REAL is non empty non trivial V35() V183() V184() V185() V189() set
NAT is non empty non trivial ordinal V35() cardinal limit_cardinal V183() V184() V185() V186() V187() V188() V189() Element of bool REAL
bool REAL is non empty non trivial V35() set
I[01] is non empty strict TopSpace-like T_0 T_1 T_2 connected compact V231() pathwise_connected SubSpace of R^1
R^1 is non empty strict TopSpace-like V231() TopStruct
the carrier of I[01] is non empty V183() V184() V185() set
COMPLEX is non empty non trivial V35() V183() V189() set
omega is non empty non trivial ordinal V35() cardinal limit_cardinal V183() V184() V185() V186() V187() V188() V189() set
bool omega is non empty non trivial V35() set
bool NAT is non empty non trivial V35() set
K194(NAT) is V53() set
1 is non empty ordinal natural V11() real ext-real positive non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
INT is non empty non trivial V35() V183() V184() V185() V186() V187() V189() set
[:1,1:] is non empty RAT -valued INT -valued V35() complex-yielding V174() V175() V176() set
RAT is non empty non trivial V35() V183() V184() V185() V186() V189() set
bool [:1,1:] is non empty V35() V39() set
[:[:1,1:],1:] is non empty RAT -valued INT -valued V35() complex-yielding V174() V175() V176() set
bool [:[:1,1:],1:] is non empty V35() V39() set
[:[:1,1:],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[:1,1:],REAL:] is non empty non trivial V35() set
[:REAL,REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
[:[:REAL,REAL:],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[:REAL,REAL:],REAL:] is non empty non trivial V35() set
2 is non empty ordinal natural V11() real ext-real positive non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
[:2,2:] is non empty RAT -valued INT -valued V35() complex-yielding V174() V175() V176() set
[:[:2,2:],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[:2,2:],REAL:] is non empty non trivial V35() set
bool [:REAL,REAL:] is non empty non trivial V35() set
K390() is non empty V132() L10()
the carrier of K390() is non empty set
K395() is non empty V132() V154() V155() V156() V158() V205() V206() V207() V208() V209() V210() L10()
K396() is non empty V132() V156() V158() V208() V209() V210() M15(K395())
K397() is non empty V132() V154() V156() V158() V208() V209() V210() V211() M18(K395(),K396())
K399() is non empty V132() V154() V156() V158() L10()
K400() is non empty V132() V154() V156() V158() V211() M15(K399())
K483() is non empty strict TopSpace-like T_0 T_1 T_2 connected compact V231() pathwise_connected TopStruct
the carrier of K483() is non empty V183() V184() V185() set
RealSpace is non empty strict Reflexive discerning symmetric triangle Discerning V231() MetrStruct
real_dist is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
MetrStruct(# REAL,real_dist #) is strict MetrStruct
0 is empty trivial ordinal natural V11() real ext-real non positive non negative Function-like functional V35() V39() cardinal {} -element FinSequence-membered V116() V117() V183() V184() V185() V186() V187() V188() V189() Element of NAT
{} is empty trivial ordinal natural V11() real ext-real non positive non negative Function-like functional V35() V39() cardinal {} -element FinSequence-membered V183() V184() V185() V186() V187() V188() V189() set
the empty trivial ordinal natural V11() real ext-real non positive non negative Function-like functional V35() V39() cardinal {} -element FinSequence-membered V183() V184() V185() V186() V187() V188() V189() set is empty trivial ordinal natural V11() real ext-real non positive non negative Function-like functional V35() V39() cardinal {} -element FinSequence-membered V183() V184() V185() V186() V187() V188() V189() set
Closed-Interval-TSpace (0,1) is non empty strict TopSpace-like V231() SubSpace of R^1
the carrier of (Closed-Interval-TSpace (0,1)) is non empty V183() V184() V185() set
TOP-REAL 2 is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict RLTopStruct
the carrier of (TOP-REAL 2) is non empty set
the carrier of (TOP-REAL 2) * is non empty functional FinSequence-membered FinSequenceSet of the carrier of (TOP-REAL 2)
[: the carrier of (TOP-REAL 2),REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [: the carrier of (TOP-REAL 2),REAL:] is non empty non trivial V35() set
bool the carrier of (TOP-REAL 2) is non empty set
the carrier of R^1 is non empty V183() V184() V185() set
{{},1} is non empty V35() V39() V183() V184() V185() V186() V187() V188() set
TOP-REAL 1 is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict RLTopStruct
the carrier of (TOP-REAL 1) is non empty set
[:COMPLEX,COMPLEX:] is non empty non trivial V35() complex-yielding set
bool [:COMPLEX,COMPLEX:] is non empty non trivial V35() set
[:[:COMPLEX,COMPLEX:],COMPLEX:] is non empty non trivial V35() complex-yielding set
bool [:[:COMPLEX,COMPLEX:],COMPLEX:] is non empty non trivial V35() set
[:RAT,RAT:] is non empty non trivial RAT -valued V35() complex-yielding V174() V175() set
bool [:RAT,RAT:] is non empty non trivial V35() set
[:[:RAT,RAT:],RAT:] is non empty non trivial RAT -valued V35() complex-yielding V174() V175() set
bool [:[:RAT,RAT:],RAT:] is non empty non trivial V35() set
[:INT,INT:] is non empty non trivial RAT -valued INT -valued V35() complex-yielding V174() V175() set
bool [:INT,INT:] is non empty non trivial V35() set
[:[:INT,INT:],INT:] is non empty non trivial RAT -valued INT -valued V35() complex-yielding V174() V175() set
bool [:[:INT,INT:],INT:] is non empty non trivial V35() set
[:NAT,NAT:] is non empty non trivial RAT -valued INT -valued V35() complex-yielding V174() V175() V176() set
[:[:NAT,NAT:],NAT:] is non empty non trivial RAT -valued INT -valued V35() complex-yielding V174() V175() V176() set
bool [:[:NAT,NAT:],NAT:] is non empty non trivial V35() set
[:COMPLEX,REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:COMPLEX,REAL:] is non empty non trivial V35() set
[:NAT,REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:NAT,REAL:] is non empty non trivial V35() set
3 is non empty ordinal natural V11() real ext-real positive non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
0. (TOP-REAL 2) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like V62( TOP-REAL 2) complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
the ZeroF of (TOP-REAL 2) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
|[0,0]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
REAL 0 is non empty functional FinSequence-membered FinSequenceSet of REAL
0 -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
REAL * is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = 0 } is set
TOP-REAL 0 is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict RLTopStruct
0. (TOP-REAL 0) is empty trivial ordinal natural V11() real ext-real non positive non negative Relation-like NAT -defined REAL -valued Function-like one-to-one constant functional V35() V36() V39() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered V62( TOP-REAL 0) complex-yielding V174() V175() V176() increasing V178() V179() V180() V183() V184() V185() V186() V187() V188() V189() Element of the carrier of (TOP-REAL 0)
the carrier of (TOP-REAL 0) is non empty set
the ZeroF of (TOP-REAL 0) is empty trivial ordinal natural V11() real ext-real non positive non negative Relation-like NAT -defined REAL -valued Function-like one-to-one constant functional V35() V36() V39() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered complex-yielding V174() V175() V176() increasing V178() V179() V180() V183() V184() V185() V186() V187() V188() V189() Element of the carrier of (TOP-REAL 0)
{(0. (TOP-REAL 0))} is non empty trivial functional V35() V39() 1 -element V183() V184() V185() V186() V187() V188() set
4 is non empty ordinal natural V11() real ext-real positive non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
[.0,1.] is V183() V184() V185() real-bounded Element of bool REAL
K484() is V11() real ext-real Element of the carrier of K483()
K485() is V11() real ext-real Element of the carrier of K483()
TopSpaceMetr RealSpace is TopStruct
sqrt 1 is V11() real ext-real Element of REAL
bool the carrier of R^1 is non empty set
(#) (0,1) is V11() real ext-real Element of the carrier of (Closed-Interval-TSpace (0,1))
(0,1) (#) is V11() real ext-real Element of the carrier of (Closed-Interval-TSpace (0,1))
Euclid 2 is non empty strict Reflexive discerning symmetric triangle Discerning MetrStruct
REAL 2 is non empty functional FinSequence-membered FinSequenceSet of REAL
2 -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = 2 } is set
Pitag_dist 2 is non empty Relation-like [:(REAL 2),(REAL 2):] -defined REAL -valued Function-like total V30([:(REAL 2),(REAL 2):], REAL ) complex-yielding V174() V175() Element of bool [:[:(REAL 2),(REAL 2):],REAL:]
[:(REAL 2),(REAL 2):] is non empty set
[:[:(REAL 2),(REAL 2):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[:(REAL 2),(REAL 2):],REAL:] is non empty non trivial V35() set
MetrStruct(# (REAL 2),(Pitag_dist 2) #) is strict MetrStruct
the carrier of (Euclid 2) is non empty set
5 is non empty ordinal natural V11() real ext-real positive non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
multreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
C is ordinal natural V11() real ext-real non negative V35() cardinal set
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict RLTopStruct
Euclid C is non empty strict Reflexive discerning symmetric triangle Discerning MetrStruct
REAL C is non empty functional FinSequence-membered FinSequenceSet of REAL
C -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = C } is set
Pitag_dist C is non empty Relation-like [:(REAL C),(REAL C):] -defined REAL -valued Function-like total V30([:(REAL C),(REAL C):], REAL ) complex-yielding V174() V175() Element of bool [:[:(REAL C),(REAL C):],REAL:]
[:(REAL C),(REAL C):] is non empty set
[:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() set
MetrStruct(# (REAL C),(Pitag_dist C) #) is strict MetrStruct
TopSpaceMetr (Euclid C) is TopStruct
the carrier of (TOP-REAL C) is non empty set
the topology of (TOP-REAL C) is non empty Element of bool (bool the carrier of (TOP-REAL C))
bool the carrier of (TOP-REAL C) is non empty set
bool (bool the carrier of (TOP-REAL C)) is non empty set
TopStruct(# the carrier of (TOP-REAL C), the topology of (TOP-REAL C) #) is non empty strict TopSpace-like TopStruct
C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
r is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
K258((TOP-REAL C),C,r) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) is non empty Relation-like [: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):] -defined the carrier of (TOP-REAL C) -valued Function-like total V30([: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C)) Element of bool [:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):]
[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):] is non empty set
[:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):] is non empty set
bool [:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):] is non empty set
the U7 of (TOP-REAL C) . (C,r) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[C,r] is non empty set
{C,r} is non empty functional V35() V39() set
{C} is non empty trivial functional V35() V39() 1 -element set
{{C,r},{C}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [C,r] is set
C + r is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
addreal .: (C,r) is set
EX2 is Element of bool the carrier of (TOP-REAL C)
C + r is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the carrier of (Euclid C) is non empty set
the carrier of (TopSpaceMetr (Euclid C)) is set
bool the carrier of (TopSpaceMetr (Euclid C)) is non empty set
t2 is Element of bool the carrier of (TopSpaceMetr (Euclid C))
EX is Element of the carrier of (Euclid C)
qt2 is V11() real ext-real set
Ball (EX,qt2) is bounded Element of bool the carrier of (Euclid C)
bool the carrier of (Euclid C) is non empty set
qt2 / 2 is V11() real ext-real Element of REAL
EX1 is Element of the carrier of (Euclid C)
Ball (EX1,(qt2 / 2)) is bounded Element of bool the carrier of (Euclid C)
p1 is Element of the carrier of (Euclid C)
Ball (p1,(qt2 / 2)) is bounded Element of bool the carrier of (Euclid C)
q4 is Element of bool the carrier of (TOP-REAL C)
r5 is Element of bool the carrier of (TOP-REAL C)
q4 + r5 is Element of bool the carrier of (TOP-REAL C)
r0 is set
q4 + r5 is Element of bool the carrier of (TOP-REAL C)
{ (b1 + b2) where b1, b2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C) : ( b1 in q4 & b2 in r5 ) } is set
Q is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
P3 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
Q + P3 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) . (Q,P3) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[Q,P3] is non empty set
{Q,P3} is non empty functional V35() V39() set
{Q} is non empty trivial functional V35() V39() 1 -element set
{{Q,P3},{Q}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [Q,P3] is set
Q + P3 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (Q,P3) is set
Q is Element of the carrier of (Euclid C)
dist (p1,Q) is V11() real ext-real Element of REAL
the distance of (Euclid C) is non empty Relation-like [: the carrier of (Euclid C), the carrier of (Euclid C):] -defined REAL -valued Function-like total V30([: the carrier of (Euclid C), the carrier of (Euclid C):], REAL ) complex-yielding V174() V175() Element of bool [:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:]
[: the carrier of (Euclid C), the carrier of (Euclid C):] is non empty set
[:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:] is non empty non trivial V35() set
the distance of (Euclid C) . (p1,Q) is V11() real ext-real Element of REAL
[p1,Q] is non empty set
{p1,Q} is non empty V35() set
{p1} is non empty trivial V35() 1 -element set
{{p1,Q},{p1}} is non empty V35() V39() set
the distance of (Euclid C) . [p1,Q] is V11() real ext-real set
z is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
r is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
z - r is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
diffreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
id REAL is non empty Relation-like REAL -defined REAL -valued Function-like one-to-one total V30( REAL , REAL ) complex-yielding V174() V175() increasing V179() Element of bool [:REAL,REAL:]
compreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
K174(REAL,addreal,(id REAL),compreal) is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
diffreal .: (z,r) is set
K324(r) is Relation-like Function-like complex-yielding set
r (#) compreal is Relation-like Function-like V35() complex-yielding V174() V175() set
K38(1) is V11() real ext-real non positive set
K38(1) * r is Relation-like Function-like set
K38(1) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (K38(1),(id REAL)) is set
r (#) (K38(1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
K295(z,K324(r)) is Relation-like Function-like set
|.(z - r).| is V11() real ext-real non negative Element of REAL
sqr (z - r) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
sqrreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
(z - r) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((z - r),(z - r)) is Relation-like Function-like set
multreal .: ((z - r),(z - r)) is set
K383((sqr (z - r))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (z - r)),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (z - r))) is V11() real ext-real Element of REAL
W3 is Element of the carrier of (Euclid C)
dist (EX1,W3) is V11() real ext-real Element of REAL
the distance of (Euclid C) . (EX1,W3) is V11() real ext-real Element of REAL
[EX1,W3] is non empty set
{EX1,W3} is non empty V35() set
{EX1} is non empty trivial V35() 1 -element set
{{EX1,W3},{EX1}} is non empty V35() V39() set
the distance of (Euclid C) . [EX1,W3] is V11() real ext-real set
W2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
q is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
W2 - q is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
diffreal .: (W2,q) is set
K324(q) is Relation-like Function-like complex-yielding set
q (#) compreal is Relation-like Function-like V35() complex-yielding V174() V175() set
K38(1) * q is Relation-like Function-like set
q (#) (K38(1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
K295(W2,K324(q)) is Relation-like Function-like set
|.(W2 - q).| is V11() real ext-real non negative Element of REAL
sqr (W2 - q) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(W2 - q) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((W2 - q),(W2 - q)) is Relation-like Function-like set
multreal .: ((W2 - q),(W2 - q)) is set
K383((sqr (W2 - q))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (W2 - q)),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (W2 - q))) is V11() real ext-real Element of REAL
(qt2 / 2) + (qt2 / 2) is V11() real ext-real Element of REAL
|.(W2 - q).| + |.(z - r).| is V11() real ext-real non negative Element of REAL
W2 + z is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
addreal .: (W2,z) is set
q + r is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
addreal .: (q,r) is set
(W2 + z) - (q + r) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
diffreal .: ((W2 + z),(q + r)) is set
K324((q + r)) is Relation-like Function-like complex-yielding set
(q + r) (#) compreal is Relation-like Function-like V35() complex-yielding V174() V175() set
K38(1) * (q + r) is Relation-like Function-like set
(q + r) (#) (K38(1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
K295((W2 + z),K324((q + r))) is Relation-like Function-like set
r + q is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
addreal .: (r,q) is set
- (r + q) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
(r + q) (#) compreal is Relation-like Function-like V35() complex-yielding V174() V175() set
K38(1) * (r + q) is Relation-like Function-like set
(r + q) (#) (K38(1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
(W2 + z) + (- (r + q)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
addreal .: ((W2 + z),(- (r + q))) is set
- r is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
- q is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
(- r) + (- q) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
addreal .: ((- r),(- q)) is set
