
((TOP-REAL 2),(TOP-REAL 2),rg) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
((TOP-REAL 2),(TOP-REAL 2),rg) `1 is complex ext-real real Element of REAL
(((TOP-REAL 2),(TOP-REAL 2),rg) `1) - (rp `1) is complex ext-real real Element of REAL
rl is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() Element of bool [: the carrier of [:(TOP-REAL 2),(TOP-REAL 2):],REAL:]
rg is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() Element of bool [: the carrier of [:(TOP-REAL 2),(TOP-REAL 2):],REAL:]
rd is Element of the carrier of [:(TOP-REAL 2),(TOP-REAL 2):]
rl . rd is complex ext-real real Element of REAL
((TOP-REAL 2),(TOP-REAL 2),rd) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
((TOP-REAL 2),(TOP-REAL 2),rd) `1 is complex ext-real real Element of REAL
(((TOP-REAL 2),(TOP-REAL 2),rd) `1) - (rp `1) is complex ext-real real Element of REAL
rg . rd is complex ext-real real Element of REAL
rp `2 is complex ext-real real Element of REAL
rl is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() Element of bool [: the carrier of [:(TOP-REAL 2),(TOP-REAL 2):],REAL:]
rg is Element of the carrier of [:(TOP-REAL 2),(TOP-REAL 2):]
rl . rg is complex ext-real real Element of REAL
((TOP-REAL 2),(TOP-REAL 2),rg) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
((TOP-REAL 2),(TOP-REAL 2),rg) `2 is complex ext-real real Element of REAL
(((TOP-REAL 2),(TOP-REAL 2),rg) `2) - (rp `2) is complex ext-real real Element of REAL
rl is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() Element of bool [: the carrier of [:(TOP-REAL 2),(TOP-REAL 2):],REAL:]
rg is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() Element of bool [: the carrier of [:(TOP-REAL 2),(TOP-REAL 2):],REAL:]
rd is Element of the carrier of [:(TOP-REAL 2),(TOP-REAL 2):]
rl . rd is complex ext-real real Element of REAL
((TOP-REAL 2),(TOP-REAL 2),rd) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
((TOP-REAL 2),(TOP-REAL 2),rd) `2 is complex ext-real real Element of REAL
(((TOP-REAL 2),(TOP-REAL 2),rd) `2) - (rp `2) is complex ext-real real Element of REAL
rg . rd is complex ext-real real Element of REAL
rp is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() Element of bool [: the carrier of [:(TOP-REAL 2),(TOP-REAL 2):],REAL:]
rl is Element of the carrier of [:(TOP-REAL 2),(TOP-REAL 2):]
rp . rl is complex ext-real real Element of REAL
((TOP-REAL 2),(TOP-REAL 2),rl) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
((TOP-REAL 2),(TOP-REAL 2),rl) `1 is complex ext-real real Element of REAL
((TOP-REAL 2),(TOP-REAL 2),rl) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
((TOP-REAL 2),(TOP-REAL 2),rl) `1 is complex ext-real real Element of REAL
(((TOP-REAL 2),(TOP-REAL 2),rl) `1) - (((TOP-REAL 2),(TOP-REAL 2),rl) `1) is complex ext-real real Element of REAL
rp is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() Element of bool [: the carrier of [:(TOP-REAL 2),(TOP-REAL 2):],REAL:]
rl is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() Element of bool [: the carrier of [:(TOP-REAL 2),(TOP-REAL 2):],REAL:]
rg is Element of the carrier of [:(TOP-REAL 2),(TOP-REAL 2):]
rp . rg is complex ext-real real Element of REAL
((TOP-REAL 2),(TOP-REAL 2),rg) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
((TOP-REAL 2),(TOP-REAL 2),rg) `1 is complex ext-real real Element of REAL
((TOP-REAL 2),(TOP-REAL 2),rg) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
((TOP-REAL 2),(TOP-REAL 2),rg) `1 is complex ext-real real Element of REAL
(((TOP-REAL 2),(TOP-REAL 2),rg) `1) - (((TOP-REAL 2),(TOP-REAL 2),rg) `1) is complex ext-real real Element of REAL
rl . rg is complex ext-real real Element of REAL
rp is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() Element of bool [: the carrier of [:(TOP-REAL 2),(TOP-REAL 2):],REAL:]
rl is Element of the carrier of [:(TOP-REAL 2),(TOP-REAL 2):]
rp . rl is complex ext-real real Element of REAL
((TOP-REAL 2),(TOP-REAL 2),rl) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
((TOP-REAL 2),(TOP-REAL 2),rl) `2 is complex ext-real real Element of REAL
((TOP-REAL 2),(TOP-REAL 2),rl) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
((TOP-REAL 2),(TOP-REAL 2),rl) `2 is complex ext-real real Element of REAL
(((TOP-REAL 2),(TOP-REAL 2),rl) `2) - (((TOP-REAL 2),(TOP-REAL 2),rl) `2) is complex ext-real real Element of REAL
rp is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() Element of bool [: the carrier of [:(TOP-REAL 2),(TOP-REAL 2):],REAL:]
rl is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() Element of bool [: the carrier of [:(TOP-REAL 2),(TOP-REAL 2):],REAL:]
rg is Element of the carrier of [:(TOP-REAL 2),(TOP-REAL 2):]
rp . rg is complex ext-real real Element of REAL
((TOP-REAL 2),(TOP-REAL 2),rg) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
((TOP-REAL 2),(TOP-REAL 2),rg) `2 is complex ext-real real Element of REAL
((TOP-REAL 2),(TOP-REAL 2),rg) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
((TOP-REAL 2),(TOP-REAL 2),rg) `2 is complex ext-real real Element of REAL
(((TOP-REAL 2),(TOP-REAL 2),rg) `2) - (((TOP-REAL 2),(TOP-REAL 2),rg) `2) is complex ext-real real Element of REAL
rl . rg is complex ext-real real Element of REAL
rp is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() Element of bool [: the carrier of [:(TOP-REAL 2),(TOP-REAL 2):],REAL:]
rl is Element of the carrier of [:(TOP-REAL 2),(TOP-REAL 2):]
rp . rl is complex ext-real real Element of REAL
((TOP-REAL 2),(TOP-REAL 2),rl) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
((TOP-REAL 2),(TOP-REAL 2),rl) `1 is complex ext-real real Element of REAL
rp is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() Element of bool [: the carrier of [:(TOP-REAL 2),(TOP-REAL 2):],REAL:]
rl is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() Element of bool [: the carrier of [:(TOP-REAL 2),(TOP-REAL 2):],REAL:]
rg is Element of the carrier of [:(TOP-REAL 2),(TOP-REAL 2):]
rp . rg is complex ext-real real Element of REAL
((TOP-REAL 2),(TOP-REAL 2),rg) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
((TOP-REAL 2),(TOP-REAL 2),rg) `1 is complex ext-real real Element of REAL
rl . rg is complex ext-real real Element of REAL
rp is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() Element of bool [: the carrier of [:(TOP-REAL 2),(TOP-REAL 2):],REAL:]
rl is Element of the carrier of [:(TOP-REAL 2),(TOP-REAL 2):]
rp . rl is complex ext-real real Element of REAL
((TOP-REAL 2),(TOP-REAL 2),rl) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
((TOP-REAL 2),(TOP-REAL 2),rl) `2 is complex ext-real real Element of REAL
rp is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() Element of bool [: the carrier of [:(TOP-REAL 2),(TOP-REAL 2):],REAL:]
rl is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() Element of bool [: the carrier of [:(TOP-REAL 2),(TOP-REAL 2):],REAL:]
rg is Element of the carrier of [:(TOP-REAL 2),(TOP-REAL 2):]
rp . rg is complex ext-real real Element of REAL
((TOP-REAL 2),(TOP-REAL 2),rg) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
((TOP-REAL 2),(TOP-REAL 2),rg) `2 is complex ext-real real Element of REAL
rl . rg is complex ext-real real Element of REAL
() is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() Element of bool [: the carrier of [:(TOP-REAL 2),(TOP-REAL 2):],REAL:]
() is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() Element of bool [: the carrier of [:(TOP-REAL 2),(TOP-REAL 2):],REAL:]
() is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() Element of bool [: the carrier of [:(TOP-REAL 2),(TOP-REAL 2):],REAL:]
() is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() Element of bool [: the carrier of [:(TOP-REAL 2),(TOP-REAL 2):],REAL:]
[: the carrier of [:(TOP-REAL 2),(TOP-REAL 2):], the carrier of R^1:] is Relation-like non empty V156() V157() V158() set
bool [: the carrier of [:(TOP-REAL 2),(TOP-REAL 2):], the carrier of R^1:] is non empty set
rp is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
(rp) is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() Element of bool [: the carrier of [:(TOP-REAL 2),(TOP-REAL 2):],REAL:]
rl is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined the carrier of R^1 -valued Function-like non empty total quasi_total V156() V157() V158() Element of bool [: the carrier of [:(TOP-REAL 2),(TOP-REAL 2):], the carrier of R^1:]
bool the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] is non empty set
rg is Element of the carrier of [:(TOP-REAL 2),(TOP-REAL 2):]
rl . rg is complex ext-real real Element of the carrier of R^1
rd is V166() V167() V168() Element of bool the carrier of R^1
((TOP-REAL 2),(TOP-REAL 2),rg) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
((TOP-REAL 2),(TOP-REAL 2),rg) `1 is complex ext-real real Element of REAL
rp `1 is complex ext-real real Element of REAL
(((TOP-REAL 2),(TOP-REAL 2),rg) `1) - (rp `1) is complex ext-real real Element of REAL
b is V166() V167() V168() open Element of bool REAL
c is complex ext-real real set
((((TOP-REAL 2),(TOP-REAL 2),rg) `1) - (rp `1)) - c is complex ext-real real Element of REAL
((((TOP-REAL 2),(TOP-REAL 2),rg) `1) - (rp `1)) + c is complex ext-real real Element of REAL
].(((((TOP-REAL 2),(TOP-REAL 2),rg) `1) - (rp `1)) - c),(((((TOP-REAL 2),(TOP-REAL 2),rg) `1) - (rp `1)) + c).[ is V166() V167() V168() non left_end non right_end bounded_below bounded_above real-bounded interval Element of bool REAL
d is complex ext-real real Element of REAL
(((TOP-REAL 2),(TOP-REAL 2),rg) `1) - d is complex ext-real real Element of REAL
(((TOP-REAL 2),(TOP-REAL 2),rg) `1) + d is complex ext-real real Element of REAL
{ |[b₁,b₂]| where b₁, b₂ is complex ext-real real Element of REAL : ( not b₁ <= (((TOP-REAL 2),(TOP-REAL 2),rg) `1) - d & not (((TOP-REAL 2),(TOP-REAL 2),rg) `1) + d <= b₁ ) } is set
pg is set
ld is complex ext-real real Element of REAL
pd is complex ext-real real Element of REAL
|[ld,pd]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
[#] (TOP-REAL 2) is functional non empty non proper non proper open open closed closed dense dense non boundary non boundary connected a_component being_Region convex Element of bool the carrier of (TOP-REAL 2)
pg is functional Element of bool the carrier of (TOP-REAL 2)
[:([#] (TOP-REAL 2)),pg:] is Relation-like Element of bool the carrier of [:(TOP-REAL 2),(TOP-REAL 2):]
rl .: [:([#] (TOP-REAL 2)),pg:] is V166() V167() V168() Element of bool the carrier of R^1
((TOP-REAL 2),(TOP-REAL 2),rg) `2 is complex ext-real real Element of REAL
|[(((TOP-REAL 2),(TOP-REAL 2),rg) `1),(((TOP-REAL 2),(TOP-REAL 2),rg) `2)]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
((TOP-REAL 2),(TOP-REAL 2),rg) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
[((TOP-REAL 2),(TOP-REAL 2),rg),((TOP-REAL 2),(TOP-REAL 2),rg)] is V15() Element of the carrier of [:(TOP-REAL 2),(TOP-REAL 2):]
{((TOP-REAL 2),(TOP-REAL 2),rg),((TOP-REAL 2),(TOP-REAL 2),rg)} is functional non empty set
{((TOP-REAL 2),(TOP-REAL 2),rg)} is functional non empty set
{{((TOP-REAL 2),(TOP-REAL 2),rg),((TOP-REAL 2),(TOP-REAL 2),rg)},{((TOP-REAL 2),(TOP-REAL 2),rg)}} is non empty set
(((TOP-REAL 2),(TOP-REAL 2),rg) `1) - 0 is complex ext-real real Element of REAL
(((TOP-REAL 2),(TOP-REAL 2),rg) `1) + 0 is complex ext-real real Element of REAL
ld is set
pd is Element of the carrier of [:(TOP-REAL 2),(TOP-REAL 2):]
rl . pd is complex ext-real real Element of the carrier of R^1
((TOP-REAL 2),(TOP-REAL 2),pd) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
((TOP-REAL 2),(TOP-REAL 2),pd) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
[((TOP-REAL 2),(TOP-REAL 2),pd),((TOP-REAL 2),(TOP-REAL 2),pd)] is V15() Element of the carrier of [:(TOP-REAL 2),(TOP-REAL 2):]
{((TOP-REAL 2),(TOP-REAL 2),pd),((TOP-REAL 2),(TOP-REAL 2),pd)} is functional non empty set
{((TOP-REAL 2),(TOP-REAL 2),pd)} is functional non empty set
{{((TOP-REAL 2),(TOP-REAL 2),pd),((TOP-REAL 2),(TOP-REAL 2),pd)},{((TOP-REAL 2),(TOP-REAL 2),pd)}} is non empty set
(rp) . pd is complex ext-real real Element of REAL
((TOP-REAL 2),(TOP-REAL 2),pd) `1 is complex ext-real real Element of REAL
(((TOP-REAL 2),(TOP-REAL 2),pd) `1) - (rp `1) is complex ext-real real Element of REAL
R is complex ext-real real Element of REAL
dR is complex ext-real real Element of REAL
|[R,dR]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
((((TOP-REAL 2),(TOP-REAL 2),rg) `1) - d) - (rp `1) is complex ext-real real Element of REAL
((((TOP-REAL 2),(TOP-REAL 2),rg) `1) + d) - (rp `1) is complex ext-real real Element of REAL
((((TOP-REAL 2),(TOP-REAL 2),rg) `1) - (rp `1)) - d is complex ext-real real Element of REAL
((((TOP-REAL 2),(TOP-REAL 2),rg) `1) - (rp `1)) + d is complex ext-real real Element of REAL
].(((((TOP-REAL 2),(TOP-REAL 2),rg) `1) - (rp `1)) - d),(((((TOP-REAL 2),(TOP-REAL 2),rg) `1) - (rp `1)) + d).[ is V166() V167() V168() non left_end non right_end bounded_below bounded_above real-bounded interval Element of bool REAL
rp is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
(rp) is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() Element of bool [: the carrier of [:(TOP-REAL 2),(TOP-REAL 2):],REAL:]
rl is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined the carrier of R^1 -valued Function-like non empty total quasi_total V156() V157() V158() Element of bool [: the carrier of [:(TOP-REAL 2),(TOP-REAL 2):], the carrier of R^1:]
bool the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] is non empty set
rg is Element of the carrier of [:(TOP-REAL 2),(TOP-REAL 2):]
rl . rg is complex ext-real real Element of the carrier of R^1
rd is V166() V167() V168() Element of bool the carrier of R^1
((TOP-REAL 2),(TOP-REAL 2),rg) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
((TOP-REAL 2),(TOP-REAL 2),rg) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
[((TOP-REAL 2),(TOP-REAL 2),rg),((TOP-REAL 2),(TOP-REAL 2),rg)] is V15() Element of the carrier of [:(TOP-REAL 2),(TOP-REAL 2):]
{((TOP-REAL 2),(TOP-REAL 2),rg),((TOP-REAL 2),(TOP-REAL 2),rg)} is functional non empty set
{((TOP-REAL 2),(TOP-REAL 2),rg)} is functional non empty set
{{((TOP-REAL 2),(TOP-REAL 2),rg),((TOP-REAL 2),(TOP-REAL 2),rg)},{((TOP-REAL 2),(TOP-REAL 2),rg)}} is non empty set
((TOP-REAL 2),(TOP-REAL 2),rg) `2 is complex ext-real real Element of REAL
rp `2 is complex ext-real real Element of REAL
(((TOP-REAL 2),(TOP-REAL 2),rg) `2) - (rp `2) is complex ext-real real Element of REAL
b is V166() V167() V168() open Element of bool REAL
c is complex ext-real real set
((((TOP-REAL 2),(TOP-REAL 2),rg) `2) - (rp `2)) - c is complex ext-real real Element of REAL
((((TOP-REAL 2),(TOP-REAL 2),rg) `2) - (rp `2)) + c is complex ext-real real Element of REAL
].(((((TOP-REAL 2),(TOP-REAL 2),rg) `2) - (rp `2)) - c),(((((TOP-REAL 2),(TOP-REAL 2),rg) `2) - (rp `2)) + c).[ is V166() V167() V168() non left_end non right_end bounded_below bounded_above real-bounded interval Element of bool REAL
d is complex ext-real real Element of REAL
(((TOP-REAL 2),(TOP-REAL 2),rg) `2) - d is complex ext-real real Element of REAL
(((TOP-REAL 2),(TOP-REAL 2),rg) `2) + d is complex ext-real real Element of REAL
{ |[b₁,b₂]| where b₁, b₂ is complex ext-real real Element of REAL : ( not b₂ <= (((TOP-REAL 2),(TOP-REAL 2),rg) `2) - d & not (((TOP-REAL 2),(TOP-REAL 2),rg) `2) + d <= b₂ ) } is set
pg is set
ld is complex ext-real real Element of REAL
pd is complex ext-real real Element of REAL
|[ld,pd]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
[#] (TOP-REAL 2) is functional non empty non proper non proper open open closed closed dense dense non boundary non boundary connected a_component being_Region convex Element of bool the carrier of (TOP-REAL 2)
pg is functional Element of bool the carrier of (TOP-REAL 2)
[:([#] (TOP-REAL 2)),pg:] is Relation-like Element of bool the carrier of [:(TOP-REAL 2),(TOP-REAL 2):]
rl .: [:([#] (TOP-REAL 2)),pg:] is V166() V167() V168() Element of bool the carrier of R^1
((TOP-REAL 2),(TOP-REAL 2),rg) `1 is complex ext-real real Element of REAL
|[(((TOP-REAL 2),(TOP-REAL 2),rg) `1),(((TOP-REAL 2),(TOP-REAL 2),rg) `2)]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
(((TOP-REAL 2),(TOP-REAL 2),rg) `2) - 0 is complex ext-real real Element of REAL
(((TOP-REAL 2),(TOP-REAL 2),rg) `2) + 0 is complex ext-real real Element of REAL
ld is set
pd is Element of the carrier of [:(TOP-REAL 2),(TOP-REAL 2):]
rl . pd is complex ext-real real Element of the carrier of R^1
((TOP-REAL 2),(TOP-REAL 2),pd) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
((TOP-REAL 2),(TOP-REAL 2),pd) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
[((TOP-REAL 2),(TOP-REAL 2),pd),((TOP-REAL 2),(TOP-REAL 2),pd)] is V15() Element of the carrier of [:(TOP-REAL 2),(TOP-REAL 2):]
{((TOP-REAL 2),(TOP-REAL 2),pd),((TOP-REAL 2),(TOP-REAL 2),pd)} is functional non empty set
{((TOP-REAL 2),(TOP-REAL 2),pd)} is functional non empty set
{{((TOP-REAL 2),(TOP-REAL 2),pd),((TOP-REAL 2),(TOP-REAL 2),pd)},{((TOP-REAL 2),(TOP-REAL 2),pd)}} is non empty set
(rp) . pd is complex ext-real real Element of REAL
((TOP-REAL 2),(TOP-REAL 2),pd) `2 is complex ext-real real Element of REAL
(((TOP-REAL 2),(TOP-REAL 2),pd) `2) - (rp `2) is complex ext-real real Element of REAL
R is complex ext-real real Element of REAL
dR is complex ext-real real Element of REAL
|[R,dR]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
((((TOP-REAL 2),(TOP-REAL 2),rg) `2) - d) - (rp `2) is complex ext-real real Element of REAL
((((TOP-REAL 2),(TOP-REAL 2),rg) `2) + d) - (rp `2) is complex ext-real real Element of REAL
((((TOP-REAL 2),(TOP-REAL 2),rg) `2) - (rp `2)) - d is complex ext-real real Element of REAL
((((TOP-REAL 2),(TOP-REAL 2),rg) `2) - (rp `2)) + d is complex ext-real real Element of REAL
].(((((TOP-REAL 2),(TOP-REAL 2),rg) `2) - (rp `2)) - d),(((((TOP-REAL 2),(TOP-REAL 2),rg) `2) - (rp `2)) + d).[ is V166() V167() V168() non left_end non right_end bounded_below bounded_above real-bounded interval Element of bool REAL
rp is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined the carrier of R^1 -valued Function-like non empty total quasi_total V156() V157() V158() Element of bool [: the carrier of [:(TOP-REAL 2),(TOP-REAL 2):], the carrier of R^1:]
bool the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] is non empty set
rl is Element of the carrier of [:(TOP-REAL 2),(TOP-REAL 2):]
rp . rl is complex ext-real real Element of the carrier of R^1
rg is V166() V167() V168() Element of bool the carrier of R^1
((TOP-REAL 2),(TOP-REAL 2),rl) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
((TOP-REAL 2),(TOP-REAL 2),rl) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
[((TOP-REAL 2),(TOP-REAL 2),rl),((TOP-REAL 2),(TOP-REAL 2),rl)] is V15() Element of the carrier of [:(TOP-REAL 2),(TOP-REAL 2):]
{((TOP-REAL 2),(TOP-REAL 2),rl),((TOP-REAL 2),(TOP-REAL 2),rl)} is functional non empty set
{((TOP-REAL 2),(TOP-REAL 2),rl)} is functional non empty set
{{((TOP-REAL 2),(TOP-REAL 2),rl),((TOP-REAL 2),(TOP-REAL 2),rl)},{((TOP-REAL 2),(TOP-REAL 2),rl)}} is non empty set
() . rl is complex ext-real real Element of REAL
((TOP-REAL 2),(TOP-REAL 2),rl) `1 is complex ext-real real Element of REAL
((TOP-REAL 2),(TOP-REAL 2),rl) `1 is complex ext-real real Element of REAL
(((TOP-REAL 2),(TOP-REAL 2),rl) `1) - (((TOP-REAL 2),(TOP-REAL 2),rl) `1) is complex ext-real real Element of REAL
a is V166() V167() V168() open Element of bool REAL
b is complex ext-real real set
((((TOP-REAL 2),(TOP-REAL 2),rl) `1) - (((TOP-REAL 2),(TOP-REAL 2),rl) `1)) - b is complex ext-real real Element of REAL
((((TOP-REAL 2),(TOP-REAL 2),rl) `1) - (((TOP-REAL 2),(TOP-REAL 2),rl) `1)) + b is complex ext-real real Element of REAL
].(((((TOP-REAL 2),(TOP-REAL 2),rl) `1) - (((TOP-REAL 2),(TOP-REAL 2),rl) `1)) - b),(((((TOP-REAL 2),(TOP-REAL 2),rl) `1) - (((TOP-REAL 2),(TOP-REAL 2),rl) `1)) + b).[ is V166() V167() V168() non left_end non right_end bounded_below bounded_above real-bounded interval Element of bool REAL
c is complex ext-real real Element of REAL
c / 2 is complex ext-real real Element of REAL
(((TOP-REAL 2),(TOP-REAL 2),rl) `1) - (c / 2) is complex ext-real real Element of REAL
(((TOP-REAL 2),(TOP-REAL 2),rl) `1) + (c / 2) is complex ext-real real Element of REAL
{ |[b₁,b₂]| where b₁, b₂ is complex ext-real real Element of REAL : ( not b₁ <= (((TOP-REAL 2),(TOP-REAL 2),rl) `1) - (c / 2) & not (((TOP-REAL 2),(TOP-REAL 2),rl) `1) + (c / 2) <= b₁ ) } is set
(((TOP-REAL 2),(TOP-REAL 2),rl) `1) - (c / 2) is complex ext-real real Element of REAL
(((TOP-REAL 2),(TOP-REAL 2),rl) `1) + (c / 2) is complex ext-real real Element of REAL
{ |[b₁,b₂]| where b₁, b₂ is complex ext-real real Element of REAL : ( not b₁ <= (((TOP-REAL 2),(TOP-REAL 2),rl) `1) - (c / 2) & not (((TOP-REAL 2),(TOP-REAL 2),rl) `1) + (c / 2) <= b₁ ) } is set
pg is set
ld is complex ext-real real Element of REAL
pd is complex ext-real real Element of REAL
|[ld,pd]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
ld is set
pd is complex ext-real real Element of REAL
R is complex ext-real real Element of REAL
|[pd,R]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
pg is functional Element of bool the carrier of (TOP-REAL 2)
ld is functional Element of bool the carrier of (TOP-REAL 2)
[:pg,ld:] is Relation-like Element of bool the carrier of [:(TOP-REAL 2),(TOP-REAL 2):]
rp .: [:pg,ld:] is V166() V167() V168() Element of bool the carrier of R^1
((TOP-REAL 2),(TOP-REAL 2),rl) `2 is complex ext-real real Element of REAL
|[(((TOP-REAL 2),(TOP-REAL 2),rl) `1),(((TOP-REAL 2),(TOP-REAL 2),rl) `2)]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
0 / 2 is Relation-like non-empty empty-yielding RAT -valued Function-like one-to-one constant functional empty complex ext-real non positive non negative real V156() V157() V158() V159() V166() V167() V168() V169() V170() V171() V172() bounded_below interval Element of REAL
(((TOP-REAL 2),(TOP-REAL 2),rl) `1) - 0 is complex ext-real real Element of REAL
(((TOP-REAL 2),(TOP-REAL 2),rl) `1) + 0 is complex ext-real real Element of REAL
((TOP-REAL 2),(TOP-REAL 2),rl) `2 is complex ext-real real Element of REAL
|[(((TOP-REAL 2),(TOP-REAL 2),rl) `1),(((TOP-REAL 2),(TOP-REAL 2),rl) `2)]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
(((TOP-REAL 2),(TOP-REAL 2),rl) `1) - 0 is complex ext-real real Element of REAL
(((TOP-REAL 2),(TOP-REAL 2),rl) `1) + 0 is complex ext-real real Element of REAL
pd is set
R is Element of the carrier of [:(TOP-REAL 2),(TOP-REAL 2):]
rp . R is complex ext-real real Element of the carrier of R^1
((TOP-REAL 2),(TOP-REAL 2),R) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
((TOP-REAL 2),(TOP-REAL 2),R) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
[((TOP-REAL 2),(TOP-REAL 2),R),((TOP-REAL 2),(TOP-REAL 2),R)] is V15() Element of the carrier of [:(TOP-REAL 2),(TOP-REAL 2):]
{((TOP-REAL 2),(TOP-REAL 2),R),((TOP-REAL 2),(TOP-REAL 2),R)} is functional non empty set
{((TOP-REAL 2),(TOP-REAL 2),R)} is functional non empty set
{{((TOP-REAL 2),(TOP-REAL 2),R),((TOP-REAL 2),(TOP-REAL 2),R)},{((TOP-REAL 2),(TOP-REAL 2),R)}} is non empty set
() . R is complex ext-real real Element of REAL
((TOP-REAL 2),(TOP-REAL 2),R) `1 is complex ext-real real Element of REAL
((TOP-REAL 2),(TOP-REAL 2),R) `1 is complex ext-real real Element of REAL
(((TOP-REAL 2),(TOP-REAL 2),R) `1) - (((TOP-REAL 2),(TOP-REAL 2),R) `1) is complex ext-real real Element of REAL
dR is complex ext-real real Element of REAL
TR is complex ext-real real Element of REAL
|[dR,TR]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
dR + (c / 2) is complex ext-real real Element of REAL
((((TOP-REAL 2),(TOP-REAL 2),rl) `1) - (c / 2)) + (c / 2) is complex ext-real real Element of REAL
(((TOP-REAL 2),(TOP-REAL 2),rl) `1) - dR is complex ext-real real Element of REAL
(((TOP-REAL 2),(TOP-REAL 2),rl) `1) - ((((TOP-REAL 2),(TOP-REAL 2),rl) `1) + (c / 2)) is complex ext-real real Element of REAL
(dR + (c / 2)) - dR is complex ext-real real Element of REAL
- (c / 2) is complex ext-real real Element of REAL
abs ((((TOP-REAL 2),(TOP-REAL 2),rl) `1) - dR) is complex ext-real real Element of REAL
C is complex ext-real real Element of REAL
P is complex ext-real real Element of REAL
|[C,P]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
C + (c / 2) is complex ext-real real Element of REAL
((((TOP-REAL 2),(TOP-REAL 2),rl) `1) - (c / 2)) + (c / 2) is complex ext-real real Element of REAL
(((TOP-REAL 2),(TOP-REAL 2),rl) `1) - C is complex ext-real real Element of REAL
(((TOP-REAL 2),(TOP-REAL 2),rl) `1) - ((((TOP-REAL 2),(TOP-REAL 2),rl) `1) + (c / 2)) is complex ext-real real Element of REAL
(C + (c / 2)) - C is complex ext-real real Element of REAL
abs ((((TOP-REAL 2),(TOP-REAL 2),rl) `1) - C) is complex ext-real real Element of REAL
(c / 2) + (c / 2) is complex ext-real real Element of REAL
(abs ((((TOP-REAL 2),(TOP-REAL 2),rl) `1) - dR)) + (abs ((((TOP-REAL 2),(TOP-REAL 2),rl) `1) - C)) is complex ext-real real Element of REAL
((((TOP-REAL 2),(TOP-REAL 2),rl) `1) - dR) - ((((TOP-REAL 2),(TOP-REAL 2),rl) `1) - C) is complex ext-real real Element of REAL
abs (((((TOP-REAL 2),(TOP-REAL 2),rl) `1) - dR) - ((((TOP-REAL 2),(TOP-REAL 2),rl) `1) - C)) is complex ext-real real Element of REAL
- (((((TOP-REAL 2),(TOP-REAL 2),rl) `1) - dR) - ((((TOP-REAL 2),(TOP-REAL 2),rl) `1) - C)) is complex ext-real real Element of REAL
abs (- (((((TOP-REAL 2),(TOP-REAL 2),rl) `1) - dR) - ((((TOP-REAL 2),(TOP-REAL 2),rl) `1) - C))) is complex ext-real real Element of REAL
dR - C is complex ext-real real Element of REAL
(dR - C) - ((((TOP-REAL 2),(TOP-REAL 2),rl) `1) - (((TOP-REAL 2),(TOP-REAL 2),rl) `1)) is complex ext-real real Element of REAL
abs ((dR - C) - ((((TOP-REAL 2),(TOP-REAL 2),rl) `1) - (((TOP-REAL 2),(TOP-REAL 2),rl) `1))) is complex ext-real real Element of REAL
((((TOP-REAL 2),(TOP-REAL 2),rl) `1) - (((TOP-REAL 2),(TOP-REAL 2),rl) `1)) - c is complex ext-real real Element of REAL
((((TOP-REAL 2),(TOP-REAL 2),rl) `1) - (((TOP-REAL 2),(TOP-REAL 2),rl) `1)) + c is complex ext-real real Element of REAL
].(((((TOP-REAL 2),(TOP-REAL 2),rl) `1) - (((TOP-REAL 2),(TOP-REAL 2),rl) `1)) - c),(((((TOP-REAL 2),(TOP-REAL 2),rl) `1) - (((TOP-REAL 2),(TOP-REAL 2),rl) `1)) + c).[ is V166() V167() V168() non left_end non right_end bounded_below bounded_above real-bounded interval Element of bool REAL
rp is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined the carrier of R^1 -valued Function-like non empty total quasi_total V156() V157() V158() Element of bool [: the carrier of [:(TOP-REAL 2),(TOP-REAL 2):], the carrier of R^1:]
bool the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] is non empty set
rl is Element of the carrier of [:(TOP-REAL 2),(TOP-REAL 2):]
rp . rl is complex ext-real real Element of the carrier of R^1
rg is V166() V167() V168() Element of bool the carrier of R^1
((TOP-REAL 2),(TOP-REAL 2),rl) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
((TOP-REAL 2),(TOP-REAL 2),rl) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
[((TOP-REAL 2),(TOP-REAL 2),rl),((TOP-REAL 2),(TOP-REAL 2),rl)] is V15() Element of the carrier of [:(TOP-REAL 2),(TOP-REAL 2):]
{((TOP-REAL 2),(TOP-REAL 2),rl),((TOP-REAL 2),(TOP-REAL 2),rl)} is functional non empty set
{((TOP-REAL 2),(TOP-REAL 2),rl)} is functional non empty set
{{((TOP-REAL 2),(TOP-REAL 2),rl),((TOP-REAL 2),(TOP-REAL 2),rl)},{((TOP-REAL 2),(TOP-REAL 2),rl)}} is non empty set
() . rl is complex ext-real real Element of REAL
((TOP-REAL 2),(TOP-REAL 2),rl) `2 is complex ext-real real Element of REAL
((TOP-REAL 2),(TOP-REAL 2),rl) `2 is complex ext-real real Element of REAL
(((TOP-REAL 2),(TOP-REAL 2),rl) `2) - (((TOP-REAL 2),(TOP-REAL 2),rl) `2) is complex ext-real real Element of REAL
a is V166() V167() V168() open Element of bool REAL
b is complex ext-real real set
((((TOP-REAL 2),(TOP-REAL 2),rl) `2) - (((TOP-REAL 2),(TOP-REAL 2),rl) `2)) - b is complex ext-real real Element of REAL
((((TOP-REAL 2),(TOP-REAL 2),rl) `2) - (((TOP-REAL 2),(TOP-REAL 2),rl) `2)) + b is complex ext-real real Element of REAL
].(((((TOP-REAL 2),(TOP-REAL 2),rl) `2) - (((TOP-REAL 2),(TOP-REAL 2),rl) `2)) - b),(((((TOP-REAL 2),(TOP-REAL 2),rl) `2) - (((TOP-REAL 2),(TOP-REAL 2),rl) `2)) + b).[ is V166() V167() V168() non left_end non right_end bounded_below bounded_above real-bounded interval Element of bool REAL
c is complex ext-real real Element of REAL
c / 2 is complex ext-real real Element of REAL
(((TOP-REAL 2),(TOP-REAL 2),rl) `2) - (c / 2) is complex ext-real real Element of REAL
(((TOP-REAL 2),(TOP-REAL 2),rl) `2) + (c / 2) is complex ext-real real Element of REAL
{ |[b₁,b₂]| where b₁, b₂ is complex ext-real real Element of REAL : ( not b₂ <= (((TOP-REAL 2),(TOP-REAL 2),rl) `2) - (c / 2) & not (((TOP-REAL 2),(TOP-REAL 2),rl) `2) + (c / 2) <= b₂ ) } is set
(((TOP-REAL 2),(TOP-REAL 2),rl) `2) - (c / 2) is complex ext-real real Element of REAL
(((TOP-REAL 2),(TOP-REAL 2),rl) `2) + (c / 2) is complex ext-real real Element of REAL
{ |[b₁,b₂]| where b₁, b₂ is complex ext-real real Element of REAL : ( not b₂ <= (((TOP-REAL 2),(TOP-REAL 2),rl) `2) - (c / 2) & not (((TOP-REAL 2),(TOP-REAL 2),rl) `2) + (c / 2) <= b₂ ) } is set
pg is set
ld is complex ext-real real Element of REAL
pd is complex ext-real real Element of REAL
|[ld,pd]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
ld is set
pd is complex ext-real real Element of REAL
R is complex ext-real real Element of REAL
|[pd,R]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
pg is functional Element of bool the carrier of (TOP-REAL 2)
ld is functional Element of bool the carrier of (TOP-REAL 2)
[:pg,ld:] is Relation-like Element of bool the carrier of [:(TOP-REAL 2),(TOP-REAL 2):]
rp .: [:pg,ld:] is V166() V167() V168() Element of bool the carrier of R^1
((TOP-REAL 2),(TOP-REAL 2),rl) `1 is complex ext-real real Element of REAL
|[(((TOP-REAL 2),(TOP-REAL 2),rl) `1),(((TOP-REAL 2),(TOP-REAL 2),rl) `2)]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
0 / 2 is Relation-like non-empty empty-yielding RAT -valued Function-like one-to-one constant functional empty complex ext-real non positive non negative real V156() V157() V158() V159() V166() V167() V168() V169() V170() V171() V172() bounded_below interval Element of REAL
(((TOP-REAL 2),(TOP-REAL 2),rl) `2) - 0 is complex ext-real real Element of REAL
(((TOP-REAL 2),(TOP-REAL 2),rl) `2) + 0 is complex ext-real real Element of REAL
((TOP-REAL 2),(TOP-REAL 2),rl) `1 is complex ext-real real Element of REAL
|[(((TOP-REAL 2),(TOP-REAL 2),rl) `1),(((TOP-REAL 2),(TOP-REAL 2),rl) `2)]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
(((TOP-REAL 2),(TOP-REAL 2),rl) `2) - 0 is complex ext-real real Element of REAL
(((TOP-REAL 2),(TOP-REAL 2),rl) `2) + 0 is complex ext-real real Element of REAL
pd is set
R is Element of the carrier of [:(TOP-REAL 2),(TOP-REAL 2):]
rp . R is complex ext-real real Element of the carrier of R^1
((TOP-REAL 2),(TOP-REAL 2),R) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
((TOP-REAL 2),(TOP-REAL 2),R) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
[((TOP-REAL 2),(TOP-REAL 2),R),((TOP-REAL 2),(TOP-REAL 2),R)] is V15() Element of the carrier of [:(TOP-REAL 2),(TOP-REAL 2):]
{((TOP-REAL 2),(TOP-REAL 2),R),((TOP-REAL 2),(TOP-REAL 2),R)} is functional non empty set
{((TOP-REAL 2),(TOP-REAL 2),R)} is functional non empty set
{{((TOP-REAL 2),(TOP-REAL 2),R),((TOP-REAL 2),(TOP-REAL 2),R)},{((TOP-REAL 2),(TOP-REAL 2),R)}} is non empty set
() . R is complex ext-real real Element of REAL
((TOP-REAL 2),(TOP-REAL 2),R) `2 is complex ext-real real Element of REAL
((TOP-REAL 2),(TOP-REAL 2),R) `2 is complex ext-real real Element of REAL
(((TOP-REAL 2),(TOP-REAL 2),R) `2) - (((TOP-REAL 2),(TOP-REAL 2),R) `2) is complex ext-real real Element of REAL
dR is complex ext-real real Element of REAL
TR is complex ext-real real Element of REAL
|[dR,TR]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
TR + (c / 2) is complex ext-real real Element of REAL
((((TOP-REAL 2),(TOP-REAL 2),rl) `2) - (c / 2)) + (c / 2) is complex ext-real real Element of REAL
(((TOP-REAL 2),(TOP-REAL 2),rl) `2) - TR is complex ext-real real Element of REAL
(((TOP-REAL 2),(TOP-REAL 2),rl) `2) - ((((TOP-REAL 2),(TOP-REAL 2),rl) `2) + (c / 2)) is complex ext-real real Element of REAL
(TR + (c / 2)) - TR is complex ext-real real Element of REAL
- (c / 2) is complex ext-real real Element of REAL
abs ((((TOP-REAL 2),(TOP-REAL 2),rl) `2) - TR) is complex ext-real real Element of REAL
C is complex ext-real real Element of REAL
P is complex ext-real real Element of REAL
|[C,P]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
P + (c / 2) is complex ext-real real Element of REAL
((((TOP-REAL 2),(TOP-REAL 2),rl) `2) - (c / 2)) + (c / 2) is complex ext-real real Element of REAL
(((TOP-REAL 2),(TOP-REAL 2),rl) `2) - P is complex ext-real real Element of REAL
(((TOP-REAL 2),(TOP-REAL 2),rl) `2) - ((((TOP-REAL 2),(TOP-REAL 2),rl) `2) + (c / 2)) is complex ext-real real Element of REAL
(P + (c / 2)) - P is complex ext-real real Element of REAL
abs ((((TOP-REAL 2),(TOP-REAL 2),rl) `2) - P) is complex ext-real real Element of REAL
(c / 2) + (c / 2) is complex ext-real real Element of REAL
(abs ((((TOP-REAL 2),(TOP-REAL 2),rl) `2) - TR)) + (abs ((((TOP-REAL 2),(TOP-REAL 2),rl) `2) - P)) is complex ext-real real Element of REAL
((((TOP-REAL 2),(TOP-REAL 2),rl) `2) - TR) - ((((TOP-REAL 2),(TOP-REAL 2),rl) `2) - P) is complex ext-real real Element of REAL
abs (((((TOP-REAL 2),(TOP-REAL 2),rl) `2) - TR) - ((((TOP-REAL 2),(TOP-REAL 2),rl) `2) - P)) is complex ext-real real Element of REAL
- (((((TOP-REAL 2),(TOP-REAL 2),rl) `2) - TR) - ((((TOP-REAL 2),(TOP-REAL 2),rl) `2) - P)) is complex ext-real real Element of REAL
abs (- (((((TOP-REAL 2),(TOP-REAL 2),rl) `2) - TR) - ((((TOP-REAL 2),(TOP-REAL 2),rl) `2) - P))) is complex ext-real real Element of REAL
TR - P is complex ext-real real Element of REAL
(TR - P) - ((((TOP-REAL 2),(TOP-REAL 2),rl) `2) - (((TOP-REAL 2),(TOP-REAL 2),rl) `2)) is complex ext-real real Element of REAL
abs ((TR - P) - ((((TOP-REAL 2),(TOP-REAL 2),rl) `2) - (((TOP-REAL 2),(TOP-REAL 2),rl) `2))) is complex ext-real real Element of REAL
((((TOP-REAL 2),(TOP-REAL 2),rl) `2) - (((TOP-REAL 2),(TOP-REAL 2),rl) `2)) - c is complex ext-real real Element of REAL
((((TOP-REAL 2),(TOP-REAL 2),rl) `2) - (((TOP-REAL 2),(TOP-REAL 2),rl) `2)) + c is complex ext-real real Element of REAL
].(((((TOP-REAL 2),(TOP-REAL 2),rl) `2) - (((TOP-REAL 2),(TOP-REAL 2),rl) `2)) - c),(((((TOP-REAL 2),(TOP-REAL 2),rl) `2) - (((TOP-REAL 2),(TOP-REAL 2),rl) `2)) + c).[ is V166() V167() V168() non left_end non right_end bounded_below bounded_above real-bounded interval Element of bool REAL
rp is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined the carrier of R^1 -valued Function-like non empty total quasi_total V156() V157() V158() Element of bool [: the carrier of [:(TOP-REAL 2),(TOP-REAL 2):], the carrier of R^1:]
bool the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] is non empty set
rl is Element of the carrier of [:(TOP-REAL 2),(TOP-REAL 2):]
rp . rl is complex ext-real real Element of the carrier of R^1
rg is V166() V167() V168() Element of bool the carrier of R^1
((TOP-REAL 2),(TOP-REAL 2),rl) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
((TOP-REAL 2),(TOP-REAL 2),rl) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
[((TOP-REAL 2),(TOP-REAL 2),rl),((TOP-REAL 2),(TOP-REAL 2),rl)] is V15() Element of the carrier of [:(TOP-REAL 2),(TOP-REAL 2):]
{((TOP-REAL 2),(TOP-REAL 2),rl),((TOP-REAL 2),(TOP-REAL 2),rl)} is functional non empty set
{((TOP-REAL 2),(TOP-REAL 2),rl)} is functional non empty set
{{((TOP-REAL 2),(TOP-REAL 2),rl),((TOP-REAL 2),(TOP-REAL 2),rl)},{((TOP-REAL 2),(TOP-REAL 2),rl)}} is non empty set
((TOP-REAL 2),(TOP-REAL 2),rl) `1 is complex ext-real real Element of REAL
rd is V166() V167() V168() open Element of bool REAL
a is complex ext-real real set
(((TOP-REAL 2),(TOP-REAL 2),rl) `1) - a is complex ext-real real Element of REAL
(((TOP-REAL 2),(TOP-REAL 2),rl) `1) + a is complex ext-real real Element of REAL
].((((TOP-REAL 2),(TOP-REAL 2),rl) `1) - a),((((TOP-REAL 2),(TOP-REAL 2),rl) `1) + a).[ is V166() V167() V168() non left_end non right_end bounded_below bounded_above real-bounded interval Element of bool REAL
b is complex ext-real real Element of REAL
(((TOP-REAL 2),(TOP-REAL 2),rl) `1) - b is complex ext-real real Element of REAL
(((TOP-REAL 2),(TOP-REAL 2),rl) `1) + b is complex ext-real real Element of REAL
{ |[b<sub>1</sub>,b<sub>2</sub>]| where b<sub>1</sub>, b<sub>2</sub> is complex ext-real real Element of REAL : ( not b<sub>1</sub> <= (((TOP-REAL 2),(TOP-REAL 2),rl) `1) - b & not (((TOP-REAL 2),(TOP-REAL 2),rl) `1) + b <= b<sub>1</sub> ) } is set
d is set
lg is complex ext-real real Element of REAL
pg is complex ext-real real Element of REAL
|[lg,pg]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
[#] (TOP-REAL 2) is functional non empty non proper non proper open open closed closed dense dense non boundary non boundary connected a_component being_Region convex Element of bool the carrier of (TOP-REAL 2)
d is functional Element of bool the carrier of (TOP-REAL 2)
[:([#] (TOP-REAL 2)),d:] is Relation-like Element of bool the carrier of [:(TOP-REAL 2),(TOP-REAL 2):]
rp .: [:([#] (TOP-REAL 2)),d:] is V166() V167() V168() Element of bool the carrier of R^1
((TOP-REAL 2),(TOP-REAL 2),rl) `2 is complex ext-real real Element of REAL
|[(((TOP-REAL 2),(TOP-REAL 2),rl) `1),(((TOP-REAL 2),(TOP-REAL 2),rl) `2)]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
(((TOP-REAL 2),(TOP-REAL 2),rl) `1) - 0 is complex ext-real real Element of REAL
(((TOP-REAL 2),(TOP-REAL 2),rl) `1) + 0 is complex ext-real real Element of REAL
lg is set
pg is Element of the carrier of [:(TOP-REAL 2),(TOP-REAL 2):]
rp . pg is complex ext-real real Element of the carrier of R^1
((TOP-REAL 2),(TOP-REAL 2),pg) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
((TOP-REAL 2),(TOP-REAL 2),pg) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
[((TOP-REAL 2),(TOP-REAL 2),pg),((TOP-REAL 2),(TOP-REAL 2),pg)] is V15() Element of the carrier of [:(TOP-REAL 2),(TOP-REAL 2):]
{((TOP-REAL 2),(TOP-REAL 2),pg),((TOP-REAL 2),(TOP-REAL 2),pg)} is functional non empty set
{((TOP-REAL 2),(TOP-REAL 2),pg)} is functional non empty set
{{((TOP-REAL 2),(TOP-REAL 2),pg),((TOP-REAL 2),(TOP-REAL 2),pg)},{((TOP-REAL 2),(TOP-REAL 2),pg)}} is non empty set
((TOP-REAL 2),(TOP-REAL 2),pg) `1 is complex ext-real real Element of REAL
ld is complex ext-real real Element of REAL
pd is complex ext-real real Element of REAL
|[ld,pd]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
ld + b is complex ext-real real Element of REAL
((((TOP-REAL 2),(TOP-REAL 2),rl) `1) - b) + b is complex ext-real real Element of REAL
(((TOP-REAL 2),(TOP-REAL 2),rl) `1) - ld is complex ext-real real Element of REAL
(((TOP-REAL 2),(TOP-REAL 2),rl) `1) - ((((TOP-REAL 2),(TOP-REAL 2),rl) `1) + b) is complex ext-real real Element of REAL
(ld + b) - ld is complex ext-real real Element of REAL
- b is complex ext-real real Element of REAL
abs ((((TOP-REAL 2),(TOP-REAL 2),rl) `1) - ld) is complex ext-real real Element of REAL
- ((((TOP-REAL 2),(TOP-REAL 2),rl) `1) - ld) is complex ext-real real Element of REAL
abs (- ((((TOP-REAL 2),(TOP-REAL 2),rl) `1) - ld)) is complex ext-real real Element of REAL
ld - (((TOP-REAL 2),(TOP-REAL 2),rl) `1) is complex ext-real real Element of REAL
abs (ld - (((TOP-REAL 2),(TOP-REAL 2),rl) `1)) is complex ext-real real Element of REAL
].((((TOP-REAL 2),(TOP-REAL 2),rl) `1) - b),((((TOP-REAL 2),(TOP-REAL 2),rl) `1) + b).[ is V166() V167() V168() non left_end non right_end bounded_below bounded_above real-bounded interval Element of bool REAL
rp is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined the carrier of R^1 -valued Function-like non empty total quasi_total V156() V157() V158() Element of bool [: the carrier of [:(TOP-REAL 2),(TOP-REAL 2):], the carrier of R^1:]
bool the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] is non empty set
rl is Element of the carrier of [:(TOP-REAL 2),(TOP-REAL 2):]
rp . rl is complex ext-real real Element of the carrier of R^1
rg is V166() V167() V168() Element of bool the carrier of R^1
((TOP-REAL 2),(TOP-REAL 2),rl) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
((TOP-REAL 2),(TOP-REAL 2),rl) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
[((TOP-REAL 2),(TOP-REAL 2),rl),((TOP-REAL 2),(TOP-REAL 2),rl)] is V15() Element of the carrier of [:(TOP-REAL 2),(TOP-REAL 2):]
{((TOP-REAL 2),(TOP-REAL 2),rl),((TOP-REAL 2),(TOP-REAL 2),rl)} is functional non empty set
{((TOP-REAL 2),(TOP-REAL 2),rl)} is functional non empty set
{{((TOP-REAL 2),(TOP-REAL 2),rl),((TOP-REAL 2),(TOP-REAL 2),rl)},{((TOP-REAL 2),(TOP-REAL 2),rl)}} is non empty set
((TOP-REAL 2),(TOP-REAL 2),rl) `2 is complex ext-real real Element of REAL
rd is V166() V167() V168() open Element of bool REAL
a is complex ext-real real set
(((TOP-REAL 2),(TOP-REAL 2),rl) `2) - a is complex ext-real real Element of REAL
(((TOP-REAL 2),(TOP-REAL 2),rl) `2) + a is complex ext-real real Element of REAL
].((((TOP-REAL 2),(TOP-REAL 2),rl) `2) - a),((((TOP-REAL 2),(TOP-REAL 2),rl) `2) + a).[ is V166() V167() V168() non left_end non right_end bounded_below bounded_above real-bounded interval Element of bool REAL
b is complex ext-real real Element of REAL
(((TOP-REAL 2),(TOP-REAL 2),rl) `2) - b is complex ext-real real Element of REAL
(((TOP-REAL 2),(TOP-REAL 2),rl) `2) + b is complex ext-real real Element of REAL
{ |[b<sub>1</sub>,b<sub>2</sub>]| where b<sub>1</sub>, b<sub>2</sub> is complex ext-real real Element of REAL : ( not b<sub>2</sub> <= (((TOP-REAL 2),(TOP-REAL 2),rl) `2) - b & not (((TOP-REAL 2),(TOP-REAL 2),rl) `2) + b <= b<sub>2</sub> ) } is set
d is set
lg is complex ext-real real Element of REAL
pg is complex ext-real real Element of REAL
|[lg,pg]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
[#] (TOP-REAL 2) is functional non empty non proper non proper open open closed closed dense dense non boundary non boundary connected a_component being_Region convex Element of bool the carrier of (TOP-REAL 2)
d is functional Element of bool the carrier of (TOP-REAL 2)
[:([#] (TOP-REAL 2)),d:] is Relation-like Element of bool the carrier of [:(TOP-REAL 2),(TOP-REAL 2):]
rp .: [:([#] (TOP-REAL 2)),d:] is V166() V167() V168() Element of bool the carrier of R^1
((TOP-REAL 2),(TOP-REAL 2),rl) `1 is complex ext-real real Element of REAL
|[(((TOP-REAL 2),(TOP-REAL 2),rl) `1),(((TOP-REAL 2),(TOP-REAL 2),rl) `2)]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
(((TOP-REAL 2),(TOP-REAL 2),rl) `2) - 0 is complex ext-real real Element of REAL
(((TOP-REAL 2),(TOP-REAL 2),rl) `2) + 0 is complex ext-real real Element of REAL
lg is set
pg is Element of the carrier of [:(TOP-REAL 2),(TOP-REAL 2):]
rp . pg is complex ext-real real Element of the carrier of R^1
((TOP-REAL 2),(TOP-REAL 2),pg) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
((TOP-REAL 2),(TOP-REAL 2),pg) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
[((TOP-REAL 2),(TOP-REAL 2),pg),((TOP-REAL 2),(TOP-REAL 2),pg)] is V15() Element of the carrier of [:(TOP-REAL 2),(TOP-REAL 2):]
{((TOP-REAL 2),(TOP-REAL 2),pg),((TOP-REAL 2),(TOP-REAL 2),pg)} is functional non empty set
{((TOP-REAL 2),(TOP-REAL 2),pg)} is functional non empty set
{{((TOP-REAL 2),(TOP-REAL 2),pg),((TOP-REAL 2),(TOP-REAL 2),pg)},{((TOP-REAL 2),(TOP-REAL 2),pg)}} is non empty set
((TOP-REAL 2),(TOP-REAL 2),pg) `2 is complex ext-real real Element of REAL
ld is complex ext-real real Element of REAL
pd is complex ext-real real Element of REAL
|[ld,pd]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
pd + b is complex ext-real real Element of REAL
((((TOP-REAL 2),(TOP-REAL 2),rl) `2) - b) + b is complex ext-real real Element of REAL
(((TOP-REAL 2),(TOP-REAL 2),rl) `2) - pd is complex ext-real real Element of REAL
(((TOP-REAL 2),(TOP-REAL 2),rl) `2) - ((((TOP-REAL 2),(TOP-REAL 2),rl) `2) + b) is complex ext-real real Element of REAL
(pd + b) - pd is complex ext-real real Element of REAL
- b is complex ext-real real Element of REAL
abs ((((TOP-REAL 2),(TOP-REAL 2),rl) `2) - pd) is complex ext-real real Element of REAL
- ((((TOP-REAL 2),(TOP-REAL 2),rl) `2) - pd) is complex ext-real real Element of REAL
abs (- ((((TOP-REAL 2),(TOP-REAL 2),rl) `2) - pd)) is complex ext-real real Element of REAL
pd - (((TOP-REAL 2),(TOP-REAL 2),rl) `2) is complex ext-real real Element of REAL
abs (pd - (((TOP-REAL 2),(TOP-REAL 2),rl) `2)) is complex ext-real real Element of REAL
].((((TOP-REAL 2),(TOP-REAL 2),rl) `2) - b),((((TOP-REAL 2),(TOP-REAL 2),rl) `2) + b).[ is V166() V167() V168() non left_end non right_end bounded_below bounded_above real-bounded interval Element of bool REAL
rp is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
(rp) is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() Element of bool [: the carrier of [:(TOP-REAL 2),(TOP-REAL 2):],REAL:]
(rp) is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() Element of bool [: the carrier of [:(TOP-REAL 2),(TOP-REAL 2):],REAL:]
rp is non empty ordinal natural complex ext-real positive non negative real V33() V119() V166() V167() V168() V169() V170() V171() left_end bounded_below Element of NAT
TOP-REAL rp is non empty TopSpace-like T_0 T_1 T_2 connected V132() V178() V179() V180() V181() V182() V183() V184() strict add-continuous Mult-continuous pathwise_connected RLTopStruct
the carrier of (TOP-REAL rp) is functional non empty set
rg is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
rl is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
rd is non empty complex ext-real positive non negative real set
Tdisk (rl,rd) is non empty TopSpace-like T_0 T_1 T_2 V270(rp) SubSpace of TOP-REAL rp
the carrier of (Tdisk (rl,rd)) is non empty set
cl_Ball (rl,rd) is functional non empty proper closed connected bounded convex Element of bool the carrier of (TOP-REAL rp)
bool the carrier of (TOP-REAL rp) is non empty set
{rg} is functional non empty proper closed compact bounded Element of bool the carrier of (TOP-REAL rp)
(cl_Ball (rl,rd)) \ {rg} is functional non empty Element of bool the carrier of (TOP-REAL rp)
(TOP-REAL rp) | ((cl_Ball (rl,rd)) \ {rg}) is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL rp
the carrier of ((TOP-REAL rp) | ((cl_Ball (rl,rd)) \ {rg})) is non empty set
Tcircle (rl,rd) is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL rp
the carrier of (Tcircle (rl,rd)) is non empty set
[: the carrier of ((TOP-REAL rp) | ((cl_Ball (rl,rd)) \ {rg})), the carrier of (Tcircle (rl,rd)):] is Relation-like non empty set
bool [: the carrier of ((TOP-REAL rp) | ((cl_Ball (rl,rd)) \ {rg})), the carrier of (Tcircle (rl,rd)):] is non empty set
b is set
c is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
HC (rg,c,rl,rd) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
b is Relation-like the carrier of ((TOP-REAL rp) | ((cl_Ball (rl,rd)) \ {rg})) -defined the carrier of (Tcircle (rl,rd)) -valued Function-like non empty total quasi_total Element of bool [: the carrier of ((TOP-REAL rp) | ((cl_Ball (rl,rd)) \ {rg})), the carrier of (Tcircle (rl,rd)):]
c is Relation-like the carrier of ((TOP-REAL rp) | ((cl_Ball (rl,rd)) \ {rg})) -defined the carrier of (Tcircle (rl,rd)) -valued Function-like non empty total quasi_total Element of bool [: the carrier of ((TOP-REAL rp) | ((cl_Ball (rl,rd)) \ {rg})), the carrier of (Tcircle (rl,rd)):]
d is Element of the carrier of ((TOP-REAL rp) | ((cl_Ball (rl,rd)) \ {rg}))
c . d is Element of the carrier of (Tcircle (rl,rd))
b is Relation-like the carrier of ((TOP-REAL rp) | ((cl_Ball (rl,rd)) \ {rg})) -defined the carrier of (Tcircle (rl,rd)) -valued Function-like non empty total quasi_total Element of bool [: the carrier of ((TOP-REAL rp) | ((cl_Ball (rl,rd)) \ {rg})), the carrier of (Tcircle (rl,rd)):]
c is Relation-like the carrier of ((TOP-REAL rp) | ((cl_Ball (rl,rd)) \ {rg})) -defined the carrier of (Tcircle (rl,rd)) -valued Function-like non empty total quasi_total Element of bool [: the carrier of ((TOP-REAL rp) | ((cl_Ball (rl,rd)) \ {rg})), the carrier of (Tcircle (rl,rd)):]
d is set
b . d is set
c . d is set
lg is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
HC (rg,lg,rl,rd) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
pg is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
HC (rg,pg,rl,rd) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
rl is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
rp is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
{rl} is functional non empty proper closed compact bounded Element of bool the carrier of (TOP-REAL 2)
rg is non empty complex ext-real positive non negative real set
Tdisk (rp,rg) is non empty TopSpace-like T_0 T_1 T_2 V82() normal T_3 T_4 compact closed V246() V270(2) pseudocompact SubSpace of TOP-REAL 2
the carrier of (Tdisk (rp,rg)) is non empty set
cl_Ball (rp,rg) is functional non empty proper closed connected bounded convex Element of bool the carrier of (TOP-REAL 2)
(cl_Ball (rp,rg)) \ {rl} is functional non empty Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | ((cl_Ball (rp,rg)) \ {rl}) is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
Tcircle (rp,rg) is non empty strict TopSpace-like T_0 T_1 T_2 V82() normal T_3 T_4 connected compact V246() being_simple_closed_curve pathwise_connected pseudocompact SubSpace of TOP-REAL 2
(2,rp,rl,rg) is Relation-like the carrier of ((TOP-REAL 2) | ((cl_Ball (rp,rg)) \ {rl})) -defined the carrier of (Tcircle (rp,rg)) -valued Function-like non empty total quasi_total Element of bool [: the carrier of ((TOP-REAL 2) | ((cl_Ball (rp,rg)) \ {rl})), the carrier of (Tcircle (rp,rg)):]
the carrier of ((TOP-REAL 2) | ((cl_Ball (rp,rg)) \ {rl})) is non empty set
the carrier of (Tcircle (rp,rg)) is non empty set
[: the carrier of ((TOP-REAL 2) | ((cl_Ball (rp,rg)) \ {rl})), the carrier of (Tcircle (rp,rg)):] is Relation-like non empty set
bool [: the carrier of ((TOP-REAL 2) | ((cl_Ball (rp,rg)) \ {rl})), the carrier of (Tcircle (rp,rg)):] is non empty set
[:((cl_Ball (rp,rg)) \ {rl}),{rl}:] is Relation-like non empty Element of bool the carrier of [:(TOP-REAL 2),(TOP-REAL 2):]
bool the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] is non empty set
(TOP-REAL 2) | {rl} is non empty strict TopSpace-like T_0 T_1 T_2 V82() normal T_3 T_4 compact V246() pseudocompact SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | {rl}) is non empty set
[:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:] is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of [:(TOP-REAL 2),(TOP-REAL 2):]
(rp) is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of [:(TOP-REAL 2),(TOP-REAL 2):],REAL:]
(rp) is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of [:(TOP-REAL 2),(TOP-REAL 2):],REAL:]
rg ^2 is complex ext-real real set
rg * rg is complex ext-real non negative real set
l is complex ext-real real Element of REAL
the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] --> l is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() Element of bool [: the carrier of [:(TOP-REAL 2),(TOP-REAL 2):],REAL:]
k is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of [:(TOP-REAL 2),(TOP-REAL 2):],REAL:]
k | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:] is Relation-like [:((cl_Ball (rp,rg)) \ {rl}),{rl}:] -defined the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]),REAL:]
the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) is non empty set
[: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]),REAL:] is Relation-like non empty V156() V157() V158() set
bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]),REAL:] is non empty set
() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:] is Relation-like [:((cl_Ball (rp,rg)) \ {rl}),{rl}:] -defined the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]),REAL:]
() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:] is Relation-like [:((cl_Ball (rp,rg)) \ {rl}),{rl}:] -defined the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]),REAL:]
() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:] is Relation-like [:((cl_Ball (rp,rg)) \ {rl}),{rl}:] -defined the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]),REAL:]
() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:] is Relation-like [:((cl_Ball (rp,rg)) \ {rl}),{rl}:] -defined the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]),REAL:]
(rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:] is Relation-like [:((cl_Ball (rp,rg)) \ {rl}),{rl}:] -defined the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]),REAL:]
(rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:] is Relation-like [:((cl_Ball (rp,rg)) \ {rl}),{rl}:] -defined the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]),REAL:]
((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) -defined REAL -valued Function-like non empty total total quasi_total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]),REAL:]
((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) -defined REAL -valued Function-like non empty total total quasi_total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]),REAL:]
(() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) -defined REAL -valued Function-like non empty total total quasi_total quasi_total V156() V157() V158() nonnegative-yielding continuous Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]),REAL:]
(() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) -defined REAL -valued Function-like non empty total total quasi_total quasi_total V156() V157() V158() nonnegative-yielding continuous Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]),REAL:]
((() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + ((() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) -defined REAL -valued Function-like non empty total total quasi_total quasi_total V156() V157() V158() nonnegative-yielding continuous Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]),REAL:]
AR is Element of the carrier of ((TOP-REAL 2) | ((cl_Ball (rp,rg)) \ {rl}))
BR is Element of the carrier of ((TOP-REAL 2) | {rl})
[AR,BR] is V15() Element of the carrier of [:((TOP-REAL 2) | ((cl_Ball (rp,rg)) \ {rl})),((TOP-REAL 2) | {rl}):]
[:((TOP-REAL 2) | ((cl_Ball (rp,rg)) \ {rl})),((TOP-REAL 2) | {rl}):] is non empty strict TopSpace-like T_0 T_1 T_2 TopStruct
the carrier of [:((TOP-REAL 2) | ((cl_Ball (rp,rg)) \ {rl})),((TOP-REAL 2) | {rl}):] is non empty set
{AR,BR} is non empty set
{AR} is non empty set
{{AR,BR},{AR}} is non empty set
(() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) . [AR,BR] is complex ext-real real set
() . [AR,BR] is complex ext-real real set
AR is Element of the carrier of ((TOP-REAL 2) | ((cl_Ball (rp,rg)) \ {rl}))
BR is Element of the carrier of ((TOP-REAL 2) | {rl})
[AR,BR] is V15() Element of the carrier of [:((TOP-REAL 2) | ((cl_Ball (rp,rg)) \ {rl})),((TOP-REAL 2) | {rl}):]