(W2 + z) + ((- r) + (- q)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
addreal .: ((W2 + z),((- r) + (- q))) is set
(W2 + z) + (- r) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
addreal .: ((W2 + z),(- r)) is set
((W2 + z) + (- r)) + (- q) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
addreal .: (((W2 + z) + (- r)),(- q)) is set
z + (- r) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
addreal .: (z,(- r)) is set
(z + (- r)) + W2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
addreal .: ((z + (- r)),W2) is set
((z + (- r)) + W2) + (- q) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
addreal .: (((z + (- r)) + W2),(- q)) is set
W2 + (- q) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
addreal .: (W2,(- q)) is set
(z + (- r)) + (W2 + (- q)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
addreal .: ((z + (- r)),(W2 + (- q))) is set
(z - r) + (W2 + (- q)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
addreal .: ((z - r),(W2 + (- q))) is set
(z - r) + (W2 - q) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
addreal .: ((z - r),(W2 - q)) is set
P2 is Element of the carrier of (Euclid C)
dist (EX,P2) is V11() real ext-real Element of REAL
the distance of (Euclid C) . (EX,P2) is V11() real ext-real Element of REAL
[EX,P2] is non empty set
{EX,P2} is non empty V35() set
{EX} is non empty trivial V35() 1 -element set
{{EX,P2},{EX}} is non empty V35() V39() set
the distance of (Euclid C) . [EX,P2] is V11() real ext-real set
(W2 - q) + (z - r) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
addreal .: ((W2 - q),(z - r)) is set
|.((W2 - q) + (z - r)).| is V11() real ext-real non negative Element of REAL
sqr ((W2 - q) + (z - r)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
((W2 - q) + (z - r)) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (((W2 - q) + (z - r)),((W2 - q) + (z - r))) is Relation-like Function-like set
multreal .: (((W2 - q) + (z - r)),((W2 - q) + (z - r))) is set
K383((sqr ((W2 - q) + (z - r)))) is V11() real ext-real Element of REAL
K195(REAL,(sqr ((W2 - q) + (z - r))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr ((W2 - q) + (z - r)))) is V11() real ext-real Element of REAL
C is V11() real ext-real Element of REAL
r is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
C * r is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
C * r is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
C multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
id REAL is non empty Relation-like REAL -defined REAL -valued Function-like one-to-one total V30( REAL , REAL ) complex-yielding V174() V175() increasing V179() Element of bool [:REAL,REAL:]
multreal [;] (C,(id REAL)) is set
r (#) (C multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
EX2 is Element of bool the carrier of (TOP-REAL C)
the carrier of (Euclid C) is non empty set
the carrier of (TopSpaceMetr (Euclid C)) is set
bool the carrier of (TopSpaceMetr (Euclid C)) is non empty set
EX is Element of bool the carrier of (TopSpaceMetr (Euclid C))
p1 is Element of the carrier of (Euclid C)
t2 is V11() real ext-real set
Ball (p1,t2) is bounded Element of bool the carrier of (Euclid C)
bool the carrier of (Euclid C) is non empty set
t2 / 2 is V11() real ext-real Element of REAL
(t2 / 2) / 2 is V11() real ext-real Element of REAL
abs C is V11() real ext-real Element of REAL
(abs C) * 1 is V11() real ext-real Element of REAL
((t2 / 2) / 2) / (abs C) is V11() real ext-real Element of REAL
r2 is non empty V11() real ext-real positive non negative Element of REAL
(abs C) * r2 is V11() real ext-real Element of REAL
r2 is non empty V11() real ext-real positive non negative Element of REAL
(abs C) * r2 is V11() real ext-real Element of REAL
r2 is non empty V11() real ext-real positive non negative Element of REAL
(abs C) * r2 is V11() real ext-real Element of REAL
EX1 is Element of the carrier of (Euclid C)
Ball (EX1,r2) is bounded Element of bool the carrier of (Euclid C)
|.r.| is V11() real ext-real non negative Element of REAL
sqr r is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
sqrreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
r (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (r,r) is Relation-like Function-like set
multreal .: (r,r) is set
K383((sqr r)) is V11() real ext-real Element of REAL
addreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K195(REAL,(sqr r),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr r)) is V11() real ext-real Element of REAL
|.r.| + r2 is non empty V11() real ext-real positive non negative Element of REAL
(t2 / 2) / (|.r.| + r2) is V11() real ext-real Element of REAL
r5 is non empty V11() real ext-real positive non negative Element of REAL
q4 is Element of bool the carrier of (TOP-REAL C)
r0 is V11() real ext-real Element of REAL
r0 - C is V11() real ext-real Element of REAL
abs (r0 - C) is V11() real ext-real Element of REAL
r0 * q4 is Element of bool the carrier of (TOP-REAL C)
{ (r0 * b1) where b1 is Element of the carrier of (TOP-REAL C) : b1 in q4 } is set
Q is set
P3 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
r0 * P3 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
r0 * P3 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
r0 multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (r0,(id REAL)) is set
P3 (#) (r0 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
P2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
W2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
q is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of C -tuples_on REAL
C |-> 0 is Relation-like empty-yielding NAT -defined NAT -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() V176() Element of C -tuples_on NAT
C -tuples_on NAT is non empty functional FinSequence-membered FinSequenceSet of NAT
NAT * is non empty functional FinSequence-membered FinSequenceSet of NAT
{ b1 where b1 is Relation-like NAT -defined NAT -valued Function-like V35() FinSequence-like FinSubsequence-like Element of NAT * : len b1 = C } is set
Seg C is V35() C -element V183() V184() V185() V186() V187() V188() Element of bool NAT
(Seg C) --> 0 is Relation-like Seg C -defined INT -valued RAT -valued {0} -valued Function-like total V30( Seg C,{0}) V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() V176() Element of bool [:(Seg C),{0}:]
{0} is non empty trivial V35() V39() 1 -element V183() V184() V185() V186() V187() V188() set
[:(Seg C),{0}:] is INT -valued RAT -valued V35() complex-yielding V174() V175() V176() set
bool [:(Seg C),{0}:] is non empty V35() V39() set
q - (C |-> 0) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
diffreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
compreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
K174(REAL,addreal,(id REAL),compreal) is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
diffreal .: (q,(C |-> 0)) is set
K324((C |-> 0)) is Relation-like Function-like complex-yielding set
(C |-> 0) (#) compreal is Relation-like Function-like V35() complex-yielding V174() V175() set
K38(1) is V11() real ext-real non positive set
K38(1) * (C |-> 0) is Relation-like Function-like set
K38(1) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (K38(1),(id REAL)) is set
(C |-> 0) (#) (K38(1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
K295(q,K324((C |-> 0))) is Relation-like Function-like set
z is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of C -tuples_on REAL
z - z is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of C -tuples_on REAL
diffreal .: (z,z) is set
K324(z) is Relation-like Function-like complex-yielding set
z (#) compreal is Relation-like Function-like V35() complex-yielding V174() V175() set
K38(1) * z is Relation-like Function-like set
z (#) (K38(1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
K295(z,K324(z)) is Relation-like Function-like set
q - (z - z) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of C -tuples_on REAL
diffreal .: (q,(z - z)) is set
K324((z - z)) is Relation-like Function-like complex-yielding set
(z - z) (#) compreal is Relation-like Function-like V35() complex-yielding V174() V175() set
K38(1) * (z - z) is Relation-like Function-like set
(z - z) (#) (K38(1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
K295(q,K324((z - z))) is Relation-like Function-like set
q - z is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of C -tuples_on REAL
diffreal .: (q,z) is set
K295(q,K324(z)) is Relation-like Function-like set
(q - z) + z is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of C -tuples_on REAL
addreal .: ((q - z),z) is set
|.W2.| is V11() real ext-real non negative Element of REAL
sqr W2 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
W2 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (W2,W2) is Relation-like Function-like set
multreal .: (W2,W2) is set
K383((sqr W2)) is V11() real ext-real Element of REAL
K195(REAL,(sqr W2),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr W2)) is V11() real ext-real Element of REAL
W2 - P2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
diffreal .: (W2,P2) is set
K324(P2) is Relation-like Function-like complex-yielding set
P2 (#) compreal is Relation-like Function-like V35() complex-yielding V174() V175() set
K38(1) * P2 is Relation-like Function-like set
P2 (#) (K38(1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
K295(W2,K324(P2)) is Relation-like Function-like set
|.(W2 - P2).| is V11() real ext-real non negative Element of REAL
sqr (W2 - P2) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(W2 - P2) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((W2 - P2),(W2 - P2)) is Relation-like Function-like set
multreal .: ((W2 - P2),(W2 - P2)) is set
K383((sqr (W2 - P2))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (W2 - P2)),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (W2 - P2))) is V11() real ext-real Element of REAL
|.P2.| is V11() real ext-real non negative Element of REAL
sqr P2 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
P2 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (P2,P2) is Relation-like Function-like set
multreal .: (P2,P2) is set
K383((sqr P2)) is V11() real ext-real Element of REAL
K195(REAL,(sqr P2),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr P2)) is V11() real ext-real Element of REAL
|.(W2 - P2).| + |.P2.| is V11() real ext-real non negative Element of REAL
W3 is Element of the carrier of (Euclid C)
dist (EX1,W3) is V11() real ext-real Element of REAL
the distance of (Euclid C) is non empty Relation-like [: the carrier of (Euclid C), the carrier of (Euclid C):] -defined REAL -valued Function-like total V30([: the carrier of (Euclid C), the carrier of (Euclid C):], REAL ) complex-yielding V174() V175() Element of bool [:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:]
[: the carrier of (Euclid C), the carrier of (Euclid C):] is non empty set
[:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:] is non empty non trivial V35() set
the distance of (Euclid C) . (EX1,W3) is V11() real ext-real Element of REAL
[EX1,W3] is non empty set
{EX1,W3} is non empty V35() set
{EX1} is non empty trivial V35() 1 -element set
{{EX1,W3},{EX1}} is non empty V35() V39() set
the distance of (Euclid C) . [EX1,W3] is V11() real ext-real set
r2 + |.r.| is non empty V11() real ext-real positive non negative Element of REAL
r5 * |.W2.| is V11() real ext-real non negative Element of REAL
r5 * (r2 + |.r.|) is V11() real ext-real non negative Element of REAL
C * P2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
P2 (#) (C multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
C * W2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
W2 (#) (C multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
- (C * W2) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
(C * W2) (#) compreal is Relation-like Function-like V35() complex-yielding V174() V175() set
K38(1) * (C * W2) is Relation-like Function-like set
(C * W2) (#) (K38(1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
(C * P2) + (- (C * W2)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
addreal .: ((C * P2),(- (C * W2))) is set
- 1 is V11() real ext-real non positive Element of REAL
(- 1) * (C * W2) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
(- 1) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] ((- 1),(id REAL)) is set
(C * W2) (#) ((- 1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
(C * P2) + ((- 1) * (C * W2)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
addreal .: ((C * P2),((- 1) * (C * W2))) is set
(- 1) * C is V11() real ext-real Element of REAL
((- 1) * C) * W2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
((- 1) * C) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (((- 1) * C),(id REAL)) is set
W2 (#) (((- 1) * C) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
(C * P2) + (((- 1) * C) * W2) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
addreal .: ((C * P2),(((- 1) * C) * W2)) is set
(- 1) * W2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
W2 (#) ((- 1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
C * ((- 1) * W2) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
((- 1) * W2) (#) (C multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
(C * P2) + (C * ((- 1) * W2)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
addreal .: ((C * P2),(C * ((- 1) * W2))) is set
P2 + ((- 1) * W2) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
addreal .: (P2,((- 1) * W2)) is set
C * (P2 + ((- 1) * W2)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
(P2 + ((- 1) * W2)) (#) (C multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
- W2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
W2 (#) compreal is Relation-like Function-like V35() complex-yielding V174() V175() set
K38(1) * W2 is Relation-like Function-like set
W2 (#) (K38(1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
P2 + (- W2) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
addreal .: (P2,(- W2)) is set
C * (P2 + (- W2)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
(P2 + (- W2)) (#) (C multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
P2 - W2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
diffreal .: (P2,W2) is set
K324(W2) is Relation-like Function-like complex-yielding set
K295(P2,K324(W2)) is Relation-like Function-like set
C * (P2 - W2) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
(P2 - W2) (#) (C multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
|.((C * P2) + (- (C * W2))).| is V11() real ext-real non negative Element of REAL
sqr ((C * P2) + (- (C * W2))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
((C * P2) + (- (C * W2))) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (((C * P2) + (- (C * W2))),((C * P2) + (- (C * W2)))) is Relation-like Function-like set
multreal .: (((C * P2) + (- (C * W2))),((C * P2) + (- (C * W2)))) is set
K383((sqr ((C * P2) + (- (C * W2))))) is V11() real ext-real Element of REAL
K195(REAL,(sqr ((C * P2) + (- (C * W2)))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr ((C * P2) + (- (C * W2))))) is V11() real ext-real Element of REAL
|.(P2 - W2).| is V11() real ext-real non negative Element of REAL
sqr (P2 - W2) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(P2 - W2) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((P2 - W2),(P2 - W2)) is Relation-like Function-like set
multreal .: ((P2 - W2),(P2 - W2)) is set
K383((sqr (P2 - W2))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (P2 - W2)),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (P2 - W2))) is V11() real ext-real Element of REAL
(abs C) * |.(P2 - W2).| is V11() real ext-real Element of REAL
r0 * W2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
W2 (#) (r0 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
- (r0 * W2) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
(r0 * W2) (#) compreal is Relation-like Function-like V35() complex-yielding V174() V175() set
K38(1) * (r0 * W2) is Relation-like Function-like set
(r0 * W2) (#) (K38(1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
(C * W2) + (- (r0 * W2)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
addreal .: ((C * W2),(- (r0 * W2))) is set
(- 1) * (r0 * W2) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
(r0 * W2) (#) ((- 1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
(C * W2) + ((- 1) * (r0 * W2)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
addreal .: ((C * W2),((- 1) * (r0 * W2))) is set
(- 1) * r0 is V11() real ext-real Element of REAL
((- 1) * r0) * W2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
((- 1) * r0) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (((- 1) * r0),(id REAL)) is set
W2 (#) (((- 1) * r0) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
(C * W2) + (((- 1) * r0) * W2) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
addreal .: ((C * W2),(((- 1) * r0) * W2)) is set
C + ((- 1) * r0) is V11() real ext-real Element of REAL
(C + ((- 1) * r0)) * W2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
(C + ((- 1) * r0)) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] ((C + ((- 1) * r0)),(id REAL)) is set
W2 (#) ((C + ((- 1) * r0)) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
|.((C * W2) + (- (r0 * W2))).| is V11() real ext-real non negative Element of REAL
sqr ((C * W2) + (- (r0 * W2))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
((C * W2) + (- (r0 * W2))) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (((C * W2) + (- (r0 * W2))),((C * W2) + (- (r0 * W2)))) is Relation-like Function-like set
multreal .: (((C * W2) + (- (r0 * W2))),((C * W2) + (- (r0 * W2)))) is set
K383((sqr ((C * W2) + (- (r0 * W2))))) is V11() real ext-real Element of REAL
K195(REAL,(sqr ((C * W2) + (- (r0 * W2)))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr ((C * W2) + (- (r0 * W2))))) is V11() real ext-real Element of REAL
C - r0 is V11() real ext-real Element of REAL
abs (C - r0) is V11() real ext-real Element of REAL
(abs (C - r0)) * |.W2.| is V11() real ext-real Element of REAL
- (C - r0) is V11() real ext-real Element of REAL
abs (- (C - r0)) is V11() real ext-real Element of REAL
(abs (- (C - r0))) * |.W2.| is V11() real ext-real Element of REAL
r5 * (|.r.| + r2) is V11() real ext-real non negative Element of REAL
((C * P2) + (- (C * W2))) + ((C * W2) + (- (r0 * W2))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
addreal .: (((C * P2) + (- (C * W2))),((C * W2) + (- (r0 * W2)))) is set