[:((TOP-REAL 2) | ((cl_Ball (rp,rg)) \ {rl})),((TOP-REAL 2) | {rl}):] is non empty strict TopSpace-like T_0 T_1 T_2 TopStruct
the carrier of [:((TOP-REAL 2) | ((cl_Ball (rp,rg)) \ {rl})),((TOP-REAL 2) | {rl}):] is non empty set
{AR,BR} is non empty set
{AR} is non empty set
{{AR,BR},{AR}} is non empty set
(() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) . [AR,BR] is complex ext-real real set
() . [AR,BR] is complex ext-real real set
AR is Element of the carrier of ((TOP-REAL 2) | ((cl_Ball (rp,rg)) \ {rl}))
BR is Element of the carrier of ((TOP-REAL 2) | {rl})
[AR,BR] is V15() Element of the carrier of [:((TOP-REAL 2) | ((cl_Ball (rp,rg)) \ {rl})),((TOP-REAL 2) | {rl}):]
[:((TOP-REAL 2) | ((cl_Ball (rp,rg)) \ {rl})),((TOP-REAL 2) | {rl}):] is non empty strict TopSpace-like T_0 T_1 T_2 TopStruct
the carrier of [:((TOP-REAL 2) | ((cl_Ball (rp,rg)) \ {rl})),((TOP-REAL 2) | {rl}):] is non empty set
{AR,BR} is non empty set
{AR} is non empty set
{{AR,BR},{AR}} is non empty set
(() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) . [AR,BR] is complex ext-real real set
() . [AR,BR] is complex ext-real real set
AR is Element of the carrier of ((TOP-REAL 2) | ((cl_Ball (rp,rg)) \ {rl}))
BR is Element of the carrier of ((TOP-REAL 2) | {rl})
[AR,BR] is V15() Element of the carrier of [:((TOP-REAL 2) | ((cl_Ball (rp,rg)) \ {rl})),((TOP-REAL 2) | {rl}):]
[:((TOP-REAL 2) | ((cl_Ball (rp,rg)) \ {rl})),((TOP-REAL 2) | {rl}):] is non empty strict TopSpace-like T_0 T_1 T_2 TopStruct
the carrier of [:((TOP-REAL 2) | ((cl_Ball (rp,rg)) \ {rl})),((TOP-REAL 2) | {rl}):] is non empty set
{AR,BR} is non empty set
{AR} is non empty set
{{AR,BR},{AR}} is non empty set
(() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) . [AR,BR] is complex ext-real real set
() . [AR,BR] is complex ext-real real set
AR is Element of the carrier of ((TOP-REAL 2) | ((cl_Ball (rp,rg)) \ {rl}))
BR is Element of the carrier of ((TOP-REAL 2) | {rl})
[AR,BR] is V15() Element of the carrier of [:((TOP-REAL 2) | ((cl_Ball (rp,rg)) \ {rl})),((TOP-REAL 2) | {rl}):]
[:((TOP-REAL 2) | ((cl_Ball (rp,rg)) \ {rl})),((TOP-REAL 2) | {rl}):] is non empty strict TopSpace-like T_0 T_1 T_2 TopStruct
the carrier of [:((TOP-REAL 2) | ((cl_Ball (rp,rg)) \ {rl})),((TOP-REAL 2) | {rl}):] is non empty set
{AR,BR} is non empty set
{AR} is non empty set
{{AR,BR},{AR}} is non empty set
(k | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) . [AR,BR] is complex ext-real real set
k . [AR,BR] is complex ext-real real set
AR is Element of the carrier of ((TOP-REAL 2) | ((cl_Ball (rp,rg)) \ {rl}))
BR is Element of the carrier of ((TOP-REAL 2) | {rl})
[AR,BR] is V15() Element of the carrier of [:((TOP-REAL 2) | ((cl_Ball (rp,rg)) \ {rl})),((TOP-REAL 2) | {rl}):]
[:((TOP-REAL 2) | ((cl_Ball (rp,rg)) \ {rl})),((TOP-REAL 2) | {rl}):] is non empty strict TopSpace-like T_0 T_1 T_2 TopStruct
the carrier of [:((TOP-REAL 2) | ((cl_Ball (rp,rg)) \ {rl})),((TOP-REAL 2) | {rl}):] is non empty set
{AR,BR} is non empty set
{AR} is non empty set
{{AR,BR},{AR}} is non empty set
((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) . [AR,BR] is complex ext-real real set
(rp) . [AR,BR] is complex ext-real real set
AR is Element of the carrier of ((TOP-REAL 2) | ((cl_Ball (rp,rg)) \ {rl}))
BR is Element of the carrier of ((TOP-REAL 2) | {rl})
[AR,BR] is V15() Element of the carrier of [:((TOP-REAL 2) | ((cl_Ball (rp,rg)) \ {rl})),((TOP-REAL 2) | {rl}):]
[:((TOP-REAL 2) | ((cl_Ball (rp,rg)) \ {rl})),((TOP-REAL 2) | {rl}):] is non empty strict TopSpace-like T_0 T_1 T_2 TopStruct
the carrier of [:((TOP-REAL 2) | ((cl_Ball (rp,rg)) \ {rl})),((TOP-REAL 2) | {rl}):] is non empty set
{AR,BR} is non empty set
{AR} is non empty set
{{AR,BR},{AR}} is non empty set
((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) . [AR,BR] is complex ext-real real set
(rp) . [AR,BR] is complex ext-real real set
AR is complex ext-real real set
rng (((() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + ((() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]))) is non empty V166() V167() V168() Element of bool REAL
dom (((() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + ((() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]))) is Relation-like (cl_Ball (rp,rg)) \ {rl} -defined {rl} -valued non empty Element of bool [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]
bool [:((cl_Ball (rp,rg)) \ {rl}),{rl}:] is non empty set
BR is set
(((() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + ((() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]))) . BR is complex ext-real real set
CR is set
DR is set
[CR,DR] is V15() set
{CR,DR} is non empty set
{CR} is non empty set
{{CR,DR},{CR}} is non empty set
Pcm is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
fcm is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
[Pcm,fcm] is V15() Element of the carrier of [:(TOP-REAL 2),(TOP-REAL 2):]
{Pcm,fcm} is functional non empty set
{Pcm} is functional non empty set
{{Pcm,fcm},{Pcm}} is non empty set
() . [Pcm,fcm] is complex ext-real real Element of REAL
((TOP-REAL 2),(TOP-REAL 2),[Pcm,fcm]) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
((TOP-REAL 2),(TOP-REAL 2),[Pcm,fcm]) `1 is complex ext-real real Element of REAL
((TOP-REAL 2),(TOP-REAL 2),[Pcm,fcm]) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
((TOP-REAL 2),(TOP-REAL 2),[Pcm,fcm]) `1 is complex ext-real real Element of REAL
(((TOP-REAL 2),(TOP-REAL 2),[Pcm,fcm]) `1) - (((TOP-REAL 2),(TOP-REAL 2),[Pcm,fcm]) `1) is complex ext-real real Element of REAL
() . [Pcm,fcm] is complex ext-real real Element of REAL
((TOP-REAL 2),(TOP-REAL 2),[Pcm,fcm]) `2 is complex ext-real real Element of REAL
((TOP-REAL 2),(TOP-REAL 2),[Pcm,fcm]) `2 is complex ext-real real Element of REAL
(((TOP-REAL 2),(TOP-REAL 2),[Pcm,fcm]) `2) - (((TOP-REAL 2),(TOP-REAL 2),[Pcm,fcm]) `2) is complex ext-real real Element of REAL
Pcm `1 is complex ext-real real Element of REAL
fcm `1 is complex ext-real real Element of REAL
(Pcm `1) - (fcm `1) is complex ext-real real Element of REAL
Pcm `2 is complex ext-real real Element of REAL
fcm `2 is complex ext-real real Element of REAL
(Pcm `2) - (fcm `2) is complex ext-real real Element of REAL
(() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) . [Pcm,fcm] is complex ext-real real set
(() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) . [Pcm,fcm] is complex ext-real real set
(((() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + ((() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]))) . [Pcm,fcm] is complex ext-real real set
((() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) . [Pcm,fcm] is complex ext-real real set
((() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) . [Pcm,fcm] is complex ext-real real set
(((() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) . [Pcm,fcm]) + (((() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) . [Pcm,fcm]) is complex ext-real real set
((() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) . [Pcm,fcm]) * ((() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) . [Pcm,fcm]) is complex ext-real non negative real set
(((() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) . [Pcm,fcm]) * ((() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) . [Pcm,fcm])) + (((() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) . [Pcm,fcm]) is complex ext-real real set
((Pcm `1) - (fcm `1)) ^2 is complex ext-real real Element of REAL
((Pcm `1) - (fcm `1)) * ((Pcm `1) - (fcm `1)) is complex ext-real non negative real set
((Pcm `2) - (fcm `2)) ^2 is complex ext-real real Element of REAL
((Pcm `2) - (fcm `2)) * ((Pcm `2) - (fcm `2)) is complex ext-real non negative real set
(((Pcm `1) - (fcm `1)) ^2) + (((Pcm `2) - (fcm `2)) ^2) is complex ext-real real Element of REAL
(((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) -defined REAL -valued Function-like non empty total total quasi_total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]),REAL:]
((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]))) (#) ((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]))) is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) -defined REAL -valued Function-like non empty total total quasi_total quasi_total V156() V157() V158() nonnegative-yielding continuous Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]),REAL:]
((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) ((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) -defined REAL -valued Function-like non empty total total quasi_total quasi_total V156() V157() V158() nonnegative-yielding continuous Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]),REAL:]
((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) ((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) -defined REAL -valued Function-like non empty total total quasi_total quasi_total V156() V157() V158() nonnegative-yielding continuous Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]),REAL:]
(((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) ((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) ((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) -defined REAL -valued Function-like non empty total total quasi_total quasi_total V156() V157() V158() nonnegative-yielding continuous Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]),REAL:]
((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) ((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) ((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]))) - (k | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) -defined REAL -valued Function-like non empty total total quasi_total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]),REAL:]
dom (((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) ((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) ((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]))) - (k | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) is Relation-like (cl_Ball (rp,rg)) \ {rl} -defined {rl} -valued non empty Element of bool [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]
DR is complex ext-real real set
rng (((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) ((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) ((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]))) - (k | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) is non empty V166() V167() V168() Element of bool REAL
Pcm is set
(((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) ((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) ((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]))) - (k | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) . Pcm is complex ext-real real set
fcm is set
V is set
[fcm,V] is V15() set
{fcm,V} is non empty set
{fcm} is non empty set
{{fcm,V},{fcm}} is non empty set
T2C is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
T2C `1 is complex ext-real real Element of REAL
rp `1 is complex ext-real real Element of REAL
(T2C `1) - (rp `1) is complex ext-real real Element of REAL
T2C `2 is complex ext-real real Element of REAL
rp `2 is complex ext-real real Element of REAL
(T2C `2) - (rp `2) is complex ext-real real Element of REAL
VP is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
[VP,T2C] is V15() Element of the carrier of [:(TOP-REAL 2),(TOP-REAL 2):]
{VP,T2C} is functional non empty set
{VP} is functional non empty set
{{VP,T2C},{VP}} is non empty set
(k | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) . [VP,T2C] is complex ext-real real set
k . [VP,T2C] is complex ext-real real Element of REAL
((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) . [VP,T2C] is complex ext-real real set
(rp) . [VP,T2C] is complex ext-real real Element of REAL
((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) . [VP,T2C] is complex ext-real real set
(rp) . [VP,T2C] is complex ext-real real Element of REAL
((TOP-REAL 2),(TOP-REAL 2),[VP,T2C]) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
((TOP-REAL 2),(TOP-REAL 2),[VP,T2C]) `1 is complex ext-real real Element of REAL
(((TOP-REAL 2),(TOP-REAL 2),[VP,T2C]) `1) - (rp `1) is complex ext-real real Element of REAL
((TOP-REAL 2),(TOP-REAL 2),[VP,T2C]) `2 is complex ext-real real Element of REAL
(((TOP-REAL 2),(TOP-REAL 2),[VP,T2C]) `2) - (rp `2) is complex ext-real real Element of REAL
(((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) ((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) ((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]))) - (k | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) . [VP,T2C] is complex ext-real real set
((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) ((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) ((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]))) . [VP,T2C] is complex ext-real real set
(((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) ((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) ((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]))) . [VP,T2C]) - ((k | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) . [VP,T2C]) is complex ext-real real set
(((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) ((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) ((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]))) . [VP,T2C]) - (rg ^2) is complex ext-real real set
(((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) ((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) . [VP,T2C] is complex ext-real real set
(((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) ((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) . [VP,T2C] is complex ext-real real set
((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) ((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) . [VP,T2C]) + ((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) ((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) . [VP,T2C]) is complex ext-real real set
(((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) ((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) . [VP,T2C]) + ((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) ((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) . [VP,T2C])) - (rg ^2) is complex ext-real real set
(((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) . [VP,T2C]) * (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) . [VP,T2C]) is complex ext-real non negative real set
((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) . [VP,T2C]) * (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) . [VP,T2C])) + ((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) ((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) . [VP,T2C]) is complex ext-real real set
(((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) . [VP,T2C]) * (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) . [VP,T2C])) + ((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) ((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) . [VP,T2C])) - (rg ^2) is complex ext-real real set
((T2C `1) - (rp `1)) ^2 is complex ext-real real Element of REAL
((T2C `1) - (rp `1)) * ((T2C `1) - (rp `1)) is complex ext-real non negative real set
((T2C `2) - (rp `2)) ^2 is complex ext-real real Element of REAL
((T2C `2) - (rp `2)) * ((T2C `2) - (rp `2)) is complex ext-real non negative real set
(((T2C `1) - (rp `1)) ^2) + (((T2C `2) - (rp `2)) ^2) is complex ext-real real Element of REAL
((((T2C `1) - (rp `1)) ^2) + (((T2C `2) - (rp `2)) ^2)) - (rg ^2) is complex ext-real real Element of REAL
T2C - rp is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
- rp is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
K270((TOP-REAL 2),T2C,(- rp)) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) is Relation-like [: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of bool [:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):]
[:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):] is Relation-like non empty set
bool [:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):] is non empty set
K224( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),T2C,(- rp)) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
|.(T2C - rp).| is complex ext-real non negative real Element of REAL
|.(T2C - rp).| ^2 is complex ext-real real Element of REAL
|.(T2C - rp).| * |.(T2C - rp).| is complex ext-real non negative real set
(T2C - rp) `1 is complex ext-real real Element of REAL
((T2C - rp) `1) ^2 is complex ext-real real Element of REAL
((T2C - rp) `1) * ((T2C - rp) `1) is complex ext-real non negative real set
(T2C - rp) `2 is complex ext-real real Element of REAL
((T2C - rp) `2) ^2 is complex ext-real real Element of REAL
((T2C - rp) `2) * ((T2C - rp) `2) is complex ext-real non negative real set
(((T2C - rp) `1) ^2) + (((T2C - rp) `2) ^2) is complex ext-real real Element of REAL
(((T2C `1) - (rp `1)) ^2) + (((T2C - rp) `2) ^2) is complex ext-real real Element of REAL
(rg ^2) - (rg ^2) is complex ext-real real set
AR is Relation-like non-empty the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() positive-yielding nonnegative-yielding continuous Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]),REAL:]
DR is Relation-like the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() nonpositive-yielding continuous Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]),REAL:]
AR (#) DR is Relation-like the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) -defined REAL -valued Function-like non empty total total quasi_total quasi_total V156() V157() V158() nonpositive-yielding continuous Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]),REAL:]
(((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]))) (#) ((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])))) - (AR (#) DR) is Relation-like the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) -defined REAL -valued Function-like non empty total total quasi_total quasi_total V156() V157() V158() nonnegative-yielding continuous Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]),REAL:]
- ((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]))) is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) -defined REAL -valued Function-like non empty total total quasi_total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]),REAL:]
sqrt ((((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]))) (#) ((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])))) - (AR (#) DR)) is Relation-like the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) -defined REAL -valued Function-like non empty total total quasi_total quasi_total V156() V157() V158() nonnegative-yielding continuous Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]),REAL:]
(- ((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])))) + (sqrt ((((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]))) (#) ((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])))) - (AR (#) DR))) is Relation-like the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) -defined REAL -valued Function-like non empty total total quasi_total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]),REAL:]
((- ((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])))) + (sqrt ((((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]))) (#) ((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])))) - (AR (#) DR)))) / AR is Relation-like the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) -defined REAL -valued Function-like non empty total total quasi_total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]),REAL:]
(((- ((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])))) + (sqrt ((((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]))) (#) ((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])))) - (AR (#) DR)))) / AR) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) -defined REAL -valued Function-like non empty total total quasi_total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]),REAL:]
(() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) + ((((- ((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])))) + (sqrt ((((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]))) (#) ((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])))) - (AR (#) DR)))) / AR) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) -defined REAL -valued Function-like non empty total total quasi_total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]),REAL:]
(((- ((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])))) + (sqrt ((((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]))) (#) ((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])))) - (AR (#) DR)))) / AR) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) -defined REAL -valued Function-like non empty total total quasi_total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]),REAL:]
(() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) + ((((- ((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])))) + (sqrt ((((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]))) (#) ((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])))) - (AR (#) DR)))) / AR) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) -defined REAL -valued Function-like non empty total total quasi_total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]),REAL:]
[: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]), the carrier of R^1:] is Relation-like non empty V156() V157() V158() set
bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]), the carrier of R^1:] is non empty set
T2C is Relation-like the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) -defined the carrier of R^1 -valued Function-like non empty total quasi_total V156() V157() V158() Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]), the carrier of R^1:]
VP is Relation-like the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) -defined the carrier of R^1 -valued Function-like non empty total quasi_total V156() V157() V158() Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]), the carrier of R^1:]
<:T2C,VP:> is Relation-like the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) -defined [: the carrier of R^1, the carrier of R^1:] -valued Function-like non empty total quasi_total Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]),[: the carrier of R^1, the carrier of R^1:]:]
[: the carrier of R^1, the carrier of R^1:] is Relation-like non empty V156() V157() V158() set
[: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]),[: the carrier of R^1, the carrier of R^1:]:] is Relation-like non empty set
bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]),[: the carrier of R^1, the carrier of R^1:]:] is non empty set
R2Homeomorphism * <:T2C,VP:> is Relation-like the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) -defined the carrier of (TOP-REAL 2) -valued Function-like Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]), the carrier of (TOP-REAL 2):]
[: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]), the carrier of (TOP-REAL 2):] is Relation-like non empty set
bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]), the carrier of (TOP-REAL 2):] is non empty set
Plk is Element of the carrier of ((TOP-REAL 2) | ((cl_Ball (rp,rg)) \ {rl}))
(2,rp,rl,rg) . Plk is Element of the carrier of (Tcircle (rp,rg))
[Plk,rl] is V15() Element of the carrier of [:((TOP-REAL 2) | ((cl_Ball (rp,rg)) \ {rl})),(TOP-REAL 2):]
[:((TOP-REAL 2) | ((cl_Ball (rp,rg)) \ {rl})),(TOP-REAL 2):] is non empty strict TopSpace-like T_0 T_1 T_2 TopStruct
the carrier of [:((TOP-REAL 2) | ((cl_Ball (rp,rg)) \ {rl})),(TOP-REAL 2):] is non empty set
{Plk,rl} is non empty set
{Plk} is non empty set
{{Plk,rl},{Plk}} is non empty set
(R2Homeomorphism * <:T2C,VP:>) . [Plk,rl] is Relation-like Function-like set
flk is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
HC (rl,flk,rp,rg) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
[flk,rl] is V15() Element of the carrier of [:(TOP-REAL 2),(TOP-REAL 2):]
{flk,rl} is functional non empty set
{flk} is functional non empty set
{{flk,rl},{flk}} is non empty set
flk `1 is complex ext-real real Element of REAL
rl `1 is complex ext-real real Element of REAL
(flk `1) - (rl `1) is complex ext-real real Element of REAL
flk `2 is complex ext-real real Element of REAL
rl `2 is complex ext-real real Element of REAL
(flk `2) - (rl `2) is complex ext-real real Element of REAL
(rl `1) - (rp `1) is complex ext-real real Element of REAL
(rl `2) - (rp `2) is complex ext-real real Element of REAL
((rl `1) - (rp `1)) * ((flk `1) - (rl `1)) is complex ext-real real Element of REAL
((rl `2) - (rp `2)) * ((flk `2) - (rl `2)) is complex ext-real real Element of REAL
(((rl `1) - (rp `1)) * ((flk `1) - (rl `1))) + (((rl `2) - (rp `2)) * ((flk `2) - (rl `2))) is complex ext-real real Element of REAL
- ((((rl `1) - (rp `1)) * ((flk `1) - (rl `1))) + (((rl `2) - (rp `2)) * ((flk `2) - (rl `2)))) is complex ext-real real Element of REAL
((((rl `1) - (rp `1)) * ((flk `1) - (rl `1))) + (((rl `2) - (rp `2)) * ((flk `2) - (rl `2)))) ^2 is complex ext-real real Element of REAL
((((rl `1) - (rp `1)) * ((flk `1) - (rl `1))) + (((rl `2) - (rp `2)) * ((flk `2) - (rl `2)))) * ((((rl `1) - (rp `1)) * ((flk `1) - (rl `1))) + (((rl `2) - (rp `2)) * ((flk `2) - (rl `2)))) is complex ext-real non negative real set
((flk `1) - (rl `1)) ^2 is complex ext-real real Element of REAL
((flk `1) - (rl `1)) * ((flk `1) - (rl `1)) is complex ext-real non negative real set
((flk `2) - (rl `2)) ^2 is complex ext-real real Element of REAL
((flk `2) - (rl `2)) * ((flk `2) - (rl `2)) is complex ext-real non negative real set
(((flk `1) - (rl `1)) ^2) + (((flk `2) - (rl `2)) ^2) is complex ext-real real Element of REAL
((rl `1) - (rp `1)) ^2 is complex ext-real real Element of REAL
((rl `1) - (rp `1)) * ((rl `1) - (rp `1)) is complex ext-real non negative real set
((rl `2) - (rp `2)) ^2 is complex ext-real real Element of REAL
((rl `2) - (rp `2)) * ((rl `2) - (rp `2)) is complex ext-real non negative real set
(((rl `1) - (rp `1)) ^2) + (((rl `2) - (rp `2)) ^2) is complex ext-real real Element of REAL
((((rl `1) - (rp `1)) ^2) + (((rl `2) - (rp `2)) ^2)) - (rg ^2) is complex ext-real real Element of REAL
((((flk `1) - (rl `1)) ^2) + (((flk `2) - (rl `2)) ^2)) * (((((rl `1) - (rp `1)) ^2) + (((rl `2) - (rp `2)) ^2)) - (rg ^2)) is complex ext-real real Element of REAL
(((((rl `1) - (rp `1)) * ((flk `1) - (rl `1))) + (((rl `2) - (rp `2)) * ((flk `2) - (rl `2)))) ^2) - (((((flk `1) - (rl `1)) ^2) + (((flk `2) - (rl `2)) ^2)) * (((((rl `1) - (rp `1)) ^2) + (((rl `2) - (rp `2)) ^2)) - (rg ^2))) is complex ext-real real Element of REAL
sqrt ((((((rl `1) - (rp `1)) * ((flk `1) - (rl `1))) + (((rl `2) - (rp `2)) * ((flk `2) - (rl `2)))) ^2) - (((((flk `1) - (rl `1)) ^2) + (((flk `2) - (rl `2)) ^2)) * (((((rl `1) - (rp `1)) ^2) + (((rl `2) - (rp `2)) ^2)) - (rg ^2)))) is complex ext-real real Element of REAL
(- ((((rl `1) - (rp `1)) * ((flk `1) - (rl `1))) + (((rl `2) - (rp `2)) * ((flk `2) - (rl `2))))) + (sqrt ((((((rl `1) - (rp `1)) * ((flk `1) - (rl `1))) + (((rl `2) - (rp `2)) * ((flk `2) - (rl `2)))) ^2) - (((((flk `1) - (rl `1)) ^2) + (((flk `2) - (rl `2)) ^2)) * (((((rl `1) - (rp `1)) ^2) + (((rl `2) - (rp `2)) ^2)) - (rg ^2))))) is complex ext-real real Element of REAL
((- ((((rl `1) - (rp `1)) * ((flk `1) - (rl `1))) + (((rl `2) - (rp `2)) * ((flk `2) - (rl `2))))) + (sqrt ((((((rl `1) - (rp `1)) * ((flk `1) - (rl `1))) + (((rl `2) - (rp `2)) * ((flk `2) - (rl `2)))) ^2) - (((((flk `1) - (rl `1)) ^2) + (((flk `2) - (rl `2)) ^2)) * (((((rl `1) - (rp `1)) ^2) + (((rl `2) - (rp `2)) ^2)) - (rg ^2)))))) / ((((flk `1) - (rl `1)) ^2) + (((flk `2) - (rl `2)) ^2)) is complex ext-real real Element of REAL
() . [flk,rl] is complex ext-real real Element of REAL
((TOP-REAL 2),(TOP-REAL 2),[flk,rl]) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
((TOP-REAL 2),(TOP-REAL 2),[flk,rl]) `1 is complex ext-real real Element of REAL
() . [flk,rl] is complex ext-real real Element of REAL
((TOP-REAL 2),(TOP-REAL 2),[flk,rl]) `2 is complex ext-real real Element of REAL
() . [flk,rl] is complex ext-real real Element of REAL
((TOP-REAL 2),(TOP-REAL 2),[flk,rl]) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
((TOP-REAL 2),(TOP-REAL 2),[flk,rl]) `1 is complex ext-real real Element of REAL
(((TOP-REAL 2),(TOP-REAL 2),[flk,rl]) `1) - (((TOP-REAL 2),(TOP-REAL 2),[flk,rl]) `1) is complex ext-real real Element of REAL
() . [flk,rl] is complex ext-real real Element of REAL
((TOP-REAL 2),(TOP-REAL 2),[flk,rl]) `2 is complex ext-real real Element of REAL
(((TOP-REAL 2),(TOP-REAL 2),[flk,rl]) `2) - (((TOP-REAL 2),(TOP-REAL 2),[flk,rl]) `2) is complex ext-real real Element of REAL
(rp) . [flk,rl] is complex ext-real real Element of REAL
(((TOP-REAL 2),(TOP-REAL 2),[flk,rl]) `1) - (rp `1) is complex ext-real real Element of REAL
(rp) . [flk,rl] is complex ext-real real Element of REAL
(((TOP-REAL 2),(TOP-REAL 2),[flk,rl]) `2) - (rp `2) is complex ext-real real Element of REAL
dom T2C is non empty Element of bool the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])
bool the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) is non empty set
dom VP is non empty Element of bool the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])
dom ((((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]))) (#) ((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])))) - (AR (#) DR)) is non empty Element of bool the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])
(() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) . [flk,rl] is complex ext-real real set
(() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) . [flk,rl] is complex ext-real real set
(k | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) . [flk,rl] is complex ext-real real set
k . [flk,rl] is complex ext-real real Element of REAL
((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) . [flk,rl] is complex ext-real real set
((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) . [flk,rl] is complex ext-real real set
AR . [flk,rl] is complex ext-real real set
((() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) . [flk,rl] is complex ext-real real set
((() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) . [flk,rl] is complex ext-real real set
(((() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) . [flk,rl]) + (((() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) . [flk,rl]) is complex ext-real real set
((() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) . [flk,rl]) * ((() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) . [flk,rl]) is complex ext-real non negative real set
(((() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) . [flk,rl]) * ((() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) . [flk,rl])) + (((() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) . [flk,rl]) is complex ext-real real set
(((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) . [flk,rl] is complex ext-real real set
(((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) . [flk,rl]) * ((() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) . [flk,rl]) is complex ext-real real set
(((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) . [flk,rl] is complex ext-real real set
(((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) . [flk,rl]) * ((() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) . [flk,rl]) is complex ext-real real set
((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]))) . [flk,rl] is complex ext-real real set
((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) . [flk,rl]) + ((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) . [flk,rl]) is complex ext-real real set
(((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]))) (#) ((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])))) . [flk,rl] is complex ext-real real set
DR . [flk,rl] is complex ext-real real set
((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) ((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) ((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]))) . [flk,rl] is complex ext-real real set
(((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) ((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) ((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]))) . [flk,rl]) - ((k | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) . [flk,rl]) is complex ext-real real set
(((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) ((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) ((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]))) . [flk,rl]) - (rg ^2) is complex ext-real real set
(((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) ((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) . [flk,rl] is complex ext-real real set
(((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) ((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) . [flk,rl] is complex ext-real real set
((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) ((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) . [flk,rl]) + ((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) ((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) . [flk,rl]) is complex ext-real real set
(((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) ((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) . [flk,rl]) + ((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) ((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) . [flk,rl])) - (rg ^2) is complex ext-real real set
(((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) . [flk,rl]) * (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) . [flk,rl]) is complex ext-real non negative real set
((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) . [flk,rl]) * (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) . [flk,rl])) + ((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) ((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) . [flk,rl]) is complex ext-real real set
(((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) . [flk,rl]) * (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) . [flk,rl])) + ((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) ((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) . [flk,rl])) - (rg ^2) is complex ext-real real set
dom (sqrt ((((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]))) (#) ((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])))) - (AR (#) DR))) is non empty Element of bool the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])
(sqrt ((((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]))) (#) ((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])))) - (AR (#) DR))) . [flk,rl] is complex ext-real real set
((((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]))) (#) ((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])))) - (AR (#) DR)) . [flk,rl] is complex ext-real real set
sqrt (((((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]))) (#) ((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])))) - (AR (#) DR)) . [flk,rl]) is complex ext-real real set
(AR (#) DR) . [flk,rl] is complex ext-real real set
((((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]))) (#) ((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])))) . [flk,rl]) - ((AR (#) DR) . [flk,rl]) is complex ext-real real set
sqrt (((((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]))) (#) ((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])))) . [flk,rl]) - ((AR (#) DR) . [flk,rl])) is complex ext-real real set
dom (((- ((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])))) + (sqrt ((((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]))) (#) ((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])))) - (AR (#) DR)))) / AR) is non empty Element of bool the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])
(((- ((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])))) + (sqrt ((((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]))) (#) ((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])))) - (AR (#) DR)))) / AR) . [flk,rl] is complex ext-real real set
((- ((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])))) + (sqrt ((((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]))) (#) ((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])))) - (AR (#) DR)))) . [flk,rl] is complex ext-real real set
(AR . [flk,rl]) " is complex ext-real real set
(((- ((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])))) + (sqrt ((((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]))) (#) ((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])))) - (AR (#) DR)))) . [flk,rl]) * ((AR . [flk,rl]) ") is complex ext-real real set
(((- ((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])))) + (sqrt ((((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]))) (#) ((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])))) - (AR (#) DR)))) . [flk,rl]) / (AR . [flk,rl]) is complex ext-real real Element of COMPLEX
(- ((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])))) . [flk,rl] is complex ext-real real set
((- ((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])))) . [flk,rl]) + ((sqrt ((((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]))) (#) ((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])))) - (AR (#) DR))) . [flk,rl]) is complex ext-real real set
(((- ((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])))) . [flk,rl]) + ((sqrt ((((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]))) (#) ((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])))) - (AR (#) DR))) . [flk,rl])) / ((((flk `1) - (rl `1)) ^2) + (((flk `2) - (rl `2)) ^2)) is complex ext-real real Element of REAL
T2C . [flk,rl] is complex ext-real real set
(() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) . [flk,rl] is complex ext-real real set
((((- ((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])))) + (sqrt ((((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]))) (#) ((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])))) - (AR (#) DR)))) / AR) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) . [flk,rl] is complex ext-real real set
((() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) . [flk,rl]) + (((((- ((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])))) + (sqrt ((((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]))) (#) ((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])))) - (AR (#) DR)))) / AR) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) . [flk,rl]) is complex ext-real real set
(rl `1) + (((((- ((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])))) + (sqrt ((((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]))) (#) ((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])))) - (AR (#) DR)))) / AR) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) . [flk,rl]) is complex ext-real real Element of REAL
(((- ((((rl `1) - (rp `1)) * ((flk `1) - (rl `1))) + (((rl `2) - (rp `2)) * ((flk `2) - (rl `2))))) + (sqrt ((((((rl `1) - (rp `1)) * ((flk `1) - (rl `1))) + (((rl `2) - (rp `2)) * ((flk `2) - (rl `2)))) ^2) - (((((flk `1) - (rl `1)) ^2) + (((flk `2) - (rl `2)) ^2)) * (((((rl `1) - (rp `1)) ^2) + (((rl `2) - (rp `2)) ^2)) - (rg ^2)))))) / ((((flk `1) - (rl `1)) ^2) + (((flk `2) - (rl `2)) ^2))) * ((flk `1) - (rl `1)) is complex ext-real real Element of REAL
(rl `1) + ((((- ((((rl `1) - (rp `1)) * ((flk `1) - (rl `1))) + (((rl `2) - (rp `2)) * ((flk `2) - (rl `2))))) + (sqrt ((((((rl `1) - (rp `1)) * ((flk `1) - (rl `1))) + (((rl `2) - (rp `2)) * ((flk `2) - (rl `2)))) ^2) - (((((flk `1) - (rl `1)) ^2) + (((flk `2) - (rl `2)) ^2)) * (((((rl `1) - (rp `1)) ^2) + (((rl `2) - (rp `2)) ^2)) - (rg ^2)))))) / ((((flk `1) - (rl `1)) ^2) + (((flk `2) - (rl `2)) ^2))) * ((flk `1) - (rl `1))) is complex ext-real real Element of REAL
VP . [flk,rl] is complex ext-real real set
(() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) . [flk,rl] is complex ext-real real set
((((- ((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])))) + (sqrt ((((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]))) (#) ((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])))) - (AR (#) DR)))) / AR) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) . [flk,rl] is complex ext-real real set
((() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) . [flk,rl]) + (((((- ((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])))) + (sqrt ((((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]))) (#) ((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])))) - (AR (#) DR)))) / AR) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) . [flk,rl]) is complex ext-real real set
(rl `2) + (((((- ((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])))) + (sqrt ((((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]))) (#) ((((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) + (((rp) | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])))) - (AR (#) DR)))) / AR) (#) (() | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) . [flk,rl]) is complex ext-real real Element of REAL
(((- ((((rl `1) - (rp `1)) * ((flk `1) - (rl `1))) + (((rl `2) - (rp `2)) * ((flk `2) - (rl `2))))) + (sqrt ((((((rl `1) - (rp `1)) * ((flk `1) - (rl `1))) + (((rl `2) - (rp `2)) * ((flk `2) - (rl `2)))) ^2) - (((((flk `1) - (rl `1)) ^2) + (((flk `2) - (rl `2)) ^2)) * (((((rl `1) - (rp `1)) ^2) + (((rl `2) - (rp `2)) ^2)) - (rg ^2)))))) / ((((flk `1) - (rl `1)) ^2) + (((flk `2) - (rl `2)) ^2))) * ((flk `2) - (rl `2)) is complex ext-real real Element of REAL
(rl `2) + ((((- ((((rl `1) - (rp `1)) * ((flk `1) - (rl `1))) + (((rl `2) - (rp `2)) * ((flk `2) - (rl `2))))) + (sqrt ((((((rl `1) - (rp `1)) * ((flk `1) - (rl `1))) + (((rl `2) - (rp `2)) * ((flk `2) - (rl `2)))) ^2) - (((((flk `1) - (rl `1)) ^2) + (((flk `2) - (rl `2)) ^2)) * (((((rl `1) - (rp `1)) ^2) + (((rl `2) - (rp `2)) ^2)) - (rg ^2)))))) / ((((flk `1) - (rl `1)) ^2) + (((flk `2) - (rl `2)) ^2))) * ((flk `2) - (rl `2))) is complex ext-real real Element of REAL
|[((rl `1) + ((((- ((((rl `1) - (rp `1)) * ((flk `1) - (rl `1))) + (((rl `2) - (rp `2)) * ((flk `2) - (rl `2))))) + (sqrt ((((((rl `1) - (rp `1)) * ((flk `1) - (rl `1))) + (((rl `2) - (rp `2)) * ((flk `2) - (rl `2)))) ^2) - (((((flk `1) - (rl `1)) ^2) + (((flk `2) - (rl `2)) ^2)) * (((((rl `1) - (rp `1)) ^2) + (((rl `2) - (rp `2)) ^2)) - (rg ^2)))))) / ((((flk `1) - (rl `1)) ^2) + (((flk `2) - (rl `2)) ^2))) * ((flk `1) - (rl `1)))),((rl `2) + ((((- ((((rl `1) - (rp `1)) * ((flk `1) - (rl `1))) + (((rl `2) - (rp `2)) * ((flk `2) - (rl `2))))) + (sqrt ((((((rl `1) - (rp `1)) * ((flk `1) - (rl `1))) + (((rl `2) - (rp `2)) * ((flk `2) - (rl `2)))) ^2) - (((((flk `1) - (rl `1)) ^2) + (((flk `2) - (rl `2)) ^2)) * (((((rl `1) - (rp `1)) ^2) + (((rl `2) - (rp `2)) ^2)) - (rg ^2)))))) / ((((flk `1) - (rl `1)) ^2) + (((flk `2) - (rl `2)) ^2))) * ((flk `2) - (rl `2))))]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
[(T2C . [flk,rl]),(VP . [flk,rl])] is V15() set
{(T2C . [flk,rl]),(VP . [flk,rl])} is non empty V166() V167() V168() set
{(T2C . [flk,rl])} is non empty V166() V167() V168() set
{{(T2C . [flk,rl]),(VP . [flk,rl])},{(T2C . [flk,rl])}} is non empty set
R2Homeomorphism . [(T2C . [flk,rl]),(VP . [flk,rl])] is Relation-like Function-like set
<:T2C,VP:> . [flk,rl] is set
R2Homeomorphism . (<:T2C,VP:> . [flk,rl]) is Relation-like Function-like set
[: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]), the carrier of [:R^1,R^1:]:] is Relation-like non empty set
bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]), the carrier of [:R^1,R^1:]:] is non empty set
bool the carrier of (Tcircle (rp,rg)) is non empty set
bool the carrier of ((TOP-REAL 2) | ((cl_Ball (rp,rg)) \ {rl})) is non empty set
flk is Element of the carrier of ((TOP-REAL 2) | ((cl_Ball (rp,rg)) \ {rl}))
(2,rp,rl,rg) . flk is Element of the carrier of (Tcircle (rp,rg))
beta is Element of bool the carrier of (Tcircle (rp,rg))
[flk,rl] is V15() Element of the carrier of [:((TOP-REAL 2) | ((cl_Ball (rp,rg)) \ {rl})),(TOP-REAL 2):]
[:((TOP-REAL 2) | ((cl_Ball (rp,rg)) \ {rl})),(TOP-REAL 2):] is non empty strict TopSpace-like T_0 T_1 T_2 TopStruct
the carrier of [:((TOP-REAL 2) | ((cl_Ball (rp,rg)) \ {rl})),(TOP-REAL 2):] is non empty set
{flk,rl} is non empty set
{flk} is non empty set
{{flk,rl},{flk}} is non empty set
[#] (Tcircle (rp,rg)) is non empty non proper open closed dense non boundary compact Element of bool the carrier of (Tcircle (rp,rg))
A is functional Element of bool the carrier of (TOP-REAL 2)
A /\ ([#] (Tcircle (rp,rg))) is Element of bool the carrier of (Tcircle (rp,rg))
Plk is Relation-like the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) -defined the carrier of [:R^1,R^1:] -valued Function-like non empty total quasi_total continuous Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]), the carrier of [:R^1,R^1:]:]
R2Homeomorphism * Plk is Relation-like the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]), the carrier of (TOP-REAL 2):]
(R2Homeomorphism * Plk) . [flk,rl] is Relation-like Function-like set
R2Homeomorphism /" is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of [:R^1,R^1:] -valued Function-like non empty total quasi_total Element of bool [: the carrier of (TOP-REAL 2), the carrier of [:R^1,R^1:]:]
[: the carrier of (TOP-REAL 2), the carrier of [:R^1,R^1:]:] is Relation-like non empty set
bool [: the carrier of (TOP-REAL 2), the carrier of [:R^1,R^1:]:] is non empty set
(R2Homeomorphism /") .: A is Element of bool the carrier of [:R^1,R^1:]
bool the carrier of [:R^1,R^1:] is non empty set
dom Plk is non empty Element of bool the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])
bool the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) is non empty set
dom R2Homeomorphism is non empty Element of bool the carrier of [:R^1,R^1:]
rng Plk is non empty Element of bool the carrier of [:R^1,R^1:]
dom (R2Homeomorphism * Plk) is non empty Element of bool the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])
rng R2Homeomorphism is functional non empty Element of bool the carrier of (TOP-REAL 2)
[#] (TOP-REAL 2) is functional non empty non proper non proper open open closed closed dense dense non boundary non boundary connected a_component being_Region convex Element of bool the carrier of (TOP-REAL 2)
(R2Homeomorphism /") * (R2Homeomorphism * Plk) is Relation-like the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) -defined the carrier of [:R^1,R^1:] -valued Function-like non empty total quasi_total Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]), the carrier of [:R^1,R^1:]:]
(R2Homeomorphism /") * R2Homeomorphism is Relation-like the carrier of [:R^1,R^1:] -defined the carrier of [:R^1,R^1:] -valued Function-like non empty total quasi_total Element of bool [: the carrier of [:R^1,R^1:], the carrier of [:R^1,R^1:]:]
[: the carrier of [:R^1,R^1:], the carrier of [:R^1,R^1:]:] is Relation-like non empty set
bool [: the carrier of [:R^1,R^1:], the carrier of [:R^1,R^1:]:] is non empty set
((R2Homeomorphism /") * R2Homeomorphism) * Plk is Relation-like the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) -defined the carrier of [:R^1,R^1:] -valued Function-like non empty total quasi_total Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]), the carrier of [:R^1,R^1:]:]
id (dom R2Homeomorphism) is Relation-like dom R2Homeomorphism -defined dom R2Homeomorphism -valued Function-like one-to-one non empty total quasi_total Element of bool [:(dom R2Homeomorphism),(dom R2Homeomorphism):]
[:(dom R2Homeomorphism),(dom R2Homeomorphism):] is Relation-like non empty set
bool [:(dom R2Homeomorphism),(dom R2Homeomorphism):] is non empty set
(id (dom R2Homeomorphism)) * Plk is Relation-like the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) -defined dom R2Homeomorphism -valued Function-like Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]),(dom R2Homeomorphism):]
[: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]),(dom R2Homeomorphism):] is Relation-like non empty set
bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]),(dom R2Homeomorphism):] is non empty set
dom (id (dom R2Homeomorphism)) is non empty Element of bool (dom R2Homeomorphism)
bool (dom R2Homeomorphism) is non empty set
dom ((id (dom R2Homeomorphism)) * Plk) is Element of bool the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])
B is set
((id (dom R2Homeomorphism)) * Plk) . B is set
Plk . B is set
(id (dom R2Homeomorphism)) . (Plk . B) is set
ra is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
rb is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
[ra,rb] is V15() Element of the carrier of [:(TOP-REAL 2),(TOP-REAL 2):]
{ra,rb} is functional non empty set
{ra} is functional non empty set
{{ra,rb},{ra}} is non empty set
(R2Homeomorphism * Plk) . [ra,rb] is Relation-like Function-like set
(R2Homeomorphism /") . ((R2Homeomorphism * Plk) . [ra,rb]) is set
((R2Homeomorphism /") * (R2Homeomorphism * Plk)) . [ra,rb] is set
B is Element of bool the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])
Plk .: B is Element of bool the carrier of [:R^1,R^1:]
[#] ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]) is non empty non proper open closed dense non boundary Element of bool the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])
t is Element of bool the carrier of [:(TOP-REAL 2),(TOP-REAL 2):]
t /\ ([#] ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) is Element of bool the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])
bool (bool the carrier of [:(TOP-REAL 2),(TOP-REAL 2):]) is non empty set
u is Element of bool (bool the carrier of [:(TOP-REAL 2),(TOP-REAL 2):])
union u is set
v is set
u is functional Element of bool the carrier of (TOP-REAL 2)
v is functional Element of bool the carrier of (TOP-REAL 2)
[:u,v:] is Relation-like Element of bool the carrier of [:(TOP-REAL 2),(TOP-REAL 2):]
v /\ ([#] ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])) is Element of bool the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:])
[#] ((TOP-REAL 2) | ((cl_Ball (rp,rg)) \ {rl})) is non empty non proper open closed dense non boundary Element of bool the carrier of ((TOP-REAL 2) | ((cl_Ball (rp,rg)) \ {rl}))
u /\ ([#] ((TOP-REAL 2) | ((cl_Ball (rp,rg)) \ {rl}))) is Element of bool the carrier of ((TOP-REAL 2) | ((cl_Ball (rp,rg)) \ {rl}))
v1 is open Element of bool the carrier of ((TOP-REAL 2) | ((cl_Ball (rp,rg)) \ {rl}))
(2,rp,rl,rg) .: v1 is Element of bool the carrier of (Tcircle (rp,rg))
fuv is set
uv is Element of the carrier of ((TOP-REAL 2) | ((cl_Ball (rp,rg)) \ {rl}))
(2,rp,rl,rg) . uv is Element of the carrier of (Tcircle (rp,rg))
[uv,rl] is V15() Element of the carrier of [:((TOP-REAL 2) | ((cl_Ball (rp,rg)) \ {rl})),(TOP-REAL 2):]
{uv,rl} is non empty set
{uv} is non empty set
{{uv,rl},{uv}} is non empty set
fau is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
[uv,fau] is V15() Element of the carrier of [:((TOP-REAL 2) | ((cl_Ball (rp,rg)) \ {rl})),(TOP-REAL 2):]
{uv,fau} is non empty set
{{uv,fau},{uv}} is non empty set
au is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
[au,fau] is V15() Element of the carrier of [:(TOP-REAL 2),(TOP-REAL 2):]
{au,fau} is functional non empty set
{au} is functional non empty set
{{au,fau},{au}} is non empty set
Plk . [au,fau] is set
Plk .: (v /\ ([#] ([:(TOP-REAL 2),(TOP-REAL 2):] | [:((cl_Ball (rp,rg)) \ {rl}),{rl}:]))) is Element of bool the carrier of [:R^1,R^1:]
R2Homeomorphism " is Relation-like Function-like set
dom (R2Homeomorphism /") is functional non empty Element of bool the carrier of (TOP-REAL 2)
R2Homeomorphism . (Plk . [au,fau]) is Relation-like Function-like set
R2Homeomorphism .: ((R2Homeomorphism /") .: A) is functional Element of bool the carrier of (TOP-REAL 2)
(R2Homeomorphism * Plk) . [au,fau] is Relation-like Function-like set
rp is non empty ordinal natural complex ext-real positive non negative real V33() V119() V166() V167() V168() V169() V170() V171() left_end bounded_below Element of NAT
TOP-REAL rp is non empty TopSpace-like T_0 T_1 T_2 connected V132() V178() V179() V180() V181() V182() V183() V184() strict add-continuous Mult-continuous pathwise_connected RLTopStruct
the carrier of (TOP-REAL rp) is functional non empty set
rg is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
rl is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
{rg} is functional non empty proper closed compact bounded Element of bool the carrier of (TOP-REAL rp)
bool the carrier of (TOP-REAL rp) is non empty set
rd is non empty complex ext-real positive non negative real set
Ball (rl,rd) is functional non empty proper open connected bounded convex Element of bool the carrier of (TOP-REAL rp)
cl_Ball (rl,rd) is functional non empty proper closed connected bounded convex Element of bool the carrier of (TOP-REAL rp)
(cl_Ball (rl,rd)) \ {rg} is functional non empty Element of bool the carrier of (TOP-REAL rp)
(TOP-REAL rp) | ((cl_Ball (rl,rd)) \ {rg}) is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL rp
the carrier of ((TOP-REAL rp) | ((cl_Ball (rl,rd)) \ {rg})) is non empty set
Tcircle (rl,rd) is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL rp
the carrier of (Tcircle (rl,rd)) is non empty set
(rp,rl,rg,rd) is Relation-like the carrier of ((TOP-REAL rp) | ((cl_Ball (rl,rd)) \ {rg})) -defined the carrier of (Tcircle (rl,rd)) -valued Function-like non empty total quasi_total Element of bool [: the carrier of ((TOP-REAL rp) | ((cl_Ball (rl,rd)) \ {rg})), the carrier of (Tcircle (rl,rd)):]
[: the carrier of ((TOP-REAL rp) | ((cl_Ball (rl,rd)) \ {rg})), the carrier of (Tcircle (rl,rd)):] is Relation-like non empty set
bool [: the carrier of ((TOP-REAL rp) | ((cl_Ball (rl,rd)) \ {rg})), the carrier of (Tcircle (rl,rd)):] is non empty set
Sphere (rl,rd) is functional non empty proper closed bounded Element of bool the carrier of (TOP-REAL rp)
(rp,rl,rg,rd) | (Sphere (rl,rd)) is Relation-like the carrier of ((TOP-REAL rp) | ((cl_Ball (rl,rd)) \ {rg})) -defined Sphere (rl,rd) -defined the carrier of ((TOP-REAL rp) | ((cl_Ball (rl,rd)) \ {rg})) -defined the carrier of (Tcircle (rl,rd)) -valued Function-like Element of bool [: the carrier of ((TOP-REAL rp) | ((cl_Ball (rl,rd)) \ {rg})), the carrier of (Tcircle (rl,rd)):]
id (Sphere (rl,rd)) is Relation-like Sphere (rl,rd) -defined Sphere (rl,rd) -valued Function-like one-to-one non empty total quasi_total Element of bool [:(Sphere (rl,rd)),(Sphere (rl,rd)):]
[:(Sphere (rl,rd)),(Sphere (rl,rd)):] is Relation-like non empty set
bool [:(Sphere (rl,rd)),(Sphere (rl,rd)):] is non empty set
Tdisk (rl,rd) is non empty TopSpace-like T_0 T_1 T_2 V270(rp) SubSpace of TOP-REAL rp
the carrier of (Tdisk (rl,rd)) is non empty set
dom (rp,rl,rg,rd) is non empty Element of bool the carrier of ((TOP-REAL rp) | ((cl_Ball (rl,rd)) \ {rg}))
bool the carrier of ((TOP-REAL rp) | ((cl_Ball (rl,rd)) \ {rg})) is non empty set
a is set
dom ((rp,rl,rg,rd) | (Sphere (rl,rd))) is functional Element of bool (Sphere (rl,rd))
bool (Sphere (rl,rd)) is non empty set
dom (id (Sphere (rl,rd))) is functional non empty Element of bool (Sphere (rl,rd))
a is set
(rp,rl,rg,rd) . a is set
b is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
HC (rg,b,rl,rd) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
halfline (rg,b) is functional non empty connected convex Element of bool the carrier of (TOP-REAL rp)
(halfline (rg,b)) /\ (Sphere (rl,rd)) is functional Element of bool the carrier of (TOP-REAL rp)
((rp,rl,rg,rd) | (Sphere (rl,rd))) . a is set
(id (Sphere (rl,rd))) . a is Relation-like Function-like set
rp is non empty ordinal natural complex ext-real positive non negative real V33() V119() V166() V167() V168() V169() V170() V171() left_end bounded_below Element of NAT
TOP-REAL rp is non empty TopSpace-like T_0 T_1 T_2 connected V132() V178() V179() V180() V181() V182() V183() V184() strict add-continuous Mult-continuous pathwise_connected RLTopStruct
the carrier of (TOP-REAL rp) is functional non empty set
rg is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
rl is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
rd is non empty complex ext-real positive non negative real set
Ball (rl,rd) is functional non empty proper open connected bounded convex Element of bool the carrier of (TOP-REAL rp)
bool the carrier of (TOP-REAL rp) is non empty set
Tcircle (rl,rd) is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL rp
the carrier of (Tcircle (rl,rd)) is non empty set
[: the carrier of (Tcircle (rl,rd)), the carrier of (Tcircle (rl,rd)):] is Relation-like non empty set
bool [: the carrier of (Tcircle (rl,rd)), the carrier of (Tcircle (rl,rd)):] is non empty set
Sphere (rl,rd) is functional non empty proper closed bounded Element of bool the carrier of (TOP-REAL rp)
b is set
cl_Ball (rl,rd) is functional non empty proper closed connected bounded convex Element of bool the carrier of (TOP-REAL rp)
c is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
Tdisk (rl,rd) is non empty TopSpace-like T_0 T_1 T_2 V270(rp) SubSpace of TOP-REAL rp
the carrier of (Tdisk (rl,rd)) is non empty set
HC (c,rg,rl,rd) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
b is Relation-like the carrier of (Tcircle (rl,rd)) -defined the carrier of (Tcircle (rl,rd)) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (Tcircle (rl,rd)), the carrier of (Tcircle (rl,rd)):]
c is Relation-like the carrier of (Tcircle (rl,rd)) -defined the carrier of (Tcircle (rl,rd)) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (Tcircle (rl,rd)), the carrier of (Tcircle (rl,rd)):]
d is Element of the carrier of (Tcircle (rl,rd))
c . d is Element of the carrier of (Tcircle (rl,rd))
b is Relation-like the carrier of (Tcircle (rl,rd)) -defined the carrier of (Tcircle (rl,rd)) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (Tcircle (rl,rd)), the carrier of (Tcircle (rl,rd)):]
c is Relation-like the carrier of (Tcircle (rl,rd)) -defined the carrier of (Tcircle (rl,rd)) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (Tcircle (rl,rd)), the carrier of (Tcircle (rl,rd)):]
d is set
b . d is set
c . d is set
lg is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
HC (lg,rg,rl,rd) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
pg is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
HC (pg,rg,rl,rd) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
rl is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
rp is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
rg is non empty complex ext-real positive non negative real set
Ball (rp,rg) is functional non empty proper open connected bounded being_Region convex Element of bool the carrier of (TOP-REAL 2)
Tcircle (rp,rg) is non empty strict TopSpace-like T_0 T_1 T_2 V82() normal T_3 T_4 connected compact V246() being_simple_closed_curve pathwise_connected pseudocompact SubSpace of TOP-REAL 2
(2,rp,rl,rg) is Relation-like the carrier of (Tcircle (rp,rg)) -defined the carrier of (Tcircle (rp,rg)) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (Tcircle (rp,rg)), the carrier of (Tcircle (rp,rg)):]
the carrier of (Tcircle (rp,rg)) is non empty set
[: the carrier of (Tcircle (rp,rg)), the carrier of (Tcircle (rp,rg)):] is Relation-like non empty set
bool [: the carrier of (Tcircle (rp,rg)), the carrier of (Tcircle (rp,rg)):] is non empty set
Tdisk (rp,rg) is non empty TopSpace-like T_0 T_1 T_2 V82() normal T_3 T_4 compact closed V246() V270(2) pseudocompact SubSpace of TOP-REAL 2
cl_Ball (rp,rg) is functional non empty proper closed connected bounded convex Element of bool the carrier of (TOP-REAL 2)
Sphere (rp,rg) is functional non empty proper closed closed connected compact bounded bounded being_simple_closed_curve with_the_max_arc Element of bool the carrier of (TOP-REAL 2)
{rl} is functional non empty proper closed compact bounded Element of bool the carrier of (TOP-REAL 2)
[:{rl},(Sphere (rp,rg)):] is Relation-like non empty Element of bool the carrier of [:(TOP-REAL 2),(TOP-REAL 2):]
bool the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] is non empty set
(TOP-REAL 2) | {rl} is non empty strict TopSpace-like T_0 T_1 T_2 V82() normal T_3 T_4 compact V246() pseudocompact SubSpace of TOP-REAL 2
(TOP-REAL 2) | (Sphere (rp,rg)) is non empty strict TopSpace-like T_0 T_1 T_2 V82() normal T_3 T_4 compact V246() pseudocompact SubSpace of TOP-REAL 2
the carrier of (Tdisk (rp,rg)) is non empty set
the carrier of ((TOP-REAL 2) | {rl}) is non empty set
the carrier of ((TOP-REAL 2) | (Sphere (rp,rg))) is non empty set
[:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):] is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of [:(TOP-REAL 2),(TOP-REAL 2):]
(rp) is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of [:(TOP-REAL 2),(TOP-REAL 2):],REAL:]
(rp) is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of [:(TOP-REAL 2),(TOP-REAL 2):],REAL:]
rg ^2 is complex ext-real real set
rg * rg is complex ext-real non negative real set
l is complex ext-real real Element of REAL
the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] --> l is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() Element of bool [: the carrier of [:(TOP-REAL 2),(TOP-REAL 2):],REAL:]
k is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of [:(TOP-REAL 2),(TOP-REAL 2):],REAL:]
k | [:{rl},(Sphere (rp,rg)):] is Relation-like [:{rl},(Sphere (rp,rg)):] -defined the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]) -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]),REAL:]
the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]) is non empty set
[: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]),REAL:] is Relation-like non empty V156() V157() V158() set
bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]),REAL:] is non empty set
() | [:{rl},(Sphere (rp,rg)):] is Relation-like [:{rl},(Sphere (rp,rg)):] -defined the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]) -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]),REAL:]
() | [:{rl},(Sphere (rp,rg)):] is Relation-like [:{rl},(Sphere (rp,rg)):] -defined the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]) -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]),REAL:]
() | [:{rl},(Sphere (rp,rg)):] is Relation-like [:{rl},(Sphere (rp,rg)):] -defined the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]) -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]),REAL:]
() | [:{rl},(Sphere (rp,rg)):] is Relation-like [:{rl},(Sphere (rp,rg)):] -defined the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]) -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]),REAL:]
(rp) | [:{rl},(Sphere (rp,rg)):] is Relation-like [:{rl},(Sphere (rp,rg)):] -defined the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]) -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]),REAL:]
(rp) | [:{rl},(Sphere (rp,rg)):] is Relation-like [:{rl},(Sphere (rp,rg)):] -defined the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]) -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]),REAL:]
((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):]) is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]) -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]) -defined REAL -valued Function-like non empty total total quasi_total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]),REAL:]
((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):]) is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]) -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]) -defined REAL -valued Function-like non empty total total quasi_total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]),REAL:]
(() | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):]) is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]) -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]) -defined REAL -valued Function-like non empty total total quasi_total quasi_total V156() V157() V158() nonnegative-yielding continuous Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]),REAL:]
(() | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):]) is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]) -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]) -defined REAL -valued Function-like non empty total total quasi_total quasi_total V156() V157() V158() nonnegative-yielding continuous Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]),REAL:]
((() | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + ((() | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]) -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]) -defined REAL -valued Function-like non empty total total quasi_total quasi_total V156() V157() V158() nonnegative-yielding continuous Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]),REAL:]
AR is Element of the carrier of ((TOP-REAL 2) | {rl})
BR is Element of the carrier of ((TOP-REAL 2) | (Sphere (rp,rg)))
[AR,BR] is V15() Element of the carrier of [:((TOP-REAL 2) | {rl}),((TOP-REAL 2) | (Sphere (rp,rg))):]
[:((TOP-REAL 2) | {rl}),((TOP-REAL 2) | (Sphere (rp,rg))):] is non empty strict TopSpace-like T_0 T_1 T_2 TopStruct
the carrier of [:((TOP-REAL 2) | {rl}),((TOP-REAL 2) | (Sphere (rp,rg))):] is non empty set
{AR,BR} is non empty set
{AR} is non empty set
{{AR,BR},{AR}} is non empty set
(() | [:{rl},(Sphere (rp,rg)):]) . [AR,BR] is complex ext-real real set
() . [AR,BR] is complex ext-real real set
AR is Element of the carrier of ((TOP-REAL 2) | {rl})
BR is Element of the carrier of ((TOP-REAL 2) | (Sphere (rp,rg)))
[AR,BR] is V15() Element of the carrier of [:((TOP-REAL 2) | {rl}),((TOP-REAL 2) | (Sphere (rp,rg))):]
[:((TOP-REAL 2) | {rl}),((TOP-REAL 2) | (Sphere (rp,rg))):] is non empty strict TopSpace-like T_0 T_1 T_2 TopStruct
the carrier of [:((TOP-REAL 2) | {rl}),((TOP-REAL 2) | (Sphere (rp,rg))):] is non empty set
{AR,BR} is non empty set
{AR} is non empty set
{{AR,BR},{AR}} is non empty set
(() | [:{rl},(Sphere (rp,rg)):]) . [AR,BR] is complex ext-real real set
() . [AR,BR] is complex ext-real real set
AR is Element of the carrier of ((TOP-REAL 2) | {rl})
BR is Element of the carrier of ((TOP-REAL 2) | (Sphere (rp,rg)))
[AR,BR] is V15() Element of the carrier of [:((TOP-REAL 2) | {rl}),((TOP-REAL 2) | (Sphere (rp,rg))):]
[:((TOP-REAL 2) | {rl}),((TOP-REAL 2) | (Sphere (rp,rg))):] is non empty strict TopSpace-like T_0 T_1 T_2 TopStruct
the carrier of [:((TOP-REAL 2) | {rl}),((TOP-REAL 2) | (Sphere (rp,rg))):] is non empty set
{AR,BR} is non empty set
{AR} is non empty set
{{AR,BR},{AR}} is non empty set
(() | [:{rl},(Sphere (rp,rg)):]) . [AR,BR] is complex ext-real real set
() . [AR,BR] is complex ext-real real set
AR is Element of the carrier of ((TOP-REAL 2) | {rl})
BR is Element of the carrier of ((TOP-REAL 2) | (Sphere (rp,rg)))
[AR,BR] is V15() Element of the carrier of [:((TOP-REAL 2) | {rl}),((TOP-REAL 2) | (Sphere (rp,rg))):]
[:((TOP-REAL 2) | {rl}),((TOP-REAL 2) | (Sphere (rp,rg))):] is non empty strict TopSpace-like T_0 T_1 T_2 TopStruct
the carrier of [:((TOP-REAL 2) | {rl}),((TOP-REAL 2) | (Sphere (rp,rg))):] is non empty set
{AR,BR} is non empty set
{AR} is non empty set
{{AR,BR},{AR}} is non empty set
(() | [:{rl},(Sphere (rp,rg)):]) . [AR,BR] is complex ext-real real set
() . [AR,BR] is complex ext-real real set
AR is Element of the carrier of ((TOP-REAL 2) | {rl})
BR is Element of the carrier of ((TOP-REAL 2) | (Sphere (rp,rg)))
[AR,BR] is V15() Element of the carrier of [:((TOP-REAL 2) | {rl}),((TOP-REAL 2) | (Sphere (rp,rg))):]
[:((TOP-REAL 2) | {rl}),((TOP-REAL 2) | (Sphere (rp,rg))):] is non empty strict TopSpace-like T_0 T_1 T_2 TopStruct
the carrier of [:((TOP-REAL 2) | {rl}),((TOP-REAL 2) | (Sphere (rp,rg))):] is non empty set
{AR,BR} is non empty set
{AR} is non empty set
{{AR,BR},{AR}} is non empty set
(k | [:{rl},(Sphere (rp,rg)):]) . [AR,BR] is complex ext-real real set
k . [AR,BR] is complex ext-real real set
AR is Element of the carrier of ((TOP-REAL 2) | {rl})
BR is Element of the carrier of ((TOP-REAL 2) | (Sphere (rp,rg)))
[AR,BR] is V15() Element of the carrier of [:((TOP-REAL 2) | {rl}),((TOP-REAL 2) | (Sphere (rp,rg))):]
[:((TOP-REAL 2) | {rl}),((TOP-REAL 2) | (Sphere (rp,rg))):] is non empty strict TopSpace-like T_0 T_1 T_2 TopStruct
the carrier of [:((TOP-REAL 2) | {rl}),((TOP-REAL 2) | (Sphere (rp,rg))):] is non empty set
{AR,BR} is non empty set
{AR} is non empty set
{{AR,BR},{AR}} is non empty set
((rp) | [:{rl},(Sphere (rp,rg)):]) . [AR,BR] is complex ext-real real set
(rp) . [AR,BR] is complex ext-real real set
AR is Element of the carrier of ((TOP-REAL 2) | {rl})
BR is Element of the carrier of ((TOP-REAL 2) | (Sphere (rp,rg)))
[AR,BR] is V15() Element of the carrier of [:((TOP-REAL 2) | {rl}),((TOP-REAL 2) | (Sphere (rp,rg))):]
[:((TOP-REAL 2) | {rl}),((TOP-REAL 2) | (Sphere (rp,rg))):] is non empty strict TopSpace-like T_0 T_1 T_2 TopStruct
the carrier of [:((TOP-REAL 2) | {rl}),((TOP-REAL 2) | (Sphere (rp,rg))):] is non empty set
{AR,BR} is non empty set
{AR} is non empty set
{{AR,BR},{AR}} is non empty set
((rp) | [:{rl},(Sphere (rp,rg)):]) . [AR,BR] is complex ext-real real set
(rp) . [AR,BR] is complex ext-real real set
AR is complex ext-real real set
rng (((() | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + ((() | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):]))) is non empty V166() V167() V168() Element of bool REAL
dom (((() | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + ((() | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):]))) is Relation-like {rl} -defined Sphere (rp,rg) -valued non empty Element of bool [:{rl},(Sphere (rp,rg)):]
bool [:{rl},(Sphere (rp,rg)):] is non empty set
BR is set
(((() | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + ((() | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):]))) . BR is complex ext-real real set
CR is set
DR is set
[CR,DR] is V15() set
{CR,DR} is non empty set
{CR} is non empty set
{{CR,DR},{CR}} is non empty set
Pcm is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
fcm is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
[Pcm,fcm] is V15() Element of the carrier of [:(TOP-REAL 2),(TOP-REAL 2):]
{Pcm,fcm} is functional non empty set
{Pcm} is functional non empty set
{{Pcm,fcm},{Pcm}} is non empty set
() . [Pcm,fcm] is complex ext-real real Element of REAL
((TOP-REAL 2),(TOP-REAL 2),[Pcm,fcm]) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
((TOP-REAL 2),(TOP-REAL 2),[Pcm,fcm]) `1 is complex ext-real real Element of REAL
((TOP-REAL 2),(TOP-REAL 2),[Pcm,fcm]) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
((TOP-REAL 2),(TOP-REAL 2),[Pcm,fcm]) `1 is complex ext-real real Element of REAL
(((TOP-REAL 2),(TOP-REAL 2),[Pcm,fcm]) `1) - (((TOP-REAL 2),(TOP-REAL 2),[Pcm,fcm]) `1) is complex ext-real real Element of REAL
() . [Pcm,fcm] is complex ext-real real Element of REAL
((TOP-REAL 2),(TOP-REAL 2),[Pcm,fcm]) `2 is complex ext-real real Element of REAL
((TOP-REAL 2),(TOP-REAL 2),[Pcm,fcm]) `2 is complex ext-real real Element of REAL
(((TOP-REAL 2),(TOP-REAL 2),[Pcm,fcm]) `2) - (((TOP-REAL 2),(TOP-REAL 2),[Pcm,fcm]) `2) is complex ext-real real Element of REAL
Pcm `1 is complex ext-real real Element of REAL
fcm `1 is complex ext-real real Element of REAL
(Pcm `1) - (fcm `1) is complex ext-real real Element of REAL
Pcm `2 is complex ext-real real Element of REAL
fcm `2 is complex ext-real real Element of REAL
(Pcm `2) - (fcm `2) is complex ext-real real Element of REAL
(() | [:{rl},(Sphere (rp,rg)):]) . [Pcm,fcm] is complex ext-real real set
(() | [:{rl},(Sphere (rp,rg)):]) . [Pcm,fcm] is complex ext-real real set
(((() | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + ((() | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):]))) . [Pcm,fcm] is complex ext-real real set
((() | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) . [Pcm,fcm] is complex ext-real real set
((() | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) . [Pcm,fcm] is complex ext-real real set
(((() | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) . [Pcm,fcm]) + (((() | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) . [Pcm,fcm]) is complex ext-real real set
((() | [:{rl},(Sphere (rp,rg)):]) . [Pcm,fcm]) * ((() | [:{rl},(Sphere (rp,rg)):]) . [Pcm,fcm]) is complex ext-real non negative real set
(((() | [:{rl},(Sphere (rp,rg)):]) . [Pcm,fcm]) * ((() | [:{rl},(Sphere (rp,rg)):]) . [Pcm,fcm])) + (((() | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) . [Pcm,fcm]) is complex ext-real real set
((Pcm `1) - (fcm `1)) ^2 is complex ext-real real Element of REAL
((Pcm `1) - (fcm `1)) * ((Pcm `1) - (fcm `1)) is complex ext-real non negative real set
((Pcm `2) - (fcm `2)) ^2 is complex ext-real real Element of REAL
((Pcm `2) - (fcm `2)) * ((Pcm `2) - (fcm `2)) is complex ext-real non negative real set
(((Pcm `1) - (fcm `1)) ^2) + (((Pcm `2) - (fcm `2)) ^2) is complex ext-real real Element of REAL
(((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]) -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]) -defined REAL -valued Function-like non empty total total quasi_total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]),REAL:]
((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):]))) (#) ((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):]))) is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]) -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]) -defined REAL -valued Function-like non empty total total quasi_total quasi_total V156() V157() V158() nonnegative-yielding continuous Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]),REAL:]
((rp) | [:{rl},(Sphere (rp,rg)):]) (#) ((rp) | [:{rl},(Sphere (rp,rg)):]) is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]) -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]) -defined REAL -valued Function-like non empty total total quasi_total quasi_total V156() V157() V158() nonnegative-yielding continuous Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]),REAL:]
((rp) | [:{rl},(Sphere (rp,rg)):]) (#) ((rp) | [:{rl},(Sphere (rp,rg)):]) is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]) -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]) -defined REAL -valued Function-like non empty total total quasi_total quasi_total V156() V157() V158() nonnegative-yielding continuous Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]),REAL:]
(((rp) | [:{rl},(Sphere (rp,rg)):]) (#) ((rp) | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) ((rp) | [:{rl},(Sphere (rp,rg)):])) is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]) -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]) -defined REAL -valued Function-like non empty total total quasi_total quasi_total V156() V157() V158() nonnegative-yielding continuous Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]),REAL:]
((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) ((rp) | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) ((rp) | [:{rl},(Sphere (rp,rg)):]))) - (k | [:{rl},(Sphere (rp,rg)):]) is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]) -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]) -defined REAL -valued Function-like non empty total total quasi_total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]),REAL:]
dom (((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) ((rp) | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) ((rp) | [:{rl},(Sphere (rp,rg)):]))) - (k | [:{rl},(Sphere (rp,rg)):])) is Relation-like {rl} -defined Sphere (rp,rg) -valued non empty Element of bool [:{rl},(Sphere (rp,rg)):]
DR is complex ext-real real set
rng (((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) ((rp) | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) ((rp) | [:{rl},(Sphere (rp,rg)):]))) - (k | [:{rl},(Sphere (rp,rg)):])) is non empty V166() V167() V168() Element of bool REAL
Pcm is set
(((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) ((rp) | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) ((rp) | [:{rl},(Sphere (rp,rg)):]))) - (k | [:{rl},(Sphere (rp,rg)):])) . Pcm is complex ext-real real set
fcm is set
V is set
[fcm,V] is V15() set
{fcm,V} is non empty set
{fcm} is non empty set
{{fcm,V},{fcm}} is non empty set
T2C is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
T2C `1 is complex ext-real real Element of REAL
rp `1 is complex ext-real real Element of REAL
(T2C `1) - (rp `1) is complex ext-real real Element of REAL
T2C `2 is complex ext-real real Element of REAL
rp `2 is complex ext-real real Element of REAL
(T2C `2) - (rp `2) is complex ext-real real Element of REAL
VP is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
[VP,T2C] is V15() Element of the carrier of [:(TOP-REAL 2),(TOP-REAL 2):]
{VP,T2C} is functional non empty set
{VP} is functional non empty set
{{VP,T2C},{VP}} is non empty set
(k | [:{rl},(Sphere (rp,rg)):]) . [VP,T2C] is complex ext-real real set
k . [VP,T2C] is complex ext-real real Element of REAL
((rp) | [:{rl},(Sphere (rp,rg)):]) . [VP,T2C] is complex ext-real real set
(rp) . [VP,T2C] is complex ext-real real Element of REAL
((rp) | [:{rl},(Sphere (rp,rg)):]) . [VP,T2C] is complex ext-real real set
(rp) . [VP,T2C] is complex ext-real real Element of REAL
((TOP-REAL 2),(TOP-REAL 2),[VP,T2C]) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
((TOP-REAL 2),(TOP-REAL 2),[VP,T2C]) `1 is complex ext-real real Element of REAL
(((TOP-REAL 2),(TOP-REAL 2),[VP,T2C]) `1) - (rp `1) is complex ext-real real Element of REAL
((TOP-REAL 2),(TOP-REAL 2),[VP,T2C]) `2 is complex ext-real real Element of REAL
(((TOP-REAL 2),(TOP-REAL 2),[VP,T2C]) `2) - (rp `2) is complex ext-real real Element of REAL
(((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) ((rp) | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) ((rp) | [:{rl},(Sphere (rp,rg)):]))) - (k | [:{rl},(Sphere (rp,rg)):])) . [VP,T2C] is complex ext-real real set
((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) ((rp) | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) ((rp) | [:{rl},(Sphere (rp,rg)):]))) . [VP,T2C] is complex ext-real real set
(((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) ((rp) | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) ((rp) | [:{rl},(Sphere (rp,rg)):]))) . [VP,T2C]) - ((k | [:{rl},(Sphere (rp,rg)):]) . [VP,T2C]) is complex ext-real real set
(((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) ((rp) | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) ((rp) | [:{rl},(Sphere (rp,rg)):]))) . [VP,T2C]) - (rg ^2) is complex ext-real real set
(((rp) | [:{rl},(Sphere (rp,rg)):]) (#) ((rp) | [:{rl},(Sphere (rp,rg)):])) . [VP,T2C] is complex ext-real real set
(((rp) | [:{rl},(Sphere (rp,rg)):]) (#) ((rp) | [:{rl},(Sphere (rp,rg)):])) . [VP,T2C] is complex ext-real real set
((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) ((rp) | [:{rl},(Sphere (rp,rg)):])) . [VP,T2C]) + ((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) ((rp) | [:{rl},(Sphere (rp,rg)):])) . [VP,T2C]) is complex ext-real real set
(((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) ((rp) | [:{rl},(Sphere (rp,rg)):])) . [VP,T2C]) + ((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) ((rp) | [:{rl},(Sphere (rp,rg)):])) . [VP,T2C])) - (rg ^2) is complex ext-real real set
(((rp) | [:{rl},(Sphere (rp,rg)):]) . [VP,T2C]) * (((rp) | [:{rl},(Sphere (rp,rg)):]) . [VP,T2C]) is complex ext-real non negative real set
((((rp) | [:{rl},(Sphere (rp,rg)):]) . [VP,T2C]) * (((rp) | [:{rl},(Sphere (rp,rg)):]) . [VP,T2C])) + ((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) ((rp) | [:{rl},(Sphere (rp,rg)):])) . [VP,T2C]) is complex ext-real real set
(((((rp) | [:{rl},(Sphere (rp,rg)):]) . [VP,T2C]) * (((rp) | [:{rl},(Sphere (rp,rg)):]) . [VP,T2C])) + ((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) ((rp) | [:{rl},(Sphere (rp,rg)):])) . [VP,T2C])) - (rg ^2) is complex ext-real real set
((T2C `1) - (rp `1)) ^2 is complex ext-real real Element of REAL
((T2C `1) - (rp `1)) * ((T2C `1) - (rp `1)) is complex ext-real non negative real set
((T2C `2) - (rp `2)) ^2 is complex ext-real real Element of REAL
((T2C `2) - (rp `2)) * ((T2C `2) - (rp `2)) is complex ext-real non negative real set
(((T2C `1) - (rp `1)) ^2) + (((T2C `2) - (rp `2)) ^2) is complex ext-real real Element of REAL
((((T2C `1) - (rp `1)) ^2) + (((T2C `2) - (rp `2)) ^2)) - (rg ^2) is complex ext-real real Element of REAL
T2C - rp is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
- rp is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
K270((TOP-REAL 2),T2C,(- rp)) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) is Relation-like [: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of bool [:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):]
[:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):] is Relation-like non empty set
bool [:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):] is non empty set
K224( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),T2C,(- rp)) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
|.(T2C - rp).| is complex ext-real non negative real Element of REAL
|.(T2C - rp).| ^2 is complex ext-real real Element of REAL
|.(T2C - rp).| * |.(T2C - rp).| is complex ext-real non negative real set
(T2C - rp) `1 is complex ext-real real Element of REAL
((T2C - rp) `1) ^2 is complex ext-real real Element of REAL
((T2C - rp) `1) * ((T2C - rp) `1) is complex ext-real non negative real set
(T2C - rp) `2 is complex ext-real real Element of REAL
((T2C - rp) `2) ^2 is complex ext-real real Element of REAL
((T2C - rp) `2) * ((T2C - rp) `2) is complex ext-real non negative real set
(((T2C - rp) `1) ^2) + (((T2C - rp) `2) ^2) is complex ext-real real Element of REAL
(((T2C `1) - (rp `1)) ^2) + (((T2C - rp) `2) ^2) is complex ext-real real Element of REAL
(rg ^2) - (rg ^2) is complex ext-real real set
AR is Relation-like non-empty the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]) -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() positive-yielding nonnegative-yielding continuous Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]),REAL:]
DR is Relation-like the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]) -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() nonpositive-yielding continuous Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]),REAL:]
AR (#) DR is Relation-like the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]) -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]) -defined REAL -valued Function-like non empty total total quasi_total quasi_total V156() V157() V158() nonpositive-yielding continuous Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]),REAL:]
(((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):]))) (#) ((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])))) - (AR (#) DR) is Relation-like the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]) -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]) -defined REAL -valued Function-like non empty total total quasi_total quasi_total V156() V157() V158() nonnegative-yielding continuous Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]),REAL:]
- ((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):]))) is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]) -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]) -defined REAL -valued Function-like non empty total total quasi_total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]),REAL:]
sqrt ((((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):]))) (#) ((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])))) - (AR (#) DR)) is Relation-like the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]) -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]) -defined REAL -valued Function-like non empty total total quasi_total quasi_total V156() V157() V158() nonnegative-yielding continuous Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]),REAL:]
(- ((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])))) + (sqrt ((((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):]))) (#) ((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])))) - (AR (#) DR))) is Relation-like the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]) -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]) -defined REAL -valued Function-like non empty total total quasi_total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]),REAL:]
((- ((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])))) + (sqrt ((((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):]))) (#) ((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])))) - (AR (#) DR)))) / AR is Relation-like the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]) -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]) -defined REAL -valued Function-like non empty total total quasi_total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]),REAL:]
(((- ((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])))) + (sqrt ((((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):]))) (#) ((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])))) - (AR (#) DR)))) / AR) (#) (() | [:{rl},(Sphere (rp,rg)):]) is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]) -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]) -defined REAL -valued Function-like non empty total total quasi_total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]),REAL:]
(() | [:{rl},(Sphere (rp,rg)):]) + ((((- ((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])))) + (sqrt ((((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):]))) (#) ((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])))) - (AR (#) DR)))) / AR) (#) (() | [:{rl},(Sphere (rp,rg)):])) is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]) -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]) -defined REAL -valued Function-like non empty total total quasi_total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]),REAL:]
(((- ((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])))) + (sqrt ((((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):]))) (#) ((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])))) - (AR (#) DR)))) / AR) (#) (() | [:{rl},(Sphere (rp,rg)):]) is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]) -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]) -defined REAL -valued Function-like non empty total total quasi_total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]),REAL:]
(() | [:{rl},(Sphere (rp,rg)):]) + ((((- ((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])))) + (sqrt ((((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):]))) (#) ((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])))) - (AR (#) DR)))) / AR) (#) (() | [:{rl},(Sphere (rp,rg)):])) is Relation-like the carrier of [:(TOP-REAL 2),(TOP-REAL 2):] -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]) -defined the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]) -defined REAL -valued Function-like non empty total total quasi_total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]),REAL:]
[: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]), the carrier of R^1:] is Relation-like non empty V156() V157() V158() set
bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]), the carrier of R^1:] is non empty set
T2C is Relation-like the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]) -defined the carrier of R^1 -valued Function-like non empty total quasi_total V156() V157() V158() Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]), the carrier of R^1:]
VP is Relation-like the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]) -defined the carrier of R^1 -valued Function-like non empty total quasi_total V156() V157() V158() Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]), the carrier of R^1:]
<:T2C,VP:> is Relation-like the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]) -defined [: the carrier of R^1, the carrier of R^1:] -valued Function-like non empty total quasi_total Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]),[: the carrier of R^1, the carrier of R^1:]:]
[: the carrier of R^1, the carrier of R^1:] is Relation-like non empty V156() V157() V158() set
[: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]),[: the carrier of R^1, the carrier of R^1:]:] is Relation-like non empty set
bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]),[: the carrier of R^1, the carrier of R^1:]:] is non empty set
R2Homeomorphism * <:T2C,VP:> is Relation-like the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]) -defined the carrier of (TOP-REAL 2) -valued Function-like Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]), the carrier of (TOP-REAL 2):]
[: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]), the carrier of (TOP-REAL 2):] is Relation-like non empty set
bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]), the carrier of (TOP-REAL 2):] is non empty set
Plk is Element of the carrier of ((TOP-REAL 2) | (Sphere (rp,rg)))
(2,rp,rl,rg) . Plk is set
[rl,Plk] is V15() Element of the carrier of [:(TOP-REAL 2),((TOP-REAL 2) | (Sphere (rp,rg))):]
[:(TOP-REAL 2),((TOP-REAL 2) | (Sphere (rp,rg))):] is non empty strict TopSpace-like T_0 T_1 T_2 TopStruct
the carrier of [:(TOP-REAL 2),((TOP-REAL 2) | (Sphere (rp,rg))):] is non empty set
{rl,Plk} is non empty set
{rl} is functional non empty set
{{rl,Plk},{rl}} is non empty set
(R2Homeomorphism * <:T2C,VP:>) . [rl,Plk] is Relation-like Function-like set
flk is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
HC (flk,rl,rp,rg) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
[rl,flk] is V15() Element of the carrier of [:(TOP-REAL 2),(TOP-REAL 2):]
{rl,flk} is functional non empty set
{{rl,flk},{rl}} is non empty set
rl `1 is complex ext-real real Element of REAL
flk `1 is complex ext-real real Element of REAL
(rl `1) - (flk `1) is complex ext-real real Element of REAL
rl `2 is complex ext-real real Element of REAL
flk `2 is complex ext-real real Element of REAL
(rl `2) - (flk `2) is complex ext-real real Element of REAL
(flk `1) - (rp `1) is complex ext-real real Element of REAL
(flk `2) - (rp `2) is complex ext-real real Element of REAL
((flk `1) - (rp `1)) * ((rl `1) - (flk `1)) is complex ext-real real Element of REAL
((flk `2) - (rp `2)) * ((rl `2) - (flk `2)) is complex ext-real real Element of REAL
(((flk `1) - (rp `1)) * ((rl `1) - (flk `1))) + (((flk `2) - (rp `2)) * ((rl `2) - (flk `2))) is complex ext-real real Element of REAL
- ((((flk `1) - (rp `1)) * ((rl `1) - (flk `1))) + (((flk `2) - (rp `2)) * ((rl `2) - (flk `2)))) is complex ext-real real Element of REAL
((((flk `1) - (rp `1)) * ((rl `1) - (flk `1))) + (((flk `2) - (rp `2)) * ((rl `2) - (flk `2)))) ^2 is complex ext-real real Element of REAL
((((flk `1) - (rp `1)) * ((rl `1) - (flk `1))) + (((flk `2) - (rp `2)) * ((rl `2) - (flk `2)))) * ((((flk `1) - (rp `1)) * ((rl `1) - (flk `1))) + (((flk `2) - (rp `2)) * ((rl `2) - (flk `2)))) is complex ext-real non negative real set
((rl `1) - (flk `1)) ^2 is complex ext-real real Element of REAL
((rl `1) - (flk `1)) * ((rl `1) - (flk `1)) is complex ext-real non negative real set
((rl `2) - (flk `2)) ^2 is complex ext-real real Element of REAL
((rl `2) - (flk `2)) * ((rl `2) - (flk `2)) is complex ext-real non negative real set
(((rl `1) - (flk `1)) ^2) + (((rl `2) - (flk `2)) ^2) is complex ext-real real Element of REAL
((flk `1) - (rp `1)) ^2 is complex ext-real real Element of REAL
((flk `1) - (rp `1)) * ((flk `1) - (rp `1)) is complex ext-real non negative real set
((flk `2) - (rp `2)) ^2 is complex ext-real real Element of REAL
((flk `2) - (rp `2)) * ((flk `2) - (rp `2)) is complex ext-real non negative real set
(((flk `1) - (rp `1)) ^2) + (((flk `2) - (rp `2)) ^2) is complex ext-real real Element of REAL
((((flk `1) - (rp `1)) ^2) + (((flk `2) - (rp `2)) ^2)) - (rg ^2) is complex ext-real real Element of REAL
((((rl `1) - (flk `1)) ^2) + (((rl `2) - (flk `2)) ^2)) * (((((flk `1) - (rp `1)) ^2) + (((flk `2) - (rp `2)) ^2)) - (rg ^2)) is complex ext-real real Element of REAL
(((((flk `1) - (rp `1)) * ((rl `1) - (flk `1))) + (((flk `2) - (rp `2)) * ((rl `2) - (flk `2)))) ^2) - (((((rl `1) - (flk `1)) ^2) + (((rl `2) - (flk `2)) ^2)) * (((((flk `1) - (rp `1)) ^2) + (((flk `2) - (rp `2)) ^2)) - (rg ^2))) is complex ext-real real Element of REAL
sqrt ((((((flk `1) - (rp `1)) * ((rl `1) - (flk `1))) + (((flk `2) - (rp `2)) * ((rl `2) - (flk `2)))) ^2) - (((((rl `1) - (flk `1)) ^2) + (((rl `2) - (flk `2)) ^2)) * (((((flk `1) - (rp `1)) ^2) + (((flk `2) - (rp `2)) ^2)) - (rg ^2)))) is complex ext-real real Element of REAL
(- ((((flk `1) - (rp `1)) * ((rl `1) - (flk `1))) + (((flk `2) - (rp `2)) * ((rl `2) - (flk `2))))) + (sqrt ((((((flk `1) - (rp `1)) * ((rl `1) - (flk `1))) + (((flk `2) - (rp `2)) * ((rl `2) - (flk `2)))) ^2) - (((((rl `1) - (flk `1)) ^2) + (((rl `2) - (flk `2)) ^2)) * (((((flk `1) - (rp `1)) ^2) + (((flk `2) - (rp `2)) ^2)) - (rg ^2))))) is complex ext-real real Element of REAL
((- ((((flk `1) - (rp `1)) * ((rl `1) - (flk `1))) + (((flk `2) - (rp `2)) * ((rl `2) - (flk `2))))) + (sqrt ((((((flk `1) - (rp `1)) * ((rl `1) - (flk `1))) + (((flk `2) - (rp `2)) * ((rl `2) - (flk `2)))) ^2) - (((((rl `1) - (flk `1)) ^2) + (((rl `2) - (flk `2)) ^2)) * (((((flk `1) - (rp `1)) ^2) + (((flk `2) - (rp `2)) ^2)) - (rg ^2)))))) / ((((rl `1) - (flk `1)) ^2) + (((rl `2) - (flk `2)) ^2)) is complex ext-real real Element of REAL
() . [rl,flk] is complex ext-real real Element of REAL
((TOP-REAL 2),(TOP-REAL 2),[rl,flk]) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
((TOP-REAL 2),(TOP-REAL 2),[rl,flk]) `1 is complex ext-real real Element of REAL
() . [rl,flk] is complex ext-real real Element of REAL
((TOP-REAL 2),(TOP-REAL 2),[rl,flk]) `2 is complex ext-real real Element of REAL
() . [rl,flk] is complex ext-real real Element of REAL
((TOP-REAL 2),(TOP-REAL 2),[rl,flk]) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
((TOP-REAL 2),(TOP-REAL 2),[rl,flk]) `1 is complex ext-real real Element of REAL
(((TOP-REAL 2),(TOP-REAL 2),[rl,flk]) `1) - (((TOP-REAL 2),(TOP-REAL 2),[rl,flk]) `1) is complex ext-real real Element of REAL
() . [rl,flk] is complex ext-real real Element of REAL
((TOP-REAL 2),(TOP-REAL 2),[rl,flk]) `2 is complex ext-real real Element of REAL
(((TOP-REAL 2),(TOP-REAL 2),[rl,flk]) `2) - (((TOP-REAL 2),(TOP-REAL 2),[rl,flk]) `2) is complex ext-real real Element of REAL
(rp) . [rl,flk] is complex ext-real real Element of REAL
(((TOP-REAL 2),(TOP-REAL 2),[rl,flk]) `1) - (rp `1) is complex ext-real real Element of REAL
(rp) . [rl,flk] is complex ext-real real Element of REAL
(((TOP-REAL 2),(TOP-REAL 2),[rl,flk]) `2) - (rp `2) is complex ext-real real Element of REAL
dom T2C is non empty Element of bool the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):])
bool the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]) is non empty set
dom VP is non empty Element of bool the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):])
dom ((((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):]))) (#) ((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])))) - (AR (#) DR)) is non empty Element of bool the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):])
(() | [:{rl},(Sphere (rp,rg)):]) . [rl,flk] is complex ext-real real set
(() | [:{rl},(Sphere (rp,rg)):]) . [rl,flk] is complex ext-real real set
(k | [:{rl},(Sphere (rp,rg)):]) . [rl,flk] is complex ext-real real set
k . [rl,flk] is complex ext-real real Element of REAL
((rp) | [:{rl},(Sphere (rp,rg)):]) . [rl,flk] is complex ext-real real set
((rp) | [:{rl},(Sphere (rp,rg)):]) . [rl,flk] is complex ext-real real set
AR . [rl,flk] is complex ext-real real set
((() | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) . [rl,flk] is complex ext-real real set
((() | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) . [rl,flk] is complex ext-real real set
(((() | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) . [rl,flk]) + (((() | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) . [rl,flk]) is complex ext-real real set
((() | [:{rl},(Sphere (rp,rg)):]) . [rl,flk]) * ((() | [:{rl},(Sphere (rp,rg)):]) . [rl,flk]) is complex ext-real non negative real set
(((() | [:{rl},(Sphere (rp,rg)):]) . [rl,flk]) * ((() | [:{rl},(Sphere (rp,rg)):]) . [rl,flk])) + (((() | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) . [rl,flk]) is complex ext-real real set
(((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) . [rl,flk] is complex ext-real real set
(((rp) | [:{rl},(Sphere (rp,rg)):]) . [rl,flk]) * ((() | [:{rl},(Sphere (rp,rg)):]) . [rl,flk]) is complex ext-real real set
(((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) . [rl,flk] is complex ext-real real set
(((rp) | [:{rl},(Sphere (rp,rg)):]) . [rl,flk]) * ((() | [:{rl},(Sphere (rp,rg)):]) . [rl,flk]) is complex ext-real real set
((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):]))) . [rl,flk] is complex ext-real real set
((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) . [rl,flk]) + ((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) . [rl,flk]) is complex ext-real real set
(((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):]))) (#) ((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])))) . [rl,flk] is complex ext-real real set
DR . [rl,flk] is complex ext-real real set
((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) ((rp) | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) ((rp) | [:{rl},(Sphere (rp,rg)):]))) . [rl,flk] is complex ext-real real set
(((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) ((rp) | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) ((rp) | [:{rl},(Sphere (rp,rg)):]))) . [rl,flk]) - ((k | [:{rl},(Sphere (rp,rg)):]) . [rl,flk]) is complex ext-real real set
(((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) ((rp) | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) ((rp) | [:{rl},(Sphere (rp,rg)):]))) . [rl,flk]) - (rg ^2) is complex ext-real real set
(((rp) | [:{rl},(Sphere (rp,rg)):]) (#) ((rp) | [:{rl},(Sphere (rp,rg)):])) . [rl,flk] is complex ext-real real set
(((rp) | [:{rl},(Sphere (rp,rg)):]) (#) ((rp) | [:{rl},(Sphere (rp,rg)):])) . [rl,flk] is complex ext-real real set
((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) ((rp) | [:{rl},(Sphere (rp,rg)):])) . [rl,flk]) + ((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) ((rp) | [:{rl},(Sphere (rp,rg)):])) . [rl,flk]) is complex ext-real real set
(((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) ((rp) | [:{rl},(Sphere (rp,rg)):])) . [rl,flk]) + ((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) ((rp) | [:{rl},(Sphere (rp,rg)):])) . [rl,flk])) - (rg ^2) is complex ext-real real set
(((rp) | [:{rl},(Sphere (rp,rg)):]) . [rl,flk]) * (((rp) | [:{rl},(Sphere (rp,rg)):]) . [rl,flk]) is complex ext-real non negative real set
((((rp) | [:{rl},(Sphere (rp,rg)):]) . [rl,flk]) * (((rp) | [:{rl},(Sphere (rp,rg)):]) . [rl,flk])) + ((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) ((rp) | [:{rl},(Sphere (rp,rg)):])) . [rl,flk]) is complex ext-real real set
(((((rp) | [:{rl},(Sphere (rp,rg)):]) . [rl,flk]) * (((rp) | [:{rl},(Sphere (rp,rg)):]) . [rl,flk])) + ((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) ((rp) | [:{rl},(Sphere (rp,rg)):])) . [rl,flk])) - (rg ^2) is complex ext-real real set
dom (sqrt ((((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):]))) (#) ((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])))) - (AR (#) DR))) is non empty Element of bool the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):])
(sqrt ((((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):]))) (#) ((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])))) - (AR (#) DR))) . [rl,flk] is complex ext-real real set
((((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):]))) (#) ((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])))) - (AR (#) DR)) . [rl,flk] is complex ext-real real set
sqrt (((((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):]))) (#) ((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])))) - (AR (#) DR)) . [rl,flk]) is complex ext-real real set
(AR (#) DR) . [rl,flk] is complex ext-real real set
((((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):]))) (#) ((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])))) . [rl,flk]) - ((AR (#) DR) . [rl,flk]) is complex ext-real real set
sqrt (((((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):]))) (#) ((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])))) . [rl,flk]) - ((AR (#) DR) . [rl,flk])) is complex ext-real real set
dom (((- ((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])))) + (sqrt ((((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):]))) (#) ((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])))) - (AR (#) DR)))) / AR) is non empty Element of bool the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):])
(((- ((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])))) + (sqrt ((((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):]))) (#) ((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])))) - (AR (#) DR)))) / AR) . [rl,flk] is complex ext-real real set
((- ((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])))) + (sqrt ((((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):]))) (#) ((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])))) - (AR (#) DR)))) . [rl,flk] is complex ext-real real set
(AR . [rl,flk]) " is complex ext-real real set
(((- ((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])))) + (sqrt ((((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):]))) (#) ((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])))) - (AR (#) DR)))) . [rl,flk]) * ((AR . [rl,flk]) ") is complex ext-real real set
(((- ((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])))) + (sqrt ((((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):]))) (#) ((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])))) - (AR (#) DR)))) . [rl,flk]) / (AR . [rl,flk]) is complex ext-real real Element of COMPLEX
(- ((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])))) . [rl,flk] is complex ext-real real set
((- ((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])))) . [rl,flk]) + ((sqrt ((((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):]))) (#) ((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])))) - (AR (#) DR))) . [rl,flk]) is complex ext-real real set
(((- ((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])))) . [rl,flk]) + ((sqrt ((((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):]))) (#) ((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])))) - (AR (#) DR))) . [rl,flk])) / ((((rl `1) - (flk `1)) ^2) + (((rl `2) - (flk `2)) ^2)) is complex ext-real real Element of REAL
T2C . [rl,flk] is complex ext-real real set
(() | [:{rl},(Sphere (rp,rg)):]) . [rl,flk] is complex ext-real real set
((((- ((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])))) + (sqrt ((((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):]))) (#) ((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])))) - (AR (#) DR)))) / AR) (#) (() | [:{rl},(Sphere (rp,rg)):])) . [rl,flk] is complex ext-real real set
((() | [:{rl},(Sphere (rp,rg)):]) . [rl,flk]) + (((((- ((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])))) + (sqrt ((((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):]))) (#) ((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])))) - (AR (#) DR)))) / AR) (#) (() | [:{rl},(Sphere (rp,rg)):])) . [rl,flk]) is complex ext-real real set
(flk `1) + (((((- ((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])))) + (sqrt ((((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):]))) (#) ((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])))) - (AR (#) DR)))) / AR) (#) (() | [:{rl},(Sphere (rp,rg)):])) . [rl,flk]) is complex ext-real real Element of REAL
(((- ((((flk `1) - (rp `1)) * ((rl `1) - (flk `1))) + (((flk `2) - (rp `2)) * ((rl `2) - (flk `2))))) + (sqrt ((((((flk `1) - (rp `1)) * ((rl `1) - (flk `1))) + (((flk `2) - (rp `2)) * ((rl `2) - (flk `2)))) ^2) - (((((rl `1) - (flk `1)) ^2) + (((rl `2) - (flk `2)) ^2)) * (((((flk `1) - (rp `1)) ^2) + (((flk `2) - (rp `2)) ^2)) - (rg ^2)))))) / ((((rl `1) - (flk `1)) ^2) + (((rl `2) - (flk `2)) ^2))) * ((rl `1) - (flk `1)) is complex ext-real real Element of REAL
(flk `1) + ((((- ((((flk `1) - (rp `1)) * ((rl `1) - (flk `1))) + (((flk `2) - (rp `2)) * ((rl `2) - (flk `2))))) + (sqrt ((((((flk `1) - (rp `1)) * ((rl `1) - (flk `1))) + (((flk `2) - (rp `2)) * ((rl `2) - (flk `2)))) ^2) - (((((rl `1) - (flk `1)) ^2) + (((rl `2) - (flk `2)) ^2)) * (((((flk `1) - (rp `1)) ^2) + (((flk `2) - (rp `2)) ^2)) - (rg ^2)))))) / ((((rl `1) - (flk `1)) ^2) + (((rl `2) - (flk `2)) ^2))) * ((rl `1) - (flk `1))) is complex ext-real real Element of REAL
VP . [rl,flk] is complex ext-real real set
(() | [:{rl},(Sphere (rp,rg)):]) . [rl,flk] is complex ext-real real set
((((- ((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])))) + (sqrt ((((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):]))) (#) ((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])))) - (AR (#) DR)))) / AR) (#) (() | [:{rl},(Sphere (rp,rg)):])) . [rl,flk] is complex ext-real real set
((() | [:{rl},(Sphere (rp,rg)):]) . [rl,flk]) + (((((- ((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])))) + (sqrt ((((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):]))) (#) ((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])))) - (AR (#) DR)))) / AR) (#) (() | [:{rl},(Sphere (rp,rg)):])) . [rl,flk]) is complex ext-real real set
(flk `2) + (((((- ((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])))) + (sqrt ((((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):]))) (#) ((((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])) + (((rp) | [:{rl},(Sphere (rp,rg)):]) (#) (() | [:{rl},(Sphere (rp,rg)):])))) - (AR (#) DR)))) / AR) (#) (() | [:{rl},(Sphere (rp,rg)):])) . [rl,flk]) is complex ext-real real Element of REAL
(((- ((((flk `1) - (rp `1)) * ((rl `1) - (flk `1))) + (((flk `2) - (rp `2)) * ((rl `2) - (flk `2))))) + (sqrt ((((((flk `1) - (rp `1)) * ((rl `1) - (flk `1))) + (((flk `2) - (rp `2)) * ((rl `2) - (flk `2)))) ^2) - (((((rl `1) - (flk `1)) ^2) + (((rl `2) - (flk `2)) ^2)) * (((((flk `1) - (rp `1)) ^2) + (((flk `2) - (rp `2)) ^2)) - (rg ^2)))))) / ((((rl `1) - (flk `1)) ^2) + (((rl `2) - (flk `2)) ^2))) * ((rl `2) - (flk `2)) is complex ext-real real Element of REAL
(flk `2) + ((((- ((((flk `1) - (rp `1)) * ((rl `1) - (flk `1))) + (((flk `2) - (rp `2)) * ((rl `2) - (flk `2))))) + (sqrt ((((((flk `1) - (rp `1)) * ((rl `1) - (flk `1))) + (((flk `2) - (rp `2)) * ((rl `2) - (flk `2)))) ^2) - (((((rl `1) - (flk `1)) ^2) + (((rl `2) - (flk `2)) ^2)) * (((((flk `1) - (rp `1)) ^2) + (((flk `2) - (rp `2)) ^2)) - (rg ^2)))))) / ((((rl `1) - (flk `1)) ^2) + (((rl `2) - (flk `2)) ^2))) * ((rl `2) - (flk `2))) is complex ext-real real Element of REAL
|[((flk `1) + ((((- ((((flk `1) - (rp `1)) * ((rl `1) - (flk `1))) + (((flk `2) - (rp `2)) * ((rl `2) - (flk `2))))) + (sqrt ((((((flk `1) - (rp `1)) * ((rl `1) - (flk `1))) + (((flk `2) - (rp `2)) * ((rl `2) - (flk `2)))) ^2) - (((((rl `1) - (flk `1)) ^2) + (((rl `2) - (flk `2)) ^2)) * (((((flk `1) - (rp `1)) ^2) + (((flk `2) - (rp `2)) ^2)) - (rg ^2)))))) / ((((rl `1) - (flk `1)) ^2) + (((rl `2) - (flk `2)) ^2))) * ((rl `1) - (flk `1)))),((flk `2) + ((((- ((((flk `1) - (rp `1)) * ((rl `1) - (flk `1))) + (((flk `2) - (rp `2)) * ((rl `2) - (flk `2))))) + (sqrt ((((((flk `1) - (rp `1)) * ((rl `1) - (flk `1))) + (((flk `2) - (rp `2)) * ((rl `2) - (flk `2)))) ^2) - (((((rl `1) - (flk `1)) ^2) + (((rl `2) - (flk `2)) ^2)) * (((((flk `1) - (rp `1)) ^2) + (((flk `2) - (rp `2)) ^2)) - (rg ^2)))))) / ((((rl `1) - (flk `1)) ^2) + (((rl `2) - (flk `2)) ^2))) * ((rl `2) - (flk `2))))]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
[(T2C . [rl,flk]),(VP . [rl,flk])] is V15() set
{(T2C . [rl,flk]),(VP . [rl,flk])} is non empty V166() V167() V168() set
{(T2C . [rl,flk])} is non empty V166() V167() V168() set
{{(T2C . [rl,flk]),(VP . [rl,flk])},{(T2C . [rl,flk])}} is non empty set
R2Homeomorphism . [(T2C . [rl,flk]),(VP . [rl,flk])] is Relation-like Function-like set
<:T2C,VP:> . [rl,flk] is set
R2Homeomorphism . (<:T2C,VP:> . [rl,flk]) is Relation-like Function-like set
[: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]), the carrier of [:R^1,R^1:]:] is Relation-like non empty set
bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]), the carrier of [:R^1,R^1:]:] is non empty set
bool the carrier of (Tcircle (rp,rg)) is non empty set
bool the carrier of ((TOP-REAL 2) | (Sphere (rp,rg))) is non empty set
flk is Element of the carrier of ((TOP-REAL 2) | (Sphere (rp,rg)))
(2,rp,rl,rg) . flk is set
beta is Element of bool the carrier of (Tcircle (rp,rg))
[rl,flk] is V15() Element of the carrier of [:(TOP-REAL 2),((TOP-REAL 2) | (Sphere (rp,rg))):]
[:(TOP-REAL 2),((TOP-REAL 2) | (Sphere (rp,rg))):] is non empty strict TopSpace-like T_0 T_1 T_2 TopStruct
the carrier of [:(TOP-REAL 2),((TOP-REAL 2) | (Sphere (rp,rg))):] is non empty set
{rl,flk} is non empty set
{rl} is functional non empty set
{{rl,flk},{rl}} is non empty set
[#] (Tcircle (rp,rg)) is non empty non proper open closed dense non boundary compact Element of bool the carrier of (Tcircle (rp,rg))
A is functional Element of bool the carrier of (TOP-REAL 2)
A /\ ([#] (Tcircle (rp,rg))) is Element of bool the carrier of (Tcircle (rp,rg))
Plk is Relation-like the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]) -defined the carrier of [:R^1,R^1:] -valued Function-like non empty total quasi_total continuous Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]), the carrier of [:R^1,R^1:]:]