|.(((C * P2) + (- (C * W2))) + ((C * W2) + (- (r0 * W2)))).| is V11() real ext-real non negative Element of REAL
sqr (((C * P2) + (- (C * W2))) + ((C * W2) + (- (r0 * W2)))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(((C * P2) + (- (C * W2))) + ((C * W2) + (- (r0 * W2)))) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((((C * P2) + (- (C * W2))) + ((C * W2) + (- (r0 * W2)))),(((C * P2) + (- (C * W2))) + ((C * W2) + (- (r0 * W2))))) is Relation-like Function-like set
multreal .: ((((C * P2) + (- (C * W2))) + ((C * W2) + (- (r0 * W2)))),(((C * P2) + (- (C * W2))) + ((C * W2) + (- (r0 * W2))))) is set
K383((sqr (((C * P2) + (- (C * W2))) + ((C * W2) + (- (r0 * W2)))))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (((C * P2) + (- (C * W2))) + ((C * W2) + (- (r0 * W2))))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (((C * P2) + (- (C * W2))) + ((C * W2) + (- (r0 * W2)))))) is V11() real ext-real Element of REAL
|.((C * P2) + (- (C * W2))).| + |.((C * W2) + (- (r0 * W2))).| is V11() real ext-real non negative Element of REAL
(t2 / 2) + (t2 / 2) is V11() real ext-real Element of REAL
(C * P2) - (r0 * W2) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
diffreal .: ((C * P2),(r0 * W2)) is set
K324((r0 * W2)) is Relation-like Function-like complex-yielding set
K295((C * P2),K324((r0 * W2))) is Relation-like Function-like set
C * z is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of C -tuples_on REAL
z (#) (C multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
(C * z) - (C |-> 0) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
diffreal .: ((C * z),(C |-> 0)) is set
K295((C * z),K324((C |-> 0))) is Relation-like Function-like set
r0 * q is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of C -tuples_on REAL
q (#) (r0 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
((C * z) - (C |-> 0)) - (r0 * q) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
diffreal .: (((C * z) - (C |-> 0)),(r0 * q)) is set
K324((r0 * q)) is Relation-like Function-like complex-yielding set
(r0 * q) (#) compreal is Relation-like Function-like V35() complex-yielding V174() V175() set
K38(1) * (r0 * q) is Relation-like Function-like set
(r0 * q) (#) (K38(1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
K295(((C * z) - (C |-> 0)),K324((r0 * q))) is Relation-like Function-like set
C * q is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of C -tuples_on REAL
q (#) (C multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
(C * q) - (C * q) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of C -tuples_on REAL
diffreal .: ((C * q),(C * q)) is set
K324((C * q)) is Relation-like Function-like complex-yielding set
(C * q) (#) compreal is Relation-like Function-like V35() complex-yielding V174() V175() set
K38(1) * (C * q) is Relation-like Function-like set
(C * q) (#) (K38(1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
K295((C * q),K324((C * q))) is Relation-like Function-like set
(C * P2) - ((C * q) - (C * q)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
diffreal .: ((C * P2),((C * q) - (C * q))) is set
K324(((C * q) - (C * q))) is Relation-like Function-like complex-yielding set
((C * q) - (C * q)) (#) compreal is Relation-like Function-like V35() complex-yielding V174() V175() set
K38(1) * ((C * q) - (C * q)) is Relation-like Function-like set
((C * q) - (C * q)) (#) (K38(1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
K295((C * P2),K324(((C * q) - (C * q)))) is Relation-like Function-like set
((C * P2) - ((C * q) - (C * q))) - (r0 * W2) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
diffreal .: (((C * P2) - ((C * q) - (C * q))),(r0 * W2)) is set
K295(((C * P2) - ((C * q) - (C * q))),K324((r0 * W2))) is Relation-like Function-like set
(C * P2) - (C * q) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
diffreal .: ((C * P2),(C * q)) is set
K295((C * P2),K324((C * q))) is Relation-like Function-like set
((C * P2) - (C * q)) + (C * q) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (((C * P2) - (C * q)),(C * q)) is set
(((C * P2) - (C * q)) + (C * q)) - (r0 * W2) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
diffreal .: ((((C * P2) - (C * q)) + (C * q)),(r0 * W2)) is set
K295((((C * P2) - (C * q)) + (C * q)),K324((r0 * W2))) is Relation-like Function-like set
(((C * P2) - (C * q)) + (C * q)) + (- (r0 * W2)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: ((((C * P2) - (C * q)) + (C * q)),(- (r0 * W2))) is set
((C * P2) - (C * q)) + ((C * W2) + (- (r0 * W2))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (((C * P2) - (C * q)),((C * W2) + (- (r0 * W2)))) is set
Q is Element of the carrier of (Euclid C)
dist (p1,Q) is V11() real ext-real Element of REAL
the distance of (Euclid C) . (p1,Q) is V11() real ext-real Element of REAL
[p1,Q] is non empty set
{p1,Q} is non empty V35() set
{p1} is non empty trivial V35() 1 -element set
{{p1,Q},{p1}} is non empty V35() V39() set
the distance of (Euclid C) . [p1,Q] is V11() real ext-real set
C is V11() real ext-real Element of REAL
p is V11() real ext-real Element of REAL
{C,p} is non empty V35() V183() V184() V185() Element of bool REAL
WH is Relation-like NAT -defined REAL -valued Function-like one-to-one V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V179() FinSequence of REAL
rng WH is V35() V183() V184() V185() Element of bool REAL
len WH is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
WH . 1 is V11() real ext-real Element of REAL
WH . 2 is V11() real ext-real Element of REAL
dom WH is V35() V183() V184() V185() V186() V187() V188() Element of bool NAT
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
p is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.p.| is V11() real ext-real non negative Element of REAL
sqr p is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
sqrreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
p (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (p,p) is Relation-like Function-like set
multreal .: (p,p) is set
K383((sqr p)) is V11() real ext-real Element of REAL
addreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K195(REAL,(sqr p),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr p)) is V11() real ext-real Element of REAL
abs |.p.| is V11() real ext-real Element of REAL
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
p is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.p.| is V11() real ext-real non negative Element of REAL
sqr p is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
sqrreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
p (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (p,p) is Relation-like Function-like set
multreal .: (p,p) is set
K383((sqr p)) is V11() real ext-real Element of REAL
addreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K195(REAL,(sqr p),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr p)) is V11() real ext-real Element of REAL
WH is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.WH.| is V11() real ext-real non negative Element of REAL
sqr WH is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
WH (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (WH,WH) is Relation-like Function-like set
multreal .: (WH,WH) is set
K383((sqr WH)) is V11() real ext-real Element of REAL
K195(REAL,(sqr WH),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr WH)) is V11() real ext-real Element of REAL
|.p.| - |.WH.| is V11() real ext-real Element of REAL
abs (|.p.| - |.WH.|) is V11() real ext-real Element of REAL
p - WH is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
- WH is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
- WH is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
compreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
WH (#) compreal is Relation-like Function-like V35() complex-yielding V174() V175() set
K38(1) is V11() real ext-real non positive set
K38(1) * WH is Relation-like Function-like set
K38(1) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
id REAL is non empty Relation-like REAL -defined REAL -valued Function-like one-to-one total V30( REAL , REAL ) complex-yielding V174() V175() increasing V179() Element of bool [:REAL,REAL:]
multreal [;] (K38(1),(id REAL)) is set
WH (#) (K38(1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
K258((TOP-REAL C),p,(- WH)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) is non empty Relation-like [: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):] -defined the carrier of (TOP-REAL C) -valued Function-like total V30([: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C)) Element of bool [:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):]
[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):] is non empty set
[:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):] is non empty set
bool [:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):] is non empty set
the U7 of (TOP-REAL C) . (p,(- WH)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[p,(- WH)] is non empty set
{p,(- WH)} is non empty functional V35() V39() set
{p} is non empty trivial functional V35() V39() 1 -element set
{{p,(- WH)},{p}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [p,(- WH)] is set