R2Homeomorphism * Plk is Relation-like the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]) -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]), the carrier of (TOP-REAL 2):]
(R2Homeomorphism * Plk) . [rl,flk] is Relation-like Function-like set
R2Homeomorphism /" is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of [:R^1,R^1:] -valued Function-like non empty total quasi_total Element of bool [: the carrier of (TOP-REAL 2), the carrier of [:R^1,R^1:]:]
[: the carrier of (TOP-REAL 2), the carrier of [:R^1,R^1:]:] is Relation-like non empty set
bool [: the carrier of (TOP-REAL 2), the carrier of [:R^1,R^1:]:] is non empty set
(R2Homeomorphism /") .: A is Element of bool the carrier of [:R^1,R^1:]
bool the carrier of [:R^1,R^1:] is non empty set
dom Plk is non empty Element of bool the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):])
bool the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]) is non empty set
dom R2Homeomorphism is non empty Element of bool the carrier of [:R^1,R^1:]
rng Plk is non empty Element of bool the carrier of [:R^1,R^1:]
dom (R2Homeomorphism * Plk) is non empty Element of bool the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):])
rng R2Homeomorphism is functional non empty Element of bool the carrier of (TOP-REAL 2)
[#] (TOP-REAL 2) is functional non empty non proper non proper open open closed closed dense dense non boundary non boundary connected a_component being_Region convex Element of bool the carrier of (TOP-REAL 2)
(R2Homeomorphism /") * (R2Homeomorphism * Plk) is Relation-like the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]) -defined the carrier of [:R^1,R^1:] -valued Function-like non empty total quasi_total Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]), the carrier of [:R^1,R^1:]:]
(R2Homeomorphism /") * R2Homeomorphism is Relation-like the carrier of [:R^1,R^1:] -defined the carrier of [:R^1,R^1:] -valued Function-like non empty total quasi_total Element of bool [: the carrier of [:R^1,R^1:], the carrier of [:R^1,R^1:]:]
[: the carrier of [:R^1,R^1:], the carrier of [:R^1,R^1:]:] is Relation-like non empty set
bool [: the carrier of [:R^1,R^1:], the carrier of [:R^1,R^1:]:] is non empty set
((R2Homeomorphism /") * R2Homeomorphism) * Plk is Relation-like the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]) -defined the carrier of [:R^1,R^1:] -valued Function-like non empty total quasi_total Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]), the carrier of [:R^1,R^1:]:]
id (dom R2Homeomorphism) is Relation-like dom R2Homeomorphism -defined dom R2Homeomorphism -valued Function-like one-to-one non empty total quasi_total Element of bool [:(dom R2Homeomorphism),(dom R2Homeomorphism):]
[:(dom R2Homeomorphism),(dom R2Homeomorphism):] is Relation-like non empty set
bool [:(dom R2Homeomorphism),(dom R2Homeomorphism):] is non empty set
(id (dom R2Homeomorphism)) * Plk is Relation-like the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]) -defined dom R2Homeomorphism -valued Function-like Element of bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]),(dom R2Homeomorphism):]
[: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]),(dom R2Homeomorphism):] is Relation-like non empty set
bool [: the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]),(dom R2Homeomorphism):] is non empty set
dom (id (dom R2Homeomorphism)) is non empty Element of bool (dom R2Homeomorphism)
bool (dom R2Homeomorphism) is non empty set
dom ((id (dom R2Homeomorphism)) * Plk) is Element of bool the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):])
B is set
((id (dom R2Homeomorphism)) * Plk) . B is set
Plk . B is set
(id (dom R2Homeomorphism)) . (Plk . B) is set
rb is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
ra is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
[rb,ra] is V15() Element of the carrier of [:(TOP-REAL 2),(TOP-REAL 2):]
{rb,ra} is functional non empty set
{rb} is functional non empty set
{{rb,ra},{rb}} is non empty set
(R2Homeomorphism * Plk) . [rb,ra] is Relation-like Function-like set
(R2Homeomorphism /") . ((R2Homeomorphism * Plk) . [rb,ra]) is set
((R2Homeomorphism /") * (R2Homeomorphism * Plk)) . [rb,ra] is set
B is Element of bool the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):])
Plk .: B is Element of bool the carrier of [:R^1,R^1:]
[#] ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]) is non empty non proper open closed dense non boundary Element of bool the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):])
t is Element of bool the carrier of [:(TOP-REAL 2),(TOP-REAL 2):]
t /\ ([#] ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):])) is Element of bool the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):])
bool (bool the carrier of [:(TOP-REAL 2),(TOP-REAL 2):]) is non empty set
u is Element of bool (bool the carrier of [:(TOP-REAL 2),(TOP-REAL 2):])
union u is set
v is set
u is functional Element of bool the carrier of (TOP-REAL 2)
v is functional Element of bool the carrier of (TOP-REAL 2)
[:u,v:] is Relation-like Element of bool the carrier of [:(TOP-REAL 2),(TOP-REAL 2):]
v /\ ([#] ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):])) is Element of bool the carrier of ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):])
[#] ((TOP-REAL 2) | (Sphere (rp,rg))) is non empty non proper open closed dense non boundary compact Element of bool the carrier of ((TOP-REAL 2) | (Sphere (rp,rg)))
v /\ ([#] ((TOP-REAL 2) | (Sphere (rp,rg)))) is Element of bool the carrier of ((TOP-REAL 2) | (Sphere (rp,rg)))
v1 is open Element of bool the carrier of ((TOP-REAL 2) | (Sphere (rp,rg)))
(2,rp,rl,rg) .: v1 is Element of bool the carrier of (Tcircle (rp,rg))
fuv is set
uv is Element of the carrier of ((TOP-REAL 2) | (Sphere (rp,rg)))
(2,rp,rl,rg) . uv is set
[rl,uv] is V15() Element of the carrier of [:(TOP-REAL 2),((TOP-REAL 2) | (Sphere (rp,rg))):]
{rl,uv} is non empty set
{{rl,uv},{rl}} is non empty set
fau is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
[fau,uv] is V15() Element of the carrier of [:(TOP-REAL 2),((TOP-REAL 2) | (Sphere (rp,rg))):]
{fau,uv} is non empty set
{fau} is functional non empty set
{{fau,uv},{fau}} is non empty set
au is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
[fau,au] is V15() Element of the carrier of [:(TOP-REAL 2),(TOP-REAL 2):]
{fau,au} is functional non empty set
{{fau,au},{fau}} is non empty set
Plk . [fau,au] is set
Plk .: (v /\ ([#] ([:(TOP-REAL 2),(TOP-REAL 2):] | [:{rl},(Sphere (rp,rg)):]))) is Element of bool the carrier of [:R^1,R^1:]
R2Homeomorphism " is Relation-like Function-like set
dom (R2Homeomorphism /") is functional non empty Element of bool the carrier of (TOP-REAL 2)
(2,rp,rl,rg) . au is set
R2Homeomorphism . (Plk . [fau,au]) is Relation-like Function-like set
R2Homeomorphism .: ((R2Homeomorphism /") .: A) is functional Element of bool the carrier of (TOP-REAL 2)
(R2Homeomorphism * Plk) . [fau,au] is Relation-like Function-like set
rp is non empty ordinal natural complex ext-real positive non negative real V33() V119() V166() V167() V168() V169() V170() V171() left_end bounded_below Element of NAT
TOP-REAL rp is non empty TopSpace-like T_0 T_1 T_2 connected V132() V178() V179() V180() V181() V182() V183() V184() strict add-continuous Mult-continuous pathwise_connected RLTopStruct
the carrier of (TOP-REAL rp) is functional non empty set
rg is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
rl is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
rd is non empty complex ext-real positive non negative real set
Ball (rl,rd) is functional non empty proper open connected bounded convex Element of bool the carrier of (TOP-REAL rp)
bool the carrier of (TOP-REAL rp) is non empty set
(rp,rl,rg,rd) is Relation-like the carrier of (Tcircle (rl,rd)) -defined the carrier of (Tcircle (rl,rd)) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (Tcircle (rl,rd)), the carrier of (Tcircle (rl,rd)):]
Tcircle (rl,rd) is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL rp
the carrier of (Tcircle (rl,rd)) is non empty set
[: the carrier of (Tcircle (rl,rd)), the carrier of (Tcircle (rl,rd)):] is Relation-like non empty set
bool [: the carrier of (Tcircle (rl,rd)), the carrier of (Tcircle (rl,rd)):] is non empty set
b is set
dom (rp,rl,rg,rd) is non empty Element of bool the carrier of (Tcircle (rl,rd))
bool the carrier of (Tcircle (rl,rd)) is non empty set
(rp,rl,rg,rd) . b is set
d is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
HC (d,rg,rl,rd) is Relation-like Function-like V49(rp) V50() V156() V157() V158() Element of the carrier of (TOP-REAL rp)
Sphere (rl,rd) is functional non empty proper closed bounded Element of bool the carrier of (TOP-REAL rp)
cl_Ball (rl,rd) is functional non empty proper closed connected bounded convex Element of bool the carrier of (TOP-REAL rp)
Tdisk (rl,rd) is non empty TopSpace-like T_0 T_1 T_2 V270(rp) SubSpace of TOP-REAL rp
the carrier of (Tdisk (rl,rd)) is non empty set
rp is functional non empty proper closed connected compact bounded being_simple_closed_curve with_the_max_arc Element of bool the carrier of (TOP-REAL 2)
rp ` is functional non empty open Element of bool the carrier of (TOP-REAL 2)
the carrier of (TOP-REAL 2) \ rp is set
(TOP-REAL 2) | (rp `) is non empty strict TopSpace-like T_0 T_1 T_2 V118( TOP-REAL 2) SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | (rp `)) is non empty set
bool the carrier of ((TOP-REAL 2) | (rp `)) is non empty set
rl is functional Element of bool the carrier of (TOP-REAL 2)
Cl rl is functional closed Element of bool the carrier of (TOP-REAL 2)
rg is Element of bool the carrier of ((TOP-REAL 2) | (rp `))
rd is Element of bool the carrier of ((TOP-REAL 2) | (rp `))
b is non empty TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
a is functional Element of bool the carrier of (TOP-REAL 2)
c is set
rp is functional non empty proper closed connected compact bounded being_simple_closed_curve with_the_max_arc Element of bool the carrier of (TOP-REAL 2)
rp ` is functional non empty open Element of bool the carrier of (TOP-REAL 2)
the carrier of (TOP-REAL 2) \ rp is set
(TOP-REAL 2) | (rp `) is non empty strict TopSpace-like T_0 T_1 T_2 V118( TOP-REAL 2) SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | (rp `)) is non empty set
bool the carrier of ((TOP-REAL 2) | (rp `)) is non empty set
rl is Element of bool the carrier of ((TOP-REAL 2) | (rp `))
((TOP-REAL 2) | (rp `)) | rl is strict TopSpace-like T_0 T_1 T_2 SubSpace of (TOP-REAL 2) | (rp `)
the carrier of (((TOP-REAL 2) | (rp `)) | rl) is set
rd is Element of the carrier of (((TOP-REAL 2) | (rp `)) | rl)
a is Element of the carrier of (((TOP-REAL 2) | (rp `)) | rl)
{} ((TOP-REAL 2) | (rp `)) is Relation-like non-empty empty-yielding RAT -valued Function-like one-to-one constant functional empty proper open closed boundary nowhere_dense connected compact V156() V157() V158() V159() V166() V167() V168() V169() V170() V171() V172() bounded_below interval Element of bool the carrier of ((TOP-REAL 2) | (rp `))
b is non empty TopSpace-like TopStruct
the carrier of b is non empty set
[: the carrier of I[01], the carrier of (((TOP-REAL 2) | (rp `)) | rl):] is Relation-like set
bool [: the carrier of I[01], the carrier of (((TOP-REAL 2) | (rp `)) | rl):] is non empty set
c is Element of the carrier of b
I[01] --> c is Relation-like the carrier of I[01] -defined the carrier of b -valued Function-like non empty total quasi_total continuous Element of bool [: the carrier of I[01], the carrier of b:]
[: the carrier of I[01], the carrier of b:] is Relation-like non empty set
bool [: the carrier of I[01], the carrier of b:] is non empty set
the carrier of I[01] --> c is Relation-like the carrier of I[01] -defined the carrier of b -valued Function-like non empty total quasi_total Element of bool [: the carrier of I[01], the carrier of b:]
d is Relation-like the carrier of I[01] -defined the carrier of (((TOP-REAL 2) | (rp `)) | rl) -valued Function-like quasi_total Element of bool [: the carrier of I[01], the carrier of (((TOP-REAL 2) | (rp `)) | rl):]
d . 0 is set
d . 1 is set
d is functional Element of bool the carrier of (TOP-REAL 2)
b is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
c is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
lg is functional Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | lg is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | lg) is set
[: the carrier of I[01], the carrier of ((TOP-REAL 2) | lg):] is Relation-like set
bool [: the carrier of I[01], the carrier of ((TOP-REAL 2) | lg):] is non empty set
pg is Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL 2) | lg) -valued Function-like quasi_total Element of bool [: the carrier of I[01], the carrier of ((TOP-REAL 2) | lg):]
pg . 0 is set
pg . 1 is set
[: the carrier of I[01], the carrier of (((TOP-REAL 2) | (rp `)) | rl):] is Relation-like set
bool [: the carrier of I[01], the carrier of (((TOP-REAL 2) | (rp `)) | rl):] is non empty set
ld is Relation-like the carrier of I[01] -defined the carrier of (((TOP-REAL 2) | (rp `)) | rl) -valued Function-like quasi_total Element of bool [: the carrier of I[01], the carrier of (((TOP-REAL 2) | (rp `)) | rl):]
ld . 0 is set
ld . 1 is set
rp is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
rl is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
rg is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
rd is functional Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | rd is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | rd) is set
id rd is Relation-like rd -defined rd -valued Function-like one-to-one total quasi_total Element of bool [:rd,rd:]
[:rd,rd:] is Relation-like set
bool [:rd,rd:] is non empty set
a is complex ext-real non negative real set
Tdisk (rg,a) is non empty TopSpace-like T_0 T_1 T_2 V82() normal T_3 T_4 compact closed V246() V270(2) pseudocompact SubSpace of TOP-REAL 2
the carrier of (Tdisk (rg,a)) is non empty set
bool the carrier of (Tdisk (rg,a)) is non empty set
[: the carrier of (Tdisk (rg,a)), the carrier of ((TOP-REAL 2) | rd):] is Relation-like set
bool [: the carrier of (Tdisk (rg,a)), the carrier of ((TOP-REAL 2) | rd):] is non empty set
d is functional non empty Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | d is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | d) is non empty set
[: the carrier of I[01], the carrier of ((TOP-REAL 2) | d):] is Relation-like non empty set
bool [: the carrier of I[01], the carrier of ((TOP-REAL 2) | d):] is non empty set
pg is Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL 2) | d) -valued Function-like non empty total quasi_total Element of bool [: the carrier of I[01], the carrier of ((TOP-REAL 2) | d):]
pg . 0 is set
pg . 1 is set
[: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of ((TOP-REAL 2) | d):] is Relation-like non empty set
bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of ((TOP-REAL 2) | d):] is non empty set
c is non empty Element of bool the carrier of (Tdisk (rg,a))
(Tdisk (rg,a)) | c is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of Tdisk (rg,a)
the carrier of ((Tdisk (rg,a)) | c) is non empty set
[: the carrier of ((Tdisk (rg,a)) | c), the carrier of (Closed-Interval-TSpace ((- 1),1)):] is Relation-like non empty V156() V157() V158() set
bool [: the carrier of ((Tdisk (rg,a)) | c), the carrier of (Closed-Interval-TSpace ((- 1),1)):] is non empty set
ld is Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined the carrier of ((TOP-REAL 2) | d) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of ((TOP-REAL 2) | d):]
ld /" is Relation-like the carrier of ((TOP-REAL 2) | d) -defined the carrier of (Closed-Interval-TSpace (0,1)) -valued Function-like non empty total quasi_total V156() V157() V158() Element of bool [: the carrier of ((TOP-REAL 2) | d), the carrier of (Closed-Interval-TSpace (0,1)):]
[: the carrier of ((TOP-REAL 2) | d), the carrier of (Closed-Interval-TSpace (0,1)):] is Relation-like non empty V156() V157() V158() set
bool [: the carrier of ((TOP-REAL 2) | d), the carrier of (Closed-Interval-TSpace (0,1)):] is non empty set
(L[01] (((#) ((- 1),1)),(((- 1),1) (#)))) * (ld /") is Relation-like the carrier of ((TOP-REAL 2) | d) -defined the carrier of (Closed-Interval-TSpace ((- 1),1)) -valued Function-like non empty total quasi_total V156() V157() V158() Element of bool [: the carrier of ((TOP-REAL 2) | d), the carrier of (Closed-Interval-TSpace ((- 1),1)):]
[: the carrier of ((TOP-REAL 2) | d), the carrier of (Closed-Interval-TSpace ((- 1),1)):] is Relation-like non empty V156() V157() V158() set
bool [: the carrier of ((TOP-REAL 2) | d), the carrier of (Closed-Interval-TSpace ((- 1),1)):] is non empty set
[: the carrier of (Tdisk (rg,a)), the carrier of (Closed-Interval-TSpace ((- 1),1)):] is Relation-like non empty V156() V157() V158() set
bool [: the carrier of (Tdisk (rg,a)), the carrier of (Closed-Interval-TSpace ((- 1),1)):] is non empty set
pd is Relation-like the carrier of ((Tdisk (rg,a)) | c) -defined the carrier of (Closed-Interval-TSpace ((- 1),1)) -valued Function-like non empty total quasi_total V156() V157() V158() Element of bool [: the carrier of ((Tdisk (rg,a)) | c), the carrier of (Closed-Interval-TSpace ((- 1),1)):]
R is Relation-like the carrier of (Tdisk (rg,a)) -defined the carrier of (Closed-Interval-TSpace ((- 1),1)) -valued Function-like non empty total quasi_total continuous V156() V157() V158() Element of bool [: the carrier of (Tdisk (rg,a)), the carrier of (Closed-Interval-TSpace ((- 1),1)):]
R | c is Relation-like the carrier of (Tdisk (rg,a)) -defined c -defined the carrier of (Tdisk (rg,a)) -defined the carrier of (Closed-Interval-TSpace ((- 1),1)) -valued Function-like V156() V157() V158() Element of bool [: the carrier of (Tdisk (rg,a)), the carrier of (Closed-Interval-TSpace ((- 1),1)):]
(L[01] (((#) ((- 1),1)),(((- 1),1) (#)))) /" is Relation-like the carrier of (Closed-Interval-TSpace ((- 1),1)) -defined the carrier of (Closed-Interval-TSpace (0,1)) -valued Function-like non empty total quasi_total V156() V157() V158() Element of bool [: the carrier of (Closed-Interval-TSpace ((- 1),1)), the carrier of (Closed-Interval-TSpace (0,1)):]
[: the carrier of (Closed-Interval-TSpace ((- 1),1)), the carrier of (Closed-Interval-TSpace (0,1)):] is Relation-like non empty V156() V157() V158() set
bool [: the carrier of (Closed-Interval-TSpace ((- 1),1)), the carrier of (Closed-Interval-TSpace (0,1)):] is non empty set
ld * ((L[01] (((#) ((- 1),1)),(((- 1),1) (#)))) /") is Relation-like the carrier of (Closed-Interval-TSpace ((- 1),1)) -defined the carrier of ((TOP-REAL 2) | d) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (Closed-Interval-TSpace ((- 1),1)), the carrier of ((TOP-REAL 2) | d):]
[: the carrier of (Closed-Interval-TSpace ((- 1),1)), the carrier of ((TOP-REAL 2) | d):] is Relation-like non empty set
bool [: the carrier of (Closed-Interval-TSpace ((- 1),1)), the carrier of ((TOP-REAL 2) | d):] is non empty set
(ld * ((L[01] (((#) ((- 1),1)),(((- 1),1) (#)))) /")) * R is Relation-like the carrier of (Tdisk (rg,a)) -defined the carrier of ((TOP-REAL 2) | d) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (Tdisk (rg,a)), the carrier of ((TOP-REAL 2) | d):]
[: the carrier of (Tdisk (rg,a)), the carrier of ((TOP-REAL 2) | d):] is Relation-like non empty set
bool [: the carrier of (Tdisk (rg,a)), the carrier of ((TOP-REAL 2) | d):] is non empty set
dR is Relation-like the carrier of (Tdisk (rg,a)) -defined the carrier of ((TOP-REAL 2) | rd) -valued Function-like quasi_total Element of bool [: the carrier of (Tdisk (rg,a)), the carrier of ((TOP-REAL 2) | rd):]
dR | rd is Relation-like rd -defined the carrier of (Tdisk (rg,a)) -defined the carrier of ((TOP-REAL 2) | rd) -valued Function-like Element of bool [: the carrier of (Tdisk (rg,a)), the carrier of ((TOP-REAL 2) | rd):]
dom dR is Element of bool the carrier of (Tdisk (rg,a))
dom (id rd) is functional Element of bool rd
bool rd is non empty set
TR is set
dom (dR | rd) is functional Element of bool rd
dom R is non empty Element of bool the carrier of (Tdisk (rg,a))
dom ((L[01] (((#) ((- 1),1)),(((- 1),1) (#)))) * (ld /")) is non empty Element of bool the carrier of ((TOP-REAL 2) | d)
bool the carrier of ((TOP-REAL 2) | d) is non empty set
(ld * ((L[01] (((#) ((- 1),1)),(((- 1),1) (#)))) /")) * ((L[01] (((#) ((- 1),1)),(((- 1),1) (#)))) * (ld /")) is Relation-like the carrier of ((TOP-REAL 2) | d) -defined the carrier of ((TOP-REAL 2) | d) -valued Function-like non empty total quasi_total Element of bool [: the carrier of ((TOP-REAL 2) | d), the carrier of ((TOP-REAL 2) | d):]
[: the carrier of ((TOP-REAL 2) | d), the carrier of ((TOP-REAL 2) | d):] is Relation-like non empty set
bool [: the carrier of ((TOP-REAL 2) | d), the carrier of ((TOP-REAL 2) | d):] is non empty set
(ld * ((L[01] (((#) ((- 1),1)),(((- 1),1) (#)))) /")) * (L[01] (((#) ((- 1),1)),(((- 1),1) (#)))) is Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined the carrier of ((TOP-REAL 2) | d) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of ((TOP-REAL 2) | d):]
((ld * ((L[01] (((#) ((- 1),1)),(((- 1),1) (#)))) /")) * (L[01] (((#) ((- 1),1)),(((- 1),1) (#))))) * (ld /") is Relation-like the carrier of ((TOP-REAL 2) | d) -defined the carrier of ((TOP-REAL 2) | d) -valued Function-like non empty total quasi_total Element of bool [: the carrier of ((TOP-REAL 2) | d), the carrier of ((TOP-REAL 2) | d):]
((L[01] (((#) ((- 1),1)),(((- 1),1) (#)))) /") * (L[01] (((#) ((- 1),1)),(((- 1),1) (#)))) is Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined the carrier of (Closed-Interval-TSpace (0,1)) -valued Function-like non empty total quasi_total V156() V157() V158() Element of bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace (0,1)):]
[: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace (0,1)):] is Relation-like non empty V156() V157() V158() set
bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace (0,1)):] is non empty set
ld * (((L[01] (((#) ((- 1),1)),(((- 1),1) (#)))) /") * (L[01] (((#) ((- 1),1)),(((- 1),1) (#))))) is Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined the carrier of ((TOP-REAL 2) | d) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of ((TOP-REAL 2) | d):]
(ld * (((L[01] (((#) ((- 1),1)),(((- 1),1) (#)))) /") * (L[01] (((#) ((- 1),1)),(((- 1),1) (#)))))) * (ld /") is Relation-like the carrier of ((TOP-REAL 2) | d) -defined the carrier of ((TOP-REAL 2) | d) -valued Function-like non empty total quasi_total Element of bool [: the carrier of ((TOP-REAL 2) | d), the carrier of ((TOP-REAL 2) | d):]
id (Closed-Interval-TSpace (0,1)) is Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined the carrier of (Closed-Interval-TSpace (0,1)) -valued Function-like one-to-one non empty total quasi_total onto bijective continuous V156() V157() V158() being_homeomorphism Homeomorphism of Closed-Interval-TSpace (0,1)
id the carrier of (Closed-Interval-TSpace (0,1)) is Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined the carrier of (Closed-Interval-TSpace (0,1)) -valued Function-like one-to-one non empty total quasi_total V156() V157() V158() V160() V162() Element of bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace (0,1)):]
ld * (id (Closed-Interval-TSpace (0,1))) is Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined the carrier of ((TOP-REAL 2) | d) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of ((TOP-REAL 2) | d):]
(ld * (id (Closed-Interval-TSpace (0,1)))) * (ld /") is Relation-like the carrier of ((TOP-REAL 2) | d) -defined the carrier of ((TOP-REAL 2) | d) -valued Function-like non empty total quasi_total Element of bool [: the carrier of ((TOP-REAL 2) | d), the carrier of ((TOP-REAL 2) | d):]
ld * (ld /") is Relation-like the carrier of ((TOP-REAL 2) | d) -defined the carrier of ((TOP-REAL 2) | d) -valued Function-like non empty total quasi_total Element of bool [: the carrier of ((TOP-REAL 2) | d), the carrier of ((TOP-REAL 2) | d):]
id ((TOP-REAL 2) | d) is Relation-like the carrier of ((TOP-REAL 2) | d) -defined the carrier of ((TOP-REAL 2) | d) -valued Function-like one-to-one non empty total quasi_total onto bijective continuous being_homeomorphism Homeomorphism of (TOP-REAL 2) | d
id the carrier of ((TOP-REAL 2) | d) is Relation-like the carrier of ((TOP-REAL 2) | d) -defined the carrier of ((TOP-REAL 2) | d) -valued Function-like one-to-one non empty total quasi_total Element of bool [: the carrier of ((TOP-REAL 2) | d), the carrier of ((TOP-REAL 2) | d):]
(dR | rd) . TR is set
dR . TR is set
R . TR is complex ext-real real set
(ld * ((L[01] (((#) ((- 1),1)),(((- 1),1) (#)))) /")) . (R . TR) is set
((L[01] (((#) ((- 1),1)),(((- 1),1) (#)))) * (ld /")) . TR is complex ext-real real set
(ld * ((L[01] (((#) ((- 1),1)),(((- 1),1) (#)))) /")) . (((L[01] (((#) ((- 1),1)),(((- 1),1) (#)))) * (ld /")) . TR) is set
(id rd) . TR is Relation-like Function-like set
rp is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
rl is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
rg is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
{rg} is functional non empty proper closed compact bounded Element of bool the carrier of (TOP-REAL 2)
rd is functional non empty proper closed connected compact bounded being_simple_closed_curve with_the_max_arc Element of bool the carrier of (TOP-REAL 2)
rd ` is functional non empty open Element of bool the carrier of (TOP-REAL 2)
the carrier of (TOP-REAL 2) \ rd is set
(TOP-REAL 2) | (rd `) is non empty strict TopSpace-like T_0 T_1 T_2 V118( TOP-REAL 2) SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | (rd `)) is non empty set
bool the carrier of ((TOP-REAL 2) | (rd `)) is non empty set
a is functional Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | a is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | a) is set
id a is Relation-like a -defined a -valued Function-like one-to-one total quasi_total Element of bool [:a,a:]
[:a,a:] is Relation-like set
bool [:a,a:] is non empty set
b is functional Element of bool the carrier of (TOP-REAL 2)
Cl b is functional closed Element of bool the carrier of (TOP-REAL 2)
b ` is functional Element of bool the carrier of (TOP-REAL 2)
the carrier of (TOP-REAL 2) \ b is set
(Cl b) /\ (b `) is functional Element of bool the carrier of (TOP-REAL 2)
c is functional Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | c is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | c) is set
d is Element of bool the carrier of ((TOP-REAL 2) | (rd `))
lg is non empty complex ext-real positive non negative real set
Ball (rg,lg) is functional non empty proper open connected bounded being_Region convex Element of bool the carrier of (TOP-REAL 2)
Tdisk (rg,lg) is non empty TopSpace-like T_0 T_1 T_2 V82() normal T_3 T_4 compact closed V246() V270(2) pseudocompact SubSpace of TOP-REAL 2
the carrier of (Tdisk (rg,lg)) is non empty set
[: the carrier of (Tdisk (rg,lg)), the carrier of ((TOP-REAL 2) | a):] is Relation-like set
bool [: the carrier of (Tdisk (rg,lg)), the carrier of ((TOP-REAL 2) | a):] is non empty set
cl_Ball (rg,lg) is functional non empty proper closed connected bounded convex Element of bool the carrier of (TOP-REAL 2)
(cl_Ball (rg,lg)) \ {rg} is functional non empty Element of bool the carrier of (TOP-REAL 2)
[: the carrier of (Tdisk (rg,lg)), the carrier of ((TOP-REAL 2) | c):] is Relation-like set
bool [: the carrier of (Tdisk (rg,lg)), the carrier of ((TOP-REAL 2) | c):] is non empty set
ld is Relation-like the carrier of (Tdisk (rg,lg)) -defined the carrier of ((TOP-REAL 2) | a) -valued Function-like quasi_total Element of bool [: the carrier of (Tdisk (rg,lg)), the carrier of ((TOP-REAL 2) | a):]
ld | a is Relation-like a -defined the carrier of (Tdisk (rg,lg)) -defined the carrier of ((TOP-REAL 2) | a) -valued Function-like Element of bool [: the carrier of (Tdisk (rg,lg)), the carrier of ((TOP-REAL 2) | a):]
pd is functional non empty Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | pd is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
rg - rg is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
- rg is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
K270((TOP-REAL 2),rg,(- rg)) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) is Relation-like [: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of bool [:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):]
[:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):] is Relation-like non empty set
bool [:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):] is non empty set
K224( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),rg,(- rg)) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
|.(rg - rg).| is complex ext-real non negative real Element of REAL
[#] (Tdisk (rg,lg)) is non empty non proper open closed dense non boundary compact Element of bool the carrier of (Tdisk (rg,lg))
bool the carrier of (Tdisk (rg,lg)) is non empty set
(Cl b) /\ ([#] (Tdisk (rg,lg))) is Element of bool the carrier of (Tdisk (rg,lg))
Sphere (rg,lg) is functional non empty proper closed closed connected compact bounded bounded being_simple_closed_curve with_the_max_arc Element of bool the carrier of (TOP-REAL 2)
C is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
(b `) /\ ([#] (Tdisk (rg,lg))) is Element of bool the carrier of (Tdisk (rg,lg))
TR is non empty Element of bool the carrier of (Tdisk (rg,lg))
(Tdisk (rg,lg)) | TR is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of Tdisk (rg,lg)
P is non empty Element of bool the carrier of (Tdisk (rg,lg))
(Tdisk (rg,lg)) | P is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of Tdisk (rg,lg)
U is non empty TopSpace-like T_0 T_1 T_2 SubSpace of Tdisk (rg,lg)
the carrier of U is non empty set
l is non empty TopSpace-like T_0 T_1 T_2 SubSpace of Tdisk (rg,lg)
the carrier of l is non empty set
R is non empty TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of R is non empty set
LJ is set
LJ is set
ld | TR is Relation-like the carrier of (Tdisk (rg,lg)) -defined TR -defined the carrier of (Tdisk (rg,lg)) -defined the carrier of ((TOP-REAL 2) | a) -valued Function-like Element of bool [: the carrier of (Tdisk (rg,lg)), the carrier of ((TOP-REAL 2) | a):]
[:TR,a:] is Relation-like set
bool [:TR,a:] is non empty set
[: the carrier of U, the carrier of R:] is Relation-like non empty set
bool [: the carrier of U, the carrier of R:] is non empty set
[: the carrier of l, the carrier of R:] is Relation-like non empty set
bool [: the carrier of l, the carrier of R:] is non empty set
id P is Relation-like P -defined P -valued Function-like one-to-one non empty total quasi_total Element of bool [:P,P:]
[:P,P:] is Relation-like non empty set
bool [:P,P:] is non empty set
[#] U is non empty non proper open closed dense non boundary Element of bool the carrier of U
bool the carrier of U is non empty set
[#] l is non empty non proper open closed dense non boundary Element of bool the carrier of l
bool the carrier of l is non empty set
([#] U) \/ ([#] l) is non empty set
x is set
x is functional closed Element of bool the carrier of (TOP-REAL 2)
x /\ (Cl b) is functional closed Element of bool the carrier of (TOP-REAL 2)
x /\ (b `) is functional Element of bool the carrier of (TOP-REAL 2)
dR is functional non empty Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | dR is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | dR) is non empty set
[: the carrier of U, the carrier of ((TOP-REAL 2) | dR):] is Relation-like non empty set
bool [: the carrier of U, the carrier of ((TOP-REAL 2) | dR):] is non empty set
A1 is Relation-like the carrier of U -defined the carrier of ((TOP-REAL 2) | dR) -valued Function-like non empty total quasi_total Element of bool [: the carrier of U, the carrier of ((TOP-REAL 2) | dR):]
LJ is Relation-like the carrier of U -defined the carrier of R -valued Function-like non empty total quasi_total Element of bool [: the carrier of U, the carrier of R:]
[: the carrier of l, the carrier of l:] is Relation-like non empty set
bool [: the carrier of l, the carrier of l:] is non empty set
A2 is Relation-like the carrier of l -defined the carrier of l -valued Function-like non empty total quasi_total Element of bool [: the carrier of l, the carrier of l:]
id l is Relation-like the carrier of l -defined the carrier of l -valued Function-like one-to-one non empty total quasi_total onto bijective continuous being_homeomorphism Homeomorphism of l
id the carrier of l is Relation-like the carrier of l -defined the carrier of l -valued Function-like one-to-one non empty total quasi_total Element of bool [: the carrier of l, the carrier of l:]
k is Relation-like the carrier of l -defined the carrier of R -valued Function-like non empty total quasi_total Element of bool [: the carrier of l, the carrier of R:]
w is set
ld . w is set
(id a) . w is Relation-like Function-like set
([#] U) /\ ([#] l) is Element of bool the carrier of l
w is set
LJ . w is set
k . w is set
ld . w is set
LJ +* k is Relation-like Function-like set
w is Relation-like the carrier of (Tdisk (rg,lg)) -defined the carrier of ((TOP-REAL 2) | c) -valued Function-like quasi_total Element of bool [: the carrier of (Tdisk (rg,lg)), the carrier of ((TOP-REAL 2) | c):]
Ux is Element of the carrier of (Tdisk (rg,lg))
w . Ux is Element of the carrier of ((TOP-REAL 2) | c)
ld . Ux is Element of the carrier of ((TOP-REAL 2) | a)
dom k is non empty Element of bool the carrier of l
LJ . Ux is set
k . Ux is set
k . Ux is set
rp is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
{rp} is functional non empty proper closed compact bounded Element of bool the carrier of (TOP-REAL 2)
rl is functional non empty proper closed connected compact bounded being_simple_closed_curve with_the_max_arc Element of bool the carrier of (TOP-REAL 2)
rl ` is functional non empty open Element of bool the carrier of (TOP-REAL 2)
the carrier of (TOP-REAL 2) \ rl is set
(TOP-REAL 2) | (rl `) is non empty strict TopSpace-like T_0 T_1 T_2 V118( TOP-REAL 2) SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | (rl `)) is non empty set
bool the carrier of ((TOP-REAL 2) | (rl `)) is non empty set
rg is functional Element of bool the carrier of (TOP-REAL 2)
Cl rg is functional closed Element of bool the carrier of (TOP-REAL 2)
rg ` is functional Element of bool the carrier of (TOP-REAL 2)
the carrier of (TOP-REAL 2) \ rg is set
(Cl rg) /\ (rg `) is functional Element of bool the carrier of (TOP-REAL 2)
rd is functional Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | rd is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | rd) is set
a is Element of bool the carrier of ((TOP-REAL 2) | (rl `))
b is Element of bool the carrier of ((TOP-REAL 2) | (rl `))
c is functional non empty Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | c is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | c) is non empty set
id c is Relation-like c -defined c -valued Function-like one-to-one non empty total quasi_total Element of bool [:c,c:]
[:c,c:] is Relation-like non empty set
bool [:c,c:] is non empty set
d is non empty complex ext-real positive non negative real set
Ball (rp,d) is functional non empty proper open connected bounded being_Region convex Element of bool the carrier of (TOP-REAL 2)
Tdisk (rp,d) is non empty TopSpace-like T_0 T_1 T_2 V82() normal T_3 T_4 compact closed V246() V270(2) pseudocompact SubSpace of TOP-REAL 2
the carrier of (Tdisk (rp,d)) is non empty set
[: the carrier of (Tdisk (rp,d)), the carrier of ((TOP-REAL 2) | c):] is Relation-like non empty set
bool [: the carrier of (Tdisk (rp,d)), the carrier of ((TOP-REAL 2) | c):] is non empty set
cl_Ball (rp,d) is functional non empty proper closed connected bounded convex Element of bool the carrier of (TOP-REAL 2)
(cl_Ball (rp,d)) \ {rp} is functional non empty Element of bool the carrier of (TOP-REAL 2)
[: the carrier of (Tdisk (rp,d)), the carrier of ((TOP-REAL 2) | rd):] is Relation-like set
bool [: the carrier of (Tdisk (rp,d)), the carrier of ((TOP-REAL 2) | rd):] is non empty set
pg is Relation-like the carrier of (Tdisk (rp,d)) -defined the carrier of ((TOP-REAL 2) | c) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (Tdisk (rp,d)), the carrier of ((TOP-REAL 2) | c):]
pg | c is Relation-like c -defined the carrier of (Tdisk (rp,d)) -defined the carrier of ((TOP-REAL 2) | c) -valued Function-like Element of bool [: the carrier of (Tdisk (rp,d)), the carrier of ((TOP-REAL 2) | c):]
ld is functional non empty Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | ld is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
rp - rp is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
- rp is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
K270((TOP-REAL 2),rp,(- rp)) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) is Relation-like [: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of bool [:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):]
[:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):] is Relation-like non empty set
bool [:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):] is non empty set
K224( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),rp,(- rp)) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
|.(rp - rp).| is complex ext-real non negative real Element of REAL
[#] (Tdisk (rp,d)) is non empty non proper open closed dense non boundary compact Element of bool the carrier of (Tdisk (rp,d))
bool the carrier of (Tdisk (rp,d)) is non empty set
(Cl rg) /\ ([#] (Tdisk (rp,d))) is Element of bool the carrier of (Tdisk (rp,d))
dR is set
(rg `) /\ ([#] (Tdisk (rp,d))) is Element of bool the carrier of (Tdisk (rp,d))
R is non empty Element of bool the carrier of (Tdisk (rp,d))
(Tdisk (rp,d)) | R is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of Tdisk (rp,d)
dR is non empty Element of bool the carrier of (Tdisk (rp,d))
(Tdisk (rp,d)) | dR is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of Tdisk (rp,d)
the carrier of ((Tdisk (rp,d)) | R) is non empty set
the carrier of ((Tdisk (rp,d)) | dR) is non empty set
the carrier of ((TOP-REAL 2) | ld) is non empty set
P is set
P is set
pd is non empty TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of pd is non empty set
[: the carrier of ((Tdisk (rp,d)) | R), the carrier of pd:] is Relation-like non empty set
bool [: the carrier of ((Tdisk (rp,d)) | R), the carrier of pd:] is non empty set
id R is Relation-like R -defined R -valued Function-like one-to-one non empty total quasi_total Element of bool [:R,R:]
[:R,R:] is Relation-like non empty set
bool [:R,R:] is non empty set
pg | dR is Relation-like the carrier of (Tdisk (rp,d)) -defined dR -defined the carrier of (Tdisk (rp,d)) -defined the carrier of ((TOP-REAL 2) | c) -valued Function-like Element of bool [: the carrier of (Tdisk (rp,d)), the carrier of ((TOP-REAL 2) | c):]
[:dR,c:] is Relation-like non empty set
bool [:dR,c:] is non empty set
[: the carrier of ((Tdisk (rp,d)) | dR), the carrier of pd:] is Relation-like non empty set
bool [: the carrier of ((Tdisk (rp,d)) | dR), the carrier of pd:] is non empty set
[#] ((Tdisk (rp,d)) | R) is non empty non proper open closed dense non boundary Element of bool the carrier of ((Tdisk (rp,d)) | R)
bool the carrier of ((Tdisk (rp,d)) | R) is non empty set
[#] ((Tdisk (rp,d)) | dR) is non empty non proper open closed dense non boundary Element of bool the carrier of ((Tdisk (rp,d)) | dR)
bool the carrier of ((Tdisk (rp,d)) | dR) is non empty set
([#] ((Tdisk (rp,d)) | R)) \/ ([#] ((Tdisk (rp,d)) | dR)) is non empty set
l is set
l is functional closed Element of bool the carrier of (TOP-REAL 2)
l /\ (Cl rg) is functional closed Element of bool the carrier of (TOP-REAL 2)
l /\ (rg `) is functional Element of bool the carrier of (TOP-REAL 2)
id ((Tdisk (rp,d)) | R) is Relation-like the carrier of ((Tdisk (rp,d)) | R) -defined the carrier of ((Tdisk (rp,d)) | R) -valued Function-like one-to-one non empty total quasi_total onto bijective continuous being_homeomorphism Homeomorphism of (Tdisk (rp,d)) | R
id the carrier of ((Tdisk (rp,d)) | R) is Relation-like the carrier of ((Tdisk (rp,d)) | R) -defined the carrier of ((Tdisk (rp,d)) | R) -valued Function-like one-to-one non empty total quasi_total Element of bool [: the carrier of ((Tdisk (rp,d)) | R), the carrier of ((Tdisk (rp,d)) | R):]
[: the carrier of ((Tdisk (rp,d)) | R), the carrier of ((Tdisk (rp,d)) | R):] is Relation-like non empty set
bool [: the carrier of ((Tdisk (rp,d)) | R), the carrier of ((Tdisk (rp,d)) | R):] is non empty set
P is Relation-like the carrier of ((Tdisk (rp,d)) | R) -defined the carrier of pd -valued Function-like non empty total quasi_total Element of bool [: the carrier of ((Tdisk (rp,d)) | R), the carrier of pd:]
[: the carrier of ((Tdisk (rp,d)) | dR), the carrier of ((TOP-REAL 2) | c):] is Relation-like non empty set
bool [: the carrier of ((Tdisk (rp,d)) | dR), the carrier of ((TOP-REAL 2) | c):] is non empty set
U is Relation-like the carrier of ((Tdisk (rp,d)) | dR) -defined the carrier of pd -valued Function-like non empty total quasi_total Element of bool [: the carrier of ((Tdisk (rp,d)) | dR), the carrier of pd:]
LJ is Relation-like the carrier of ((Tdisk (rp,d)) | dR) -defined the carrier of ((TOP-REAL 2) | c) -valued Function-like non empty total quasi_total Element of bool [: the carrier of ((Tdisk (rp,d)) | dR), the carrier of ((TOP-REAL 2) | c):]
k is set
pg . k is set
(id c) . k is Relation-like Function-like set
([#] ((Tdisk (rp,d)) | R)) /\ ([#] ((Tdisk (rp,d)) | dR)) is Element of bool the carrier of ((Tdisk (rp,d)) | dR)
k is set
P . k is set
U . k is set
pg . k is set
P +* U is Relation-like Function-like set
k is Relation-like the carrier of (Tdisk (rp,d)) -defined the carrier of ((TOP-REAL 2) | rd) -valued Function-like quasi_total Element of bool [: the carrier of (Tdisk (rp,d)), the carrier of ((TOP-REAL 2) | rd):]
x is Element of the carrier of (Tdisk (rp,d))
k . x is Element of the carrier of ((TOP-REAL 2) | rd)
pg . x is Element of the carrier of ((TOP-REAL 2) | c)
dom U is non empty Element of bool the carrier of ((Tdisk (rp,d)) | dR)
P . x is set
U . x is set
U . x is set
rp is functional non empty proper closed connected compact bounded being_simple_closed_curve with_the_max_arc Element of bool the carrier of (TOP-REAL 2)
rp ` is functional non empty open Element of bool the carrier of (TOP-REAL 2)
the carrier of (TOP-REAL 2) \ rp is set
(TOP-REAL 2) | (rp `) is non empty strict TopSpace-like T_0 T_1 T_2 V118( TOP-REAL 2) SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | (rp `)) is non empty set
bool the carrier of ((TOP-REAL 2) | (rp `)) is non empty set
BDD rp is functional open Element of bool the carrier of (TOP-REAL 2)
{ b₁ where b₁ is functional Element of bool the carrier of (TOP-REAL 2) : b₁ is_inside_component_of rp } is set
union { b₁ where b₁ is functional Element of bool the carrier of (TOP-REAL 2) : b₁ is_inside_component_of rp } is set
rl is functional Element of bool the carrier of (TOP-REAL 2)
Fr rl is functional closed Element of bool the carrier of (TOP-REAL 2)
Cl rl is functional closed Element of bool the carrier of (TOP-REAL 2)
rl ` is functional Element of bool the carrier of (TOP-REAL 2)
the carrier of (TOP-REAL 2) \ rl is set
Cl (rl `) is functional closed Element of bool the carrier of (TOP-REAL 2)
(Cl rl) /\ (Cl (rl `)) is functional closed Element of bool the carrier of (TOP-REAL 2)
rg is Element of bool the carrier of ((TOP-REAL 2) | (rp `))
rd is non empty TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
a is functional open Element of bool the carrier of (TOP-REAL 2)
Fr a is functional closed boundary nowhere_dense Element of bool the carrier of (TOP-REAL 2)
Cl a is functional closed Element of bool the carrier of (TOP-REAL 2)
a ` is functional closed Element of bool the carrier of (TOP-REAL 2)
the carrier of (TOP-REAL 2) \ a is set
Cl (a `) is functional closed Element of bool the carrier of (TOP-REAL 2)
(Cl a) /\ (Cl (a `)) is functional closed Element of bool the carrier of (TOP-REAL 2)
(Cl a) /\ (a `) is functional closed Element of bool the carrier of (TOP-REAL 2)
{ b₁ where b₁ is Element of bool the carrier of ((TOP-REAL 2) | (rp `)) : ( b<sub>1</sub> is a_component & not b<sub>1</sub> = rg ) } is set
union { b<sub>1</sub> where b<sub>1</sub> is Element of bool the carrier of ((TOP-REAL 2) | (rp `)) : ( b₁ is a_component & not b₁ = rg ) } is set
(union { b₁ where b₁ is Element of bool the carrier of ((TOP-REAL 2) | (rp `)) : ( b<sub>1</sub> is a_component & not b<sub>1</sub> = rg ) } ) \/ rg is set
((union { b<sub>1</sub> where b<sub>1</sub> is Element of bool the carrier of ((TOP-REAL 2) | (rp `)) : ( b₁ is a_component & not b₁ = rg ) } ) \/ rg) \/ rp is non empty set
d is set
lg is set
pg is Element of bool the carrier of ((TOP-REAL 2) | (rp `))
d is set
lg is Element of the carrier of ((TOP-REAL 2) | (rp `))
Component_of lg is Element of bool the carrier of ((TOP-REAL 2) | (rp `))
d is set
lg is set
pg is Element of bool the carrier of ((TOP-REAL 2) | (rp `))
d is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
lg is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
pg is functional Element of bool the carrier of (TOP-REAL 2)
{} ((TOP-REAL 2) | (rp `)) is Relation-like non-empty empty-yielding RAT -valued Function-like one-to-one constant functional empty proper open closed boundary nowhere_dense connected compact V156() V157() V158() V159() V166() V167() V168() V169() V170() V171() V172() bounded_below interval Element of bool the carrier of ((TOP-REAL 2) | (rp `))
pd is set
ld is functional proper bounded Element of bool the carrier of (TOP-REAL 2)
ld \/ rp is functional non empty Element of bool the carrier of (TOP-REAL 2)
Euclid 2 is non empty strict Reflexive discerning symmetric triangle Discerning MetrStruct
the carrier of (Euclid 2) is non empty set
bool the carrier of (Euclid 2) is non empty set
dR is bounded Element of bool the carrier of (Euclid 2)
R is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
TR is non empty complex ext-real positive non negative real set
Ball (R,TR) is functional non empty proper open connected bounded being_Region convex Element of bool the carrier of (TOP-REAL 2)
Tdisk (R,TR) is non empty TopSpace-like T_0 T_1 T_2 V82() normal T_3 T_4 compact closed V246() V270(2) pseudocompact SubSpace of TOP-REAL 2
Tcircle (R,TR) is non empty strict TopSpace-like T_0 T_1 T_2 V82() normal T_3 T_4 connected compact V246() being_simple_closed_curve pathwise_connected pseudocompact SubSpace of TOP-REAL 2
cl_Ball (R,TR) is functional non empty proper closed connected bounded convex Element of bool the carrier of (TOP-REAL 2)
{R} is functional non empty proper closed compact bounded Element of bool the carrier of (TOP-REAL 2)
(cl_Ball (R,TR)) \ {R} is functional non empty Element of bool the carrier of (TOP-REAL 2)
the carrier of (Tcircle (R,TR)) is non empty set
Sphere (R,TR) is functional non empty proper closed closed connected compact bounded bounded being_simple_closed_curve with_the_max_arc Element of bool the carrier of (TOP-REAL 2)
the carrier of (Tdisk (R,TR)) is non empty set
bool the carrier of (Tdisk (R,TR)) is non empty set
(TOP-REAL 2) | pg is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | pg) is set
[: the carrier of (Tdisk (R,TR)), the carrier of ((TOP-REAL 2) | pg):] is Relation-like set
bool [: the carrier of (Tdisk (R,TR)), the carrier of ((TOP-REAL 2) | pg):] is non empty set
id pg is Relation-like pg -defined pg -valued Function-like one-to-one total quasi_total Element of bool [:pg,pg:]
[:pg,pg:] is Relation-like set
bool [:pg,pg:] is non empty set
l is Relation-like the carrier of (Tdisk (R,TR)) -defined the carrier of ((TOP-REAL 2) | pg) -valued Function-like quasi_total Element of bool [: the carrier of (Tdisk (R,TR)), the carrier of ((TOP-REAL 2) | pg):]
l | pg is Relation-like pg -defined the carrier of (Tdisk (R,TR)) -defined the carrier of ((TOP-REAL 2) | pg) -valued Function-like Element of bool [: the carrier of (Tdisk (R,TR)), the carrier of ((TOP-REAL 2) | pg):]
(TOP-REAL 2) | ((cl_Ball (R,TR)) \ {R}) is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | ((cl_Ball (R,TR)) \ {R})) is non empty set
[: the carrier of (Tdisk (R,TR)), the carrier of ((TOP-REAL 2) | ((cl_Ball (R,TR)) \ {R})):] is Relation-like non empty set
bool [: the carrier of (Tdisk (R,TR)), the carrier of ((TOP-REAL 2) | ((cl_Ball (R,TR)) \ {R})):] is non empty set
Cl ld is functional proper closed closed bounded Element of bool the carrier of (TOP-REAL 2)
ld ` is functional non empty Element of bool the carrier of (TOP-REAL 2)
the carrier of (TOP-REAL 2) \ ld is set
LJ is Relation-like the carrier of (Tdisk (R,TR)) -defined the carrier of ((TOP-REAL 2) | ((cl_Ball (R,TR)) \ {R})) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (Tdisk (R,TR)), the carrier of ((TOP-REAL 2) | ((cl_Ball (R,TR)) \ {R})):]
(2,R,R,TR) is Relation-like the carrier of ((TOP-REAL 2) | ((cl_Ball (R,TR)) \ {R})) -defined the carrier of (Tcircle (R,TR)) -valued Function-like non empty total quasi_total Element of bool [: the carrier of ((TOP-REAL 2) | ((cl_Ball (R,TR)) \ {R})), the carrier of (Tcircle (R,TR)):]
[: the carrier of ((TOP-REAL 2) | ((cl_Ball (R,TR)) \ {R})), the carrier of (Tcircle (R,TR)):] is Relation-like non empty set
bool [: the carrier of ((TOP-REAL 2) | ((cl_Ball (R,TR)) \ {R})), the carrier of (Tcircle (R,TR)):] is non empty set
(2,R,R,TR) is Relation-like the carrier of (Tcircle (R,TR)) -defined the carrier of (Tcircle (R,TR)) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (Tcircle (R,TR)), the carrier of (Tcircle (R,TR)):]
[: the carrier of (Tcircle (R,TR)), the carrier of (Tcircle (R,TR)):] is Relation-like non empty set
bool [: the carrier of (Tcircle (R,TR)), the carrier of (Tcircle (R,TR)):] is non empty set
[: the carrier of (Tdisk (R,TR)), the carrier of (Tdisk (R,TR)):] is Relation-like non empty set
bool [: the carrier of (Tdisk (R,TR)), the carrier of (Tdisk (R,TR)):] is non empty set
(2,R,R,TR) * LJ is Relation-like the carrier of (Tdisk (R,TR)) -defined the carrier of (Tcircle (R,TR)) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (Tdisk (R,TR)), the carrier of (Tcircle (R,TR)):]
[: the carrier of (Tdisk (R,TR)), the carrier of (Tcircle (R,TR)):] is Relation-like non empty set
bool [: the carrier of (Tdisk (R,TR)), the carrier of (Tcircle (R,TR)):] is non empty set
(2,R,R,TR) * ((2,R,R,TR) * LJ) is Relation-like the carrier of (Tdisk (R,TR)) -defined the carrier of (Tcircle (R,TR)) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (Tdisk (R,TR)), the carrier of (Tcircle (R,TR)):]
R - R is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
- R is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
K270((TOP-REAL 2),R,(- R)) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) is Relation-like [: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of bool [:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):]
[:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):] is Relation-like non empty set
bool [:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):] is non empty set
K224( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),R,(- R)) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
|.(R - R).| is complex ext-real non negative real Element of REAL
A1 is Relation-like the carrier of (Tdisk (R,TR)) -defined the carrier of (Tdisk (R,TR)) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (Tdisk (R,TR)), the carrier of (Tdisk (R,TR)):]
A2 is set
dom A1 is non empty Element of bool the carrier of (Tdisk (R,TR))
(Ball (R,TR)) \/ (Sphere (R,TR)) is functional non empty Element of bool the carrier of (TOP-REAL 2)
A1 . A2 is set
dom LJ is non empty Element of bool the carrier of (Tdisk (R,TR))
(2,R,R,TR) | (Sphere (R,TR)) is Relation-like Sphere (R,TR) -defined the carrier of ((TOP-REAL 2) | ((cl_Ball (R,TR)) \ {R})) -defined the carrier of (Tcircle (R,TR)) -valued Function-like Element of bool [: the carrier of ((TOP-REAL 2) | ((cl_Ball (R,TR)) \ {R})), the carrier of (Tcircle (R,TR)):]
id (Sphere (R,TR)) is Relation-like Sphere (R,TR) -defined Sphere (R,TR) -valued Function-like one-to-one non empty total quasi_total Element of bool [:(Sphere (R,TR)),(Sphere (R,TR)):]
[:(Sphere (R,TR)),(Sphere (R,TR)):] is Relation-like non empty set
bool [:(Sphere (R,TR)),(Sphere (R,TR)):] is non empty set
dom (2,R,R,TR) is non empty Element of bool the carrier of (Tcircle (R,TR))
bool the carrier of (Tcircle (R,TR)) is non empty set
A1 . A2 is set
((2,R,R,TR) * LJ) . A2 is set
(2,R,R,TR) . (((2,R,R,TR) * LJ) . A2) is set
LJ . A2 is set
(2,R,R,TR) . (LJ . A2) is set
(2,R,R,TR) . ((2,R,R,TR) . (LJ . A2)) is set
(2,R,R,TR) . A2 is set
(2,R,R,TR) . ((2,R,R,TR) . A2) is set
(id (Sphere (R,TR))) . A2 is Relation-like Function-like set
(2,R,R,TR) . ((id (Sphere (R,TR))) . A2) is set
(2,R,R,TR) . A2 is set
A1 . A2 is set
A1 . A2 is set
A2 is set
dom A1 is non empty Element of bool the carrier of (Tdisk (R,TR))
A2 is set
dom A1 is non empty Element of bool the carrier of (Tdisk (R,TR))
ld is set
pd is set
R is functional Element of bool the carrier of (TOP-REAL 2)
Euclid 2 is non empty strict Reflexive discerning symmetric triangle Discerning MetrStruct
the carrier of (Euclid 2) is non empty set
bool the carrier of (Euclid 2) is non empty set
dR is Element of bool the carrier of ((TOP-REAL 2) | (rp `))
C is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
TR is functional non empty proper open bounded Element of bool the carrier of (TOP-REAL 2)
TR \/ rp is functional non empty Element of bool the carrier of (TOP-REAL 2)
P is bounded Element of bool the carrier of (Euclid 2)
U is non empty complex ext-real positive non negative real set
Ball (C,U) is functional non empty proper open connected bounded being_Region convex Element of bool the carrier of (TOP-REAL 2)
l is set
LJ is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
LJ - C is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
- C is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
K270((TOP-REAL 2),LJ,(- C)) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) is Relation-like [: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of bool [:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):]
[:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):] is Relation-like non empty set
bool [:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):] is non empty set
K224( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),LJ,(- C)) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
|.(LJ - C).| is complex ext-real non negative real Element of REAL
x is non empty complex ext-real positive non negative real set
Ball (C,x) is functional non empty proper open connected bounded being_Region convex Element of bool the carrier of (TOP-REAL 2)
Fr (Ball (C,x)) is functional proper closed closed boundary nowhere_dense bounded Element of bool the carrier of (TOP-REAL 2)
Cl (Ball (C,x)) is functional non empty proper closed closed bounded Element of bool the carrier of (TOP-REAL 2)
(Ball (C,x)) ` is functional non empty closed Element of bool the carrier of (TOP-REAL 2)
the carrier of (TOP-REAL 2) \ (Ball (C,x)) is set
Cl ((Ball (C,x)) `) is functional non empty closed Element of bool the carrier of (TOP-REAL 2)
(Cl (Ball (C,x))) /\ (Cl ((Ball (C,x)) `)) is functional closed Element of bool the carrier of (TOP-REAL 2)
Sphere (C,x) is functional non empty proper closed closed connected compact bounded bounded being_simple_closed_curve with_the_max_arc Element of bool the carrier of (TOP-REAL 2)
Tdisk (C,x) is non empty TopSpace-like T_0 T_1 T_2 V82() normal T_3 T_4 compact closed V246() V270(2) pseudocompact SubSpace of TOP-REAL 2
Tcircle (C,x) is non empty strict TopSpace-like T_0 T_1 T_2 V82() normal T_3 T_4 connected compact V246() being_simple_closed_curve pathwise_connected pseudocompact SubSpace of TOP-REAL 2
cl_Ball (C,x) is functional non empty proper closed connected bounded convex Element of bool the carrier of (TOP-REAL 2)
{C} is functional non empty proper closed compact bounded Element of bool the carrier of (TOP-REAL 2)
(cl_Ball (C,x)) \ {C} is functional non empty Element of bool the carrier of (TOP-REAL 2)
the carrier of (Tcircle (C,x)) is non empty set
the carrier of (Tdisk (C,x)) is non empty set
bool the carrier of (Tdisk (C,x)) is non empty set
(TOP-REAL 2) | pg is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | pg) is set
[: the carrier of (Tdisk (C,x)), the carrier of ((TOP-REAL 2) | pg):] is Relation-like set
bool [: the carrier of (Tdisk (C,x)), the carrier of ((TOP-REAL 2) | pg):] is non empty set
id pg is Relation-like pg -defined pg -valued Function-like one-to-one total quasi_total Element of bool [:pg,pg:]
[:pg,pg:] is Relation-like set
bool [:pg,pg:] is non empty set
Ux is Relation-like the carrier of (Tdisk (C,x)) -defined the carrier of ((TOP-REAL 2) | pg) -valued Function-like quasi_total Element of bool [: the carrier of (Tdisk (C,x)), the carrier of ((TOP-REAL 2) | pg):]
Ux | pg is Relation-like pg -defined the carrier of (Tdisk (C,x)) -defined the carrier of ((TOP-REAL 2) | pg) -valued Function-like Element of bool [: the carrier of (Tdisk (C,x)), the carrier of ((TOP-REAL 2) | pg):]
(TOP-REAL 2) | ((cl_Ball (C,x)) \ {C}) is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | ((cl_Ball (C,x)) \ {C})) is non empty set
[: the carrier of (Tdisk (C,x)), the carrier of ((TOP-REAL 2) | ((cl_Ball (C,x)) \ {C})):] is Relation-like non empty set
bool [: the carrier of (Tdisk (C,x)), the carrier of ((TOP-REAL 2) | ((cl_Ball (C,x)) \ {C})):] is non empty set
Pml is Relation-like the carrier of (Tdisk (C,x)) -defined the carrier of ((TOP-REAL 2) | ((cl_Ball (C,x)) \ {C})) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (Tdisk (C,x)), the carrier of ((TOP-REAL 2) | ((cl_Ball (C,x)) \ {C})):]
(2,C,C,x) is Relation-like the carrier of ((TOP-REAL 2) | ((cl_Ball (C,x)) \ {C})) -defined the carrier of (Tcircle (C,x)) -valued Function-like non empty total quasi_total Element of bool [: the carrier of ((TOP-REAL 2) | ((cl_Ball (C,x)) \ {C})), the carrier of (Tcircle (C,x)):]
[: the carrier of ((TOP-REAL 2) | ((cl_Ball (C,x)) \ {C})), the carrier of (Tcircle (C,x)):] is Relation-like non empty set
bool [: the carrier of ((TOP-REAL 2) | ((cl_Ball (C,x)) \ {C})), the carrier of (Tcircle (C,x)):] is non empty set
(2,C,C,x) is Relation-like the carrier of (Tcircle (C,x)) -defined the carrier of (Tcircle (C,x)) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (Tcircle (C,x)), the carrier of (Tcircle (C,x)):]
[: the carrier of (Tcircle (C,x)), the carrier of (Tcircle (C,x)):] is Relation-like non empty set
bool [: the carrier of (Tcircle (C,x)), the carrier of (Tcircle (C,x)):] is non empty set
[: the carrier of (Tdisk (C,x)), the carrier of (Tdisk (C,x)):] is Relation-like non empty set
bool [: the carrier of (Tdisk (C,x)), the carrier of (Tdisk (C,x)):] is non empty set
(2,C,C,x) * Pml is Relation-like the carrier of (Tdisk (C,x)) -defined the carrier of (Tcircle (C,x)) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (Tdisk (C,x)), the carrier of (Tcircle (C,x)):]
[: the carrier of (Tdisk (C,x)), the carrier of (Tcircle (C,x)):] is Relation-like non empty set
bool [: the carrier of (Tdisk (C,x)), the carrier of (Tcircle (C,x)):] is non empty set
(2,C,C,x) * ((2,C,C,x) * Pml) is Relation-like the carrier of (Tdisk (C,x)) -defined the carrier of (Tcircle (C,x)) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (Tdisk (C,x)), the carrier of (Tcircle (C,x)):]
C - C is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
K270((TOP-REAL 2),C,(- C)) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
K224( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),C,(- C)) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
|.(C - C).| is complex ext-real non negative real Element of REAL
kj is Relation-like the carrier of (Tdisk (C,x)) -defined the carrier of (Tdisk (C,x)) -valued Function-like non empty total quasi_total Element of bool [: the carrier of (Tdisk (C,x)), the carrier of (Tdisk (C,x)):]
X is set
dom kj is non empty Element of bool the carrier of (Tdisk (C,x))
(Ball (C,x)) \/ (Sphere (C,x)) is functional non empty Element of bool the carrier of (TOP-REAL 2)
kj . X is set
dom Pml is non empty Element of bool the carrier of (Tdisk (C,x))
BR is set
CR is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
CR - C is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
K270((TOP-REAL 2),CR,(- C)) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
K224( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),CR,(- C)) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
|.(CR - C).| is complex ext-real non negative real Element of REAL
BR is Element of bool the carrier of ((TOP-REAL 2) | (rp `))
(2,C,C,x) | (Sphere (C,x)) is Relation-like Sphere (C,x) -defined the carrier of ((TOP-REAL 2) | ((cl_Ball (C,x)) \ {C})) -defined the carrier of (Tcircle (C,x)) -valued Function-like Element of bool [: the carrier of ((TOP-REAL 2) | ((cl_Ball (C,x)) \ {C})), the carrier of (Tcircle (C,x)):]
id (Sphere (C,x)) is Relation-like Sphere (C,x) -defined Sphere (C,x) -valued Function-like one-to-one non empty total quasi_total Element of bool [:(Sphere (C,x)),(Sphere (C,x)):]
[:(Sphere (C,x)),(Sphere (C,x)):] is Relation-like non empty set
bool [:(Sphere (C,x)),(Sphere (C,x)):] is non empty set
dom (2,C,C,x) is non empty Element of bool the carrier of (Tcircle (C,x))
bool the carrier of (Tcircle (C,x)) is non empty set
kj . X is set
((2,C,C,x) * Pml) . X is set
(2,C,C,x) . (((2,C,C,x) * Pml) . X) is set
Pml . X is set
(2,C,C,x) . (Pml . X) is set
(2,C,C,x) . ((2,C,C,x) . (Pml . X)) is set
(2,C,C,x) . X is set
(2,C,C,x) . ((2,C,C,x) . X) is set
(id (Sphere (C,x))) . X is Relation-like Function-like set
(2,C,C,x) . ((id (Sphere (C,x))) . X) is set
(2,C,C,x) . X is set
kj . X is set
kj . X is set
X is set
dom kj is non empty Element of bool the carrier of (Tdisk (C,x))
X is set
dom kj is non empty Element of bool the carrier of (Tdisk (C,x))
- 3 is complex ext-real non positive real Element of REAL
|[0,3]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
|[0,(- 3)]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
|[(- 1),3]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
|[1,3]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
|[(- 1),(- 3)]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
|[1,(- 3)]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
closed_inside_of_rectangle ((- 1),1,(- 3),3) is functional closed connected convex Element of bool the carrier of (TOP-REAL 2)
{ b₁ where b₁ is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2) : ( - 1 <= b₁ `1 & b<sub>1</sub> `1 <= 1 & - 3 <= b₁ `2 & b<sub>1</sub> `2 <= 3 ) } is set
rectangle ((- 1),1,(- 3),3) is functional non empty proper closed compact bounded Element of bool the carrier of (TOP-REAL 2)
Trectangle ((- 1),1,(- 3),3) is non empty TopSpace-like T_0 T_1 T_2 V270(2) SubSpace of TOP-REAL 2
(TOP-REAL 2) | (closed_inside_of_rectangle ((- 1),1,(- 3),3)) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
|[(- 1),0]| `1 is complex ext-real real Element of REAL
|[1,0]| `1 is complex ext-real real Element of REAL
|[(- 1),0]| `2 is complex ext-real real Element of REAL
|[1,0]| `2 is complex ext-real real Element of REAL
|[0,3]| `1 is complex ext-real real Element of REAL
|[0,3]| `2 is complex ext-real real Element of REAL
|[0,(- 3)]| `1 is complex ext-real real Element of REAL
|[0,(- 3)]| `2 is complex ext-real real Element of REAL
|[(- 1),3]| `1 is complex ext-real real Element of REAL
|[(- 1),3]| `2 is complex ext-real real Element of REAL
|[(- 1),(- 3)]| `1 is complex ext-real real Element of REAL
|[(- 1),(- 3)]| `2 is complex ext-real real Element of REAL
|[1,3]| `1 is complex ext-real real Element of REAL
|[1,3]| `2 is complex ext-real real Element of REAL
|[1,(- 3)]| `1 is complex ext-real real Element of REAL
|[1,(- 3)]| `2 is complex ext-real real Element of REAL
|[(|[(- 1),(- 3)]| `1),(|[(- 1),(- 3)]| `2)]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
|[(|[(- 1),3]| `1),(|[(- 1),3]| `2)]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
|[(|[1,(- 3)]| `1),(|[1,(- 3)]| `2)]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
|[(|[1,3]| `1),(|[1,3]| `2)]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
LSeg (|[(- 1),(- 3)]|,|[(- 1),3]|) is functional proper closed closed boundary nowhere_dense connected compact compact bounded bounded Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * |[(- 1),(- 3)]|) + (b₁ * |[(- 1),3]|)) where b₁ is complex ext-real real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
LSeg (|[(- 1),3]|,|[1,3]|) is functional proper closed closed boundary nowhere_dense connected compact compact bounded bounded Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * |[(- 1),3]|) + (b₁ * |[1,3]|)) where b₁ is complex ext-real real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg (|[(- 1),(- 3)]|,|[(- 1),3]|)) \/ (LSeg (|[(- 1),3]|,|[1,3]|)) is functional closed Element of bool the carrier of (TOP-REAL 2)
LSeg (|[1,3]|,|[1,(- 3)]|) is functional proper closed closed boundary nowhere_dense connected compact compact bounded bounded Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * |[1,3]|) + (b₁ * |[1,(- 3)]|)) where b₁ is complex ext-real real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
LSeg (|[1,(- 3)]|,|[(- 1),(- 3)]|) is functional proper closed closed boundary nowhere_dense connected compact compact bounded bounded Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * |[1,(- 3)]|) + (b₁ * |[(- 1),(- 3)]|)) where b₁ is complex ext-real real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg (|[1,3]|,|[1,(- 3)]|)) \/ (LSeg (|[1,(- 3)]|,|[(- 1),(- 3)]|)) is functional closed Element of bool the carrier of (TOP-REAL 2)
((LSeg (|[(- 1),(- 3)]|,|[(- 1),3]|)) \/ (LSeg (|[(- 1),3]|,|[1,3]|))) \/ ((LSeg (|[1,3]|,|[1,(- 3)]|)) \/ (LSeg (|[1,(- 3)]|,|[(- 1),(- 3)]|))) is functional closed Element of bool the carrier of (TOP-REAL 2)
LSeg (|[1,(- 3)]|,|[1,3]|) is functional proper closed closed boundary nowhere_dense connected compact compact bounded bounded Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * |[1,(- 3)]|) + (b₁ * |[1,3]|)) where b₁ is complex ext-real real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
LSeg (|[(- 1),0]|,|[(- 1),3]|) is functional proper closed closed boundary nowhere_dense connected compact compact bounded bounded Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * |[(- 1),0]|) + (b₁ * |[(- 1),3]|)) where b₁ is complex ext-real real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
LSeg (|[(- 1),0]|,|[(- 1),(- 3)]|) is functional proper closed closed boundary nowhere_dense connected compact compact bounded bounded Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * |[(- 1),0]|) + (b₁ * |[(- 1),(- 3)]|)) where b₁ is complex ext-real real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
LSeg (|[1,0]|,|[1,3]|) is functional proper closed closed boundary nowhere_dense connected compact compact bounded bounded Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * |[1,0]|) + (b₁ * |[1,3]|)) where b₁ is complex ext-real real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
LSeg (|[1,0]|,|[1,(- 3)]|) is functional proper closed closed boundary nowhere_dense connected compact compact bounded bounded Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * |[1,0]|) + (b₁ * |[1,(- 3)]|)) where b₁ is complex ext-real real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
LSeg (|[(- 1),(- 3)]|,|[0,(- 3)]|) is functional proper closed closed boundary nowhere_dense connected compact compact bounded bounded Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * |[(- 1),(- 3)]|) + (b₁ * |[0,(- 3)]|)) where b₁ is complex ext-real real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
LSeg (|[1,(- 3)]|,|[0,(- 3)]|) is functional proper closed closed boundary nowhere_dense connected compact compact bounded bounded Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * |[1,(- 3)]|) + (b₁ * |[0,(- 3)]|)) where b₁ is complex ext-real real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
LSeg (|[(- 1),3]|,|[0,3]|) is functional proper closed closed boundary nowhere_dense connected compact compact bounded bounded Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * |[(- 1),3]|) + (b₁ * |[0,3]|)) where b₁ is complex ext-real real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
LSeg (|[1,3]|,|[0,3]|) is functional proper closed closed boundary nowhere_dense connected compact compact bounded bounded Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * |[1,3]|) + (b₁ * |[0,3]|)) where b₁ is complex ext-real real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
LSeg (|[(- 1),(- 3)]|,|[1,(- 3)]|) is functional proper closed closed boundary nowhere_dense connected compact compact bounded bounded Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * |[(- 1),(- 3)]|) + (b₁ * |[1,(- 3)]|)) where b₁ is complex ext-real real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
{ b₁ where b₁ is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2) : ( ( b₁ `1 = - 1 & b<sub>1</sub> `2 <= 3 & - 3 <= b₁ `2 ) or ( b<sub>1</sub> `1 <= 1 & - 1 <= b₁ `1 & b<sub>1</sub> `2 = 3 ) or ( b₁ `1 <= 1 & - 1 <= b<sub>1</sub> `1 & b₁ `2 = - 3 ) or ( b<sub>1</sub> `1 = 1 & b₁ `2 <= 3 & - 3 <= b<sub>1</sub> `2 ) ) } is set
2 + 1 is non empty ordinal natural complex ext-real positive non negative real Element of REAL
(2 + 1) ^2 is complex ext-real real Element of REAL
(2 + 1) * (2 + 1) is ordinal natural complex ext-real non negative real set
4 + 4 is non empty ordinal natural complex ext-real positive non negative real Element of REAL
(4 + 4) + 1 is non empty ordinal natural complex ext-real positive non negative real Element of REAL
9 is non empty ordinal natural complex ext-real positive non negative real V33() V119() V166() V167() V168() V169() V170() V171() left_end bounded_below Element of NAT
sqrt 9 is non empty complex ext-real positive non negative real Element of REAL
dist (|[(- 1),0]|,|[1,0]|) is complex ext-real non negative real Element of REAL
(|[(- 1),0]| `1) - (|[1,0]| `1) is complex ext-real real Element of REAL
((|[(- 1),0]| `1) - (|[1,0]| `1)) ^2 is complex ext-real real Element of REAL
((|[(- 1),0]| `1) - (|[1,0]| `1)) * ((|[(- 1),0]| `1) - (|[1,0]| `1)) is complex ext-real non negative real set
(|[(- 1),0]| `2) - (|[1,0]| `2) is complex ext-real real Element of REAL
((|[(- 1),0]| `2) - (|[1,0]| `2)) ^2 is complex ext-real real Element of REAL
((|[(- 1),0]| `2) - (|[1,0]| `2)) * ((|[(- 1),0]| `2) - (|[1,0]| `2)) is complex ext-real non negative real set
(((|[(- 1),0]| `1) - (|[1,0]| `1)) ^2) + (((|[(- 1),0]| `2) - (|[1,0]| `2)) ^2) is complex ext-real real Element of REAL
sqrt ((((|[(- 1),0]| `1) - (|[1,0]| `1)) ^2) + (((|[(- 1),0]| `2) - (|[1,0]| `2)) ^2)) is complex ext-real real Element of REAL
- 2 is complex ext-real non positive real Element of REAL
- (- 2) is complex ext-real non negative real Element of REAL
C is functional non empty proper closed connected compact bounded being_simple_closed_curve with_the_max_arc Element of bool the carrier of (TOP-REAL 2)
P is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like one-to-one non empty total quasi_total onto bijective continuous being_homeomorphism Homeomorphism of TOP-REAL 2
P .: C is functional non empty Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | C is non empty strict TopSpace-like T_0 T_1 T_2 V82() normal T_3 T_4 compact V246() pseudocompact SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | C) is non empty set
[: the carrier of ((TOP-REAL 2) | R^2-unit_square), the carrier of ((TOP-REAL 2) | C):] is Relation-like non empty set
bool [: the carrier of ((TOP-REAL 2) | R^2-unit_square), the carrier of ((TOP-REAL 2) | C):] is non empty set
U is Relation-like the carrier of ((TOP-REAL 2) | R^2-unit_square) -defined the carrier of ((TOP-REAL 2) | C) -valued Function-like non empty total quasi_total Element of bool [: the carrier of ((TOP-REAL 2) | R^2-unit_square), the carrier of ((TOP-REAL 2) | C):]
(TOP-REAL 2) | (P .: C) is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | (P .: C)) is non empty set
[: the carrier of ((TOP-REAL 2) | C), the carrier of ((TOP-REAL 2) | (P .: C)):] is Relation-like non empty set
bool [: the carrier of ((TOP-REAL 2) | C), the carrier of ((TOP-REAL 2) | (P .: C)):] is non empty set
P | C is Relation-like the carrier of (TOP-REAL 2) -defined C -defined the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like Element of bool [: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):]
l is Relation-like the carrier of ((TOP-REAL 2) | C) -defined the carrier of ((TOP-REAL 2) | (P .: C)) -valued Function-like non empty total quasi_total Element of bool [: the carrier of ((TOP-REAL 2) | C), the carrier of ((TOP-REAL 2) | (P .: C)):]
l * U is Relation-like the carrier of ((TOP-REAL 2) | R^2-unit_square) -defined the carrier of ((TOP-REAL 2) | (P .: C)) -valued Function-like non empty total quasi_total Element of bool [: the carrier of ((TOP-REAL 2) | R^2-unit_square), the carrier of ((TOP-REAL 2) | (P .: C)):]
[: the carrier of ((TOP-REAL 2) | R^2-unit_square), the carrier of ((TOP-REAL 2) | (P .: C)):] is Relation-like non empty set
bool [: the carrier of ((TOP-REAL 2) | R^2-unit_square), the carrier of ((TOP-REAL 2) | (P .: C)):] is non empty set
C is functional Element of bool the carrier of (TOP-REAL 2)
P is set
U is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
dist (|[(- 1),0]|,U) is complex ext-real non negative real Element of REAL
U `1 is complex ext-real real Element of REAL
(- 1) - (U `1) is complex ext-real real Element of REAL
((- 1) - (U `1)) ^2 is complex ext-real real Element of REAL
((- 1) - (U `1)) * ((- 1) - (U `1)) is complex ext-real non negative real set
U `2 is complex ext-real real Element of REAL
0 - (U `2) is complex ext-real real Element of REAL
(0 - (U `2)) ^2 is complex ext-real real Element of REAL
(0 - (U `2)) * (0 - (U `2)) is complex ext-real non negative real set
(((- 1) - (U `1)) ^2) + ((0 - (U `2)) ^2) is complex ext-real real Element of REAL
sqrt ((((- 1) - (U `1)) ^2) + ((0 - (U `2)) ^2)) is complex ext-real real Element of REAL
(U `2) ^2 is complex ext-real real Element of REAL
(U `2) * (U `2) is complex ext-real non negative real set
(((- 1) - (U `1)) ^2) + ((U `2) ^2) is complex ext-real real Element of REAL
sqrt ((((- 1) - (U `1)) ^2) + ((U `2) ^2)) is complex ext-real real Element of REAL
0 + 9 is non empty ordinal natural complex ext-real positive non negative real Element of REAL
LSeg (U,|[1,0]|) is functional proper closed closed boundary nowhere_dense connected compact compact bounded bounded Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * U) + (b<sub>1</sub> * |[1,0]|)) where b<sub>1</sub> is complex ext-real real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
Vertical_Line (- 1) is functional Element of bool the carrier of (TOP-REAL 2)
l is set
LJ is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
LJ `1 is complex ext-real real Element of REAL
dist (U,|[1,0]|) is complex ext-real non negative real Element of REAL
dist (U,LJ) is complex ext-real non negative real Element of REAL
dist (LJ,|[1,0]|) is complex ext-real non negative real Element of REAL
(dist (U,LJ)) + (dist (LJ,|[1,0]|)) is complex ext-real non negative real Element of REAL
(LJ `1) - (|[1,0]| `1) is complex ext-real real Element of REAL
((LJ `1) - (|[1,0]| `1)) ^2 is complex ext-real real Element of REAL
((LJ `1) - (|[1,0]| `1)) * ((LJ `1) - (|[1,0]| `1)) is complex ext-real non negative real set
LJ `2 is complex ext-real real Element of REAL
(LJ `2) - (|[1,0]| `2) is complex ext-real real Element of REAL
((LJ `2) - (|[1,0]| `2)) ^2 is complex ext-real real Element of REAL
((LJ `2) - (|[1,0]| `2)) * ((LJ `2) - (|[1,0]| `2)) is complex ext-real non negative real set
(((LJ `1) - (|[1,0]| `1)) ^2) + (((LJ `2) - (|[1,0]| `2)) ^2) is complex ext-real real Element of REAL
sqrt ((((LJ `1) - (|[1,0]| `1)) ^2) + (((LJ `2) - (|[1,0]| `2)) ^2)) is complex ext-real real Element of REAL
(- 2) ^2 is complex ext-real real Element of REAL
(- 2) * (- 2) is complex ext-real non negative real set
(LJ `2) - 0 is complex ext-real real Element of REAL
((LJ `2) - 0) ^2 is complex ext-real real Element of REAL
((LJ `2) - 0) * ((LJ `2) - 0) is complex ext-real non negative real set
((- 2) ^2) + (((LJ `2) - 0) ^2) is complex ext-real real Element of REAL
sqrt (((- 2) ^2) + (((LJ `2) - 0) ^2)) is complex ext-real real Element of REAL
(LJ `2) ^2 is complex ext-real real Element of REAL
(LJ `2) * (LJ `2) is complex ext-real non negative real set
4 + ((LJ `2) ^2) is complex ext-real real Element of REAL
sqrt (4 + ((LJ `2) ^2)) is complex ext-real real Element of REAL
4 + 0 is non empty ordinal natural complex ext-real positive non negative real Element of REAL
(dist (U,|[1,0]|)) + 0 is complex ext-real non negative real Element of REAL
(dist (|[(- 1),0]|,|[1,0]|)) + 0 is complex ext-real non negative real Element of REAL
LSeg (U,|[(- 1),0]|) is functional proper closed closed boundary nowhere_dense connected compact compact bounded bounded Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * U) + (b₁ * |[(- 1),0]|)) where b₁ is complex ext-real real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
Vertical_Line 1 is functional Element of bool the carrier of (TOP-REAL 2)
l is set
LJ is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
LJ `1 is complex ext-real real Element of REAL
dist (U,|[(- 1),0]|) is complex ext-real non negative real Element of REAL
dist (U,LJ) is complex ext-real non negative real Element of REAL
dist (LJ,|[(- 1),0]|) is complex ext-real non negative real Element of REAL
(dist (U,LJ)) + (dist (LJ,|[(- 1),0]|)) is complex ext-real non negative real Element of REAL
(LJ `1) - (|[(- 1),0]| `1) is complex ext-real real Element of REAL
((LJ `1) - (|[(- 1),0]| `1)) ^2 is complex ext-real real Element of REAL
((LJ `1) - (|[(- 1),0]| `1)) * ((LJ `1) - (|[(- 1),0]| `1)) is complex ext-real non negative real set
LJ `2 is complex ext-real real Element of REAL
(LJ `2) - (|[(- 1),0]| `2) is complex ext-real real Element of REAL
((LJ `2) - (|[(- 1),0]| `2)) ^2 is complex ext-real real Element of REAL
((LJ `2) - (|[(- 1),0]| `2)) * ((LJ `2) - (|[(- 1),0]| `2)) is complex ext-real non negative real set
(((LJ `1) - (|[(- 1),0]| `1)) ^2) + (((LJ `2) - (|[(- 1),0]| `2)) ^2) is complex ext-real real Element of REAL
sqrt ((((LJ `1) - (|[(- 1),0]| `1)) ^2) + (((LJ `2) - (|[(- 1),0]| `2)) ^2)) is complex ext-real real Element of REAL
(LJ `2) ^2 is complex ext-real real Element of REAL
(LJ `2) * (LJ `2) is complex ext-real non negative real set
4 + ((LJ `2) ^2) is complex ext-real real Element of REAL
sqrt (4 + ((LJ `2) ^2)) is complex ext-real real Element of REAL
(dist (U,|[(- 1),0]|)) + 0 is complex ext-real non negative real Element of REAL
(- 3) ^2 is complex ext-real real Element of REAL
(- 3) * (- 3) is complex ext-real non negative real set
LSeg (|[0,3]|,|[1,3]|) is functional proper closed closed boundary nowhere_dense connected compact compact bounded bounded Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * |[0,3]|) + (b<sub>1</sub> * |[1,3]|)) where b<sub>1</sub> is complex ext-real real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
LSeg (|[1,3]|,|[1,0]|) is functional proper closed closed boundary nowhere_dense connected compact compact bounded bounded Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * |[1,3]|) + (b<sub>1</sub> * |[1,0]|)) where b<sub>1</sub> is complex ext-real real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
C is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
C `2 is complex ext-real real Element of REAL
P is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
P `1 is complex ext-real real Element of REAL
P `2 is complex ext-real real Element of REAL
LSeg (|[0,(- 3)]|,|[1,(- 3)]|) is functional proper closed closed boundary nowhere_dense connected compact compact bounded bounded Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * |[0,(- 3)]|) + (b₁ * |[1,(- 3)]|)) where b₁ is complex ext-real real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
LSeg (|[1,(- 3)]|,|[1,0]|) is functional proper closed closed boundary nowhere_dense connected compact compact bounded bounded Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * |[1,(- 3)]|) + (b₁ * |[1,0]|)) where b₁ is complex ext-real real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
C is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
C `2 is complex ext-real real Element of REAL
P is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
P `1 is complex ext-real real Element of REAL
P `2 is complex ext-real real Element of REAL
C is functional Element of bool the carrier of (TOP-REAL 2)
P is set
U is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
U `2 is complex ext-real real Element of REAL
dist (|[(- 1),0]|,U) is complex ext-real non negative real Element of REAL
U `1 is complex ext-real real Element of REAL
(|[(- 1),0]| `1) - (U `1) is complex ext-real real Element of REAL
((|[(- 1),0]| `1) - (U `1)) ^2 is complex ext-real real Element of REAL
((|[(- 1),0]| `1) - (U `1)) * ((|[(- 1),0]| `1) - (U `1)) is complex ext-real non negative real set
(|[(- 1),0]| `2) - (U `2) is complex ext-real real Element of REAL
((|[(- 1),0]| `2) - (U `2)) ^2 is complex ext-real real Element of REAL
((|[(- 1),0]| `2) - (U `2)) * ((|[(- 1),0]| `2) - (U `2)) is complex ext-real non negative real set
(((|[(- 1),0]| `1) - (U `1)) ^2) + (((|[(- 1),0]| `2) - (U `2)) ^2) is complex ext-real real Element of REAL
sqrt ((((|[(- 1),0]| `1) - (U `1)) ^2) + (((|[(- 1),0]| `2) - (U `2)) ^2)) is complex ext-real real Element of REAL
(- 1) - (U `1) is complex ext-real real Element of REAL
((- 1) - (U `1)) ^2 is complex ext-real real Element of REAL
((- 1) - (U `1)) * ((- 1) - (U `1)) is complex ext-real non negative real set
3 ^2 is complex ext-real real Element of REAL
3 * 3 is ordinal natural complex ext-real non negative real set
(((- 1) - (U `1)) ^2) + (3 ^2) is complex ext-real real Element of REAL
sqrt ((((- 1) - (U `1)) ^2) + (3 ^2)) is complex ext-real real Element of REAL
(((- 1) - (U `1)) ^2) + 9 is complex ext-real real Element of REAL
0 + 4 is non empty ordinal natural complex ext-real positive non negative real Element of REAL
C is functional Element of bool the carrier of (TOP-REAL 2)
P is set
U is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
U `2 is complex ext-real real Element of REAL
dist (|[(- 1),0]|,U) is complex ext-real non negative real Element of REAL
U `1 is complex ext-real real Element of REAL
(|[(- 1),0]| `1) - (U `1) is complex ext-real real Element of REAL
((|[(- 1),0]| `1) - (U `1)) ^2 is complex ext-real real Element of REAL
((|[(- 1),0]| `1) - (U `1)) * ((|[(- 1),0]| `1) - (U `1)) is complex ext-real non negative real set
(|[(- 1),0]| `2) - (U `2) is complex ext-real real Element of REAL
((|[(- 1),0]| `2) - (U `2)) ^2 is complex ext-real real Element of REAL
((|[(- 1),0]| `2) - (U `2)) * ((|[(- 1),0]| `2) - (U `2)) is complex ext-real non negative real set
(((|[(- 1),0]| `1) - (U `1)) ^2) + (((|[(- 1),0]| `2) - (U `2)) ^2) is complex ext-real real Element of REAL
sqrt ((((|[(- 1),0]| `1) - (U `1)) ^2) + (((|[(- 1),0]| `2) - (U `2)) ^2)) is complex ext-real real Element of REAL
(- 1) - (U `1) is complex ext-real real Element of REAL
((- 1) - (U `1)) ^2 is complex ext-real real Element of REAL
((- 1) - (U `1)) * ((- 1) - (U `1)) is complex ext-real non negative real set
- (- 3) is complex ext-real non negative real Element of REAL
(- (- 3)) ^2 is complex ext-real real Element of REAL
(- (- 3)) * (- (- 3)) is complex ext-real non negative real set
(((- 1) - (U `1)) ^2) + ((- (- 3)) ^2) is complex ext-real real Element of REAL
sqrt ((((- 1) - (U `1)) ^2) + ((- (- 3)) ^2)) is complex ext-real real Element of REAL
(((- 1) - (U `1)) ^2) + 9 is complex ext-real real Element of REAL
0 + 4 is non empty ordinal natural complex ext-real positive non negative real Element of REAL
{|[(- 1),0]|,|[1,0]|} is functional non empty Element of bool the carrier of (TOP-REAL 2)
C is functional Element of bool the carrier of (TOP-REAL 2)
C /\ (rectangle ((- 1),1,(- 3),3)) is functional Element of bool the carrier of (TOP-REAL 2)
P is set
U is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
U `1 is complex ext-real real Element of REAL
U `2 is complex ext-real real Element of REAL
U `2 is complex ext-real real Element of REAL
(U `2) ^2 is complex ext-real real Element of REAL
(U `2) * (U `2) is complex ext-real non negative real set
dist (|[1,0]|,U) is complex ext-real non negative real Element of REAL
1 - (- 1) is non empty complex ext-real positive non negative real Element of REAL
(1 - (- 1)) ^2 is complex ext-real real Element of REAL
(1 - (- 1)) * (1 - (- 1)) is complex ext-real non negative real set
0 - (U `2) is complex ext-real real Element of REAL
(0 - (U `2)) ^2 is complex ext-real real Element of REAL
(0 - (U `2)) * (0 - (U `2)) is complex ext-real non negative real set
((1 - (- 1)) ^2) + ((0 - (U `2)) ^2) is complex ext-real real Element of REAL
sqrt (((1 - (- 1)) ^2) + ((0 - (U `2)) ^2)) is complex ext-real real Element of REAL
4 + ((U `2) ^2) is complex ext-real real Element of REAL
sqrt (4 + ((U `2) ^2)) is complex ext-real real Element of REAL
((U `2) ^2) + 4 is complex ext-real real Element of REAL
0 + 4 is non empty ordinal natural complex ext-real positive non negative real Element of REAL
sqrt (((U `2) ^2) + 4) is complex ext-real real Element of REAL
U `2 is complex ext-real real Element of REAL
U is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
U is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
U `1 is complex ext-real real Element of REAL
U `2 is complex ext-real real Element of REAL
U `2 is complex ext-real real Element of REAL
(U `2) ^2 is complex ext-real real Element of REAL
(U `2) * (U `2) is complex ext-real non negative real set
dist (U,|[(- 1),0]|) is complex ext-real non negative real Element of REAL
(U `1) - (|[(- 1),0]| `1) is complex ext-real real Element of REAL
((U `1) - (|[(- 1),0]| `1)) ^2 is complex ext-real real Element of REAL
((U `1) - (|[(- 1),0]| `1)) * ((U `1) - (|[(- 1),0]| `1)) is complex ext-real non negative real set
(U `2) - (|[(- 1),0]| `2) is complex ext-real real Element of REAL
((U `2) - (|[(- 1),0]| `2)) ^2 is complex ext-real real Element of REAL
((U `2) - (|[(- 1),0]| `2)) * ((U `2) - (|[(- 1),0]| `2)) is complex ext-real non negative real set
(((U `1) - (|[(- 1),0]| `1)) ^2) + (((U `2) - (|[(- 1),0]| `2)) ^2) is complex ext-real real Element of REAL
sqrt ((((U `1) - (|[(- 1),0]| `1)) ^2) + (((U `2) - (|[(- 1),0]| `2)) ^2)) is complex ext-real real Element of REAL
4 + ((U `2) ^2) is complex ext-real real Element of REAL
sqrt (4 + ((U `2) ^2)) is complex ext-real real Element of REAL
((U `2) ^2) + 4 is complex ext-real real Element of REAL
0 + 4 is non empty ordinal natural complex ext-real positive non negative real Element of REAL
sqrt (((U `2) ^2) + 4) is complex ext-real real Element of REAL
U `2 is complex ext-real real Element of REAL
U is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
U is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
P is set
C is functional non empty proper closed connected compact bounded being_simple_closed_curve with_the_max_arc Element of bool the carrier of (TOP-REAL 2)
C /\ (rectangle ((- 1),1,(- 3),3)) is functional proper closed compact bounded Element of bool the carrier of (TOP-REAL 2)
P is set
U is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
(rectangle ((- 1),1,(- 3),3)) /\ C is functional proper closed compact bounded Element of bool the carrier of (TOP-REAL 2)
C is functional non empty proper closed connected compact bounded being_simple_closed_curve with_the_max_arc Element of bool the carrier of (TOP-REAL 2)
C /\ (rectangle ((- 1),1,(- 3),3)) is functional proper closed compact bounded Element of bool the carrier of (TOP-REAL 2)
P is set
U is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
(rectangle ((- 1),1,(- 3),3)) /\ C is functional proper closed compact bounded Element of bool the carrier of (TOP-REAL 2)
C is functional non empty proper closed connected compact bounded being_simple_closed_curve with_the_max_arc Element of bool the carrier of (TOP-REAL 2)
C /\ (rectangle ((- 1),1,(- 3),3)) is functional proper closed compact bounded Element of bool the carrier of (TOP-REAL 2)
P is set
U is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
(rectangle ((- 1),1,(- 3),3)) /\ C is functional proper closed compact bounded Element of bool the carrier of (TOP-REAL 2)
C is functional non empty proper closed connected compact bounded being_simple_closed_curve with_the_max_arc Element of bool the carrier of (TOP-REAL 2)
C /\ (rectangle ((- 1),1,(- 3),3)) is functional proper closed compact bounded Element of bool the carrier of (TOP-REAL 2)
P is set
U is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
(rectangle ((- 1),1,(- 3),3)) /\ C is functional proper closed compact bounded Element of bool the carrier of (TOP-REAL 2)
C is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
LSeg (C,|[(- 1),3]|) is functional proper closed closed boundary nowhere_dense connected compact compact bounded bounded Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * C) + (b<sub>1</sub> * |[(- 1),3]|)) where b<sub>1</sub> is complex ext-real real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
P is functional non empty proper closed connected compact bounded being_simple_closed_curve with_the_max_arc Element of bool the carrier of (TOP-REAL 2)
P ` is functional non empty open Element of bool the carrier of (TOP-REAL 2)
the carrier of (TOP-REAL 2) \ P is set
P /\ (rectangle ((- 1),1,(- 3),3)) is functional proper closed compact bounded Element of bool the carrier of (TOP-REAL 2)
U is set
C `1 is complex ext-real real Element of REAL
C `2 is complex ext-real real Element of REAL
l is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
(rectangle ((- 1),1,(- 3),3)) /\ P is functional proper closed compact bounded Element of bool the carrier of (TOP-REAL 2)
|[(C `1),(C `2)]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
C is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
LSeg (C,|[1,3]|) is functional proper closed closed boundary nowhere_dense connected compact compact bounded bounded Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * C) + (b₁ * |[1,3]|)) where b₁ is complex ext-real real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
P is functional non empty proper closed connected compact bounded being_simple_closed_curve with_the_max_arc Element of bool the carrier of (TOP-REAL 2)
P ` is functional non empty open Element of bool the carrier of (TOP-REAL 2)
the carrier of (TOP-REAL 2) \ P is set
P /\ (rectangle ((- 1),1,(- 3),3)) is functional proper closed compact bounded Element of bool the carrier of (TOP-REAL 2)
U is set
C `1 is complex ext-real real Element of REAL
C `2 is complex ext-real real Element of REAL
l is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
(rectangle ((- 1),1,(- 3),3)) /\ P is functional proper closed compact bounded Element of bool the carrier of (TOP-REAL 2)
|[(C `1),(C `2)]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
C is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
LSeg (C,|[(- 1),(- 3)]|) is functional proper closed closed boundary nowhere_dense connected compact compact bounded bounded Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * C) + (b<sub>1</sub> * |[(- 1),(- 3)]|)) where b<sub>1</sub> is complex ext-real real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
P is functional non empty proper closed connected compact bounded being_simple_closed_curve with_the_max_arc Element of bool the carrier of (TOP-REAL 2)
P ` is functional non empty open Element of bool the carrier of (TOP-REAL 2)
the carrier of (TOP-REAL 2) \ P is set
P /\ (rectangle ((- 1),1,(- 3),3)) is functional proper closed compact bounded Element of bool the carrier of (TOP-REAL 2)
U is set
C `1 is complex ext-real real Element of REAL
C `2 is complex ext-real real Element of REAL
l is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
(rectangle ((- 1),1,(- 3),3)) /\ P is functional proper closed compact bounded Element of bool the carrier of (TOP-REAL 2)
|[(C `1),(C `2)]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
C is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
LSeg (C,|[1,(- 3)]|) is functional proper closed closed boundary nowhere_dense connected compact compact bounded bounded Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * C) + (b₁ * |[1,(- 3)]|)) where b₁ is complex ext-real real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
P is functional non empty proper closed connected compact bounded being_simple_closed_curve with_the_max_arc Element of bool the carrier of (TOP-REAL 2)
P ` is functional non empty open Element of bool the carrier of (TOP-REAL 2)
the carrier of (TOP-REAL 2) \ P is set
P /\ (rectangle ((- 1),1,(- 3),3)) is functional proper closed compact bounded Element of bool the carrier of (TOP-REAL 2)
U is set
C `1 is complex ext-real real Element of REAL
C `2 is complex ext-real real Element of REAL
l is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
(rectangle ((- 1),1,(- 3),3)) /\ P is functional proper closed compact bounded Element of bool the carrier of (TOP-REAL 2)
|[(C `1),(C `2)]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
C is complex ext-real real set
|[0,C]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
P is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
P `1 is complex ext-real real Element of REAL
P `2 is complex ext-real real Element of REAL
C is functional Element of bool the carrier of (TOP-REAL 2)
W-bound C is complex ext-real real Element of REAL
(TOP-REAL 2) | C is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj1 | C is Relation-like C -defined the carrier of (TOP-REAL 2) -defined the carrier of ((TOP-REAL 2) | C) -defined REAL -valued Function-like total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ((TOP-REAL 2) | C),REAL:]
the carrier of ((TOP-REAL 2) | C) is set
[: the carrier of ((TOP-REAL 2) | C),REAL:] is Relation-like V156() V157() V158() set
bool [: the carrier of ((TOP-REAL 2) | C),REAL:] is non empty set
lower_bound (proj1 | C) is complex ext-real real Element of REAL
(proj1 | C) .: the carrier of ((TOP-REAL 2) | C) is V166() V167() V168() Element of bool REAL
K663(((proj1 | C) .: the carrier of ((TOP-REAL 2) | C))) is complex ext-real real Element of REAL
P is functional non empty Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | P is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | P) is non empty set
proj1 | P is Relation-like P -defined the carrier of (TOP-REAL 2) -defined the carrier of ((TOP-REAL 2) | P) -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ((TOP-REAL 2) | P),REAL:]
[: the carrier of ((TOP-REAL 2) | P),REAL:] is Relation-like non empty V156() V157() V158() set
bool [: the carrier of ((TOP-REAL 2) | P),REAL:] is non empty set
(proj1 | P) .: the carrier of ((TOP-REAL 2) | P) is non empty V166() V167() V168() Element of bool REAL
U is V166() V167() V168() Element of bool REAL
l is complex ext-real real set
LJ is set
(proj1 | P) . LJ is complex ext-real real set
k is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
k `1 is complex ext-real real Element of REAL
k `2 is complex ext-real real Element of REAL
l is complex ext-real real set
(proj1 | P) . |[(- 1),0]| is complex ext-real real set
C is functional Element of bool the carrier of (TOP-REAL 2)
E-bound C is complex ext-real real Element of REAL
(TOP-REAL 2) | C is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj1 | C is Relation-like C -defined the carrier of (TOP-REAL 2) -defined the carrier of ((TOP-REAL 2) | C) -defined REAL -valued Function-like total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ((TOP-REAL 2) | C),REAL:]
the carrier of ((TOP-REAL 2) | C) is set
[: the carrier of ((TOP-REAL 2) | C),REAL:] is Relation-like V156() V157() V158() set
bool [: the carrier of ((TOP-REAL 2) | C),REAL:] is non empty set
upper_bound (proj1 | C) is complex ext-real real Element of REAL
(proj1 | C) .: the carrier of ((TOP-REAL 2) | C) is V166() V167() V168() Element of bool REAL
K662(((proj1 | C) .: the carrier of ((TOP-REAL 2) | C))) is complex ext-real real Element of REAL
P is functional non empty Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | P is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | P) is non empty set
proj1 | P is Relation-like P -defined the carrier of (TOP-REAL 2) -defined the carrier of ((TOP-REAL 2) | P) -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ((TOP-REAL 2) | P),REAL:]
[: the carrier of ((TOP-REAL 2) | P),REAL:] is Relation-like non empty V156() V157() V158() set
bool [: the carrier of ((TOP-REAL 2) | P),REAL:] is non empty set
(proj1 | P) .: the carrier of ((TOP-REAL 2) | P) is non empty V166() V167() V168() Element of bool REAL
U is V166() V167() V168() Element of bool REAL
l is complex ext-real real set
LJ is set
(proj1 | P) . LJ is complex ext-real real set
k is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
k `1 is complex ext-real real Element of REAL
k `2 is complex ext-real real Element of REAL
l is complex ext-real real set
(proj1 | P) . |[1,0]| is complex ext-real real set
{|[(- 1),0]|} is functional non empty proper closed compact bounded Element of bool the carrier of (TOP-REAL 2)
C is functional proper closed compact bounded Element of bool the carrier of (TOP-REAL 2)
W-most C is functional Element of bool the carrier of (TOP-REAL 2)
SW-corner C is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
W-bound C is complex ext-real real Element of REAL
(TOP-REAL 2) | C is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj1 | C is Relation-like C -defined the carrier of (TOP-REAL 2) -defined the carrier of ((TOP-REAL 2) | C) -defined REAL -valued Function-like total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ((TOP-REAL 2) | C),REAL:]
the carrier of ((TOP-REAL 2) | C) is set
[: the carrier of ((TOP-REAL 2) | C),REAL:] is Relation-like V156() V157() V158() set
bool [: the carrier of ((TOP-REAL 2) | C),REAL:] is non empty set
lower_bound (proj1 | C) is complex ext-real real Element of REAL
(proj1 | C) .: the carrier of ((TOP-REAL 2) | C) is V166() V167() V168() Element of bool REAL
K663(((proj1 | C) .: the carrier of ((TOP-REAL 2) | C))) is complex ext-real real Element of REAL
S-bound C is complex ext-real real Element of REAL
proj2 | C is Relation-like C -defined the carrier of (TOP-REAL 2) -defined the carrier of ((TOP-REAL 2) | C) -defined REAL -valued Function-like total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ((TOP-REAL 2) | C),REAL:]
lower_bound (proj2 | C) is complex ext-real real Element of REAL
(proj2 | C) .: the carrier of ((TOP-REAL 2) | C) is V166() V167() V168() Element of bool REAL
K663(((proj2 | C) .: the carrier of ((TOP-REAL 2) | C))) is complex ext-real real Element of REAL
|[(W-bound C),(S-bound C)]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
NW-corner C is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
N-bound C is complex ext-real real Element of REAL
upper_bound (proj2 | C) is complex ext-real real Element of REAL
K662(((proj2 | C) .: the carrier of ((TOP-REAL 2) | C))) is complex ext-real real Element of REAL
|[(W-bound C),(N-bound C)]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner C),(NW-corner C)) is functional proper closed closed boundary nowhere_dense connected compact compact bounded bounded vertical Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (SW-corner C)) + (b<sub>1</sub> * (NW-corner C))) where b<sub>1</sub> is complex ext-real real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg ((SW-corner C),(NW-corner C))) /\ C is functional proper closed compact bounded Element of bool the carrier of (TOP-REAL 2)
(SW-corner C) `1 is complex ext-real real Element of REAL
|[(- 1),(S-bound C)]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
|[(- 1),(S-bound C)]| `1 is complex ext-real real Element of REAL
(NW-corner C) `1 is complex ext-real real Element of REAL
|[(- 1),(N-bound C)]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
|[(- 1),(N-bound C)]| `1 is complex ext-real real Element of REAL
U is set
l is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
l `1 is complex ext-real real Element of REAL
LJ is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
LJ `1 is complex ext-real real Element of REAL
LJ `2 is complex ext-real real Element of REAL
C /\ (rectangle ((- 1),1,(- 3),3)) is functional proper closed compact bounded Element of bool the carrier of (TOP-REAL 2)
U is set
(SW-corner C) `2 is complex ext-real real Element of REAL
(NW-corner C) `2 is complex ext-real real Element of REAL
{|[1,0]|} is functional non empty proper closed compact bounded Element of bool the carrier of (TOP-REAL 2)
C is functional proper closed compact bounded Element of bool the carrier of (TOP-REAL 2)
E-most C is functional Element of bool the carrier of (TOP-REAL 2)
SE-corner C is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
E-bound C is complex ext-real real Element of REAL
(TOP-REAL 2) | C is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj1 | C is Relation-like C -defined the carrier of (TOP-REAL 2) -defined the carrier of ((TOP-REAL 2) | C) -defined REAL -valued Function-like total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ((TOP-REAL 2) | C),REAL:]
the carrier of ((TOP-REAL 2) | C) is set
[: the carrier of ((TOP-REAL 2) | C),REAL:] is Relation-like V156() V157() V158() set
bool [: the carrier of ((TOP-REAL 2) | C),REAL:] is non empty set
upper_bound (proj1 | C) is complex ext-real real Element of REAL
(proj1 | C) .: the carrier of ((TOP-REAL 2) | C) is V166() V167() V168() Element of bool REAL
K662(((proj1 | C) .: the carrier of ((TOP-REAL 2) | C))) is complex ext-real real Element of REAL
S-bound C is complex ext-real real Element of REAL
proj2 | C is Relation-like C -defined the carrier of (TOP-REAL 2) -defined the carrier of ((TOP-REAL 2) | C) -defined REAL -valued Function-like total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ((TOP-REAL 2) | C),REAL:]
lower_bound (proj2 | C) is complex ext-real real Element of REAL
(proj2 | C) .: the carrier of ((TOP-REAL 2) | C) is V166() V167() V168() Element of bool REAL
K663(((proj2 | C) .: the carrier of ((TOP-REAL 2) | C))) is complex ext-real real Element of REAL
|[(E-bound C),(S-bound C)]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
NE-corner C is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
N-bound C is complex ext-real real Element of REAL
upper_bound (proj2 | C) is complex ext-real real Element of REAL
K662(((proj2 | C) .: the carrier of ((TOP-REAL 2) | C))) is complex ext-real real Element of REAL
|[(E-bound C),(N-bound C)]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner C),(NE-corner C)) is functional proper closed closed boundary nowhere_dense connected compact compact bounded bounded vertical Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SE-corner C)) + (b₁ * (NE-corner C))) where b₁ is complex ext-real real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((SE-corner C),(NE-corner C))) /\ C is functional proper closed compact bounded Element of bool the carrier of (TOP-REAL 2)
(SE-corner C) `1 is complex ext-real real Element of REAL
|[1,(S-bound C)]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
|[1,(S-bound C)]| `1 is complex ext-real real Element of REAL
(NE-corner C) `1 is complex ext-real real Element of REAL
|[1,(N-bound C)]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
|[1,(N-bound C)]| `1 is complex ext-real real Element of REAL
U is set
l is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
l `1 is complex ext-real real Element of REAL
LJ is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
LJ `1 is complex ext-real real Element of REAL
LJ `2 is complex ext-real real Element of REAL
C /\ (rectangle ((- 1),1,(- 3),3)) is functional proper closed compact bounded Element of bool the carrier of (TOP-REAL 2)
U is set
(SE-corner C) `2 is complex ext-real real Element of REAL
(NE-corner C) `2 is complex ext-real real Element of REAL
C is functional proper closed compact bounded Element of bool the carrier of (TOP-REAL 2)
W-min C is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
W-bound C is complex ext-real real Element of REAL
(TOP-REAL 2) | C is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj1 | C is Relation-like C -defined the carrier of (TOP-REAL 2) -defined the carrier of ((TOP-REAL 2) | C) -defined REAL -valued Function-like total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ((TOP-REAL 2) | C),REAL:]
the carrier of ((TOP-REAL 2) | C) is set
[: the carrier of ((TOP-REAL 2) | C),REAL:] is Relation-like V156() V157() V158() set
bool [: the carrier of ((TOP-REAL 2) | C),REAL:] is non empty set
lower_bound (proj1 | C) is complex ext-real real Element of REAL
(proj1 | C) .: the carrier of ((TOP-REAL 2) | C) is V166() V167() V168() Element of bool REAL
K663(((proj1 | C) .: the carrier of ((TOP-REAL 2) | C))) is complex ext-real real Element of REAL
W-most C is functional Element of bool the carrier of (TOP-REAL 2)
SW-corner C is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
S-bound C is complex ext-real real Element of REAL
proj2 | C is Relation-like C -defined the carrier of (TOP-REAL 2) -defined the carrier of ((TOP-REAL 2) | C) -defined REAL -valued Function-like total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ((TOP-REAL 2) | C),REAL:]
lower_bound (proj2 | C) is complex ext-real real Element of REAL
(proj2 | C) .: the carrier of ((TOP-REAL 2) | C) is V166() V167() V168() Element of bool REAL
K663(((proj2 | C) .: the carrier of ((TOP-REAL 2) | C))) is complex ext-real real Element of REAL
|[(W-bound C),(S-bound C)]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
NW-corner C is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
N-bound C is complex ext-real real Element of REAL
upper_bound (proj2 | C) is complex ext-real real Element of REAL
K662(((proj2 | C) .: the carrier of ((TOP-REAL 2) | C))) is complex ext-real real Element of REAL
|[(W-bound C),(N-bound C)]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner C),(NW-corner C)) is functional proper closed closed boundary nowhere_dense connected compact compact bounded bounded vertical Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (SW-corner C)) + (b<sub>1</sub> * (NW-corner C))) where b<sub>1</sub> is complex ext-real real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg ((SW-corner C),(NW-corner C))) /\ C is functional proper closed compact bounded Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (W-most C) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj2 | (W-most C) is Relation-like W-most C -defined the carrier of (TOP-REAL 2) -defined the carrier of ((TOP-REAL 2) | (W-most C)) -defined REAL -valued Function-like total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ((TOP-REAL 2) | (W-most C)),REAL:]
the carrier of ((TOP-REAL 2) | (W-most C)) is set
[: the carrier of ((TOP-REAL 2) | (W-most C)),REAL:] is Relation-like V156() V157() V158() set
bool [: the carrier of ((TOP-REAL 2) | (W-most C)),REAL:] is non empty set
lower_bound (proj2 | (W-most C)) is complex ext-real real Element of REAL
(proj2 | (W-most C)) .: the carrier of ((TOP-REAL 2) | (W-most C)) is V166() V167() V168() Element of bool REAL
K663(((proj2 | (W-most C)) .: the carrier of ((TOP-REAL 2) | (W-most C)))) is complex ext-real real Element of REAL
|[(W-bound C),(lower_bound (proj2 | (W-most C)))]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
W-max C is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
upper_bound (proj2 | (W-most C)) is complex ext-real real Element of REAL
K662(((proj2 | (W-most C)) .: the carrier of ((TOP-REAL 2) | (W-most C)))) is complex ext-real real Element of REAL
|[(W-bound C),(upper_bound (proj2 | (W-most C)))]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
dom (proj2 | (W-most C)) is functional Element of bool (W-most C)
bool (W-most C) is non empty set
Im ((proj2 | (W-most C)),|[(- 1),0]|) is V166() V167() V168() set
{|[(- 1),0]|} is functional non empty set
(proj2 | (W-most C)) .: {|[(- 1),0]|} is V166() V167() V168() set
(proj2 | (W-most C)) . |[(- 1),0]| is complex ext-real real set
{((proj2 | (W-most C)) . |[(- 1),0]|)} is non empty V166() V167() V168() set
proj2 . |[(- 1),0]| is complex ext-real real Element of REAL
{(proj2 . |[(- 1),0]|)} is non empty V166() V167() V168() Element of bool REAL
{(|[(- 1),0]| `2)} is non empty V166() V167() V168() Element of bool REAL
|[(|[(- 1),0]| `1),(|[(- 1),0]| `2)]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
C is functional proper closed compact bounded Element of bool the carrier of (TOP-REAL 2)
E-min C is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
E-bound C is complex ext-real real Element of REAL
(TOP-REAL 2) | C is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj1 | C is Relation-like C -defined the carrier of (TOP-REAL 2) -defined the carrier of ((TOP-REAL 2) | C) -defined REAL -valued Function-like total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ((TOP-REAL 2) | C),REAL:]
the carrier of ((TOP-REAL 2) | C) is set
[: the carrier of ((TOP-REAL 2) | C),REAL:] is Relation-like V156() V157() V158() set
bool [: the carrier of ((TOP-REAL 2) | C),REAL:] is non empty set
upper_bound (proj1 | C) is complex ext-real real Element of REAL