p + (- WH) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (p,(- WH)) is set
p - WH is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
diffreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K174(REAL,addreal,(id REAL),compreal) is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
diffreal .: (p,WH) is set
K324(WH) is Relation-like Function-like complex-yielding set
K295(p,K324(WH)) is Relation-like Function-like set
|.(p - WH).| is V11() real ext-real non negative Element of REAL
sqr (p - WH) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(p - WH) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((p - WH),(p - WH)) is Relation-like Function-like set
multreal .: ((p - WH),(p - WH)) is set
K383((sqr (p - WH))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (p - WH)),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (p - WH))) is V11() real ext-real Element of REAL
|.WH.| - |.p.| is V11() real ext-real Element of REAL
WH - p is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
- p is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
- p is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
p (#) compreal is Relation-like Function-like V35() complex-yielding V174() V175() set
K38(1) * p is Relation-like Function-like set
p (#) (K38(1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
K258((TOP-REAL C),WH,(- p)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) . (WH,(- p)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[WH,(- p)] is non empty set
{WH,(- p)} is non empty functional V35() V39() set
{WH} is non empty trivial functional V35() V39() 1 -element set
{{WH,(- p)},{WH}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [WH,(- p)] is set
WH + (- p) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (WH,(- p)) is set
WH - p is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
diffreal .: (WH,p) is set
K324(p) is Relation-like Function-like complex-yielding set
K295(WH,K324(p)) is Relation-like Function-like set
|.(WH - p).| is V11() real ext-real non negative Element of REAL
sqr (WH - p) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(WH - p) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((WH - p),(WH - p)) is Relation-like Function-like set
multreal .: ((WH - p),(WH - p)) is set
K383((sqr (WH - p))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (WH - p)),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (WH - p))) is V11() real ext-real Element of REAL
abs (|.WH.| - |.p.|) is V11() real ext-real Element of REAL
C is V11() real ext-real Element of REAL
|[C]| is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
|.|[C]|.| is V11() real ext-real non negative Element of REAL
sqr |[C]| is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
sqrreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
|[C]| (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (|[C]|,|[C]|) is Relation-like Function-like set
multreal .: (|[C]|,|[C]|) is set
K383((sqr |[C]|)) is V11() real ext-real Element of REAL
addreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K195(REAL,(sqr |[C]|),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr |[C]|)) is V11() real ext-real Element of REAL
abs C is V11() real ext-real Element of REAL
REAL 1 is non empty functional FinSequence-membered FinSequenceSet of REAL
1 -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = 1 } is set
WH is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of REAL 1
sqr WH is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of 1 -tuples_on REAL
WH (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (WH,WH) is Relation-like Function-like set
multreal .: (WH,WH) is set
C ^2 is V11() real ext-real Element of REAL
K37(C,C) is V11() real ext-real set
<*(C ^2)*> is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() FinSequence of REAL
sqrt (C ^2) is V11() real ext-real Element of REAL
C is ordinal natural V11() real ext-real non negative V35() cardinal set
Euclid C is non empty strict Reflexive discerning symmetric triangle Discerning MetrStruct
REAL C is non empty functional FinSequence-membered FinSequenceSet of REAL
C -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = C } is set
Pitag_dist C is non empty Relation-like [:(REAL C),(REAL C):] -defined REAL -valued Function-like total V30([:(REAL C),(REAL C):], REAL ) complex-yielding V174() V175() Element of bool [:[:(REAL C),(REAL C):],REAL:]
[:(REAL C),(REAL C):] is non empty set
[:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() set
MetrStruct(# (REAL C),(Pitag_dist C) #) is strict MetrStruct
the carrier of (Euclid C) is non empty set
0* C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
C |-> 0 is Relation-like empty-yielding NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of C -tuples_on REAL
Seg C is V35() C -element V183() V184() V185() V186() V187() V188() Element of bool NAT
(Seg C) --> 0 is Relation-like Seg C -defined INT -valued RAT -valued {0} -valued Function-like total V30( Seg C,{0}) V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() V176() Element of bool [:(Seg C),{0}:]
{0} is non empty trivial V35() V39() 1 -element V183() V184() V185() V186() V187() V188() set
[:(Seg C),{0}:] is INT -valued RAT -valued V35() complex-yielding V174() V175() V176() set
bool [:(Seg C),{0}:] is non empty V35() V39() set
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
p is V11() real ext-real Element of REAL
WH is Element of the carrier of (Euclid C)
p12 is Element of the carrier of (Euclid C)
C is Element of the carrier of (Euclid C)
dist (WH,p12) is V11() real ext-real Element of REAL
the distance of (Euclid C) is non empty Relation-like [: the carrier of (Euclid C), the carrier of (Euclid C):] -defined REAL -valued Function-like total V30([: the carrier of (Euclid C), the carrier of (Euclid C):], REAL ) complex-yielding V174() V175() Element of bool [:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:]
[: the carrier of (Euclid C), the carrier of (Euclid C):] is non empty set
[:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:] is non empty non trivial V35() set
the distance of (Euclid C) . (WH,p12) is V11() real ext-real Element of REAL
[WH,p12] is non empty set
{WH,p12} is non empty V35() set
{WH} is non empty trivial V35() 1 -element set
{{WH,p12},{WH}} is non empty V35() V39() set
the distance of (Euclid C) . [WH,p12] is V11() real ext-real set
p * (dist (WH,p12)) is V11() real ext-real Element of REAL
dist (WH,C) is V11() real ext-real Element of REAL
the distance of (Euclid C) . (WH,C) is V11() real ext-real Element of REAL
[WH,C] is non empty set
{WH,C} is non empty V35() set
{{WH,C},{WH}} is non empty V35() V39() set
the distance of (Euclid C) . [WH,C] is V11() real ext-real set
r is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
p * r is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
p * r is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
p multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
id REAL is non empty Relation-like REAL -defined REAL -valued Function-like one-to-one total V30( REAL , REAL ) complex-yielding V174() V175() increasing V179() Element of bool [:REAL,REAL:]
multreal [;] (p,(id REAL)) is set
r (#) (p multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
(Pitag_dist C) . (WH,C) is set
(Pitag_dist C) . [WH,C] is V11() real ext-real set
EX2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
EX1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
p * EX1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
EX1 (#) (p multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
EX2 - (p * EX1) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
diffreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
addreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
compreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
K174(REAL,addreal,(id REAL),compreal) is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
diffreal .: (EX2,(p * EX1)) is set
K324((p * EX1)) is Relation-like Function-like complex-yielding set
(p * EX1) (#) compreal is Relation-like Function-like V35() complex-yielding V174() V175() set
K38(1) is V11() real ext-real non positive set
K38(1) * (p * EX1) is Relation-like Function-like set
K38(1) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (K38(1),(id REAL)) is set
(p * EX1) (#) (K38(1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
K295(EX2,K324((p * EX1))) is Relation-like Function-like set
|.(EX2 - (p * EX1)).| is V11() real ext-real non negative Element of REAL
sqr (EX2 - (p * EX1)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
sqrreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
(EX2 - (p * EX1)) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((EX2 - (p * EX1)),(EX2 - (p * EX1))) is Relation-like Function-like set
multreal .: ((EX2 - (p * EX1)),(EX2 - (p * EX1))) is set
K383((sqr (EX2 - (p * EX1)))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (EX2 - (p * EX1))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (EX2 - (p * EX1)))) is V11() real ext-real Element of REAL
p * EX2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
EX2 (#) (p multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
0 * p is V11() real ext-real Element of REAL