(proj1 | C) .: the carrier of ((TOP-REAL 2) | C) is V166() V167() V168() Element of bool REAL
K662(((proj1 | C) .: the carrier of ((TOP-REAL 2) | C))) is complex ext-real real Element of REAL
E-most C is functional Element of bool the carrier of (TOP-REAL 2)
SE-corner C is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
S-bound C is complex ext-real real Element of REAL
proj2 | C is Relation-like C -defined the carrier of (TOP-REAL 2) -defined the carrier of ((TOP-REAL 2) | C) -defined REAL -valued Function-like total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ((TOP-REAL 2) | C),REAL:]
lower_bound (proj2 | C) is complex ext-real real Element of REAL
(proj2 | C) .: the carrier of ((TOP-REAL 2) | C) is V166() V167() V168() Element of bool REAL
K663(((proj2 | C) .: the carrier of ((TOP-REAL 2) | C))) is complex ext-real real Element of REAL
|[(E-bound C),(S-bound C)]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
NE-corner C is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
N-bound C is complex ext-real real Element of REAL
upper_bound (proj2 | C) is complex ext-real real Element of REAL
K662(((proj2 | C) .: the carrier of ((TOP-REAL 2) | C))) is complex ext-real real Element of REAL
|[(E-bound C),(N-bound C)]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner C),(NE-corner C)) is functional proper closed closed boundary nowhere_dense connected compact compact bounded bounded vertical Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SE-corner C)) + (b₁ * (NE-corner C))) where b₁ is complex ext-real real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((SE-corner C),(NE-corner C))) /\ C is functional proper closed compact bounded Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (E-most C) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj2 | (E-most C) is Relation-like E-most C -defined the carrier of (TOP-REAL 2) -defined the carrier of ((TOP-REAL 2) | (E-most C)) -defined REAL -valued Function-like total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ((TOP-REAL 2) | (E-most C)),REAL:]
the carrier of ((TOP-REAL 2) | (E-most C)) is set
[: the carrier of ((TOP-REAL 2) | (E-most C)),REAL:] is Relation-like V156() V157() V158() set
bool [: the carrier of ((TOP-REAL 2) | (E-most C)),REAL:] is non empty set
lower_bound (proj2 | (E-most C)) is complex ext-real real Element of REAL
(proj2 | (E-most C)) .: the carrier of ((TOP-REAL 2) | (E-most C)) is V166() V167() V168() Element of bool REAL
K663(((proj2 | (E-most C)) .: the carrier of ((TOP-REAL 2) | (E-most C)))) is complex ext-real real Element of REAL
|[(E-bound C),(lower_bound (proj2 | (E-most C)))]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
E-max C is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
upper_bound (proj2 | (E-most C)) is complex ext-real real Element of REAL
K662(((proj2 | (E-most C)) .: the carrier of ((TOP-REAL 2) | (E-most C)))) is complex ext-real real Element of REAL
|[(E-bound C),(upper_bound (proj2 | (E-most C)))]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
dom (proj2 | (E-most C)) is functional Element of bool (E-most C)
bool (E-most C) is non empty set
Im ((proj2 | (E-most C)),|[1,0]|) is V166() V167() V168() set
{|[1,0]|} is functional non empty set
(proj2 | (E-most C)) .: {|[1,0]|} is V166() V167() V168() set
(proj2 | (E-most C)) . |[1,0]| is complex ext-real real set
{((proj2 | (E-most C)) . |[1,0]|)} is non empty V166() V167() V168() set
proj2 . |[1,0]| is complex ext-real real Element of REAL
{(proj2 . |[1,0]|)} is non empty V166() V167() V168() Element of bool REAL
{(|[1,0]| `2)} is non empty V166() V167() V168() Element of bool REAL
|[(|[1,0]| `1),(|[1,0]| `2)]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
C is functional Element of bool the carrier of (TOP-REAL 2)
W-bound C is complex ext-real real Element of REAL
(TOP-REAL 2) | C is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj1 | C is Relation-like C -defined the carrier of (TOP-REAL 2) -defined the carrier of ((TOP-REAL 2) | C) -defined REAL -valued Function-like total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ((TOP-REAL 2) | C),REAL:]
the carrier of ((TOP-REAL 2) | C) is set
[: the carrier of ((TOP-REAL 2) | C),REAL:] is Relation-like V156() V157() V158() set
bool [: the carrier of ((TOP-REAL 2) | C),REAL:] is non empty set
lower_bound (proj1 | C) is complex ext-real real Element of REAL
(proj1 | C) .: the carrier of ((TOP-REAL 2) | C) is V166() V167() V168() Element of bool REAL
K663(((proj1 | C) .: the carrier of ((TOP-REAL 2) | C))) is complex ext-real real Element of REAL
E-bound C is complex ext-real real Element of REAL
upper_bound (proj1 | C) is complex ext-real real Element of REAL
K662(((proj1 | C) .: the carrier of ((TOP-REAL 2) | C))) is complex ext-real real Element of REAL
(W-bound C) + (E-bound C) is complex ext-real real Element of REAL
((W-bound C) + (E-bound C)) / 2 is complex ext-real real Element of REAL
C is functional Element of bool the carrier of (TOP-REAL 2)
W-bound C is complex ext-real real Element of REAL
(TOP-REAL 2) | C is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj1 | C is Relation-like C -defined the carrier of (TOP-REAL 2) -defined the carrier of ((TOP-REAL 2) | C) -defined REAL -valued Function-like total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ((TOP-REAL 2) | C),REAL:]
the carrier of ((TOP-REAL 2) | C) is set
[: the carrier of ((TOP-REAL 2) | C),REAL:] is Relation-like V156() V157() V158() set
bool [: the carrier of ((TOP-REAL 2) | C),REAL:] is non empty set
lower_bound (proj1 | C) is complex ext-real real Element of REAL
(proj1 | C) .: the carrier of ((TOP-REAL 2) | C) is V166() V167() V168() Element of bool REAL
K663(((proj1 | C) .: the carrier of ((TOP-REAL 2) | C))) is complex ext-real real Element of REAL
E-bound C is complex ext-real real Element of REAL
upper_bound (proj1 | C) is complex ext-real real Element of REAL
K662(((proj1 | C) .: the carrier of ((TOP-REAL 2) | C))) is complex ext-real real Element of REAL
(W-bound C) + (E-bound C) is complex ext-real real Element of REAL
((W-bound C) + (E-bound C)) / 2 is complex ext-real real Element of REAL
C is functional Element of bool the carrier of (TOP-REAL 2)
UMP C is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
E-bound C is complex ext-real real Element of REAL
(TOP-REAL 2) | C is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj1 | C is Relation-like C -defined the carrier of (TOP-REAL 2) -defined the carrier of ((TOP-REAL 2) | C) -defined REAL -valued Function-like total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ((TOP-REAL 2) | C),REAL:]
the carrier of ((TOP-REAL 2) | C) is set
[: the carrier of ((TOP-REAL 2) | C),REAL:] is Relation-like V156() V157() V158() set
bool [: the carrier of ((TOP-REAL 2) | C),REAL:] is non empty set
upper_bound (proj1 | C) is complex ext-real real Element of REAL
(proj1 | C) .: the carrier of ((TOP-REAL 2) | C) is V166() V167() V168() Element of bool REAL
K662(((proj1 | C) .: the carrier of ((TOP-REAL 2) | C))) is complex ext-real real Element of REAL
W-bound C is complex ext-real real Element of REAL
lower_bound (proj1 | C) is complex ext-real real Element of REAL
K663(((proj1 | C) .: the carrier of ((TOP-REAL 2) | C))) is complex ext-real real Element of REAL
(E-bound C) + (W-bound C) is complex ext-real real Element of REAL
((E-bound C) + (W-bound C)) / 2 is complex ext-real real Element of REAL
Vertical_Line (((E-bound C) + (W-bound C)) / 2) is functional Element of bool the carrier of (TOP-REAL 2)
C /\ (Vertical_Line (((E-bound C) + (W-bound C)) / 2)) is functional Element of bool the carrier of (TOP-REAL 2)
proj2 .: (C /\ (Vertical_Line (((E-bound C) + (W-bound C)) / 2))) is V166() V167() V168() Element of bool REAL
K662((proj2 .: (C /\ (Vertical_Line (((E-bound C) + (W-bound C)) / 2))))) is complex ext-real real Element of REAL
|[(((E-bound C) + (W-bound C)) / 2),K662((proj2 .: (C /\ (Vertical_Line (((E-bound C) + (W-bound C)) / 2)))))]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
LSeg (|[0,3]|,(UMP C)) is functional proper closed closed boundary nowhere_dense connected compact compact bounded bounded Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * |[0,3]|) + (b<sub>1</sub> * (UMP C))) where b<sub>1</sub> is complex ext-real real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(W-bound C) + (E-bound C) is complex ext-real real Element of REAL
((W-bound C) + (E-bound C)) / 2 is complex ext-real real Element of REAL
(UMP C) `1 is complex ext-real real Element of REAL
C is functional Element of bool the carrier of (TOP-REAL 2)
LMP C is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
E-bound C is complex ext-real real Element of REAL
(TOP-REAL 2) | C is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj1 | C is Relation-like C -defined the carrier of (TOP-REAL 2) -defined the carrier of ((TOP-REAL 2) | C) -defined REAL -valued Function-like total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ((TOP-REAL 2) | C),REAL:]
the carrier of ((TOP-REAL 2) | C) is set
[: the carrier of ((TOP-REAL 2) | C),REAL:] is Relation-like V156() V157() V158() set
bool [: the carrier of ((TOP-REAL 2) | C),REAL:] is non empty set
upper_bound (proj1 | C) is complex ext-real real Element of REAL
(proj1 | C) .: the carrier of ((TOP-REAL 2) | C) is V166() V167() V168() Element of bool REAL
K662(((proj1 | C) .: the carrier of ((TOP-REAL 2) | C))) is complex ext-real real Element of REAL
W-bound C is complex ext-real real Element of REAL
lower_bound (proj1 | C) is complex ext-real real Element of REAL
K663(((proj1 | C) .: the carrier of ((TOP-REAL 2) | C))) is complex ext-real real Element of REAL
(E-bound C) + (W-bound C) is complex ext-real real Element of REAL
((E-bound C) + (W-bound C)) / 2 is complex ext-real real Element of REAL
Vertical_Line (((E-bound C) + (W-bound C)) / 2) is functional Element of bool the carrier of (TOP-REAL 2)
C /\ (Vertical_Line (((E-bound C) + (W-bound C)) / 2)) is functional Element of bool the carrier of (TOP-REAL 2)
proj2 .: (C /\ (Vertical_Line (((E-bound C) + (W-bound C)) / 2))) is V166() V167() V168() Element of bool REAL
K663((proj2 .: (C /\ (Vertical_Line (((E-bound C) + (W-bound C)) / 2))))) is complex ext-real real Element of REAL
|[(((E-bound C) + (W-bound C)) / 2),K663((proj2 .: (C /\ (Vertical_Line (((E-bound C) + (W-bound C)) / 2)))))]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
LSeg ((LMP C),|[0,(- 3)]|) is functional proper closed closed boundary nowhere_dense connected compact compact bounded bounded Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (LMP C)) + (b₁ * |[0,(- 3)]|)) where b₁ is complex ext-real real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(W-bound C) + (E-bound C) is complex ext-real real Element of REAL
((W-bound C) + (E-bound C)) / 2 is complex ext-real real Element of REAL
(LMP C) `1 is complex ext-real real Element of REAL
C is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
C `2 is complex ext-real real Element of REAL
P is functional Element of bool the carrier of (TOP-REAL 2)
P /\ (rectangle ((- 1),1,(- 3),3)) is functional Element of bool the carrier of (TOP-REAL 2)
U is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
U `1 is complex ext-real real Element of REAL
U `2 is complex ext-real real Element of REAL
U is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
U `1 is complex ext-real real Element of REAL
U `2 is complex ext-real real Element of REAL
C is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
C `2 is complex ext-real real Element of REAL
P is functional Element of bool the carrier of (TOP-REAL 2)
P /\ (rectangle ((- 1),1,(- 3),3)) is functional Element of bool the carrier of (TOP-REAL 2)
U is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
U `1 is complex ext-real real Element of REAL
U `2 is complex ext-real real Element of REAL
U is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
U `1 is complex ext-real real Element of REAL
U `2 is complex ext-real real Element of REAL
C is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
C `2 is complex ext-real real Element of REAL
P is functional non empty proper closed compact bounded with_the_max_arc Element of bool the carrier of (TOP-REAL 2)
UMP P is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
E-bound P is complex ext-real real Element of REAL
(TOP-REAL 2) | P is non empty strict TopSpace-like T_0 T_1 T_2 V82() normal T_3 T_4 compact V246() pseudocompact SubSpace of TOP-REAL 2
proj1 | P is Relation-like P -defined the carrier of (TOP-REAL 2) -defined the carrier of ((TOP-REAL 2) | P) -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ((TOP-REAL 2) | P),REAL:]
the carrier of ((TOP-REAL 2) | P) is non empty set
[: the carrier of ((TOP-REAL 2) | P),REAL:] is Relation-like non empty V156() V157() V158() set
bool [: the carrier of ((TOP-REAL 2) | P),REAL:] is non empty set
upper_bound (proj1 | P) is complex ext-real real Element of REAL
(proj1 | P) .: the carrier of ((TOP-REAL 2) | P) is non empty V166() V167() V168() Element of bool REAL
K662(((proj1 | P) .: the carrier of ((TOP-REAL 2) | P))) is complex ext-real real Element of REAL
W-bound P is complex ext-real real Element of REAL
lower_bound (proj1 | P) is complex ext-real real Element of REAL
K663(((proj1 | P) .: the carrier of ((TOP-REAL 2) | P))) is complex ext-real real Element of REAL
(E-bound P) + (W-bound P) is complex ext-real real Element of REAL
((E-bound P) + (W-bound P)) / 2 is complex ext-real real Element of REAL
Vertical_Line (((E-bound P) + (W-bound P)) / 2) is functional Element of bool the carrier of (TOP-REAL 2)
P /\ (Vertical_Line (((E-bound P) + (W-bound P)) / 2)) is functional Element of bool the carrier of (TOP-REAL 2)
proj2 .: (P /\ (Vertical_Line (((E-bound P) + (W-bound P)) / 2))) is V166() V167() V168() Element of bool REAL
K662((proj2 .: (P /\ (Vertical_Line (((E-bound P) + (W-bound P)) / 2))))) is complex ext-real real Element of REAL
|[(((E-bound P) + (W-bound P)) / 2),K662((proj2 .: (P /\ (Vertical_Line (((E-bound P) + (W-bound P)) / 2)))))]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
LSeg (|[0,3]|,(UMP P)) is functional proper closed closed boundary nowhere_dense connected compact compact bounded bounded Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * |[0,3]|) + (b₁ * (UMP P))) where b₁ is complex ext-real real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(UMP P) `2 is complex ext-real real Element of REAL
|[(|[0,3]| `1),(|[0,3]| `2)]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
(UMP P) `1 is complex ext-real real Element of REAL
|[((UMP P) `1),((UMP P) `2)]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
C is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
C `2 is complex ext-real real Element of REAL
P is functional non empty proper closed compact bounded with_the_max_arc Element of bool the carrier of (TOP-REAL 2)
LMP P is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
E-bound P is complex ext-real real Element of REAL
(TOP-REAL 2) | P is non empty strict TopSpace-like T_0 T_1 T_2 V82() normal T_3 T_4 compact V246() pseudocompact SubSpace of TOP-REAL 2
proj1 | P is Relation-like P -defined the carrier of (TOP-REAL 2) -defined the carrier of ((TOP-REAL 2) | P) -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ((TOP-REAL 2) | P),REAL:]
the carrier of ((TOP-REAL 2) | P) is non empty set
[: the carrier of ((TOP-REAL 2) | P),REAL:] is Relation-like non empty V156() V157() V158() set
bool [: the carrier of ((TOP-REAL 2) | P),REAL:] is non empty set
upper_bound (proj1 | P) is complex ext-real real Element of REAL
(proj1 | P) .: the carrier of ((TOP-REAL 2) | P) is non empty V166() V167() V168() Element of bool REAL
K662(((proj1 | P) .: the carrier of ((TOP-REAL 2) | P))) is complex ext-real real Element of REAL
W-bound P is complex ext-real real Element of REAL
lower_bound (proj1 | P) is complex ext-real real Element of REAL
K663(((proj1 | P) .: the carrier of ((TOP-REAL 2) | P))) is complex ext-real real Element of REAL
(E-bound P) + (W-bound P) is complex ext-real real Element of REAL
((E-bound P) + (W-bound P)) / 2 is complex ext-real real Element of REAL
Vertical_Line (((E-bound P) + (W-bound P)) / 2) is functional Element of bool the carrier of (TOP-REAL 2)
P /\ (Vertical_Line (((E-bound P) + (W-bound P)) / 2)) is functional Element of bool the carrier of (TOP-REAL 2)
proj2 .: (P /\ (Vertical_Line (((E-bound P) + (W-bound P)) / 2))) is V166() V167() V168() Element of bool REAL
K663((proj2 .: (P /\ (Vertical_Line (((E-bound P) + (W-bound P)) / 2))))) is complex ext-real real Element of REAL
|[(((E-bound P) + (W-bound P)) / 2),K663((proj2 .: (P /\ (Vertical_Line (((E-bound P) + (W-bound P)) / 2)))))]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
LSeg ((LMP P),|[0,(- 3)]|) is functional proper closed closed boundary nowhere_dense connected compact compact bounded bounded Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (LMP P)) + (b<sub>1</sub> * |[0,(- 3)]|)) where b<sub>1</sub> is complex ext-real real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LMP P) `2 is complex ext-real real Element of REAL
|[(|[0,(- 3)]| `1),(|[0,(- 3)]| `2)]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
(LMP P) `1 is complex ext-real real Element of REAL
|[((LMP P) `1),((LMP P) `2)]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
C is functional non empty proper closed compact bounded with_the_max_arc Element of bool the carrier of (TOP-REAL 2)
UMP C is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
E-bound C is complex ext-real real Element of REAL
(TOP-REAL 2) | C is non empty strict TopSpace-like T_0 T_1 T_2 V82() normal T_3 T_4 compact V246() pseudocompact SubSpace of TOP-REAL 2
proj1 | C is Relation-like C -defined the carrier of (TOP-REAL 2) -defined the carrier of ((TOP-REAL 2) | C) -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ((TOP-REAL 2) | C),REAL:]
the carrier of ((TOP-REAL 2) | C) is non empty set
[: the carrier of ((TOP-REAL 2) | C),REAL:] is Relation-like non empty V156() V157() V158() set
bool [: the carrier of ((TOP-REAL 2) | C),REAL:] is non empty set
upper_bound (proj1 | C) is complex ext-real real Element of REAL
(proj1 | C) .: the carrier of ((TOP-REAL 2) | C) is non empty V166() V167() V168() Element of bool REAL
K662(((proj1 | C) .: the carrier of ((TOP-REAL 2) | C))) is complex ext-real real Element of REAL
W-bound C is complex ext-real real Element of REAL
lower_bound (proj1 | C) is complex ext-real real Element of REAL
K663(((proj1 | C) .: the carrier of ((TOP-REAL 2) | C))) is complex ext-real real Element of REAL
(E-bound C) + (W-bound C) is complex ext-real real Element of REAL
((E-bound C) + (W-bound C)) / 2 is complex ext-real real Element of REAL
Vertical_Line (((E-bound C) + (W-bound C)) / 2) is functional Element of bool the carrier of (TOP-REAL 2)
C /\ (Vertical_Line (((E-bound C) + (W-bound C)) / 2)) is functional Element of bool the carrier of (TOP-REAL 2)
proj2 .: (C /\ (Vertical_Line (((E-bound C) + (W-bound C)) / 2))) is V166() V167() V168() Element of bool REAL
K662((proj2 .: (C /\ (Vertical_Line (((E-bound C) + (W-bound C)) / 2))))) is complex ext-real real Element of REAL
|[(((E-bound C) + (W-bound C)) / 2),K662((proj2 .: (C /\ (Vertical_Line (((E-bound C) + (W-bound C)) / 2)))))]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
LSeg (|[0,3]|,(UMP C)) is functional proper closed closed boundary nowhere_dense connected compact compact bounded bounded Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * |[0,3]|) + (b<sub>1</sub> * (UMP C))) where b<sub>1</sub> is complex ext-real real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
north_halfline (UMP C) is functional non empty connected convex Element of bool the carrier of (TOP-REAL 2)
U is set
l is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
l `1 is complex ext-real real Element of REAL
(UMP C) `1 is complex ext-real real Element of REAL
(UMP C) `2 is complex ext-real real Element of REAL
l `2 is complex ext-real real Element of REAL
C is functional non empty proper closed compact bounded with_the_max_arc Element of bool the carrier of (TOP-REAL 2)
LMP C is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
E-bound C is complex ext-real real Element of REAL
(TOP-REAL 2) | C is non empty strict TopSpace-like T_0 T_1 T_2 V82() normal T_3 T_4 compact V246() pseudocompact SubSpace of TOP-REAL 2
proj1 | C is Relation-like C -defined the carrier of (TOP-REAL 2) -defined the carrier of ((TOP-REAL 2) | C) -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ((TOP-REAL 2) | C),REAL:]
the carrier of ((TOP-REAL 2) | C) is non empty set
[: the carrier of ((TOP-REAL 2) | C),REAL:] is Relation-like non empty V156() V157() V158() set
bool [: the carrier of ((TOP-REAL 2) | C),REAL:] is non empty set
upper_bound (proj1 | C) is complex ext-real real Element of REAL
(proj1 | C) .: the carrier of ((TOP-REAL 2) | C) is non empty V166() V167() V168() Element of bool REAL
K662(((proj1 | C) .: the carrier of ((TOP-REAL 2) | C))) is complex ext-real real Element of REAL
W-bound C is complex ext-real real Element of REAL
lower_bound (proj1 | C) is complex ext-real real Element of REAL
K663(((proj1 | C) .: the carrier of ((TOP-REAL 2) | C))) is complex ext-real real Element of REAL
(E-bound C) + (W-bound C) is complex ext-real real Element of REAL
((E-bound C) + (W-bound C)) / 2 is complex ext-real real Element of REAL
Vertical_Line (((E-bound C) + (W-bound C)) / 2) is functional Element of bool the carrier of (TOP-REAL 2)
C /\ (Vertical_Line (((E-bound C) + (W-bound C)) / 2)) is functional Element of bool the carrier of (TOP-REAL 2)
proj2 .: (C /\ (Vertical_Line (((E-bound C) + (W-bound C)) / 2))) is V166() V167() V168() Element of bool REAL
K663((proj2 .: (C /\ (Vertical_Line (((E-bound C) + (W-bound C)) / 2))))) is complex ext-real real Element of REAL
|[(((E-bound C) + (W-bound C)) / 2),K663((proj2 .: (C /\ (Vertical_Line (((E-bound C) + (W-bound C)) / 2)))))]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
LSeg ((LMP C),|[0,(- 3)]|) is functional proper closed closed boundary nowhere_dense connected compact compact bounded bounded Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (LMP C)) + (b<sub>1</sub> * |[0,(- 3)]|)) where b<sub>1</sub> is complex ext-real real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
south_halfline (LMP C) is functional non empty connected convex Element of bool the carrier of (TOP-REAL 2)
U is set
l is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
l `1 is complex ext-real real Element of REAL
(LMP C) `1 is complex ext-real real Element of REAL
|[(|[0,(- 3)]| `1),(|[0,(- 3)]| `2)]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
(LMP C) `2 is complex ext-real real Element of REAL
|[((LMP C) `1),((LMP C) `2)]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
l `2 is complex ext-real real Element of REAL
C is functional non empty proper closed connected compact bounded being_simple_closed_curve with_the_max_arc Element of bool the carrier of (TOP-REAL 2)
UMP C is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
E-bound C is complex ext-real real Element of REAL
(TOP-REAL 2) | C is non empty strict TopSpace-like T_0 T_1 T_2 V82() normal T_3 T_4 compact V246() pseudocompact SubSpace of TOP-REAL 2
proj1 | C is Relation-like C -defined the carrier of (TOP-REAL 2) -defined the carrier of ((TOP-REAL 2) | C) -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ((TOP-REAL 2) | C),REAL:]
the carrier of ((TOP-REAL 2) | C) is non empty set
[: the carrier of ((TOP-REAL 2) | C),REAL:] is Relation-like non empty V156() V157() V158() set
bool [: the carrier of ((TOP-REAL 2) | C),REAL:] is non empty set
upper_bound (proj1 | C) is complex ext-real real Element of REAL
(proj1 | C) .: the carrier of ((TOP-REAL 2) | C) is non empty V166() V167() V168() Element of bool REAL
K662(((proj1 | C) .: the carrier of ((TOP-REAL 2) | C))) is complex ext-real real Element of REAL
W-bound C is complex ext-real real Element of REAL
lower_bound (proj1 | C) is complex ext-real real Element of REAL
K663(((proj1 | C) .: the carrier of ((TOP-REAL 2) | C))) is complex ext-real real Element of REAL
(E-bound C) + (W-bound C) is complex ext-real real Element of REAL
((E-bound C) + (W-bound C)) / 2 is complex ext-real real Element of REAL
Vertical_Line (((E-bound C) + (W-bound C)) / 2) is functional Element of bool the carrier of (TOP-REAL 2)
C /\ (Vertical_Line (((E-bound C) + (W-bound C)) / 2)) is functional Element of bool the carrier of (TOP-REAL 2)
proj2 .: (C /\ (Vertical_Line (((E-bound C) + (W-bound C)) / 2))) is V166() V167() V168() Element of bool REAL
K662((proj2 .: (C /\ (Vertical_Line (((E-bound C) + (W-bound C)) / 2))))) is complex ext-real real Element of REAL
|[(((E-bound C) + (W-bound C)) / 2),K662((proj2 .: (C /\ (Vertical_Line (((E-bound C) + (W-bound C)) / 2)))))]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
LSeg (|[0,3]|,(UMP C)) is functional proper closed closed boundary nowhere_dense connected compact compact bounded bounded Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * |[0,3]|) + (b<sub>1</sub> * (UMP C))) where b<sub>1</sub> is complex ext-real real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
P is functional Element of bool the carrier of (TOP-REAL 2)
C ` is functional non empty open Element of bool the carrier of (TOP-REAL 2)
the carrier of (TOP-REAL 2) \ C is set
(TOP-REAL 2) | (C `) is non empty strict TopSpace-like T_0 T_1 T_2 V118( TOP-REAL 2) SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | (C `)) is non empty set
bool the carrier of ((TOP-REAL 2) | (C `)) is non empty set
Euclid 2 is non empty strict Reflexive discerning symmetric triangle Discerning MetrStruct
the carrier of (Euclid 2) is non empty set
bool the carrier of (Euclid 2) is non empty set
{(UMP C)} is functional non empty proper closed compact bounded Element of bool the carrier of (TOP-REAL 2)
(LSeg (|[0,3]|,(UMP C))) \ {(UMP C)} is functional Element of bool the carrier of (TOP-REAL 2)
((LSeg (|[0,3]|,(UMP C))) \ {(UMP C)}) \/ {(UMP C)} is functional non empty Element of bool the carrier of (TOP-REAL 2)
north_halfline (UMP C) is functional non empty connected convex Element of bool the carrier of (TOP-REAL 2)
(north_halfline (UMP C)) \ {(UMP C)} is functional Element of bool the carrier of (TOP-REAL 2)
UBD C is functional non empty open connected being_Region Element of bool the carrier of (TOP-REAL 2)
{ b<sub>1</sub> where b<sub>1</sub> is functional Element of bool the carrier of (TOP-REAL 2) : b<sub>1</sub> is_outside_component_of C } is set
union { b<sub>1</sub> where b<sub>1</sub> is functional Element of bool the carrier of (TOP-REAL 2) : b<sub>1</sub> is_outside_component_of C } is set
LJ is Element of bool the carrier of ((TOP-REAL 2) | (C `))
C is functional non empty proper closed connected compact bounded being_simple_closed_curve with_the_max_arc Element of bool the carrier of (TOP-REAL 2)
LMP C is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
E-bound C is complex ext-real real Element of REAL
(TOP-REAL 2) | C is non empty strict TopSpace-like T_0 T_1 T_2 V82() normal T_3 T_4 compact V246() pseudocompact SubSpace of TOP-REAL 2
proj1 | C is Relation-like C -defined the carrier of (TOP-REAL 2) -defined the carrier of ((TOP-REAL 2) | C) -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ((TOP-REAL 2) | C),REAL:]
the carrier of ((TOP-REAL 2) | C) is non empty set
[: the carrier of ((TOP-REAL 2) | C),REAL:] is Relation-like non empty V156() V157() V158() set
bool [: the carrier of ((TOP-REAL 2) | C),REAL:] is non empty set
upper_bound (proj1 | C) is complex ext-real real Element of REAL
(proj1 | C) .: the carrier of ((TOP-REAL 2) | C) is non empty V166() V167() V168() Element of bool REAL
K662(((proj1 | C) .: the carrier of ((TOP-REAL 2) | C))) is complex ext-real real Element of REAL
W-bound C is complex ext-real real Element of REAL
lower_bound (proj1 | C) is complex ext-real real Element of REAL
K663(((proj1 | C) .: the carrier of ((TOP-REAL 2) | C))) is complex ext-real real Element of REAL
(E-bound C) + (W-bound C) is complex ext-real real Element of REAL
((E-bound C) + (W-bound C)) / 2 is complex ext-real real Element of REAL
Vertical_Line (((E-bound C) + (W-bound C)) / 2) is functional Element of bool the carrier of (TOP-REAL 2)
C /\ (Vertical_Line (((E-bound C) + (W-bound C)) / 2)) is functional Element of bool the carrier of (TOP-REAL 2)
proj2 .: (C /\ (Vertical_Line (((E-bound C) + (W-bound C)) / 2))) is V166() V167() V168() Element of bool REAL
K663((proj2 .: (C /\ (Vertical_Line (((E-bound C) + (W-bound C)) / 2))))) is complex ext-real real Element of REAL
|[(((E-bound C) + (W-bound C)) / 2),K663((proj2 .: (C /\ (Vertical_Line (((E-bound C) + (W-bound C)) / 2)))))]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
LSeg ((LMP C),|[0,(- 3)]|) is functional proper closed closed boundary nowhere_dense connected compact compact bounded bounded Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (LMP C)) + (b₁ * |[0,(- 3)]|)) where b₁ is complex ext-real real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
P is functional Element of bool the carrier of (TOP-REAL 2)
C ` is functional non empty open Element of bool the carrier of (TOP-REAL 2)
the carrier of (TOP-REAL 2) \ C is set
(TOP-REAL 2) | (C `) is non empty strict TopSpace-like T_0 T_1 T_2 V118( TOP-REAL 2) SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | (C `)) is non empty set
bool the carrier of ((TOP-REAL 2) | (C `)) is non empty set
Euclid 2 is non empty strict Reflexive discerning symmetric triangle Discerning MetrStruct
the carrier of (Euclid 2) is non empty set
bool the carrier of (Euclid 2) is non empty set
{(LMP C)} is functional non empty proper closed compact bounded Element of bool the carrier of (TOP-REAL 2)
(LSeg ((LMP C),|[0,(- 3)]|)) \ {(LMP C)} is functional Element of bool the carrier of (TOP-REAL 2)
((LSeg ((LMP C),|[0,(- 3)]|)) \ {(LMP C)}) \/ {(LMP C)} is functional non empty Element of bool the carrier of (TOP-REAL 2)
south_halfline (LMP C) is functional non empty connected convex Element of bool the carrier of (TOP-REAL 2)
(south_halfline (LMP C)) \ {(LMP C)} is functional Element of bool the carrier of (TOP-REAL 2)
UBD C is functional non empty open connected being_Region Element of bool the carrier of (TOP-REAL 2)
{ b₁ where b₁ is functional Element of bool the carrier of (TOP-REAL 2) : b₁ is_outside_component_of C } is set
union { b₁ where b₁ is functional Element of bool the carrier of (TOP-REAL 2) : b₁ is_outside_component_of C } is set
LJ is Element of bool the carrier of ((TOP-REAL 2) | (C `))
C is functional non empty proper closed compact bounded with_the_max_arc Element of bool the carrier of (TOP-REAL 2)
UMP C is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
E-bound C is complex ext-real real Element of REAL
(TOP-REAL 2) | C is non empty strict TopSpace-like T_0 T_1 T_2 V82() normal T_3 T_4 compact V246() pseudocompact SubSpace of TOP-REAL 2
proj1 | C is Relation-like C -defined the carrier of (TOP-REAL 2) -defined the carrier of ((TOP-REAL 2) | C) -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ((TOP-REAL 2) | C),REAL:]
the carrier of ((TOP-REAL 2) | C) is non empty set
[: the carrier of ((TOP-REAL 2) | C),REAL:] is Relation-like non empty V156() V157() V158() set
bool [: the carrier of ((TOP-REAL 2) | C),REAL:] is non empty set
upper_bound (proj1 | C) is complex ext-real real Element of REAL
(proj1 | C) .: the carrier of ((TOP-REAL 2) | C) is non empty V166() V167() V168() Element of bool REAL
K662(((proj1 | C) .: the carrier of ((TOP-REAL 2) | C))) is complex ext-real real Element of REAL
W-bound C is complex ext-real real Element of REAL
lower_bound (proj1 | C) is complex ext-real real Element of REAL
K663(((proj1 | C) .: the carrier of ((TOP-REAL 2) | C))) is complex ext-real real Element of REAL
(E-bound C) + (W-bound C) is complex ext-real real Element of REAL
((E-bound C) + (W-bound C)) / 2 is complex ext-real real Element of REAL
Vertical_Line (((E-bound C) + (W-bound C)) / 2) is functional Element of bool the carrier of (TOP-REAL 2)
C /\ (Vertical_Line (((E-bound C) + (W-bound C)) / 2)) is functional Element of bool the carrier of (TOP-REAL 2)
proj2 .: (C /\ (Vertical_Line (((E-bound C) + (W-bound C)) / 2))) is V166() V167() V168() Element of bool REAL
K662((proj2 .: (C /\ (Vertical_Line (((E-bound C) + (W-bound C)) / 2))))) is complex ext-real real Element of REAL
|[(((E-bound C) + (W-bound C)) / 2),K662((proj2 .: (C /\ (Vertical_Line (((E-bound C) + (W-bound C)) / 2)))))]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
LSeg (|[0,3]|,(UMP C)) is functional proper closed closed boundary nowhere_dense connected compact compact bounded bounded Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * |[0,3]|) + (b<sub>1</sub> * (UMP C))) where b<sub>1</sub> is complex ext-real real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg (|[0,3]|,(UMP C))) /\ C is functional proper closed compact bounded Element of bool the carrier of (TOP-REAL 2)
{(UMP C)} is functional non empty proper closed compact bounded Element of bool the carrier of (TOP-REAL 2)
(W-bound C) + (E-bound C) is complex ext-real real Element of REAL
((W-bound C) + (E-bound C)) / 2 is complex ext-real real Element of REAL
(UMP C) `1 is complex ext-real real Element of REAL
l is set
LJ is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
LJ `1 is complex ext-real real Element of REAL
Vertical_Line (((W-bound C) + (E-bound C)) / 2) is functional Element of bool the carrier of (TOP-REAL 2)
C /\ (Vertical_Line (((W-bound C) + (E-bound C)) / 2)) is functional Element of bool the carrier of (TOP-REAL 2)
LJ `2 is complex ext-real real Element of REAL
(UMP C) `2 is complex ext-real real Element of REAL
l is set
C is functional non empty proper closed compact bounded with_the_max_arc Element of bool the carrier of (TOP-REAL 2)
LMP C is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
E-bound C is complex ext-real real Element of REAL
(TOP-REAL 2) | C is non empty strict TopSpace-like T_0 T_1 T_2 V82() normal T_3 T_4 compact V246() pseudocompact SubSpace of TOP-REAL 2
proj1 | C is Relation-like C -defined the carrier of (TOP-REAL 2) -defined the carrier of ((TOP-REAL 2) | C) -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ((TOP-REAL 2) | C),REAL:]
the carrier of ((TOP-REAL 2) | C) is non empty set
[: the carrier of ((TOP-REAL 2) | C),REAL:] is Relation-like non empty V156() V157() V158() set
bool [: the carrier of ((TOP-REAL 2) | C),REAL:] is non empty set
upper_bound (proj1 | C) is complex ext-real real Element of REAL
(proj1 | C) .: the carrier of ((TOP-REAL 2) | C) is non empty V166() V167() V168() Element of bool REAL
K662(((proj1 | C) .: the carrier of ((TOP-REAL 2) | C))) is complex ext-real real Element of REAL
W-bound C is complex ext-real real Element of REAL
lower_bound (proj1 | C) is complex ext-real real Element of REAL
K663(((proj1 | C) .: the carrier of ((TOP-REAL 2) | C))) is complex ext-real real Element of REAL
(E-bound C) + (W-bound C) is complex ext-real real Element of REAL
((E-bound C) + (W-bound C)) / 2 is complex ext-real real Element of REAL
Vertical_Line (((E-bound C) + (W-bound C)) / 2) is functional Element of bool the carrier of (TOP-REAL 2)
C /\ (Vertical_Line (((E-bound C) + (W-bound C)) / 2)) is functional Element of bool the carrier of (TOP-REAL 2)
proj2 .: (C /\ (Vertical_Line (((E-bound C) + (W-bound C)) / 2))) is V166() V167() V168() Element of bool REAL
K663((proj2 .: (C /\ (Vertical_Line (((E-bound C) + (W-bound C)) / 2))))) is complex ext-real real Element of REAL
|[(((E-bound C) + (W-bound C)) / 2),K663((proj2 .: (C /\ (Vertical_Line (((E-bound C) + (W-bound C)) / 2)))))]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
LSeg (|[0,(- 3)]|,(LMP C)) is functional proper closed closed boundary nowhere_dense connected compact compact bounded bounded Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * |[0,(- 3)]|) + (b<sub>1</sub> * (LMP C))) where b<sub>1</sub> is complex ext-real real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg (|[0,(- 3)]|,(LMP C))) /\ C is functional proper closed compact bounded Element of bool the carrier of (TOP-REAL 2)
{(LMP C)} is functional non empty proper closed compact bounded Element of bool the carrier of (TOP-REAL 2)
(W-bound C) + (E-bound C) is complex ext-real real Element of REAL
((W-bound C) + (E-bound C)) / 2 is complex ext-real real Element of REAL
(LMP C) `1 is complex ext-real real Element of REAL
l is set
LJ is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
LJ `1 is complex ext-real real Element of REAL
Vertical_Line (((W-bound C) + (E-bound C)) / 2) is functional Element of bool the carrier of (TOP-REAL 2)
C /\ (Vertical_Line (((W-bound C) + (E-bound C)) / 2)) is functional Element of bool the carrier of (TOP-REAL 2)
(LMP C) `2 is complex ext-real real Element of REAL
LJ `2 is complex ext-real real Element of REAL
l is set
C is functional Element of bool the carrier of (TOP-REAL 2)
P is functional Element of bool the carrier of (TOP-REAL 2)
U is set
(closed_inside_of_rectangle ((- 1),1,(- 3),3)) ` is functional open Element of bool the carrier of (TOP-REAL 2)
the carrier of (TOP-REAL 2) \ (closed_inside_of_rectangle ((- 1),1,(- 3),3)) is set
C ` is functional Element of bool the carrier of (TOP-REAL 2)
the carrier of (TOP-REAL 2) \ C is set
l is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
l `1 is complex ext-real real Element of REAL
l `2 is complex ext-real real Element of REAL
east_halfline l is functional non empty connected convex Element of bool the carrier of (TOP-REAL 2)
k is set
x is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
x `1 is complex ext-real real Element of REAL
A1 is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
A1 `1 is complex ext-real real Element of REAL
A1 `2 is complex ext-real real Element of REAL
UBD C is functional Element of bool the carrier of (TOP-REAL 2)
{ b₁ where b₁ is functional Element of bool the carrier of (TOP-REAL 2) : b₁ is_outside_component_of C } is set
union { b₁ where b₁ is functional Element of bool the carrier of (TOP-REAL 2) : b₁ is_outside_component_of C } is set
west_halfline l is functional non empty connected convex Element of bool the carrier of (TOP-REAL 2)
k is set
x is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
x `1 is complex ext-real real Element of REAL
A1 is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
A1 `1 is complex ext-real real Element of REAL
A1 `2 is complex ext-real real Element of REAL
UBD C is functional Element of bool the carrier of (TOP-REAL 2)
{ b<sub>1</sub> where b<sub>1</sub> is functional Element of bool the carrier of (TOP-REAL 2) : b<sub>1</sub> is_outside_component_of C } is set
union { b<sub>1</sub> where b<sub>1</sub> is functional Element of bool the carrier of (TOP-REAL 2) : b<sub>1</sub> is_outside_component_of C } is set
10 is non empty ordinal natural complex ext-real positive non negative real V33() V119() V166() V167() V168() V169() V170() V171() left_end bounded_below Element of NAT
C is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
Ball (C,10) is functional non empty proper open connected bounded being_Region convex Element of bool the carrier of (TOP-REAL 2)
P is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
P `1 is complex ext-real real Element of REAL
P `2 is complex ext-real real Element of REAL
U is set
l is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
LJ is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
LJ `1 is complex ext-real real Element of REAL
LJ `2 is complex ext-real real Element of REAL
Euclid 2 is non empty strict Reflexive discerning symmetric triangle Discerning MetrStruct
the carrier of (Euclid 2) is non empty set
dist (P,LJ) is complex ext-real non negative real Element of REAL
1 - (- 1) is non empty complex ext-real positive non negative real Element of REAL
3 - (- 3) is non empty complex ext-real positive non negative real Element of REAL
(1 - (- 1)) + (3 - (- 3)) is non empty complex ext-real positive non negative real Element of REAL
l - C is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
- C is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
K270((TOP-REAL 2),l,(- C)) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) is Relation-like [: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of bool [:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):]
[:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):] is Relation-like non empty set
bool [:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):] is non empty set
K224( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),l,(- C)) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
|.(l - C).| is complex ext-real non negative real Element of REAL
k is Element of the carrier of (Euclid 2)
x is Element of the carrier of (Euclid 2)
dist (k,x) is complex ext-real non negative real Element of REAL
LSeg (|[0,3]|,|[0,(- 3)]|) is functional proper closed closed boundary nowhere_dense connected compact compact bounded bounded Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * |[0,3]|) + (b₁ * |[0,(- 3)]|)) where b₁ is complex ext-real real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
C is functional non empty proper closed connected compact bounded being_simple_closed_curve with_the_max_arc Element of bool the carrier of (TOP-REAL 2)
Upper_Arc C is functional non empty proper closed compact bounded with_the_max_arc Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (LSeg (|[0,3]|,|[0,(- 3)]|)) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | (LSeg (|[0,3]|,|[0,(- 3)]|))) is set
[: the carrier of I[01], the carrier of ((TOP-REAL 2) | (LSeg (|[0,3]|,|[0,(- 3)]|))):] is Relation-like set
bool [: the carrier of I[01], the carrier of ((TOP-REAL 2) | (LSeg (|[0,3]|,|[0,(- 3)]|))):] is non empty set
l is Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL 2) | (LSeg (|[0,3]|,|[0,(- 3)]|))) -valued Function-like quasi_total Element of bool [: the carrier of I[01], the carrier of ((TOP-REAL 2) | (LSeg (|[0,3]|,|[0,(- 3)]|))):]
rng l is Element of bool the carrier of ((TOP-REAL 2) | (LSeg (|[0,3]|,|[0,(- 3)]|)))
bool the carrier of ((TOP-REAL 2) | (LSeg (|[0,3]|,|[0,(- 3)]|))) is non empty set
U is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total continuous Path of |[0,3]|,|[0,(- 3)]|
W-min C is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
W-bound C is complex ext-real real Element of REAL
(TOP-REAL 2) | C is non empty strict TopSpace-like T_0 T_1 T_2 V82() normal T_3 T_4 compact V246() pseudocompact SubSpace of TOP-REAL 2
proj1 | C is Relation-like C -defined the carrier of (TOP-REAL 2) -defined the carrier of ((TOP-REAL 2) | C) -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ((TOP-REAL 2) | C),REAL:]
the carrier of ((TOP-REAL 2) | C) is non empty set
[: the carrier of ((TOP-REAL 2) | C),REAL:] is Relation-like non empty V156() V157() V158() set
bool [: the carrier of ((TOP-REAL 2) | C),REAL:] is non empty set
lower_bound (proj1 | C) is complex ext-real real Element of REAL
(proj1 | C) .: the carrier of ((TOP-REAL 2) | C) is non empty V166() V167() V168() Element of bool REAL
K663(((proj1 | C) .: the carrier of ((TOP-REAL 2) | C))) is complex ext-real real Element of REAL
W-most C is functional non empty proper closed compact bounded Element of bool the carrier of (TOP-REAL 2)
SW-corner C is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
S-bound C is complex ext-real real Element of REAL
proj2 | C is Relation-like C -defined the carrier of (TOP-REAL 2) -defined the carrier of ((TOP-REAL 2) | C) -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ((TOP-REAL 2) | C),REAL:]
lower_bound (proj2 | C) is complex ext-real real Element of REAL
(proj2 | C) .: the carrier of ((TOP-REAL 2) | C) is non empty V166() V167() V168() Element of bool REAL
K663(((proj2 | C) .: the carrier of ((TOP-REAL 2) | C))) is complex ext-real real Element of REAL
|[(W-bound C),(S-bound C)]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
NW-corner C is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
N-bound C is complex ext-real real Element of REAL
upper_bound (proj2 | C) is complex ext-real real Element of REAL
K662(((proj2 | C) .: the carrier of ((TOP-REAL 2) | C))) is complex ext-real real Element of REAL
|[(W-bound C),(N-bound C)]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner C),(NW-corner C)) is functional proper closed closed boundary nowhere_dense connected compact compact bounded bounded vertical Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SW-corner C)) + (b₁ * (NW-corner C))) where b₁ is complex ext-real real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((SW-corner C),(NW-corner C))) /\ C is functional proper closed compact bounded Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (W-most C) is non empty strict TopSpace-like T_0 T_1 T_2 V82() normal T_3 T_4 compact V246() pseudocompact SubSpace of TOP-REAL 2
proj2 | (W-most C) is Relation-like W-most C -defined the carrier of (TOP-REAL 2) -defined the carrier of ((TOP-REAL 2) | (W-most C)) -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ((TOP-REAL 2) | (W-most C)),REAL:]
the carrier of ((TOP-REAL 2) | (W-most C)) is non empty set
[: the carrier of ((TOP-REAL 2) | (W-most C)),REAL:] is Relation-like non empty V156() V157() V158() set
bool [: the carrier of ((TOP-REAL 2) | (W-most C)),REAL:] is non empty set
lower_bound (proj2 | (W-most C)) is complex ext-real real Element of REAL
(proj2 | (W-most C)) .: the carrier of ((TOP-REAL 2) | (W-most C)) is non empty V166() V167() V168() Element of bool REAL
K663(((proj2 | (W-most C)) .: the carrier of ((TOP-REAL 2) | (W-most C)))) is complex ext-real real Element of REAL
|[(W-bound C),(lower_bound (proj2 | (W-most C)))]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
E-max C is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
E-bound C is complex ext-real real Element of REAL
upper_bound (proj1 | C) is complex ext-real real Element of REAL
K662(((proj1 | C) .: the carrier of ((TOP-REAL 2) | C))) is complex ext-real real Element of REAL
E-most C is functional non empty proper closed compact bounded Element of bool the carrier of (TOP-REAL 2)
SE-corner C is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
|[(E-bound C),(S-bound C)]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
NE-corner C is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
|[(E-bound C),(N-bound C)]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner C),(NE-corner C)) is functional proper closed closed boundary nowhere_dense connected compact compact bounded bounded vertical Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SE-corner C)) + (b₁ * (NE-corner C))) where b₁ is complex ext-real real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((SE-corner C),(NE-corner C))) /\ C is functional proper closed compact bounded Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (E-most C) is non empty strict TopSpace-like T_0 T_1 T_2 V82() normal T_3 T_4 compact V246() pseudocompact SubSpace of TOP-REAL 2
proj2 | (E-most C) is Relation-like E-most C -defined the carrier of (TOP-REAL 2) -defined the carrier of ((TOP-REAL 2) | (E-most C)) -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ((TOP-REAL 2) | (E-most C)),REAL:]
the carrier of ((TOP-REAL 2) | (E-most C)) is non empty set
[: the carrier of ((TOP-REAL 2) | (E-most C)),REAL:] is Relation-like non empty V156() V157() V158() set
bool [: the carrier of ((TOP-REAL 2) | (E-most C)),REAL:] is non empty set
upper_bound (proj2 | (E-most C)) is complex ext-real real Element of REAL
(proj2 | (E-most C)) .: the carrier of ((TOP-REAL 2) | (E-most C)) is non empty V166() V167() V168() Element of bool REAL
K662(((proj2 | (E-most C)) .: the carrier of ((TOP-REAL 2) | (E-most C)))) is complex ext-real real Element of REAL
|[(E-bound C),(upper_bound (proj2 | (E-most C)))]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (Upper_Arc C) is non empty strict TopSpace-like T_0 T_1 T_2 V82() normal T_3 T_4 compact V246() pseudocompact SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | (Upper_Arc C)) is non empty set
[: the carrier of I[01], the carrier of ((TOP-REAL 2) | (Upper_Arc C)):] is Relation-like non empty set
bool [: the carrier of I[01], the carrier of ((TOP-REAL 2) | (Upper_Arc C)):] is non empty set
k is Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL 2) | (Upper_Arc C)) -valued Function-like non empty total quasi_total Element of bool [: the carrier of I[01], the carrier of ((TOP-REAL 2) | (Upper_Arc C)):]
rng k is non empty Element of bool the carrier of ((TOP-REAL 2) | (Upper_Arc C))
bool the carrier of ((TOP-REAL 2) | (Upper_Arc C)) is non empty set
LJ is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total continuous Path of |[(- 1),0]|,|[1,0]|
the carrier of (Trectangle ((- 1),1,(- 3),3)) is non empty set
rng LJ is functional non empty Element of bool the carrier of (TOP-REAL 2)
x is Element of the carrier of (Trectangle ((- 1),1,(- 3),3))
A1 is Element of the carrier of (Trectangle ((- 1),1,(- 3),3))
A2 is Element of the carrier of (Trectangle ((- 1),1,(- 3),3))
w is Element of the carrier of (Trectangle ((- 1),1,(- 3),3))
Ux is Relation-like the carrier of I[01] -defined the carrier of (Trectangle ((- 1),1,(- 3),3)) -valued Function-like non empty total quasi_total Path of x,A1
Pml is Relation-like the carrier of I[01] -defined the carrier of (Trectangle ((- 1),1,(- 3),3)) -valued Function-like non empty total quasi_total Path of A2,w
ml is complex ext-real real Element of the carrier of I[01]
Ux . ml is Element of the carrier of (Trectangle ((- 1),1,(- 3),3))
Pkj is complex ext-real real Element of the carrier of I[01]
Pml . Pkj is Element of the carrier of (Trectangle ((- 1),1,(- 3),3))
dom Ux is non empty V166() V167() V168() Element of bool the carrier of I[01]
bool the carrier of I[01] is non empty set
dom Pml is non empty V166() V167() V168() Element of bool the carrier of I[01]
rng U is functional non empty Element of bool the carrier of (TOP-REAL 2)
C is functional non empty proper closed connected compact bounded being_simple_closed_curve with_the_max_arc Element of bool the carrier of (TOP-REAL 2)
UMP C is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
E-bound C is complex ext-real real Element of REAL
(TOP-REAL 2) | C is non empty strict TopSpace-like T_0 T_1 T_2 V82() normal T_3 T_4 compact V246() pseudocompact SubSpace of TOP-REAL 2
proj1 | C is Relation-like C -defined the carrier of (TOP-REAL 2) -defined the carrier of ((TOP-REAL 2) | C) -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ((TOP-REAL 2) | C),REAL:]
the carrier of ((TOP-REAL 2) | C) is non empty set
[: the carrier of ((TOP-REAL 2) | C),REAL:] is Relation-like non empty V156() V157() V158() set
bool [: the carrier of ((TOP-REAL 2) | C),REAL:] is non empty set
upper_bound (proj1 | C) is complex ext-real real Element of REAL
(proj1 | C) .: the carrier of ((TOP-REAL 2) | C) is non empty V166() V167() V168() Element of bool REAL
K662(((proj1 | C) .: the carrier of ((TOP-REAL 2) | C))) is complex ext-real real Element of REAL
W-bound C is complex ext-real real Element of REAL
lower_bound (proj1 | C) is complex ext-real real Element of REAL
K663(((proj1 | C) .: the carrier of ((TOP-REAL 2) | C))) is complex ext-real real Element of REAL
(E-bound C) + (W-bound C) is complex ext-real real Element of REAL
((E-bound C) + (W-bound C)) / 2 is complex ext-real real Element of REAL
Vertical_Line (((E-bound C) + (W-bound C)) / 2) is functional Element of bool the carrier of (TOP-REAL 2)
C /\ (Vertical_Line (((E-bound C) + (W-bound C)) / 2)) is functional Element of bool the carrier of (TOP-REAL 2)
proj2 .: (C /\ (Vertical_Line (((E-bound C) + (W-bound C)) / 2))) is V166() V167() V168() Element of bool REAL
K662((proj2 .: (C /\ (Vertical_Line (((E-bound C) + (W-bound C)) / 2))))) is complex ext-real real Element of REAL
|[(((E-bound C) + (W-bound C)) / 2),K662((proj2 .: (C /\ (Vertical_Line (((E-bound C) + (W-bound C)) / 2)))))]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
LMP C is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
K663((proj2 .: (C /\ (Vertical_Line (((E-bound C) + (W-bound C)) / 2))))) is complex ext-real real Element of REAL
|[(((E-bound C) + (W-bound C)) / 2),K663((proj2 .: (C /\ (Vertical_Line (((E-bound C) + (W-bound C)) / 2)))))]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
Upper_Arc C is functional non empty proper closed compact bounded with_the_max_arc Element of bool the carrier of (TOP-REAL 2)
Lower_Arc C is functional non empty proper closed compact bounded with_the_max_arc Element of bool the carrier of (TOP-REAL 2)
(Upper_Arc C) \/ (Lower_Arc C) is functional non empty closed Element of bool the carrier of (TOP-REAL 2)
W-min C is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
W-most C is functional non empty proper closed compact bounded Element of bool the carrier of (TOP-REAL 2)
SW-corner C is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
S-bound C is complex ext-real real Element of REAL
proj2 | C is Relation-like C -defined the carrier of (TOP-REAL 2) -defined the carrier of ((TOP-REAL 2) | C) -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ((TOP-REAL 2) | C),REAL:]
lower_bound (proj2 | C) is complex ext-real real Element of REAL
(proj2 | C) .: the carrier of ((TOP-REAL 2) | C) is non empty V166() V167() V168() Element of bool REAL
K663(((proj2 | C) .: the carrier of ((TOP-REAL 2) | C))) is complex ext-real real Element of REAL
|[(W-bound C),(S-bound C)]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
NW-corner C is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
N-bound C is complex ext-real real Element of REAL
upper_bound (proj2 | C) is complex ext-real real Element of REAL
K662(((proj2 | C) .: the carrier of ((TOP-REAL 2) | C))) is complex ext-real real Element of REAL
|[(W-bound C),(N-bound C)]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner C),(NW-corner C)) is functional proper closed closed boundary nowhere_dense connected compact compact bounded bounded vertical Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SW-corner C)) + (b₁ * (NW-corner C))) where b₁ is complex ext-real real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((SW-corner C),(NW-corner C))) /\ C is functional proper closed compact bounded Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (W-most C) is non empty strict TopSpace-like T_0 T_1 T_2 V82() normal T_3 T_4 compact V246() pseudocompact SubSpace of TOP-REAL 2
proj2 | (W-most C) is Relation-like W-most C -defined the carrier of (TOP-REAL 2) -defined the carrier of ((TOP-REAL 2) | (W-most C)) -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ((TOP-REAL 2) | (W-most C)),REAL:]
the carrier of ((TOP-REAL 2) | (W-most C)) is non empty set