C |-> (0 * p) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of C -tuples_on REAL
(Seg C) --> (0 * p) is Relation-like Seg C -defined {(0 * p)} -valued Function-like total V30( Seg C,{(0 * p)}) V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of bool [:(Seg C),{(0 * p)}:]
{(0 * p)} is non empty trivial V35() 1 -element V183() V184() V185() set
[:(Seg C),{(0 * p)}:] is V35() complex-yielding V174() V175() set
bool [:(Seg C),{(0 * p)}:] is non empty V35() V39() set
(Pitag_dist C) . (WH,p12) is set
(Pitag_dist C) . [WH,p12] is V11() real ext-real set
EX2 - EX1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
diffreal .: (EX2,EX1) is set
K324(EX1) is Relation-like Function-like complex-yielding set
EX1 (#) compreal is Relation-like Function-like V35() complex-yielding V174() V175() set
K38(1) * EX1 is Relation-like Function-like set
EX1 (#) (K38(1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
K295(EX2,K324(EX1)) is Relation-like Function-like set
|.(EX2 - EX1).| is V11() real ext-real non negative Element of REAL
sqr (EX2 - EX1) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(EX2 - EX1) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((EX2 - EX1),(EX2 - EX1)) is Relation-like Function-like set
multreal .: ((EX2 - EX1),(EX2 - EX1)) is set
K383((sqr (EX2 - EX1))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (EX2 - EX1)),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (EX2 - EX1))) is V11() real ext-real Element of REAL
abs p is V11() real ext-real Element of REAL
(abs p) * |.(EX2 - EX1).| is V11() real ext-real Element of REAL
p * (EX2 - EX1) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
(EX2 - EX1) (#) (p multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
|.(p * (EX2 - EX1)).| is V11() real ext-real non negative Element of REAL
sqr (p * (EX2 - EX1)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(p * (EX2 - EX1)) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((p * (EX2 - EX1)),(p * (EX2 - EX1))) is Relation-like Function-like set
multreal .: ((p * (EX2 - EX1)),(p * (EX2 - EX1))) is set
K383((sqr (p * (EX2 - EX1)))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (p * (EX2 - EX1))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (p * (EX2 - EX1)))) is V11() real ext-real Element of REAL
- EX1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
p * (- EX1) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
(- EX1) (#) (p multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
(p * EX2) + (p * (- EX1)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
addreal .: ((p * EX2),(p * (- EX1))) is set
|.((p * EX2) + (p * (- EX1))).| is V11() real ext-real non negative Element of REAL
sqr ((p * EX2) + (p * (- EX1))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
((p * EX2) + (p * (- EX1))) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (((p * EX2) + (p * (- EX1))),((p * EX2) + (p * (- EX1)))) is Relation-like Function-like set
multreal .: (((p * EX2) + (p * (- EX1))),((p * EX2) + (p * (- EX1)))) is set
K383((sqr ((p * EX2) + (p * (- EX1))))) is V11() real ext-real Element of REAL
K195(REAL,(sqr ((p * EX2) + (p * (- EX1)))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr ((p * EX2) + (p * (- EX1))))) is V11() real ext-real Element of REAL
- 1 is V11() real ext-real non positive Element of REAL
(- 1) * p is V11() real ext-real Element of REAL
((- 1) * p) * EX1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
((- 1) * p) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (((- 1) * p),(id REAL)) is set
EX1 (#) (((- 1) * p) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
(p * EX2) + (((- 1) * p) * EX1) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
addreal .: ((p * EX2),(((- 1) * p) * EX1)) is set
|.((p * EX2) + (((- 1) * p) * EX1)).| is V11() real ext-real non negative Element of REAL
sqr ((p * EX2) + (((- 1) * p) * EX1)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
((p * EX2) + (((- 1) * p) * EX1)) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (((p * EX2) + (((- 1) * p) * EX1)),((p * EX2) + (((- 1) * p) * EX1))) is Relation-like Function-like set
multreal .: (((p * EX2) + (((- 1) * p) * EX1)),((p * EX2) + (((- 1) * p) * EX1))) is set
K383((sqr ((p * EX2) + (((- 1) * p) * EX1)))) is V11() real ext-real Element of REAL
K195(REAL,(sqr ((p * EX2) + (((- 1) * p) * EX1))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr ((p * EX2) + (((- 1) * p) * EX1)))) is V11() real ext-real Element of REAL
C is ordinal natural V11() real ext-real non negative V35() cardinal set
Euclid C is non empty strict Reflexive discerning symmetric triangle Discerning MetrStruct
REAL C is non empty functional FinSequence-membered FinSequenceSet of REAL
C -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = C } is set
Pitag_dist C is non empty Relation-like [:(REAL C),(REAL C):] -defined REAL -valued Function-like total V30([:(REAL C),(REAL C):], REAL ) complex-yielding V174() V175() Element of bool [:[:(REAL C),(REAL C):],REAL:]
[:(REAL C),(REAL C):] is non empty set
[:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() set
MetrStruct(# (REAL C),(Pitag_dist C) #) is strict MetrStruct
the carrier of (Euclid C) is non empty set
0* C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
C |-> 0 is Relation-like empty-yielding NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of C -tuples_on REAL
Seg C is V35() C -element V183() V184() V185() V186() V187() V188() Element of bool NAT
(Seg C) --> 0 is Relation-like Seg C -defined INT -valued RAT -valued {0} -valued Function-like total V30( Seg C,{0}) V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() V176() Element of bool [:(Seg C),{0}:]
{0} is non empty trivial V35() V39() 1 -element V183() V184() V185() V186() V187() V188() set
[:(Seg C),{0}:] is INT -valued RAT -valued V35() complex-yielding V174() V175() V176() set
bool [:(Seg C),{0}:] is non empty V35() V39() set
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
bool the carrier of (TOP-REAL C) is non empty set
p is V11() real ext-real Element of REAL
WH is V11() real ext-real Element of REAL
p * WH is V11() real ext-real Element of REAL
p12 is Element of the carrier of (Euclid C)
Ball (p12,WH) is bounded Element of bool the carrier of (Euclid C)
bool the carrier of (Euclid C) is non empty set
Ball (p12,(p * WH)) is bounded Element of bool the carrier of (Euclid C)
C is Element of bool the carrier of (TOP-REAL C)
p * C is Element of bool the carrier of (TOP-REAL C)
{ (p * b1) where b1 is Element of the carrier of (TOP-REAL C) : b1 in C } is set
r is set
EX2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
p * EX2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
p * EX2 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
p multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
id REAL is non empty Relation-like REAL -defined REAL -valued Function-like one-to-one total V30( REAL , REAL ) complex-yielding V174() V175() increasing V179() Element of bool [:REAL,REAL:]
multreal [;] (p,(id REAL)) is set
EX2 (#) (p multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
{ b1 where b1 is Element of the carrier of (Euclid C) : not WH <= dist (p12,b1) } is set
EX1 is Element of the carrier of (Euclid C)
dist (p12,EX1) is V11() real ext-real Element of REAL
the distance of (Euclid C) is non empty Relation-like [: the carrier of (Euclid C), the carrier of (Euclid C):] -defined REAL -valued Function-like total V30([: the carrier of (Euclid C), the carrier of (Euclid C):], REAL ) complex-yielding V174() V175() Element of bool [:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:]
[: the carrier of (Euclid C), the carrier of (Euclid C):] is non empty set
[:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:] is non empty non trivial V35() set
the distance of (Euclid C) . (p12,EX1) is V11() real ext-real Element of REAL
[p12,EX1] is non empty set
{p12,EX1} is non empty V35() set
{p12} is non empty trivial V35() 1 -element set
{{p12,EX1},{p12}} is non empty V35() V39() set
the distance of (Euclid C) . [p12,EX1] is V11() real ext-real set
p * (dist (p12,EX1)) is V11() real ext-real Element of REAL
p1 is Element of the carrier of (Euclid C)
dist (p12,p1) is V11() real ext-real Element of REAL
the distance of (Euclid C) . (p12,p1) is V11() real ext-real Element of REAL
[p12,p1] is non empty set
{p12,p1} is non empty V35() set
{{p12,p1},{p12}} is non empty V35() V39() set
the distance of (Euclid C) . [p12,p1] is V11() real ext-real set
{ b1 where b1 is Element of the carrier of (Euclid C) : not p * WH <= dist (p12,b1) } is set
r is set
{ b1 where b1 is Element of the carrier of (Euclid C) : not p * WH <= dist (p12,b1) } is set
EX2 is Element of the carrier of (Euclid C)
dist (p12,EX2) is V11() real ext-real Element of REAL
the distance of (Euclid C) is non empty Relation-like [: the carrier of (Euclid C), the carrier of (Euclid C):] -defined REAL -valued Function-like total V30([: the carrier of (Euclid C), the carrier of (Euclid C):], REAL ) complex-yielding V174() V175() Element of bool [:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:]
[: the carrier of (Euclid C), the carrier of (Euclid C):] is non empty set
[:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:] is non empty non trivial V35() set