[: the carrier of ((TOP-REAL 2) | (W-most C)),REAL:] is Relation-like non empty V156() V157() V158() set
bool [: the carrier of ((TOP-REAL 2) | (W-most C)),REAL:] is non empty set
lower_bound (proj2 | (W-most C)) is complex ext-real real Element of REAL
(proj2 | (W-most C)) .: the carrier of ((TOP-REAL 2) | (W-most C)) is non empty V166() V167() V168() Element of bool REAL
K663(((proj2 | (W-most C)) .: the carrier of ((TOP-REAL 2) | (W-most C)))) is complex ext-real real Element of REAL
|[(W-bound C),(lower_bound (proj2 | (W-most C)))]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
E-max C is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
E-most C is functional non empty proper closed compact bounded Element of bool the carrier of (TOP-REAL 2)
SE-corner C is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
|[(E-bound C),(S-bound C)]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
NE-corner C is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
|[(E-bound C),(N-bound C)]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner C),(NE-corner C)) is functional proper closed closed boundary nowhere_dense connected compact compact bounded bounded vertical Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (SE-corner C)) + (b₁ * (NE-corner C))) where b₁ is complex ext-real real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((SE-corner C),(NE-corner C))) /\ C is functional proper closed compact bounded Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (E-most C) is non empty strict TopSpace-like T_0 T_1 T_2 V82() normal T_3 T_4 compact V246() pseudocompact SubSpace of TOP-REAL 2
proj2 | (E-most C) is Relation-like E-most C -defined the carrier of (TOP-REAL 2) -defined the carrier of ((TOP-REAL 2) | (E-most C)) -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ((TOP-REAL 2) | (E-most C)),REAL:]
the carrier of ((TOP-REAL 2) | (E-most C)) is non empty set
[: the carrier of ((TOP-REAL 2) | (E-most C)),REAL:] is Relation-like non empty V156() V157() V158() set
bool [: the carrier of ((TOP-REAL 2) | (E-most C)),REAL:] is non empty set
upper_bound (proj2 | (E-most C)) is complex ext-real real Element of REAL
(proj2 | (E-most C)) .: the carrier of ((TOP-REAL 2) | (E-most C)) is non empty V166() V167() V168() Element of bool REAL
K662(((proj2 | (E-most C)) .: the carrier of ((TOP-REAL 2) | (E-most C)))) is complex ext-real real Element of REAL
|[(E-bound C),(upper_bound (proj2 | (E-most C)))]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
W-bound (Upper_Arc C) is complex ext-real real Element of REAL
(TOP-REAL 2) | (Upper_Arc C) is non empty strict TopSpace-like T_0 T_1 T_2 V82() normal T_3 T_4 compact V246() pseudocompact SubSpace of TOP-REAL 2
proj1 | (Upper_Arc C) is Relation-like Upper_Arc C -defined the carrier of (TOP-REAL 2) -defined the carrier of ((TOP-REAL 2) | (Upper_Arc C)) -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ((TOP-REAL 2) | (Upper_Arc C)),REAL:]
the carrier of ((TOP-REAL 2) | (Upper_Arc C)) is non empty set
[: the carrier of ((TOP-REAL 2) | (Upper_Arc C)),REAL:] is Relation-like non empty V156() V157() V158() set
bool [: the carrier of ((TOP-REAL 2) | (Upper_Arc C)),REAL:] is non empty set
lower_bound (proj1 | (Upper_Arc C)) is complex ext-real real Element of REAL
(proj1 | (Upper_Arc C)) .: the carrier of ((TOP-REAL 2) | (Upper_Arc C)) is non empty V166() V167() V168() Element of bool REAL
K663(((proj1 | (Upper_Arc C)) .: the carrier of ((TOP-REAL 2) | (Upper_Arc C)))) is complex ext-real real Element of REAL
E-bound (Upper_Arc C) is complex ext-real real Element of REAL
upper_bound (proj1 | (Upper_Arc C)) is complex ext-real real Element of REAL
K662(((proj1 | (Upper_Arc C)) .: the carrier of ((TOP-REAL 2) | (Upper_Arc C)))) is complex ext-real real Element of REAL
(Upper_Arc C) /\ (Lower_Arc C) is functional proper closed compact bounded Element of bool the carrier of (TOP-REAL 2)
W-bound (Lower_Arc C) is complex ext-real real Element of REAL
(TOP-REAL 2) | (Lower_Arc C) is non empty strict TopSpace-like T_0 T_1 T_2 V82() normal T_3 T_4 compact V246() pseudocompact SubSpace of TOP-REAL 2
proj1 | (Lower_Arc C) is Relation-like Lower_Arc C -defined the carrier of (TOP-REAL 2) -defined the carrier of ((TOP-REAL 2) | (Lower_Arc C)) -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ((TOP-REAL 2) | (Lower_Arc C)),REAL:]
the carrier of ((TOP-REAL 2) | (Lower_Arc C)) is non empty set
[: the carrier of ((TOP-REAL 2) | (Lower_Arc C)),REAL:] is Relation-like non empty V156() V157() V158() set
bool [: the carrier of ((TOP-REAL 2) | (Lower_Arc C)),REAL:] is non empty set
lower_bound (proj1 | (Lower_Arc C)) is complex ext-real real Element of REAL
(proj1 | (Lower_Arc C)) .: the carrier of ((TOP-REAL 2) | (Lower_Arc C)) is non empty V166() V167() V168() Element of bool REAL
K663(((proj1 | (Lower_Arc C)) .: the carrier of ((TOP-REAL 2) | (Lower_Arc C)))) is complex ext-real real Element of REAL
E-bound (Lower_Arc C) is complex ext-real real Element of REAL
upper_bound (proj1 | (Lower_Arc C)) is complex ext-real real Element of REAL
K662(((proj1 | (Lower_Arc C)) .: the carrier of ((TOP-REAL 2) | (Lower_Arc C)))) is complex ext-real real Element of REAL
(Lower_Arc C) \/ (Upper_Arc C) is functional non empty closed Element of bool the carrier of (TOP-REAL 2)
(Lower_Arc C) /\ (Upper_Arc C) is functional proper closed compact bounded Element of bool the carrier of (TOP-REAL 2)
C is functional non empty proper closed connected compact bounded being_simple_closed_curve with_the_max_arc Element of bool the carrier of (TOP-REAL 2)
UMP C is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
E-bound C is complex ext-real real Element of REAL
(TOP-REAL 2) | C is non empty strict TopSpace-like T_0 T_1 T_2 V82() normal T_3 T_4 compact V246() pseudocompact SubSpace of TOP-REAL 2
proj1 | C is Relation-like C -defined the carrier of (TOP-REAL 2) -defined the carrier of ((TOP-REAL 2) | C) -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ((TOP-REAL 2) | C),REAL:]
the carrier of ((TOP-REAL 2) | C) is non empty set
[: the carrier of ((TOP-REAL 2) | C),REAL:] is Relation-like non empty V156() V157() V158() set
bool [: the carrier of ((TOP-REAL 2) | C),REAL:] is non empty set
upper_bound (proj1 | C) is complex ext-real real Element of REAL
(proj1 | C) .: the carrier of ((TOP-REAL 2) | C) is non empty V166() V167() V168() Element of bool REAL
K662(((proj1 | C) .: the carrier of ((TOP-REAL 2) | C))) is complex ext-real real Element of REAL
W-bound C is complex ext-real real Element of REAL
lower_bound (proj1 | C) is complex ext-real real Element of REAL
K663(((proj1 | C) .: the carrier of ((TOP-REAL 2) | C))) is complex ext-real real Element of REAL
(E-bound C) + (W-bound C) is complex ext-real real Element of REAL
((E-bound C) + (W-bound C)) / 2 is complex ext-real real Element of REAL
Vertical_Line (((E-bound C) + (W-bound C)) / 2) is functional Element of bool the carrier of (TOP-REAL 2)
C /\ (Vertical_Line (((E-bound C) + (W-bound C)) / 2)) is functional Element of bool the carrier of (TOP-REAL 2)
proj2 .: (C /\ (Vertical_Line (((E-bound C) + (W-bound C)) / 2))) is V166() V167() V168() Element of bool REAL
K662((proj2 .: (C /\ (Vertical_Line (((E-bound C) + (W-bound C)) / 2))))) is complex ext-real real Element of REAL
|[(((E-bound C) + (W-bound C)) / 2),K662((proj2 .: (C /\ (Vertical_Line (((E-bound C) + (W-bound C)) / 2)))))]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
LMP C is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
K663((proj2 .: (C /\ (Vertical_Line (((E-bound C) + (W-bound C)) / 2))))) is complex ext-real real Element of REAL
|[(((E-bound C) + (W-bound C)) / 2),K663((proj2 .: (C /\ (Vertical_Line (((E-bound C) + (W-bound C)) / 2)))))]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
C ` is functional non empty open Element of bool the carrier of (TOP-REAL 2)
the carrier of (TOP-REAL 2) \ C is set
(TOP-REAL 2) | (C `) is non empty strict TopSpace-like T_0 T_1 T_2 V118( TOP-REAL 2) SubSpace of TOP-REAL 2
l is functional non empty proper closed compact bounded with_the_max_arc Element of bool the carrier of (TOP-REAL 2)
LJ is functional non empty proper closed compact bounded with_the_max_arc Element of bool the carrier of (TOP-REAL 2)
l \/ LJ is functional non empty closed Element of bool the carrier of (TOP-REAL 2)
l /\ LJ is functional proper closed compact bounded Element of bool the carrier of (TOP-REAL 2)
W-bound l is complex ext-real real Element of REAL
(TOP-REAL 2) | l is non empty strict TopSpace-like T_0 T_1 T_2 V82() normal T_3 T_4 compact V246() pseudocompact SubSpace of TOP-REAL 2
proj1 | l is Relation-like l -defined the carrier of (TOP-REAL 2) -defined the carrier of ((TOP-REAL 2) | l) -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ((TOP-REAL 2) | l),REAL:]
the carrier of ((TOP-REAL 2) | l) is non empty set
[: the carrier of ((TOP-REAL 2) | l),REAL:] is Relation-like non empty V156() V157() V158() set
bool [: the carrier of ((TOP-REAL 2) | l),REAL:] is non empty set
lower_bound (proj1 | l) is complex ext-real real Element of REAL
(proj1 | l) .: the carrier of ((TOP-REAL 2) | l) is non empty V166() V167() V168() Element of bool REAL
K663(((proj1 | l) .: the carrier of ((TOP-REAL 2) | l))) is complex ext-real real Element of REAL
E-bound l is complex ext-real real Element of REAL
upper_bound (proj1 | l) is complex ext-real real Element of REAL
K662(((proj1 | l) .: the carrier of ((TOP-REAL 2) | l))) is complex ext-real real Element of REAL
LMP l is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
(E-bound l) + (W-bound l) is complex ext-real real Element of REAL
((E-bound l) + (W-bound l)) / 2 is complex ext-real real Element of REAL
Vertical_Line (((E-bound l) + (W-bound l)) / 2) is functional Element of bool the carrier of (TOP-REAL 2)
l /\ (Vertical_Line (((E-bound l) + (W-bound l)) / 2)) is functional Element of bool the carrier of (TOP-REAL 2)
proj2 .: (l /\ (Vertical_Line (((E-bound l) + (W-bound l)) / 2))) is V166() V167() V168() Element of bool REAL
K663((proj2 .: (l /\ (Vertical_Line (((E-bound l) + (W-bound l)) / 2))))) is complex ext-real real Element of REAL
|[(((E-bound l) + (W-bound l)) / 2),K663((proj2 .: (l /\ (Vertical_Line (((E-bound l) + (W-bound l)) / 2)))))]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
LSeg ((LMP l),|[0,(- 3)]|) is functional proper closed closed boundary nowhere_dense connected compact compact bounded bounded Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (LMP l)) + (b₁ * |[0,(- 3)]|)) where b₁ is complex ext-real real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ is functional proper closed compact bounded Element of bool the carrier of (TOP-REAL 2)
UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
E-bound ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ) is complex ext-real real Element of REAL
(TOP-REAL 2) | ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj1 | ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ) is Relation-like (LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ -defined the carrier of (TOP-REAL 2) -defined the carrier of ((TOP-REAL 2) | ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) -defined REAL -valued Function-like total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ((TOP-REAL 2) | ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)),REAL:]
the carrier of ((TOP-REAL 2) | ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) is set
[: the carrier of ((TOP-REAL 2) | ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)),REAL:] is Relation-like V156() V157() V158() set
bool [: the carrier of ((TOP-REAL 2) | ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)),REAL:] is non empty set
upper_bound (proj1 | ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) is complex ext-real real Element of REAL
(proj1 | ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) .: the carrier of ((TOP-REAL 2) | ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) is V166() V167() V168() Element of bool REAL
K662(((proj1 | ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) .: the carrier of ((TOP-REAL 2) | ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)))) is complex ext-real real Element of REAL
W-bound ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ) is complex ext-real real Element of REAL
lower_bound (proj1 | ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) is complex ext-real real Element of REAL
K663(((proj1 | ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) .: the carrier of ((TOP-REAL 2) | ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)))) is complex ext-real real Element of REAL
(E-bound ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (W-bound ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) is complex ext-real real Element of REAL
((E-bound ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (W-bound ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ))) / 2 is complex ext-real real Element of REAL
Vertical_Line (((E-bound ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (W-bound ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ))) / 2) is functional Element of bool the carrier of (TOP-REAL 2)
((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ) /\ (Vertical_Line (((E-bound ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (W-bound ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ))) / 2)) is functional Element of bool the carrier of (TOP-REAL 2)
proj2 .: (((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ) /\ (Vertical_Line (((E-bound ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (W-bound ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ))) / 2))) is V166() V167() V168() Element of bool REAL
K662((proj2 .: (((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ) /\ (Vertical_Line (((E-bound ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (W-bound ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ))) / 2))))) is complex ext-real real Element of REAL
|[(((E-bound ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (W-bound ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ))) / 2),K662((proj2 .: (((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ) /\ (Vertical_Line (((E-bound ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (W-bound ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ))) / 2)))))]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
(UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) is Relation-like [: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of bool [:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):]
[:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):] is Relation-like non empty set
bool [:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):] is non empty set
K224( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),(UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)),(LMP l)) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
(1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l)) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
Down (((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),(C `)) is Element of the carrier of ((TOP-REAL 2) | (C `))
the carrier of ((TOP-REAL 2) | (C `)) is non empty set
Component_of (Down (((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),(C `))) is Element of bool the carrier of ((TOP-REAL 2) | (C `))
bool the carrier of ((TOP-REAL 2) | (C `)) is non empty set
(W-bound C) + (E-bound C) is complex ext-real real Element of REAL
((W-bound C) + (E-bound C)) / 2 is complex ext-real real Element of REAL
Ux is functional Element of bool the carrier of (TOP-REAL 2)
(UMP C) `2 is complex ext-real real Element of REAL
(LMP l) `1 is complex ext-real real Element of REAL
(UMP C) `1 is complex ext-real real Element of REAL
Pml is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total continuous Path of UMP C, LMP l
rng Pml is functional non empty Element of bool the carrier of (TOP-REAL 2)
(LMP C) `2 is complex ext-real real Element of REAL
(LMP C) `1 is complex ext-real real Element of REAL
Vertical_Line (((W-bound C) + (E-bound C)) / 2) is functional Element of bool the carrier of (TOP-REAL 2)
C /\ (Vertical_Line (((W-bound C) + (E-bound C)) / 2)) is functional Element of bool the carrier of (TOP-REAL 2)
(LMP l) `2 is complex ext-real real Element of REAL
(UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) `1 is complex ext-real real Element of REAL
Pkj is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total continuous Path of UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ), LMP C
rng Pkj is functional non empty Element of bool the carrier of (TOP-REAL 2)
LSeg ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)),(LMP l)) is functional proper closed closed boundary nowhere_dense connected compact compact bounded bounded Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ))) + (b<sub>1</sub> * (LMP l))) where b<sub>1</sub> is complex ext-real real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
LSeg ((LMP l),(UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ))) is functional proper closed closed boundary nowhere_dense connected compact compact bounded bounded Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (LMP l)) + (b<sub>1</sub> * (UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)))) where b<sub>1</sub> is complex ext-real real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
|[((LMP l) `1),((LMP l) `2)]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
(UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) `2 is complex ext-real real Element of REAL
|[((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) `1),((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) `2)]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
|[(|[0,(- 3)]| `1),(|[0,(- 3)]| `2)]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
{(LMP l),(UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ))} is functional non empty Element of bool the carrier of (TOP-REAL 2)
(LSeg ((LMP l),(UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)))) \ {(LMP l),(UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ))} is functional Element of bool the carrier of (TOP-REAL 2)
X is set
AR is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
AR `1 is complex ext-real real Element of REAL
l /\ (Vertical_Line (((W-bound C) + (E-bound C)) / 2)) is functional Element of bool the carrier of (TOP-REAL 2)
AR `2 is complex ext-real real Element of REAL
W-bound (LSeg ((LMP l),|[0,(- 3)]|)) is complex ext-real real Element of REAL
(TOP-REAL 2) | (LSeg ((LMP l),|[0,(- 3)]|)) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj1 | (LSeg ((LMP l),|[0,(- 3)]|)) is Relation-like LSeg ((LMP l),|[0,(- 3)]|) -defined the carrier of (TOP-REAL 2) -defined the carrier of ((TOP-REAL 2) | (LSeg ((LMP l),|[0,(- 3)]|))) -defined REAL -valued Function-like total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ((TOP-REAL 2) | (LSeg ((LMP l),|[0,(- 3)]|))),REAL:]
the carrier of ((TOP-REAL 2) | (LSeg ((LMP l),|[0,(- 3)]|))) is set
[: the carrier of ((TOP-REAL 2) | (LSeg ((LMP l),|[0,(- 3)]|))),REAL:] is Relation-like V156() V157() V158() set
bool [: the carrier of ((TOP-REAL 2) | (LSeg ((LMP l),|[0,(- 3)]|))),REAL:] is non empty set
lower_bound (proj1 | (LSeg ((LMP l),|[0,(- 3)]|))) is complex ext-real real Element of REAL
(proj1 | (LSeg ((LMP l),|[0,(- 3)]|))) .: the carrier of ((TOP-REAL 2) | (LSeg ((LMP l),|[0,(- 3)]|))) is V166() V167() V168() Element of bool REAL
K663(((proj1 | (LSeg ((LMP l),|[0,(- 3)]|))) .: the carrier of ((TOP-REAL 2) | (LSeg ((LMP l),|[0,(- 3)]|))))) is complex ext-real real Element of REAL
E-bound (LSeg ((LMP l),|[0,(- 3)]|)) is complex ext-real real Element of REAL
upper_bound (proj1 | (LSeg ((LMP l),|[0,(- 3)]|))) is complex ext-real real Element of REAL
K662(((proj1 | (LSeg ((LMP l),|[0,(- 3)]|))) .: the carrier of ((TOP-REAL 2) | (LSeg ((LMP l),|[0,(- 3)]|))))) is complex ext-real real Element of REAL
(W-bound ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (E-bound ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) is complex ext-real real Element of REAL
((W-bound ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (E-bound ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ))) / 2 is complex ext-real real Element of REAL
Vertical_Line (((W-bound ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (E-bound ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ))) / 2) is functional Element of bool the carrier of (TOP-REAL 2)
((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ) /\ (Vertical_Line (((W-bound ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (E-bound ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ))) / 2)) is functional Element of bool the carrier of (TOP-REAL 2)
AR `2 is complex ext-real real Element of REAL
Component_of (((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),(C `)) is functional Element of bool the carrier of (TOP-REAL 2)
X is Element of bool the carrier of ((TOP-REAL 2) | (C `))
the carrier of (Trectangle ((- 1),1,(- 3),3)) is non empty set
LSeg (|[0,3]|,(UMP C)) is functional proper closed closed boundary nowhere_dense connected compact compact bounded bounded Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * |[0,3]|) + (b<sub>1</sub> * (UMP C))) where b<sub>1</sub> is complex ext-real real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(TOP-REAL 2) | (LSeg (|[0,3]|,(UMP C))) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | (LSeg (|[0,3]|,(UMP C)))) is set
[: the carrier of I[01], the carrier of ((TOP-REAL 2) | (LSeg (|[0,3]|,(UMP C)))):] is Relation-like set
bool [: the carrier of I[01], the carrier of ((TOP-REAL 2) | (LSeg (|[0,3]|,(UMP C)))):] is non empty set
fcm is Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL 2) | (LSeg (|[0,3]|,(UMP C)))) -valued Function-like quasi_total Element of bool [: the carrier of I[01], the carrier of ((TOP-REAL 2) | (LSeg (|[0,3]|,(UMP C)))):]
rng fcm is Element of bool the carrier of ((TOP-REAL 2) | (LSeg (|[0,3]|,(UMP C))))
bool the carrier of ((TOP-REAL 2) | (LSeg (|[0,3]|,(UMP C)))) is non empty set
Pcm is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total continuous Path of |[0,3]|, UMP C
Ball (((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),10) is functional non empty proper open connected bounded being_Region convex Element of bool the carrier of (TOP-REAL 2)
V is set
VP is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
T2C is functional Element of bool the carrier of (TOP-REAL 2)
VP is Element of bool the carrier of ((TOP-REAL 2) | (C `))
((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))) `1 is complex ext-real real Element of REAL
((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l)) `1 is complex ext-real real Element of REAL
(1 / 2) * (((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l)) `1) is complex ext-real real Element of REAL
((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) `1) + ((LMP l) `1) is complex ext-real real Element of REAL
(1 / 2) * (((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) `1) + ((LMP l) `1)) is complex ext-real real Element of REAL
LSeg (|[0,(- 3)]|,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l)))) is functional proper closed closed boundary nowhere_dense connected compact compact bounded bounded Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * |[0,(- 3)]|) + (b<sub>1</sub> * ((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))))) where b<sub>1</sub> is complex ext-real real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))) `2 is complex ext-real real Element of REAL
|[(((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))) `1),(((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))) `2)]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
LSeg (|[0,(- 3)]|,(LMP l)) is functional proper closed closed boundary nowhere_dense connected compact compact bounded bounded Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * |[0,(- 3)]|) + (b₁ * (LMP l))) where b₁ is complex ext-real real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
Pjd is set
fjd is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
fjd `2 is complex ext-real real Element of REAL
fjd `1 is complex ext-real real Element of REAL
l /\ (Vertical_Line (((W-bound C) + (E-bound C)) / 2)) is functional Element of bool the carrier of (TOP-REAL 2)
First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3))) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
Fr (closed_inside_of_rectangle ((- 1),1,(- 3),3)) is functional closed boundary nowhere_dense Element of bool the carrier of (TOP-REAL 2)
Cl (closed_inside_of_rectangle ((- 1),1,(- 3),3)) is functional closed Element of bool the carrier of (TOP-REAL 2)
(closed_inside_of_rectangle ((- 1),1,(- 3),3)) ` is functional open Element of bool the carrier of (TOP-REAL 2)
the carrier of (TOP-REAL 2) \ (closed_inside_of_rectangle ((- 1),1,(- 3),3)) is set
Cl ((closed_inside_of_rectangle ((- 1),1,(- 3),3)) `) is functional closed Element of bool the carrier of (TOP-REAL 2)
(Cl (closed_inside_of_rectangle ((- 1),1,(- 3),3))) /\ (Cl ((closed_inside_of_rectangle ((- 1),1,(- 3),3)) `)) is functional closed Element of bool the carrier of (TOP-REAL 2)
T2C \ (closed_inside_of_rectangle ((- 1),1,(- 3),3)) is functional Element of bool the carrier of (TOP-REAL 2)
{} (TOP-REAL 2) is Relation-like non-empty empty-yielding RAT -valued Function-like one-to-one constant functional empty proper open closed boundary nowhere_dense connected compact V156() V157() V158() V159() V166() V167() V168() V169() V170() V171() V172() bounded being_Region horizontal vertical bounded_below interval Element of bool the carrier of (TOP-REAL 2)
T2C /\ (rectangle ((- 1),1,(- 3),3)) is functional Element of bool the carrier of (TOP-REAL 2)
Segment (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),(First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3))))) is functional Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (LSeg (|[0,(- 3)]|,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))))) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | (LSeg (|[0,(- 3)]|,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l)))))) is set
[: the carrier of I[01], the carrier of ((TOP-REAL 2) | (LSeg (|[0,(- 3)]|,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l)))))):] is Relation-like set
bool [: the carrier of I[01], the carrier of ((TOP-REAL 2) | (LSeg (|[0,(- 3)]|,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l)))))):] is non empty set
flk is Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL 2) | (LSeg (|[0,(- 3)]|,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l)))))) -valued Function-like quasi_total Element of bool [: the carrier of I[01], the carrier of ((TOP-REAL 2) | (LSeg (|[0,(- 3)]|,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l)))))):]
rng flk is Element of bool the carrier of ((TOP-REAL 2) | (LSeg (|[0,(- 3)]|,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))))))
bool the carrier of ((TOP-REAL 2) | (LSeg (|[0,(- 3)]|,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l)))))) is non empty set
Plk is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total continuous Path of |[0,(- 3)]|,(1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))
[: the carrier of I[01], the carrier of ((TOP-REAL 2) | l):] is Relation-like non empty set
bool [: the carrier of I[01], the carrier of ((TOP-REAL 2) | l):] is non empty set
ra is Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL 2) | l) -valued Function-like non empty total quasi_total Element of bool [: the carrier of I[01], the carrier of ((TOP-REAL 2) | l):]
rng ra is non empty Element of bool the carrier of ((TOP-REAL 2) | l)
bool the carrier of ((TOP-REAL 2) | l) is non empty set
beta is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total continuous Path of |[(- 1),0]|,|[1,0]|
(TOP-REAL 2) | LJ is non empty strict TopSpace-like T_0 T_1 T_2 V82() normal T_3 T_4 compact V246() pseudocompact SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | LJ) is non empty set
[: the carrier of I[01], the carrier of ((TOP-REAL 2) | LJ):] is Relation-like non empty set
bool [: the carrier of I[01], the carrier of ((TOP-REAL 2) | LJ):] is non empty set
A is Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL 2) | LJ) -valued Function-like non empty total quasi_total Element of bool [: the carrier of I[01], the carrier of ((TOP-REAL 2) | LJ):]
rng A is non empty Element of bool the carrier of ((TOP-REAL 2) | LJ)
bool the carrier of ((TOP-REAL 2) | LJ) is non empty set
rb is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total continuous Path of |[(- 1),0]|,|[1,0]|
(TOP-REAL 2) | (Segment (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),(First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))))) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | (Segment (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),(First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3))))))) is set
[: the carrier of I[01], the carrier of ((TOP-REAL 2) | (Segment (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),(First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3))))))):] is Relation-like set
bool [: the carrier of I[01], the carrier of ((TOP-REAL 2) | (Segment (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),(First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3))))))):] is non empty set
t is Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL 2) | (Segment (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),(First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3))))))) -valued Function-like quasi_total Element of bool [: the carrier of I[01], the carrier of ((TOP-REAL 2) | (Segment (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),(First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3))))))):]
rng t is Element of bool the carrier of ((TOP-REAL 2) | (Segment (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),(First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))))))
bool the carrier of ((TOP-REAL 2) | (Segment (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),(First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3))))))) is non empty set
B is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total continuous Path of (1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l)), First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))
rng beta is functional non empty Element of bool the carrier of (TOP-REAL 2)
AR is Element of the carrier of (Trectangle ((- 1),1,(- 3),3))
BR is Element of the carrier of (Trectangle ((- 1),1,(- 3),3))
rng rb is functional non empty Element of bool the carrier of (TOP-REAL 2)
LSeg ((LMP l),((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l)))) is functional proper closed closed boundary nowhere_dense connected compact compact bounded bounded Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (LMP l)) + (b<sub>1</sub> * ((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))))) where b<sub>1</sub> is complex ext-real real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(TOP-REAL 2) | (LSeg ((LMP l),((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))))) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | (LSeg ((LMP l),((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l)))))) is set
[: the carrier of I[01], the carrier of ((TOP-REAL 2) | (LSeg ((LMP l),((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l)))))):] is Relation-like set
bool [: the carrier of I[01], the carrier of ((TOP-REAL 2) | (LSeg ((LMP l),((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l)))))):] is non empty set
v is Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL 2) | (LSeg ((LMP l),((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l)))))) -valued Function-like quasi_total Element of bool [: the carrier of I[01], the carrier of ((TOP-REAL 2) | (LSeg ((LMP l),((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l)))))):]
rng v is Element of bool the carrier of ((TOP-REAL 2) | (LSeg ((LMP l),((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))))))
bool the carrier of ((TOP-REAL 2) | (LSeg ((LMP l),((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l)))))) is non empty set
u is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total continuous Path of LMP l,(1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))
Pcm + Pml is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total continuous Path of |[0,3]|, LMP l
(Pcm + Pml) + u is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total continuous Path of |[0,3]|,(1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))
rng ((Pcm + Pml) + u) is functional non empty Element of bool the carrier of (TOP-REAL 2)
rng Pcm is functional non empty Element of bool the carrier of (TOP-REAL 2)
(rng Pcm) \/ (rng Pml) is functional non empty Element of bool the carrier of (TOP-REAL 2)
rng u is functional non empty Element of bool the carrier of (TOP-REAL 2)
((rng Pcm) \/ (rng Pml)) \/ (rng u) is functional non empty Element of bool the carrier of (TOP-REAL 2)
v1 is set
(LSeg (|[0,3]|,(UMP C))) /\ C is functional proper closed compact bounded Element of bool the carrier of (TOP-REAL 2)
{(UMP C)} is functional non empty proper closed compact bounded Element of bool the carrier of (TOP-REAL 2)
v1 is set
{(LMP l)} is functional non empty proper closed compact bounded Element of bool the carrier of (TOP-REAL 2)
(LSeg ((LMP l),((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))))) \ {(LMP l)} is functional Element of bool the carrier of (TOP-REAL 2)
((LSeg ((LMP l),((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))))) \ {(LMP l)}) \/ {(LMP l)} is functional non empty Element of bool the carrier of (TOP-REAL 2)
v1 is set
(First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))) `2 is complex ext-real real Element of REAL
LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[(- 1),(- 3)]|) is functional proper closed closed boundary nowhere_dense connected compact compact bounded bounded Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3))))) + (b₁ * |[(- 1),(- 3)]|)) where b₁ is complex ext-real real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(TOP-REAL 2) | (LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[(- 1),(- 3)]|)) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | (LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[(- 1),(- 3)]|))) is set
[: the carrier of I[01], the carrier of ((TOP-REAL 2) | (LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[(- 1),(- 3)]|))):] is Relation-like set
bool [: the carrier of I[01], the carrier of ((TOP-REAL 2) | (LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[(- 1),(- 3)]|))):] is non empty set
fuv is Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL 2) | (LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[(- 1),(- 3)]|))) -valued Function-like quasi_total Element of bool [: the carrier of I[01], the carrier of ((TOP-REAL 2) | (LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[(- 1),(- 3)]|))):]
rng fuv is Element of bool the carrier of ((TOP-REAL 2) | (LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[(- 1),(- 3)]|)))
bool the carrier of ((TOP-REAL 2) | (LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[(- 1),(- 3)]|))) is non empty set
v1 is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total continuous Path of First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3))),|[(- 1),(- 3)]|
(TOP-REAL 2) | (LSeg (|[(- 1),(- 3)]|,|[0,(- 3)]|)) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | (LSeg (|[(- 1),(- 3)]|,|[0,(- 3)]|))) is set
[: the carrier of I[01], the carrier of ((TOP-REAL 2) | (LSeg (|[(- 1),(- 3)]|,|[0,(- 3)]|))):] is Relation-like set
bool [: the carrier of I[01], the carrier of ((TOP-REAL 2) | (LSeg (|[(- 1),(- 3)]|,|[0,(- 3)]|))):] is non empty set
au is Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL 2) | (LSeg (|[(- 1),(- 3)]|,|[0,(- 3)]|))) -valued Function-like quasi_total Element of bool [: the carrier of I[01], the carrier of ((TOP-REAL 2) | (LSeg (|[(- 1),(- 3)]|,|[0,(- 3)]|))):]
rng au is Element of bool the carrier of ((TOP-REAL 2) | (LSeg (|[(- 1),(- 3)]|,|[0,(- 3)]|)))
bool the carrier of ((TOP-REAL 2) | (LSeg (|[(- 1),(- 3)]|,|[0,(- 3)]|))) is non empty set
uv is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total continuous Path of |[(- 1),(- 3)]|,|[0,(- 3)]|
(First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))) `1 is complex ext-real real Element of REAL
fau is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
fau `1 is complex ext-real real Element of REAL
fau `2 is complex ext-real real Element of REAL
((Pcm + Pml) + u) + B is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total continuous Path of |[0,3]|, First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))
(((Pcm + Pml) + u) + B) + v1 is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total continuous Path of |[0,3]|,|[(- 1),(- 3)]|
((((Pcm + Pml) + u) + B) + v1) + uv is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total continuous Path of |[0,3]|,|[0,(- 3)]|
rng (((((Pcm + Pml) + u) + B) + v1) + uv) is functional non empty Element of bool the carrier of (TOP-REAL 2)
rng B is functional non empty Element of bool the carrier of (TOP-REAL 2)
(rng ((Pcm + Pml) + u)) \/ (rng B) is functional non empty Element of bool the carrier of (TOP-REAL 2)
rng v1 is functional non empty Element of bool the carrier of (TOP-REAL 2)
((rng ((Pcm + Pml) + u)) \/ (rng B)) \/ (rng v1) is functional non empty Element of bool the carrier of (TOP-REAL 2)
rng uv is functional non empty Element of bool the carrier of (TOP-REAL 2)
(((rng ((Pcm + Pml) + u)) \/ (rng B)) \/ (rng v1)) \/ (rng uv) is functional non empty Element of bool the carrier of (TOP-REAL 2)
CR is Element of the carrier of (Trectangle ((- 1),1,(- 3),3))
DR is Element of the carrier of (Trectangle ((- 1),1,(- 3),3))
v is Relation-like the carrier of I[01] -defined the carrier of (Trectangle ((- 1),1,(- 3),3)) -valued Function-like non empty total quasi_total Path of AR,BR
vb is Relation-like the carrier of I[01] -defined the carrier of (Trectangle ((- 1),1,(- 3),3)) -valued Function-like non empty total quasi_total Path of CR,DR
fvb is complex ext-real real Element of the carrier of I[01]
v . fvb is Element of the carrier of (Trectangle ((- 1),1,(- 3),3))
AB is complex ext-real real Element of the carrier of I[01]
vb . AB is Element of the carrier of (Trectangle ((- 1),1,(- 3),3))
dom v is non empty V166() V167() V168() Element of bool the carrier of I[01]
bool the carrier of I[01] is non empty set
dom vb is non empty V166() V167() V168() Element of bool the carrier of I[01]
LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[0,(- 3)]|) is functional proper closed closed boundary nowhere_dense connected compact compact bounded bounded Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3))))) + (b<sub>1</sub> * |[0,(- 3)]|)) where b<sub>1</sub> is complex ext-real real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(TOP-REAL 2) | (LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[0,(- 3)]|)) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | (LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[0,(- 3)]|))) is set
[: the carrier of I[01], the carrier of ((TOP-REAL 2) | (LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[0,(- 3)]|))):] is Relation-like set
bool [: the carrier of I[01], the carrier of ((TOP-REAL 2) | (LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[0,(- 3)]|))):] is non empty set
fuv is Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL 2) | (LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[0,(- 3)]|))) -valued Function-like quasi_total Element of bool [: the carrier of I[01], the carrier of ((TOP-REAL 2) | (LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[0,(- 3)]|))):]
rng fuv is Element of bool the carrier of ((TOP-REAL 2) | (LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[0,(- 3)]|)))
bool the carrier of ((TOP-REAL 2) | (LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[0,(- 3)]|))) is non empty set
v1 is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total continuous Path of First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3))),|[0,(- 3)]|
((Pcm + Pml) + u) + B is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total continuous Path of |[0,3]|, First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))
(((Pcm + Pml) + u) + B) + v1 is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total continuous Path of |[0,3]|,|[0,(- 3)]|
(First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))) `1 is complex ext-real real Element of REAL
rng ((((Pcm + Pml) + u) + B) + v1) is functional non empty Element of bool the carrier of (TOP-REAL 2)
rng B is functional non empty Element of bool the carrier of (TOP-REAL 2)
(rng ((Pcm + Pml) + u)) \/ (rng B) is functional non empty Element of bool the carrier of (TOP-REAL 2)
rng v1 is functional non empty Element of bool the carrier of (TOP-REAL 2)
((rng ((Pcm + Pml) + u)) \/ (rng B)) \/ (rng v1) is functional non empty Element of bool the carrier of (TOP-REAL 2)
CR is Element of the carrier of (Trectangle ((- 1),1,(- 3),3))
DR is Element of the carrier of (Trectangle ((- 1),1,(- 3),3))
v is Relation-like the carrier of I[01] -defined the carrier of (Trectangle ((- 1),1,(- 3),3)) -valued Function-like non empty total quasi_total Path of AR,BR
au is Relation-like the carrier of I[01] -defined the carrier of (Trectangle ((- 1),1,(- 3),3)) -valued Function-like non empty total quasi_total Path of CR,DR
fau is complex ext-real real Element of the carrier of I[01]
v . fau is Element of the carrier of (Trectangle ((- 1),1,(- 3),3))
vb is complex ext-real real Element of the carrier of I[01]
au . vb is Element of the carrier of (Trectangle ((- 1),1,(- 3),3))
dom v is non empty V166() V167() V168() Element of bool the carrier of I[01]
bool the carrier of I[01] is non empty set
dom au is non empty V166() V167() V168() Element of bool the carrier of I[01]
LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[0,(- 3)]|) is functional proper closed closed boundary nowhere_dense connected compact compact bounded bounded Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3))))) + (b₁ * |[0,(- 3)]|)) where b₁ is complex ext-real real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(TOP-REAL 2) | (LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[0,(- 3)]|)) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | (LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[0,(- 3)]|))) is set
[: the carrier of I[01], the carrier of ((TOP-REAL 2) | (LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[0,(- 3)]|))):] is Relation-like set
bool [: the carrier of I[01], the carrier of ((TOP-REAL 2) | (LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[0,(- 3)]|))):] is non empty set
fuv is Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL 2) | (LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[0,(- 3)]|))) -valued Function-like quasi_total Element of bool [: the carrier of I[01], the carrier of ((TOP-REAL 2) | (LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[0,(- 3)]|))):]
rng fuv is Element of bool the carrier of ((TOP-REAL 2) | (LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[0,(- 3)]|)))
bool the carrier of ((TOP-REAL 2) | (LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[0,(- 3)]|))) is non empty set
v1 is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total continuous Path of First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3))),|[0,(- 3)]|
((Pcm + Pml) + u) + B is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total continuous Path of |[0,3]|, First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))
(((Pcm + Pml) + u) + B) + v1 is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total continuous Path of |[0,3]|,|[0,(- 3)]|
(First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))) `1 is complex ext-real real Element of REAL
rng ((((Pcm + Pml) + u) + B) + v1) is functional non empty Element of bool the carrier of (TOP-REAL 2)
rng B is functional non empty Element of bool the carrier of (TOP-REAL 2)
(rng ((Pcm + Pml) + u)) \/ (rng B) is functional non empty Element of bool the carrier of (TOP-REAL 2)
rng v1 is functional non empty Element of bool the carrier of (TOP-REAL 2)
((rng ((Pcm + Pml) + u)) \/ (rng B)) \/ (rng v1) is functional non empty Element of bool the carrier of (TOP-REAL 2)
CR is Element of the carrier of (Trectangle ((- 1),1,(- 3),3))
DR is Element of the carrier of (Trectangle ((- 1),1,(- 3),3))
v is Relation-like the carrier of I[01] -defined the carrier of (Trectangle ((- 1),1,(- 3),3)) -valued Function-like non empty total quasi_total Path of AR,BR
au is Relation-like the carrier of I[01] -defined the carrier of (Trectangle ((- 1),1,(- 3),3)) -valued Function-like non empty total quasi_total Path of CR,DR
fau is complex ext-real real Element of the carrier of I[01]
v . fau is Element of the carrier of (Trectangle ((- 1),1,(- 3),3))
vb is complex ext-real real Element of the carrier of I[01]
au . vb is Element of the carrier of (Trectangle ((- 1),1,(- 3),3))
dom v is non empty V166() V167() V168() Element of bool the carrier of I[01]
bool the carrier of I[01] is non empty set
dom au is non empty V166() V167() V168() Element of bool the carrier of I[01]
LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[1,(- 3)]|) is functional proper closed closed boundary nowhere_dense connected compact compact bounded bounded Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3))))) + (b<sub>1</sub> * |[1,(- 3)]|)) where b<sub>1</sub> is complex ext-real real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(TOP-REAL 2) | (LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[1,(- 3)]|)) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | (LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[1,(- 3)]|))) is set
[: the carrier of I[01], the carrier of ((TOP-REAL 2) | (LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[1,(- 3)]|))):] is Relation-like set
bool [: the carrier of I[01], the carrier of ((TOP-REAL 2) | (LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[1,(- 3)]|))):] is non empty set
fuv is Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL 2) | (LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[1,(- 3)]|))) -valued Function-like quasi_total Element of bool [: the carrier of I[01], the carrier of ((TOP-REAL 2) | (LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[1,(- 3)]|))):]
rng fuv is Element of bool the carrier of ((TOP-REAL 2) | (LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[1,(- 3)]|)))
bool the carrier of ((TOP-REAL 2) | (LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[1,(- 3)]|))) is non empty set
v1 is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total continuous Path of First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3))),|[1,(- 3)]|
(TOP-REAL 2) | (LSeg (|[1,(- 3)]|,|[0,(- 3)]|)) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | (LSeg (|[1,(- 3)]|,|[0,(- 3)]|))) is set
[: the carrier of I[01], the carrier of ((TOP-REAL 2) | (LSeg (|[1,(- 3)]|,|[0,(- 3)]|))):] is Relation-like set
bool [: the carrier of I[01], the carrier of ((TOP-REAL 2) | (LSeg (|[1,(- 3)]|,|[0,(- 3)]|))):] is non empty set
au is Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL 2) | (LSeg (|[1,(- 3)]|,|[0,(- 3)]|))) -valued Function-like quasi_total Element of bool [: the carrier of I[01], the carrier of ((TOP-REAL 2) | (LSeg (|[1,(- 3)]|,|[0,(- 3)]|))):]
rng au is Element of bool the carrier of ((TOP-REAL 2) | (LSeg (|[1,(- 3)]|,|[0,(- 3)]|)))
bool the carrier of ((TOP-REAL 2) | (LSeg (|[1,(- 3)]|,|[0,(- 3)]|))) is non empty set
uv is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total continuous Path of |[1,(- 3)]|,|[0,(- 3)]|
(First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))) `1 is complex ext-real real Element of REAL
fau is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
fau `1 is complex ext-real real Element of REAL
fau `2 is complex ext-real real Element of REAL
((Pcm + Pml) + u) + B is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total continuous Path of |[0,3]|, First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))
(((Pcm + Pml) + u) + B) + v1 is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total continuous Path of |[0,3]|,|[1,(- 3)]|
((((Pcm + Pml) + u) + B) + v1) + uv is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total continuous Path of |[0,3]|,|[0,(- 3)]|
rng (((((Pcm + Pml) + u) + B) + v1) + uv) is functional non empty Element of bool the carrier of (TOP-REAL 2)
rng B is functional non empty Element of bool the carrier of (TOP-REAL 2)
(rng ((Pcm + Pml) + u)) \/ (rng B) is functional non empty Element of bool the carrier of (TOP-REAL 2)
rng v1 is functional non empty Element of bool the carrier of (TOP-REAL 2)
((rng ((Pcm + Pml) + u)) \/ (rng B)) \/ (rng v1) is functional non empty Element of bool the carrier of (TOP-REAL 2)
rng uv is functional non empty Element of bool the carrier of (TOP-REAL 2)
(((rng ((Pcm + Pml) + u)) \/ (rng B)) \/ (rng v1)) \/ (rng uv) is functional non empty Element of bool the carrier of (TOP-REAL 2)
CR is Element of the carrier of (Trectangle ((- 1),1,(- 3),3))
DR is Element of the carrier of (Trectangle ((- 1),1,(- 3),3))
v is Relation-like the carrier of I[01] -defined the carrier of (Trectangle ((- 1),1,(- 3),3)) -valued Function-like non empty total quasi_total Path of AR,BR
vb is Relation-like the carrier of I[01] -defined the carrier of (Trectangle ((- 1),1,(- 3),3)) -valued Function-like non empty total quasi_total Path of CR,DR
fvb is complex ext-real real Element of the carrier of I[01]
v . fvb is Element of the carrier of (Trectangle ((- 1),1,(- 3),3))
AB is complex ext-real real Element of the carrier of I[01]
vb . AB is Element of the carrier of (Trectangle ((- 1),1,(- 3),3))
dom v is non empty V166() V167() V168() Element of bool the carrier of I[01]
bool the carrier of I[01] is non empty set
dom vb is non empty V166() V167() V168() Element of bool the carrier of I[01]
(First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))) `2 is complex ext-real real Element of REAL
LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[(- 1),3]|) is functional proper closed closed boundary nowhere_dense connected compact compact bounded bounded Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3))))) + (b<sub>1</sub> * |[(- 1),3]|)) where b<sub>1</sub> is complex ext-real real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(TOP-REAL 2) | (LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[(- 1),3]|)) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | (LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[(- 1),3]|))) is set
[: the carrier of I[01], the carrier of ((TOP-REAL 2) | (LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[(- 1),3]|))):] is Relation-like set
bool [: the carrier of I[01], the carrier of ((TOP-REAL 2) | (LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[(- 1),3]|))):] is non empty set
fuv is Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL 2) | (LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[(- 1),3]|))) -valued Function-like quasi_total Element of bool [: the carrier of I[01], the carrier of ((TOP-REAL 2) | (LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[(- 1),3]|))):]
rng fuv is Element of bool the carrier of ((TOP-REAL 2) | (LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[(- 1),3]|)))
bool the carrier of ((TOP-REAL 2) | (LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[(- 1),3]|))) is non empty set
v1 is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total continuous Path of First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3))),|[(- 1),3]|
(TOP-REAL 2) | (LSeg (|[(- 1),3]|,|[0,3]|)) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | (LSeg (|[(- 1),3]|,|[0,3]|))) is set
[: the carrier of I[01], the carrier of ((TOP-REAL 2) | (LSeg (|[(- 1),3]|,|[0,3]|))):] is Relation-like set
bool [: the carrier of I[01], the carrier of ((TOP-REAL 2) | (LSeg (|[(- 1),3]|,|[0,3]|))):] is non empty set
au is Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL 2) | (LSeg (|[(- 1),3]|,|[0,3]|))) -valued Function-like quasi_total Element of bool [: the carrier of I[01], the carrier of ((TOP-REAL 2) | (LSeg (|[(- 1),3]|,|[0,3]|))):]
rng au is Element of bool the carrier of ((TOP-REAL 2) | (LSeg (|[(- 1),3]|,|[0,3]|)))
bool the carrier of ((TOP-REAL 2) | (LSeg (|[(- 1),3]|,|[0,3]|))) is non empty set
uv is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total continuous Path of |[(- 1),3]|,|[0,3]|
(First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))) `1 is complex ext-real real Element of REAL
fau is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
fau `1 is complex ext-real real Element of REAL
fau `2 is complex ext-real real Element of REAL
Plk + B is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total continuous Path of |[0,(- 3)]|, First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))
(Plk + B) + v1 is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total continuous Path of |[0,(- 3)]|,|[(- 1),3]|
((Plk + B) + v1) + uv is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total continuous Path of |[0,(- 3)]|,|[0,3]|
rng (((Plk + B) + v1) + uv) is functional non empty Element of bool the carrier of (TOP-REAL 2)
rng Plk is functional non empty Element of bool the carrier of (TOP-REAL 2)
rng B is functional non empty Element of bool the carrier of (TOP-REAL 2)
(rng Plk) \/ (rng B) is functional non empty Element of bool the carrier of (TOP-REAL 2)
rng v1 is functional non empty Element of bool the carrier of (TOP-REAL 2)
((rng Plk) \/ (rng B)) \/ (rng v1) is functional non empty Element of bool the carrier of (TOP-REAL 2)
rng uv is functional non empty Element of bool the carrier of (TOP-REAL 2)
(((rng Plk) \/ (rng B)) \/ (rng v1)) \/ (rng uv) is functional non empty Element of bool the carrier of (TOP-REAL 2)
- (((Plk + B) + v1) + uv) is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total continuous Path of |[0,3]|,|[0,(- 3)]|
rng (- (((Plk + B) + v1) + uv)) is functional non empty Element of bool the carrier of (TOP-REAL 2)
CR is Element of the carrier of (Trectangle ((- 1),1,(- 3),3))
DR is Element of the carrier of (Trectangle ((- 1),1,(- 3),3))
u is Relation-like the carrier of I[01] -defined the carrier of (Trectangle ((- 1),1,(- 3),3)) -valued Function-like non empty total quasi_total Path of AR,BR
vb is Relation-like the carrier of I[01] -defined the carrier of (Trectangle ((- 1),1,(- 3),3)) -valued Function-like non empty total quasi_total Path of CR,DR
fvb is complex ext-real real Element of the carrier of I[01]
u . fvb is Element of the carrier of (Trectangle ((- 1),1,(- 3),3))
AB is complex ext-real real Element of the carrier of I[01]
vb . AB is Element of the carrier of (Trectangle ((- 1),1,(- 3),3))
dom u is non empty V166() V167() V168() Element of bool the carrier of I[01]
bool the carrier of I[01] is non empty set
dom vb is non empty V166() V167() V168() Element of bool the carrier of I[01]
LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[0,3]|) is functional proper closed closed boundary nowhere_dense connected compact compact bounded bounded Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3))))) + (b₁ * |[0,3]|)) where b₁ is complex ext-real real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(TOP-REAL 2) | (LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[0,3]|)) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | (LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[0,3]|))) is set
[: the carrier of I[01], the carrier of ((TOP-REAL 2) | (LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[0,3]|))):] is Relation-like set
bool [: the carrier of I[01], the carrier of ((TOP-REAL 2) | (LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[0,3]|))):] is non empty set
fuv is Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL 2) | (LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[0,3]|))) -valued Function-like quasi_total Element of bool [: the carrier of I[01], the carrier of ((TOP-REAL 2) | (LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[0,3]|))):]
rng fuv is Element of bool the carrier of ((TOP-REAL 2) | (LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[0,3]|)))
bool the carrier of ((TOP-REAL 2) | (LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[0,3]|))) is non empty set
v1 is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total continuous Path of First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3))),|[0,3]|
Plk + B is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total continuous Path of |[0,(- 3)]|, First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))
(Plk + B) + v1 is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total continuous Path of |[0,(- 3)]|,|[0,3]|
(First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))) `1 is complex ext-real real Element of REAL
rng ((Plk + B) + v1) is functional non empty Element of bool the carrier of (TOP-REAL 2)
rng Plk is functional non empty Element of bool the carrier of (TOP-REAL 2)
rng B is functional non empty Element of bool the carrier of (TOP-REAL 2)
(rng Plk) \/ (rng B) is functional non empty Element of bool the carrier of (TOP-REAL 2)
rng v1 is functional non empty Element of bool the carrier of (TOP-REAL 2)
((rng Plk) \/ (rng B)) \/ (rng v1) is functional non empty Element of bool the carrier of (TOP-REAL 2)
- ((Plk + B) + v1) is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total continuous Path of |[0,3]|,|[0,(- 3)]|
rng (- ((Plk + B) + v1)) is functional non empty Element of bool the carrier of (TOP-REAL 2)
CR is Element of the carrier of (Trectangle ((- 1),1,(- 3),3))
DR is Element of the carrier of (Trectangle ((- 1),1,(- 3),3))
u is Relation-like the carrier of I[01] -defined the carrier of (Trectangle ((- 1),1,(- 3),3)) -valued Function-like non empty total quasi_total Path of AR,BR
au is Relation-like the carrier of I[01] -defined the carrier of (Trectangle ((- 1),1,(- 3),3)) -valued Function-like non empty total quasi_total Path of CR,DR
fau is complex ext-real real Element of the carrier of I[01]
u . fau is Element of the carrier of (Trectangle ((- 1),1,(- 3),3))
vb is complex ext-real real Element of the carrier of I[01]
au . vb is Element of the carrier of (Trectangle ((- 1),1,(- 3),3))
dom u is non empty V166() V167() V168() Element of bool the carrier of I[01]
bool the carrier of I[01] is non empty set
dom au is non empty V166() V167() V168() Element of bool the carrier of I[01]
LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[0,3]|) is functional proper closed closed boundary nowhere_dense connected compact compact bounded bounded Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3))))) + (b₁ * |[0,3]|)) where b₁ is complex ext-real real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(TOP-REAL 2) | (LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[0,3]|)) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | (LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[0,3]|))) is set
[: the carrier of I[01], the carrier of ((TOP-REAL 2) | (LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[0,3]|))):] is Relation-like set
bool [: the carrier of I[01], the carrier of ((TOP-REAL 2) | (LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[0,3]|))):] is non empty set
fuv is Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL 2) | (LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[0,3]|))) -valued Function-like quasi_total Element of bool [: the carrier of I[01], the carrier of ((TOP-REAL 2) | (LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[0,3]|))):]
rng fuv is Element of bool the carrier of ((TOP-REAL 2) | (LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[0,3]|)))
bool the carrier of ((TOP-REAL 2) | (LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[0,3]|))) is non empty set
v1 is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total continuous Path of First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3))),|[0,3]|
Plk + B is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total continuous Path of |[0,(- 3)]|, First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))
(Plk + B) + v1 is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total continuous Path of |[0,(- 3)]|,|[0,3]|
(First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))) `1 is complex ext-real real Element of REAL
LSeg (|[0,3]|,(First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3))))) is functional proper closed closed boundary nowhere_dense connected compact compact bounded bounded Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * |[0,3]|) + (b₁ * (First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))))) where b₁ is complex ext-real real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
rng ((Plk + B) + v1) is functional non empty Element of bool the carrier of (TOP-REAL 2)
rng Plk is functional non empty Element of bool the carrier of (TOP-REAL 2)
rng B is functional non empty Element of bool the carrier of (TOP-REAL 2)
(rng Plk) \/ (rng B) is functional non empty Element of bool the carrier of (TOP-REAL 2)
rng v1 is functional non empty Element of bool the carrier of (TOP-REAL 2)
((rng Plk) \/ (rng B)) \/ (rng v1) is functional non empty Element of bool the carrier of (TOP-REAL 2)
- ((Plk + B) + v1) is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total continuous Path of |[0,3]|,|[0,(- 3)]|
rng (- ((Plk + B) + v1)) is functional non empty Element of bool the carrier of (TOP-REAL 2)
CR is Element of the carrier of (Trectangle ((- 1),1,(- 3),3))
DR is Element of the carrier of (Trectangle ((- 1),1,(- 3),3))
u is Relation-like the carrier of I[01] -defined the carrier of (Trectangle ((- 1),1,(- 3),3)) -valued Function-like non empty total quasi_total Path of AR,BR
au is Relation-like the carrier of I[01] -defined the carrier of (Trectangle ((- 1),1,(- 3),3)) -valued Function-like non empty total quasi_total Path of CR,DR
fau is complex ext-real real Element of the carrier of I[01]
u . fau is Element of the carrier of (Trectangle ((- 1),1,(- 3),3))
vb is complex ext-real real Element of the carrier of I[01]
au . vb is Element of the carrier of (Trectangle ((- 1),1,(- 3),3))
dom u is non empty V166() V167() V168() Element of bool the carrier of I[01]
bool the carrier of I[01] is non empty set
dom au is non empty V166() V167() V168() Element of bool the carrier of I[01]
LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[1,3]|) is functional proper closed closed boundary nowhere_dense connected compact compact bounded bounded Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3))))) + (b₁ * |[1,3]|)) where b₁ is complex ext-real real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(TOP-REAL 2) | (LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[1,3]|)) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | (LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[1,3]|))) is set
[: the carrier of I[01], the carrier of ((TOP-REAL 2) | (LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[1,3]|))):] is Relation-like set
bool [: the carrier of I[01], the carrier of ((TOP-REAL 2) | (LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[1,3]|))):] is non empty set
fuv is Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL 2) | (LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[1,3]|))) -valued Function-like quasi_total Element of bool [: the carrier of I[01], the carrier of ((TOP-REAL 2) | (LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[1,3]|))):]
rng fuv is Element of bool the carrier of ((TOP-REAL 2) | (LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[1,3]|)))
bool the carrier of ((TOP-REAL 2) | (LSeg ((First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))),|[1,3]|))) is non empty set
v1 is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total continuous Path of First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3))),|[1,3]|
(TOP-REAL 2) | (LSeg (|[1,3]|,|[0,3]|)) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | (LSeg (|[1,3]|,|[0,3]|))) is set
[: the carrier of I[01], the carrier of ((TOP-REAL 2) | (LSeg (|[1,3]|,|[0,3]|))):] is Relation-like set
bool [: the carrier of I[01], the carrier of ((TOP-REAL 2) | (LSeg (|[1,3]|,|[0,3]|))):] is non empty set
au is Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL 2) | (LSeg (|[1,3]|,|[0,3]|))) -valued Function-like quasi_total Element of bool [: the carrier of I[01], the carrier of ((TOP-REAL 2) | (LSeg (|[1,3]|,|[0,3]|))):]
rng au is Element of bool the carrier of ((TOP-REAL 2) | (LSeg (|[1,3]|,|[0,3]|)))
bool the carrier of ((TOP-REAL 2) | (LSeg (|[1,3]|,|[0,3]|))) is non empty set
uv is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total continuous Path of |[1,3]|,|[0,3]|
(First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))) `1 is complex ext-real real Element of REAL
fau is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
fau `1 is complex ext-real real Element of REAL
fau `2 is complex ext-real real Element of REAL
Plk + B is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total continuous Path of |[0,(- 3)]|, First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))
(Plk + B) + v1 is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total continuous Path of |[0,(- 3)]|,|[1,3]|
((Plk + B) + v1) + uv is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total continuous Path of |[0,(- 3)]|,|[0,3]|
rng (((Plk + B) + v1) + uv) is functional non empty Element of bool the carrier of (TOP-REAL 2)
rng Plk is functional non empty Element of bool the carrier of (TOP-REAL 2)
rng B is functional non empty Element of bool the carrier of (TOP-REAL 2)
(rng Plk) \/ (rng B) is functional non empty Element of bool the carrier of (TOP-REAL 2)
rng v1 is functional non empty Element of bool the carrier of (TOP-REAL 2)
((rng Plk) \/ (rng B)) \/ (rng v1) is functional non empty Element of bool the carrier of (TOP-REAL 2)
rng uv is functional non empty Element of bool the carrier of (TOP-REAL 2)
(((rng Plk) \/ (rng B)) \/ (rng v1)) \/ (rng uv) is functional non empty Element of bool the carrier of (TOP-REAL 2)
- (((Plk + B) + v1) + uv) is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total continuous Path of |[0,3]|,|[0,(- 3)]|
rng (- (((Plk + B) + v1) + uv)) is functional non empty Element of bool the carrier of (TOP-REAL 2)
CR is Element of the carrier of (Trectangle ((- 1),1,(- 3),3))
DR is Element of the carrier of (Trectangle ((- 1),1,(- 3),3))
u is Relation-like the carrier of I[01] -defined the carrier of (Trectangle ((- 1),1,(- 3),3)) -valued Function-like non empty total quasi_total Path of AR,BR
vb is Relation-like the carrier of I[01] -defined the carrier of (Trectangle ((- 1),1,(- 3),3)) -valued Function-like non empty total quasi_total Path of CR,DR
fvb is complex ext-real real Element of the carrier of I[01]
u . fvb is Element of the carrier of (Trectangle ((- 1),1,(- 3),3))
AB is complex ext-real real Element of the carrier of I[01]
vb . AB is Element of the carrier of (Trectangle ((- 1),1,(- 3),3))
dom u is non empty V166() V167() V168() Element of bool the carrier of I[01]
bool the carrier of I[01] is non empty set
dom vb is non empty V166() V167() V168() Element of bool the carrier of I[01]
(First_Point (T2C,((1 / 2) * ((UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)) + (LMP l))),VP,(rectangle ((- 1),1,(- 3),3)))) `2 is complex ext-real real Element of REAL
V is functional Element of bool the carrier of (TOP-REAL 2)
Euclid 2 is non empty strict Reflexive discerning symmetric triangle Discerning MetrStruct
the carrier of (Euclid 2) is non empty set
bool the carrier of (Euclid 2) is non empty set
VP is Element of bool the carrier of ((TOP-REAL 2) | (C `))
{} ((TOP-REAL 2) | (C `)) is Relation-like non-empty empty-yielding RAT -valued Function-like one-to-one constant functional empty proper open closed boundary nowhere_dense connected compact V156() V157() V158() V159() V166() V167() V168() V169() V170() V171() V172() bounded_below interval Element of bool the carrier of ((TOP-REAL 2) | (C `))
T2C is non empty TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of T2C is non empty set
bool the carrier of T2C is non empty set
LSeg ((LMP C),|[0,(- 3)]|) is functional proper closed closed boundary nowhere_dense connected compact compact bounded bounded Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (LMP C)) + (b₁ * |[0,(- 3)]|)) where b₁ is complex ext-real real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(TOP-REAL 2) | (LSeg ((LMP C),|[0,(- 3)]|)) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | (LSeg ((LMP C),|[0,(- 3)]|))) is set
[: the carrier of I[01], the carrier of ((TOP-REAL 2) | (LSeg ((LMP C),|[0,(- 3)]|))):] is Relation-like set
bool [: the carrier of I[01], the carrier of ((TOP-REAL 2) | (LSeg ((LMP C),|[0,(- 3)]|))):] is non empty set
fjd is Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL 2) | (LSeg ((LMP C),|[0,(- 3)]|))) -valued Function-like quasi_total Element of bool [: the carrier of I[01], the carrier of ((TOP-REAL 2) | (LSeg ((LMP C),|[0,(- 3)]|))):]
rng fjd is Element of bool the carrier of ((TOP-REAL 2) | (LSeg ((LMP C),|[0,(- 3)]|)))
bool the carrier of ((TOP-REAL 2) | (LSeg ((LMP C),|[0,(- 3)]|))) is non empty set
Pjd is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total continuous Path of LMP C,|[0,(- 3)]|
(TOP-REAL 2) | (LSeg ((LMP l),(UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)))) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | (LSeg ((LMP l),(UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ))))) is set
[: the carrier of I[01], the carrier of ((TOP-REAL 2) | (LSeg ((LMP l),(UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ))))):] is Relation-like set
bool [: the carrier of I[01], the carrier of ((TOP-REAL 2) | (LSeg ((LMP l),(UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ))))):] is non empty set
flk is Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL 2) | (LSeg ((LMP l),(UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ))))) -valued Function-like quasi_total Element of bool [: the carrier of I[01], the carrier of ((TOP-REAL 2) | (LSeg ((LMP l),(UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ))))):]
rng flk is Element of bool the carrier of ((TOP-REAL 2) | (LSeg ((LMP l),(UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)))))
bool the carrier of ((TOP-REAL 2) | (LSeg ((LMP l),(UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ))))) is non empty set
Plk is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total continuous Path of LMP l, UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)
Pcm + Pml is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total continuous Path of |[0,3]|, LMP l
(Pcm + Pml) + Plk is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total continuous Path of |[0,3]|, UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)
((Pcm + Pml) + Plk) + Pkj is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total continuous Path of |[0,3]|, LMP C
(((Pcm + Pml) + Plk) + Pkj) + Pjd is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total continuous Path of |[0,3]|,|[0,(- 3)]|
rng ((((Pcm + Pml) + Plk) + Pkj) + Pjd) is functional non empty Element of bool the carrier of (TOP-REAL 2)
rng Pcm is functional non empty Element of bool the carrier of (TOP-REAL 2)
(rng Pcm) \/ (rng Pml) is functional non empty Element of bool the carrier of (TOP-REAL 2)
rng Plk is functional non empty Element of bool the carrier of (TOP-REAL 2)
((rng Pcm) \/ (rng Pml)) \/ (rng Plk) is functional non empty Element of bool the carrier of (TOP-REAL 2)
(((rng Pcm) \/ (rng Pml)) \/ (rng Plk)) \/ (rng Pkj) is functional non empty Element of bool the carrier of (TOP-REAL 2)
rng Pjd is functional non empty Element of bool the carrier of (TOP-REAL 2)
((((rng Pcm) \/ (rng Pml)) \/ (rng Plk)) \/ (rng Pkj)) \/ (rng Pjd) is functional non empty Element of bool the carrier of (TOP-REAL 2)
dom ((((Pcm + Pml) + Plk) + Pkj) + Pjd) is non empty V166() V167() V168() Element of bool the carrier of I[01]
bool the carrier of I[01] is non empty set
[#] I[01] is non empty non proper open closed dense non boundary compact V166() V167() V168() Element of bool the carrier of I[01]
((((Pcm + Pml) + Plk) + Pkj) + Pjd) .: (dom ((((Pcm + Pml) + Plk) + Pkj) + Pjd)) is functional non empty Element of bool the carrier of (TOP-REAL 2)
ra is set
((LSeg ((LMP l),(UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)))) \ {(LMP l),(UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ))}) \/ {(LMP l),(UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ))} is functional non empty Element of bool the carrier of (TOP-REAL 2)
ra is set
(LSeg (|[0,3]|,(UMP C))) \/ (rng Pml) is functional non empty Element of bool the carrier of (TOP-REAL 2)
((LSeg (|[0,3]|,(UMP C))) \/ (rng Pml)) \/ (LSeg ((LMP l),(UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ)))) is functional non empty Element of bool the carrier of (TOP-REAL 2)
|[((UMP C) `1),((UMP C) `2)]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
|[(|[0,3]| `1),(|[0,3]| `2)]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
|[((LMP C) `1),((LMP C) `2)]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
(((LSeg (|[0,3]|,(UMP C))) \/ (rng Pml)) \/ (LSeg ((LMP l),(UMP ((LSeg ((LMP l),|[0,(- 3)]|)) /\ LJ))))) \/ (rng Pkj) is functional non empty Element of bool the carrier of (TOP-REAL 2)
ra is non empty complex ext-real positive non negative real set
Ball (|[(- 1),0]|,ra) is functional non empty proper open connected bounded being_Region convex Element of bool the carrier of (TOP-REAL 2)
rb is non empty complex ext-real positive non negative real set
Ball (|[1,0]|,rb) is functional non empty proper open connected bounded being_Region convex Element of bool the carrier of (TOP-REAL 2)
VP is non empty Element of bool the carrier of T2C
t is set
{ b₁ where b₁ is functional Element of bool the carrier of (TOP-REAL 2) : b₁ is_inside_component_of C } is set
BDD C is functional open Element of bool the carrier of (TOP-REAL 2)
union { b₁ where b₁ is functional Element of bool the carrier of (TOP-REAL 2) : b₁ is_inside_component_of C } is set
Fr V is functional closed Element of bool the carrier of (TOP-REAL 2)
Cl V is functional closed Element of bool the carrier of (TOP-REAL 2)
V ` is functional Element of bool the carrier of (TOP-REAL 2)
the carrier of (TOP-REAL 2) \ V is set
Cl (V `) is functional closed Element of bool the carrier of (TOP-REAL 2)
(Cl V) /\ (Cl (V `)) is functional closed Element of bool the carrier of (TOP-REAL 2)
u is set
v is set
T2C | VP is non empty strict TopSpace-like T_0 T_1 T_2 SubSpace of T2C
the carrier of (T2C | VP) is non empty set
u is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
v is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
u1 is Element of the carrier of (T2C | VP)
v1 is Element of the carrier of (T2C | VP)
[: the carrier of I[01], the carrier of (T2C | VP):] is Relation-like non empty set
bool [: the carrier of I[01], the carrier of (T2C | VP):] is non empty set
fuv is Relation-like the carrier of I[01] -defined the carrier of (T2C | VP) -valued Function-like non empty total quasi_total Element of bool [: the carrier of I[01], the carrier of (T2C | VP):]
fuv . 0 is set
fuv . 1 is set
(TOP-REAL 2) | V is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
rng fuv is non empty Element of bool the carrier of (T2C | VP)
bool the carrier of (T2C | VP) is non empty set
uv is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total continuous Path of u,v
rng uv is functional non empty Element of bool the carrier of (TOP-REAL 2)
LSeg (|[(- 1),0]|,u) is functional proper closed closed boundary nowhere_dense connected compact compact bounded bounded Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * |[(- 1),0]|) + (b<sub>1</sub> * u)) where b<sub>1</sub> is complex ext-real real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(TOP-REAL 2) | (LSeg (|[(- 1),0]|,u)) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | (LSeg (|[(- 1),0]|,u))) is set
[: the carrier of I[01], the carrier of ((TOP-REAL 2) | (LSeg (|[(- 1),0]|,u))):] is Relation-like set
bool [: the carrier of I[01], the carrier of ((TOP-REAL 2) | (LSeg (|[(- 1),0]|,u))):] is non empty set
fau is Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL 2) | (LSeg (|[(- 1),0]|,u))) -valued Function-like quasi_total Element of bool [: the carrier of I[01], the carrier of ((TOP-REAL 2) | (LSeg (|[(- 1),0]|,u))):]
rng fau is Element of bool the carrier of ((TOP-REAL 2) | (LSeg (|[(- 1),0]|,u)))
bool the carrier of ((TOP-REAL 2) | (LSeg (|[(- 1),0]|,u))) is non empty set
au is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total continuous Path of |[(- 1),0]|,u
LSeg (v,|[1,0]|) is functional proper closed closed boundary nowhere_dense connected compact compact bounded bounded Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * v) + (b<sub>1</sub> * |[1,0]|)) where b<sub>1</sub> is complex ext-real real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(TOP-REAL 2) | (LSeg (v,|[1,0]|)) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | (LSeg (v,|[1,0]|))) is set
[: the carrier of I[01], the carrier of ((TOP-REAL 2) | (LSeg (v,|[1,0]|))):] is Relation-like set
bool [: the carrier of I[01], the carrier of ((TOP-REAL 2) | (LSeg (v,|[1,0]|))):] is non empty set
fvb is Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL 2) | (LSeg (v,|[1,0]|))) -valued Function-like quasi_total Element of bool [: the carrier of I[01], the carrier of ((TOP-REAL 2) | (LSeg (v,|[1,0]|))):]
rng fvb is Element of bool the carrier of ((TOP-REAL 2) | (LSeg (v,|[1,0]|)))
bool the carrier of ((TOP-REAL 2) | (LSeg (v,|[1,0]|))) is non empty set
vb is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total continuous Path of v,|[1,0]|
au + uv is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total continuous Path of |[(- 1),0]|,v
(au + uv) + vb is Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total continuous Path of |[(- 1),0]|,|[1,0]|
rng ((au + uv) + vb) is functional non empty Element of bool the carrier of (TOP-REAL 2)
rng au is functional non empty Element of bool the carrier of (TOP-REAL 2)
(rng au) \/ (rng uv) is functional non empty Element of bool the carrier of (TOP-REAL 2)
rng vb is functional non empty Element of bool the carrier of (TOP-REAL 2)
((rng au) \/ (rng uv)) \/ (rng vb) is functional non empty Element of bool the carrier of (TOP-REAL 2)
(LSeg (|[(- 1),0]|,u)) \/ (rng uv) is functional non empty Element of bool the carrier of (TOP-REAL 2)
AR is Element of the carrier of (Trectangle ((- 1),1,(- 3),3))
BR is Element of the carrier of (Trectangle ((- 1),1,(- 3),3))
CR is Element of the carrier of (Trectangle ((- 1),1,(- 3),3))
DR is Element of the carrier of (Trectangle ((- 1),1,(- 3),3))
h is Relation-like the carrier of I[01] -defined the carrier of (Trectangle ((- 1),1,(- 3),3)) -valued Function-like non empty total quasi_total Path of AR,BR
v is Relation-like the carrier of I[01] -defined the carrier of (Trectangle ((- 1),1,(- 3),3)) -valued Function-like non empty total quasi_total Path of CR,DR
s is complex ext-real real Element of the carrier of I[01]
h . s is Element of the carrier of (Trectangle ((- 1),1,(- 3),3))
t is complex ext-real real Element of the carrier of I[01]
v . t is Element of the carrier of (Trectangle ((- 1),1,(- 3),3))
dom h is non empty V166() V167() V168() Element of bool the carrier of I[01]
dom v is non empty V166() V167() V168() Element of bool the carrier of I[01]
C is functional non empty proper closed connected compact bounded being_simple_closed_curve with_the_max_arc Element of bool the carrier of (TOP-REAL 2)
UMP C is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
E-bound C is complex ext-real real Element of REAL
(TOP-REAL 2) | C is non empty strict TopSpace-like T_0 T_1 T_2 V82() normal T_3 T_4 compact V246() pseudocompact SubSpace of TOP-REAL 2
proj1 | C is Relation-like C -defined the carrier of (TOP-REAL 2) -defined the carrier of ((TOP-REAL 2) | C) -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ((TOP-REAL 2) | C),REAL:]
the carrier of ((TOP-REAL 2) | C) is non empty set
[: the carrier of ((TOP-REAL 2) | C),REAL:] is Relation-like non empty V156() V157() V158() set
bool [: the carrier of ((TOP-REAL 2) | C),REAL:] is non empty set
upper_bound (proj1 | C) is complex ext-real real Element of REAL
(proj1 | C) .: the carrier of ((TOP-REAL 2) | C) is non empty V166() V167() V168() Element of bool REAL
K662(((proj1 | C) .: the carrier of ((TOP-REAL 2) | C))) is complex ext-real real Element of REAL
W-bound C is complex ext-real real Element of REAL
lower_bound (proj1 | C) is complex ext-real real Element of REAL
K663(((proj1 | C) .: the carrier of ((TOP-REAL 2) | C))) is complex ext-real real Element of REAL
(E-bound C) + (W-bound C) is complex ext-real real Element of REAL
((E-bound C) + (W-bound C)) / 2 is complex ext-real real Element of REAL
Vertical_Line (((E-bound C) + (W-bound C)) / 2) is functional Element of bool the carrier of (TOP-REAL 2)
C /\ (Vertical_Line (((E-bound C) + (W-bound C)) / 2)) is functional Element of bool the carrier of (TOP-REAL 2)
proj2 .: (C /\ (Vertical_Line (((E-bound C) + (W-bound C)) / 2))) is V166() V167() V168() Element of bool REAL
K662((proj2 .: (C /\ (Vertical_Line (((E-bound C) + (W-bound C)) / 2))))) is complex ext-real real Element of REAL
|[(((E-bound C) + (W-bound C)) / 2),K662((proj2 .: (C /\ (Vertical_Line (((E-bound C) + (W-bound C)) / 2)))))]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
LMP C is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
K663((proj2 .: (C /\ (Vertical_Line (((E-bound C) + (W-bound C)) / 2))))) is complex ext-real real Element of REAL
|[(((E-bound C) + (W-bound C)) / 2),K663((proj2 .: (C /\ (Vertical_Line (((E-bound C) + (W-bound C)) / 2)))))]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
BDD C is functional open Element of bool the carrier of (TOP-REAL 2)
{ b<sub>1</sub> where b<sub>1</sub> is functional Element of bool the carrier of (TOP-REAL 2) : b<sub>1</sub> is_inside_component_of C } is set
union { b<sub>1</sub> where b<sub>1</sub> is functional Element of bool the carrier of (TOP-REAL 2) : b<sub>1</sub> is_inside_component_of C } is set
C ` is functional non empty open Element of bool the carrier of (TOP-REAL 2)
the carrier of (TOP-REAL 2) \ C is set
(TOP-REAL 2) | (C `) is non empty strict TopSpace-like T_0 T_1 T_2 V118( TOP-REAL 2) SubSpace of TOP-REAL 2
P is functional non empty proper closed compact bounded with_the_max_arc Element of bool the carrier of (TOP-REAL 2)
U is functional non empty proper closed compact bounded with_the_max_arc Element of bool the carrier of (TOP-REAL 2)
P \/ U is functional non empty closed Element of bool the carrier of (TOP-REAL 2)
P /\ U is functional proper closed compact bounded Element of bool the carrier of (TOP-REAL 2)
W-bound P is complex ext-real real Element of REAL
(TOP-REAL 2) | P is non empty strict TopSpace-like T_0 T_1 T_2 V82() normal T_3 T_4 compact V246() pseudocompact SubSpace of TOP-REAL 2
proj1 | P is Relation-like P -defined the carrier of (TOP-REAL 2) -defined the carrier of ((TOP-REAL 2) | P) -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ((TOP-REAL 2) | P),REAL:]
the carrier of ((TOP-REAL 2) | P) is non empty set
[: the carrier of ((TOP-REAL 2) | P),REAL:] is Relation-like non empty V156() V157() V158() set
bool [: the carrier of ((TOP-REAL 2) | P),REAL:] is non empty set
lower_bound (proj1 | P) is complex ext-real real Element of REAL
(proj1 | P) .: the carrier of ((TOP-REAL 2) | P) is non empty V166() V167() V168() Element of bool REAL
K663(((proj1 | P) .: the carrier of ((TOP-REAL 2) | P))) is complex ext-real real Element of REAL
E-bound P is complex ext-real real Element of REAL
upper_bound (proj1 | P) is complex ext-real real Element of REAL
K662(((proj1 | P) .: the carrier of ((TOP-REAL 2) | P))) is complex ext-real real Element of REAL
LMP P is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
(E-bound P) + (W-bound P) is complex ext-real real Element of REAL
((E-bound P) + (W-bound P)) / 2 is complex ext-real real Element of REAL
Vertical_Line (((E-bound P) + (W-bound P)) / 2) is functional Element of bool the carrier of (TOP-REAL 2)
P /\ (Vertical_Line (((E-bound P) + (W-bound P)) / 2)) is functional Element of bool the carrier of (TOP-REAL 2)
proj2 .: (P /\ (Vertical_Line (((E-bound P) + (W-bound P)) / 2))) is V166() V167() V168() Element of bool REAL
K663((proj2 .: (P /\ (Vertical_Line (((E-bound P) + (W-bound P)) / 2))))) is complex ext-real real Element of REAL
|[(((E-bound P) + (W-bound P)) / 2),K663((proj2 .: (P /\ (Vertical_Line (((E-bound P) + (W-bound P)) / 2)))))]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
LSeg ((LMP P),|[0,(- 3)]|) is functional proper closed closed boundary nowhere_dense connected compact compact bounded bounded Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (LMP P)) + (b<sub>1</sub> * |[0,(- 3)]|)) where b<sub>1</sub> is complex ext-real real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg ((LMP P),|[0,(- 3)]|)) /\ U is functional proper closed compact bounded Element of bool the carrier of (TOP-REAL 2)
UMP ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
E-bound ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U) is complex ext-real real Element of REAL
(TOP-REAL 2) | ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj1 | ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U) is Relation-like (LSeg ((LMP P),|[0,(- 3)]|)) /\ U -defined the carrier of (TOP-REAL 2) -defined the carrier of ((TOP-REAL 2) | ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U)) -defined REAL -valued Function-like total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ((TOP-REAL 2) | ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U)),REAL:]
the carrier of ((TOP-REAL 2) | ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U)) is set
[: the carrier of ((TOP-REAL 2) | ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U)),REAL:] is Relation-like V156() V157() V158() set
bool [: the carrier of ((TOP-REAL 2) | ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U)),REAL:] is non empty set
upper_bound (proj1 | ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U)) is complex ext-real real Element of REAL
(proj1 | ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U)) .: the carrier of ((TOP-REAL 2) | ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U)) is V166() V167() V168() Element of bool REAL
K662(((proj1 | ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U)) .: the carrier of ((TOP-REAL 2) | ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U)))) is complex ext-real real Element of REAL
W-bound ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U) is complex ext-real real Element of REAL
lower_bound (proj1 | ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U)) is complex ext-real real Element of REAL
K663(((proj1 | ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U)) .: the carrier of ((TOP-REAL 2) | ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U)))) is complex ext-real real Element of REAL
(E-bound ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U)) + (W-bound ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U)) is complex ext-real real Element of REAL
((E-bound ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U)) + (W-bound ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U))) / 2 is complex ext-real real Element of REAL
Vertical_Line (((E-bound ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U)) + (W-bound ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U))) / 2) is functional Element of bool the carrier of (TOP-REAL 2)
((LSeg ((LMP P),|[0,(- 3)]|)) /\ U) /\ (Vertical_Line (((E-bound ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U)) + (W-bound ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U))) / 2)) is functional Element of bool the carrier of (TOP-REAL 2)
proj2 .: (((LSeg ((LMP P),|[0,(- 3)]|)) /\ U) /\ (Vertical_Line (((E-bound ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U)) + (W-bound ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U))) / 2))) is V166() V167() V168() Element of bool REAL
K662((proj2 .: (((LSeg ((LMP P),|[0,(- 3)]|)) /\ U) /\ (Vertical_Line (((E-bound ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U)) + (W-bound ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U))) / 2))))) is complex ext-real real Element of REAL
|[(((E-bound ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U)) + (W-bound ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U))) / 2),K662((proj2 .: (((LSeg ((LMP P),|[0,(- 3)]|)) /\ U) /\ (Vertical_Line (((E-bound ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U)) + (W-bound ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U))) / 2)))))]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
(UMP ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U)) + (LMP P) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) is Relation-like [: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of bool [:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):]
[:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):] is Relation-like non empty set
bool [:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):] is non empty set
K224( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),(UMP ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U)),(LMP P)) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
(1 / 2) * ((UMP ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U)) + (LMP P)) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
Down (((1 / 2) * ((UMP ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U)) + (LMP P))),(C `)) is Element of the carrier of ((TOP-REAL 2) | (C `))
the carrier of ((TOP-REAL 2) | (C `)) is non empty set
Component_of (Down (((1 / 2) * ((UMP ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U)) + (LMP P))),(C `))) is Element of bool the carrier of ((TOP-REAL 2) | (C `))
bool the carrier of ((TOP-REAL 2) | (C `)) is non empty set
l is functional Element of bool the carrier of (TOP-REAL 2)
k is set
x is set
A1 is functional Element of bool the carrier of (TOP-REAL 2)
C is functional non empty proper closed connected compact bounded being_simple_closed_curve with_the_max_arc Element of bool the carrier of (TOP-REAL 2)
UMP C is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
E-bound C is complex ext-real real Element of REAL
(TOP-REAL 2) | C is non empty strict TopSpace-like T_0 T_1 T_2 V82() normal T_3 T_4 compact V246() pseudocompact SubSpace of TOP-REAL 2
proj1 | C is Relation-like C -defined the carrier of (TOP-REAL 2) -defined the carrier of ((TOP-REAL 2) | C) -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ((TOP-REAL 2) | C),REAL:]
the carrier of ((TOP-REAL 2) | C) is non empty set
[: the carrier of ((TOP-REAL 2) | C),REAL:] is Relation-like non empty V156() V157() V158() set
bool [: the carrier of ((TOP-REAL 2) | C),REAL:] is non empty set
upper_bound (proj1 | C) is complex ext-real real Element of REAL
(proj1 | C) .: the carrier of ((TOP-REAL 2) | C) is non empty V166() V167() V168() Element of bool REAL
K662(((proj1 | C) .: the carrier of ((TOP-REAL 2) | C))) is complex ext-real real Element of REAL
W-bound C is complex ext-real real Element of REAL
lower_bound (proj1 | C) is complex ext-real real Element of REAL
K663(((proj1 | C) .: the carrier of ((TOP-REAL 2) | C))) is complex ext-real real Element of REAL
(E-bound C) + (W-bound C) is complex ext-real real Element of REAL
((E-bound C) + (W-bound C)) / 2 is complex ext-real real Element of REAL
Vertical_Line (((E-bound C) + (W-bound C)) / 2) is functional Element of bool the carrier of (TOP-REAL 2)
C /\ (Vertical_Line (((E-bound C) + (W-bound C)) / 2)) is functional Element of bool the carrier of (TOP-REAL 2)
proj2 .: (C /\ (Vertical_Line (((E-bound C) + (W-bound C)) / 2))) is V166() V167() V168() Element of bool REAL
K662((proj2 .: (C /\ (Vertical_Line (((E-bound C) + (W-bound C)) / 2))))) is complex ext-real real Element of REAL
|[(((E-bound C) + (W-bound C)) / 2),K662((proj2 .: (C /\ (Vertical_Line (((E-bound C) + (W-bound C)) / 2)))))]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
LMP C is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
K663((proj2 .: (C /\ (Vertical_Line (((E-bound C) + (W-bound C)) / 2))))) is complex ext-real real Element of REAL
|[(((E-bound C) + (W-bound C)) / 2),K663((proj2 .: (C /\ (Vertical_Line (((E-bound C) + (W-bound C)) / 2)))))]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
P is functional non empty proper closed compact bounded with_the_max_arc Element of bool the carrier of (TOP-REAL 2)
U is functional non empty proper closed compact bounded with_the_max_arc Element of bool the carrier of (TOP-REAL 2)
P \/ U is functional non empty closed Element of bool the carrier of (TOP-REAL 2)
P /\ U is functional proper closed compact bounded Element of bool the carrier of (TOP-REAL 2)
W-bound P is complex ext-real real Element of REAL
(TOP-REAL 2) | P is non empty strict TopSpace-like T_0 T_1 T_2 V82() normal T_3 T_4 compact V246() pseudocompact SubSpace of TOP-REAL 2
proj1 | P is Relation-like P -defined the carrier of (TOP-REAL 2) -defined the carrier of ((TOP-REAL 2) | P) -defined REAL -valued Function-like non empty total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ((TOP-REAL 2) | P),REAL:]
the carrier of ((TOP-REAL 2) | P) is non empty set
[: the carrier of ((TOP-REAL 2) | P),REAL:] is Relation-like non empty V156() V157() V158() set
bool [: the carrier of ((TOP-REAL 2) | P),REAL:] is non empty set
lower_bound (proj1 | P) is complex ext-real real Element of REAL
(proj1 | P) .: the carrier of ((TOP-REAL 2) | P) is non empty V166() V167() V168() Element of bool REAL
K663(((proj1 | P) .: the carrier of ((TOP-REAL 2) | P))) is complex ext-real real Element of REAL
E-bound P is complex ext-real real Element of REAL
upper_bound (proj1 | P) is complex ext-real real Element of REAL
K662(((proj1 | P) .: the carrier of ((TOP-REAL 2) | P))) is complex ext-real real Element of REAL
LMP P is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
(E-bound P) + (W-bound P) is complex ext-real real Element of REAL
((E-bound P) + (W-bound P)) / 2 is complex ext-real real Element of REAL
Vertical_Line (((E-bound P) + (W-bound P)) / 2) is functional Element of bool the carrier of (TOP-REAL 2)
P /\ (Vertical_Line (((E-bound P) + (W-bound P)) / 2)) is functional Element of bool the carrier of (TOP-REAL 2)
proj2 .: (P /\ (Vertical_Line (((E-bound P) + (W-bound P)) / 2))) is V166() V167() V168() Element of bool REAL
K663((proj2 .: (P /\ (Vertical_Line (((E-bound P) + (W-bound P)) / 2))))) is complex ext-real real Element of REAL
|[(((E-bound P) + (W-bound P)) / 2),K663((proj2 .: (P /\ (Vertical_Line (((E-bound P) + (W-bound P)) / 2)))))]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
LSeg ((LMP P),|[0,(- 3)]|) is functional proper closed closed boundary nowhere_dense connected compact compact bounded bounded Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b<sub>1</sub>) * (LMP P)) + (b<sub>1</sub> * |[0,(- 3)]|)) where b<sub>1</sub> is complex ext-real real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
(LSeg ((LMP P),|[0,(- 3)]|)) /\ U is functional proper closed compact bounded Element of bool the carrier of (TOP-REAL 2)
UMP ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
E-bound ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U) is complex ext-real real Element of REAL
(TOP-REAL 2) | ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U) is strict TopSpace-like T_0 T_1 T_2 SubSpace of TOP-REAL 2
proj1 | ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U) is Relation-like (LSeg ((LMP P),|[0,(- 3)]|)) /\ U -defined the carrier of (TOP-REAL 2) -defined the carrier of ((TOP-REAL 2) | ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U)) -defined REAL -valued Function-like total quasi_total V156() V157() V158() continuous Element of bool [: the carrier of ((TOP-REAL 2) | ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U)),REAL:]
the carrier of ((TOP-REAL 2) | ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U)) is set
[: the carrier of ((TOP-REAL 2) | ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U)),REAL:] is Relation-like V156() V157() V158() set
bool [: the carrier of ((TOP-REAL 2) | ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U)),REAL:] is non empty set
upper_bound (proj1 | ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U)) is complex ext-real real Element of REAL
(proj1 | ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U)) .: the carrier of ((TOP-REAL 2) | ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U)) is V166() V167() V168() Element of bool REAL
K662(((proj1 | ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U)) .: the carrier of ((TOP-REAL 2) | ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U)))) is complex ext-real real Element of REAL
W-bound ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U) is complex ext-real real Element of REAL
lower_bound (proj1 | ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U)) is complex ext-real real Element of REAL
K663(((proj1 | ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U)) .: the carrier of ((TOP-REAL 2) | ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U)))) is complex ext-real real Element of REAL
(E-bound ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U)) + (W-bound ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U)) is complex ext-real real Element of REAL
((E-bound ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U)) + (W-bound ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U))) / 2 is complex ext-real real Element of REAL
Vertical_Line (((E-bound ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U)) + (W-bound ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U))) / 2) is functional Element of bool the carrier of (TOP-REAL 2)
((LSeg ((LMP P),|[0,(- 3)]|)) /\ U) /\ (Vertical_Line (((E-bound ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U)) + (W-bound ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U))) / 2)) is functional Element of bool the carrier of (TOP-REAL 2)
proj2 .: (((LSeg ((LMP P),|[0,(- 3)]|)) /\ U) /\ (Vertical_Line (((E-bound ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U)) + (W-bound ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U))) / 2))) is V166() V167() V168() Element of bool REAL
K662((proj2 .: (((LSeg ((LMP P),|[0,(- 3)]|)) /\ U) /\ (Vertical_Line (((E-bound ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U)) + (W-bound ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U))) / 2))))) is complex ext-real real Element of REAL
|[(((E-bound ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U)) + (W-bound ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U))) / 2),K662((proj2 .: (((LSeg ((LMP P),|[0,(- 3)]|)) /\ U) /\ (Vertical_Line (((E-bound ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U)) + (W-bound ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U))) / 2)))))]| is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
(UMP ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U)) + (LMP P) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) is Relation-like [: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):] -defined the carrier of (TOP-REAL 2) -valued Function-like non empty total quasi_total Element of bool [:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):]
[:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):] is Relation-like non empty set
bool [:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):] is non empty set
K224( the carrier of (TOP-REAL 2), the U7 of (TOP-REAL 2),(UMP ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U)),(LMP P)) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
(1 / 2) * ((UMP ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U)) + (LMP P)) is Relation-like Function-like V49(2) V50() V156() V157() V158() Element of the carrier of (TOP-REAL 2)
C ` is functional non empty open Element of bool the carrier of (TOP-REAL 2)
the carrier of (TOP-REAL 2) \ C is set
(TOP-REAL 2) | (C `) is non empty strict TopSpace-like T_0 T_1 T_2 V118( TOP-REAL 2) SubSpace of TOP-REAL 2
Down (((1 / 2) * ((UMP ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U)) + (LMP P))),(C `)) is Element of the carrier of ((TOP-REAL 2) | (C `))
the carrier of ((TOP-REAL 2) | (C `)) is non empty set
Component_of (Down (((1 / 2) * ((UMP ((LSeg ((LMP P),|[0,(- 3)]|)) /\ U)) + (LMP P))),(C `))) is Element of bool the carrier of ((TOP-REAL 2) | (C `))
bool the carrier of ((TOP-REAL 2) | (C `)) is non empty set
BDD C is functional open Element of bool the carrier of (TOP-REAL 2)
{ b<sub>1</sub> where b<sub>1</sub> is functional Element of bool the carrier of (TOP-REAL 2) : b<sub>1</sub> is_inside_component_of C } is set
union { b<sub>1</sub> where b<sub>1</sub> is functional Element of bool the carrier of (TOP-REAL 2) : b<sub>1</sub> is_inside_component_of C } is set
UBD C is functional non empty open connected being_Region Element of bool the carrier of (TOP-REAL 2)
{ b<sub>1</sub> where b<sub>1</sub> is functional Element of bool the carrier of (TOP-REAL 2) : b<sub>1</sub> is_outside_component_of C } is set
union { b<sub>1</sub> where b<sub>1</sub> is functional Element of bool the carrier of (TOP-REAL 2) : b<sub>1</sub> is_outside_component_of C } is set
A1 is functional non empty open connected being_Region Element of bool the carrier of (TOP-REAL 2)
Cl A1 is functional non empty closed Element of bool the carrier of (TOP-REAL 2)
(Cl A1) \ A1 is functional Element of bool the carrier of (TOP-REAL 2)
A2 is functional open Element of bool the carrier of (TOP-REAL 2)
A1 \/ A2 is functional non empty open Element of bool the carrier of (TOP-REAL 2)
Cl A2 is functional closed Element of bool the carrier of (TOP-REAL 2)
(Cl A2) \ A2 is functional Element of bool the carrier of (TOP-REAL 2)
{} ((TOP-REAL 2) | (C `)) is Relation-like non-empty empty-yielding RAT -valued Function-like one-to-one constant functional empty proper open closed boundary nowhere_dense connected compact V156() V157() V158() V159() V166() V167() V168() V169() V170() V171() V172() bounded_below interval Element of bool the carrier of ((TOP-REAL 2) | (C `))
Fr A1 is functional closed boundary nowhere_dense Element of bool the carrier of (TOP-REAL 2)
A1 ` is functional closed Element of bool the carrier of (TOP-REAL 2)
the carrier of (TOP-REAL 2) \ A1 is set
Cl (A1 `) is functional closed Element of bool the carrier of (TOP-REAL 2)
(Cl A1) /\ (Cl (A1 `)) is functional closed Element of bool the carrier of (TOP-REAL 2)
w is Element of bool the carrier of ((TOP-REAL 2) | (C `))
Fr A2 is functional closed boundary nowhere_dense Element of bool the carrier of (TOP-REAL 2)
A2 ` is functional closed Element of bool the carrier of (TOP-REAL 2)
the carrier of (TOP-REAL 2) \ A2 is set
Cl (A2 `) is functional closed Element of bool the carrier of (TOP-REAL 2)
(Cl A2) /\ (Cl (A2 `)) is functional closed Element of bool the carrier of (TOP-REAL 2)
A2 \/ C is functional non empty Element of bool the carrier of (TOP-REAL 2)
A2 \/ A1 is functional non empty open Element of bool the carrier of (TOP-REAL 2)
(A2 \/ A1) ` is functional closed Element of bool the carrier of (TOP-REAL 2)
the carrier of (TOP-REAL 2) \ (A2 \/ A1) is set
((A2 \/ A1) `) /\ (C `) is functional Element of bool the carrier of (TOP-REAL 2)
(A2 \/ A1) \/ C is functional non empty Element of bool the carrier of (TOP-REAL 2)
((A2 \/ A1) \/ C) ` is functional Element of bool the carrier of (TOP-REAL 2)
the carrier of (TOP-REAL 2) \ ((A2 \/ A1) \/ C) is set
(A2 \/ C) \/ A1 is functional non empty Element of bool the carrier of (TOP-REAL 2)
((A2 \/ C) \/ A1) ` is functional Element of bool the carrier of (TOP-REAL 2)
the carrier of (TOP-REAL 2) \ ((A2 \/ C) \/ A1) is set
(A2 \/ C) ` is functional Element of bool the carrier of (TOP-REAL 2)
the carrier of (TOP-REAL 2) \ (A2 \/ C) is set
((A2 \/ C) `) /\ (A1 `) is functional Element of bool the carrier of (TOP-REAL 2)
A1 \/ C is functional non empty Element of bool the carrier of (TOP-REAL 2)
(A1 \/ A2) ` is functional closed Element of bool the carrier of (TOP-REAL 2)
the carrier of (TOP-REAL 2) \ (A1 \/ A2) is set
((A1 \/ A2) `) /\ (C `) is functional Element of bool the carrier of (TOP-REAL 2)
(A1 \/ A2) \/ C is functional non empty Element of bool the carrier of (TOP-REAL 2)
((A1 \/ A2) \/ C) ` is functional Element of bool the carrier of (TOP-REAL 2)
the carrier of (TOP-REAL 2) \ ((A1 \/ A2) \/ C) is set
(A1 \/ C) \/ A2 is functional non empty Element of bool the carrier of (TOP-REAL 2)
((A1 \/ C) \/ A2) ` is functional Element of bool the carrier of (TOP-REAL 2)
the carrier of (TOP-REAL 2) \ ((A1 \/ C) \/ A2) is set
(A1 \/ C) ` is functional Element of bool the carrier of (TOP-REAL 2)
the carrier of (TOP-REAL 2) \ (A1 \/ C) is set
((A1 \/ C) `) /\ (A2 `) is functional Element of bool the carrier of (TOP-REAL 2)
w is Element of bool the carrier of ((TOP-REAL 2) | (C `))
Ux is Element of bool the carrier of ((TOP-REAL 2) | (C `))
Pml is Element of bool the carrier of ((TOP-REAL 2) | (C `))
C is functional non empty proper closed connected compact bounded being_simple_closed_curve with_the_max_arc Element of bool the carrier of (TOP-REAL 2)
P is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued Function-like one-to-one non empty total quasi_total onto bijective continuous being_homeomorphism Homeomorphism of TOP-REAL 2
P .: C is functional non empty Element of bool the carrier of (TOP-REAL 2)
P /" is Relation-like the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -defined the carrier of (TOP-REAL 2) -valued the carrier of (TOP-REAL 2) -valued Function-like one-to-one non empty total quasi_total quasi_total onto bijective continuous being_homeomorphism Element of bool [: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):]
(P /") .: (P .: C) is functional non empty Element of bool the carrier of (TOP-REAL 2)
P " is Relation-like Function-like one-to-one set
dom P is functional non empty Element of bool the carrier of (TOP-REAL 2)
C is functional non empty proper closed connected compact bounded being_simple_closed_curve with_the_max_arc Element of bool the carrier of (TOP-REAL 2)
BDD C is functional open Element of bool the carrier of (TOP-REAL 2)
{ b<sub>1</sub> where b<sub>1</sub> is functional Element of bool the carrier of (TOP-REAL 2) : b<sub>1</sub> is_inside_component_of C } is set
union { b<sub>1</sub> where b<sub>1</sub> is functional Element of bool the carrier of (TOP-REAL 2) : b<sub>1</sub> is_inside_component_of C } is set
C ` is functional non empty open Element of bool the carrier of (TOP-REAL 2)
the carrier of (TOP-REAL 2) \ C is set
(TOP-REAL 2) | (C `) is non empty strict TopSpace-like T_0 T_1 T_2 V118( TOP-REAL 2) SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | (C `)) is non empty set
bool the carrier of ((TOP-REAL 2) | (C `)) is non empty set
{} ((TOP-REAL 2) | (C `)) is Relation-like non-empty empty-yielding RAT -valued Function-like one-to-one constant functional empty proper open closed boundary nowhere_dense connected compact V156() V157() V158() V159() V166() V167() V168() V169() V170() V171() V172() bounded_below interval Element of bool the carrier of ((TOP-REAL 2) | (C `))
P is Element of bool the carrier of ((TOP-REAL 2) | (C `))
C is functional non empty proper closed connected compact bounded being_simple_closed_curve with_the_max_arc Element of bool the carrier of (TOP-REAL 2)
C ` is functional non empty open Element of bool the carrier of (TOP-REAL 2)
the carrier of (TOP-REAL 2) \ C is set
(TOP-REAL 2) | (C `) is non empty strict TopSpace-like T_0 T_1 T_2 V118( TOP-REAL 2) SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | (C `)) is non empty set
bool the carrier of ((TOP-REAL 2) | (C `)) is non empty set
P is functional Element of bool the carrier of (TOP-REAL 2)
Fr P is functional closed Element of bool the carrier of (TOP-REAL 2)
Cl P is functional closed Element of bool the carrier of (TOP-REAL 2)
P ` is functional Element of bool the carrier of (TOP-REAL 2)
the carrier of (TOP-REAL 2) \ P is set
Cl (P `) is functional closed Element of bool the carrier of (TOP-REAL 2)
(Cl P) /\ (Cl (P `)) is functional closed Element of bool the carrier of (TOP-REAL 2)
U is Element of bool the carrier of ((TOP-REAL 2) | (C `))
BDD C is functional non empty open Element of bool the carrier of (TOP-REAL 2)
{ b₁ where b₁ is functional Element of bool the carrier of (TOP-REAL 2) : b₁ is_inside_component_of C } is set
union { b₁ where b₁ is functional Element of bool the carrier of (TOP-REAL 2) : b₁ is_inside_component_of C } is set
C is functional non empty proper closed connected compact bounded being_simple_closed_curve with_the_max_arc Element of bool the carrier of (TOP-REAL 2)
C ` is functional non empty open Element of bool the carrier of (TOP-REAL 2)
the carrier of (TOP-REAL 2) \ C is set
(TOP-REAL 2) | (C `) is non empty strict TopSpace-like T_0 T_1 T_2 V118( TOP-REAL 2) SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | (C `)) is non empty set
bool the carrier of ((TOP-REAL 2) | (C `)) is non empty set
C is functional non empty proper closed connected compact bounded being_simple_closed_curve with_the_max_arc Element of bool the carrier of (TOP-REAL 2)