the distance of (Euclid C) . (p12,EX2) is V11() real ext-real Element of REAL
[p12,EX2] is non empty set
{p12,EX2} is non empty V35() set
{p12} is non empty trivial V35() 1 -element set
{{p12,EX2},{p12}} is non empty V35() V39() set
the distance of (Euclid C) . [p12,EX2] is V11() real ext-real set
EX1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
p " is V11() real ext-real Element of REAL
(p ") * EX1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
(p ") * EX1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(p ") multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
id REAL is non empty Relation-like REAL -defined REAL -valued Function-like one-to-one total V30( REAL , REAL ) complex-yielding V174() V175() increasing V179() Element of bool [:REAL,REAL:]
multreal [;] ((p "),(id REAL)) is set
EX1 (#) ((p ") multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
1 * EX1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
1 * EX1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
1 multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (1,(id REAL)) is set
EX1 (#) (1 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
(p ") * p is V11() real ext-real Element of REAL
((p ") * p) * EX1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
((p ") * p) * EX1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
((p ") * p) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (((p ") * p),(id REAL)) is set
EX1 (#) (((p ") * p) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
p * ((p ") * EX1) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
p * ((p ") * EX1) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
p multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (p,(id REAL)) is set
((p ") * EX1) (#) (p multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
EX is Element of the carrier of (Euclid C)
dist (p12,EX) is V11() real ext-real Element of REAL
the distance of (Euclid C) . (p12,EX) is V11() real ext-real Element of REAL
[p12,EX] is non empty set
{p12,EX} is non empty V35() set
{{p12,EX},{p12}} is non empty V35() V39() set
the distance of (Euclid C) . [p12,EX] is V11() real ext-real set
(p ") * (dist (p12,EX2)) is V11() real ext-real Element of REAL
1 * WH is V11() real ext-real Element of REAL
(p ") " is V11() real ext-real Element of REAL
(p ") * ((p ") ") is V11() real ext-real Element of REAL
((p ") * ((p ") ")) * WH is V11() real ext-real Element of REAL
(p ") * (p * WH) is V11() real ext-real Element of REAL
{ b1 where b1 is Element of the carrier of (Euclid C) : not WH <= dist (p12,b1) } is set
C is ordinal natural V11() real ext-real non negative V35() cardinal set
Euclid C is non empty strict Reflexive discerning symmetric triangle Discerning MetrStruct
REAL C is non empty functional FinSequence-membered FinSequenceSet of REAL
C -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = C } is set
Pitag_dist C is non empty Relation-like [:(REAL C),(REAL C):] -defined REAL -valued Function-like total V30([:(REAL C),(REAL C):], REAL ) complex-yielding V174() V175() Element of bool [:[:(REAL C),(REAL C):],REAL:]
[:(REAL C),(REAL C):] is non empty set
[:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() set
MetrStruct(# (REAL C),(Pitag_dist C) #) is strict MetrStruct
the carrier of (Euclid C) is non empty set
0* C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
C |-> 0 is Relation-like empty-yielding NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of C -tuples_on REAL
Seg C is V35() C -element V183() V184() V185() V186() V187() V188() Element of bool NAT
(Seg C) --> 0 is Relation-like Seg C -defined INT -valued RAT -valued {0} -valued Function-like total V30( Seg C,{0}) V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() V176() Element of bool [:(Seg C),{0}:]
{0} is non empty trivial V35() V39() 1 -element V183() V184() V185() V186() V187() V188() set
[:(Seg C),{0}:] is INT -valued RAT -valued V35() complex-yielding V174() V175() V176() set
bool [:(Seg C),{0}:] is non empty V35() V39() set
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
bool the carrier of (TOP-REAL C) is non empty set
WH is V11() real ext-real Element of REAL
p12 is V11() real ext-real Element of REAL
p is V11() real ext-real Element of REAL
C is Element of the carrier of (Euclid C)
Ball (C,p) is bounded Element of bool the carrier of (Euclid C)
bool the carrier of (Euclid C) is non empty set
r is Element of bool the carrier of (TOP-REAL C)
WH * r is Element of bool the carrier of (TOP-REAL C)
{ (WH * b1) where b1 is Element of the carrier of (TOP-REAL C) : b1 in r } is set
p12 * r is Element of bool the carrier of (TOP-REAL C)
{ (p12 * b1) where b1 is Element of the carrier of (TOP-REAL C) : b1 in r } is set
EX2 is set
EX1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
WH * EX1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
WH * EX1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
WH multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
id REAL is non empty Relation-like REAL -defined REAL -valued Function-like one-to-one total V30( REAL , REAL ) complex-yielding V174() V175() increasing V179() Element of bool [:REAL,REAL:]
multreal [;] (WH,(id REAL)) is set
EX1 (#) (WH multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
{ b1 where b1 is Element of the carrier of (Euclid C) : not p <= dist (C,b1) } is set
p1 is Element of the carrier of (Euclid C)
dist (C,p1) is V11() real ext-real Element of REAL
the distance of (Euclid C) is non empty Relation-like [: the carrier of (Euclid C), the carrier of (Euclid C):] -defined REAL -valued Function-like total V30([: the carrier of (Euclid C), the carrier of (Euclid C):], REAL ) complex-yielding V174() V175() Element of bool [:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:]
[: the carrier of (Euclid C), the carrier of (Euclid C):] is non empty set
[:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:] is non empty non trivial V35() set
the distance of (Euclid C) . (C,p1) is V11() real ext-real Element of REAL
[C,p1] is non empty set
{C,p1} is non empty V35() set
{C} is non empty trivial V35() 1 -element set
{{C,p1},{C}} is non empty V35() V39() set
the distance of (Euclid C) . [C,p1] is V11() real ext-real set
WH / p12 is V11() real ext-real Element of REAL
(WH / p12) * EX1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
(WH / p12) * EX1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(WH / p12) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] ((WH / p12),(id REAL)) is set
EX1 (#) ((WH / p12) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
p12 * (WH / p12) is V11() real ext-real Element of REAL
(p12 * (WH / p12)) * EX1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
(p12 * (WH / p12)) * EX1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(p12 * (WH / p12)) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] ((p12 * (WH / p12)),(id REAL)) is set
EX1 (#) ((p12 * (WH / p12)) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
p12 * ((WH / p12) * EX1) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
p12 * ((WH / p12) * EX1) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
p12 multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (p12,(id REAL)) is set
((WH / p12) * EX1) (#) (p12 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
t2 is Element of the carrier of (Euclid C)
dist (C,t2) is V11() real ext-real Element of REAL
the distance of (Euclid C) . (C,t2) is V11() real ext-real Element of REAL
[C,t2] is non empty set
{C,t2} is non empty V35() set
{{C,t2},{C}} is non empty V35() V39() set
the distance of (Euclid C) . [C,t2] is V11() real ext-real set
(WH / p12) * (dist (C,p1)) is V11() real ext-real Element of REAL
C is ordinal natural V11() real ext-real non negative V35() cardinal set
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
bool the carrier of (TOP-REAL C) is non empty set
Euclid C is non empty strict Reflexive discerning symmetric triangle Discerning MetrStruct
REAL C is non empty functional FinSequence-membered FinSequenceSet of REAL
C -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = C } is set
Pitag_dist C is non empty Relation-like [:(REAL C),(REAL C):] -defined REAL -valued Function-like total V30([:(REAL C),(REAL C):], REAL ) complex-yielding V174() V175() Element of bool [:[:(REAL C),(REAL C):],REAL:]
[:(REAL C),(REAL C):] is non empty set
[:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() set
MetrStruct(# (REAL C),(Pitag_dist C) #) is strict MetrStruct
the carrier of (Euclid C) is non empty set
bool the carrier of (Euclid C) is non empty set
p is Element of bool the carrier of (TOP-REAL C)
0* C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
C |-> 0 is Relation-like empty-yielding NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of C -tuples_on REAL
Seg C is V35() C -element V183() V184() V185() V186() V187() V188() Element of bool NAT
(Seg C) --> 0 is Relation-like Seg C -defined INT -valued RAT -valued {0} -valued Function-like total V30( Seg C,{0}) V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() V176() Element of bool [:(Seg C),{0}:]
{0} is non empty trivial V35() V39() 1 -element V183() V184() V185() V186() V187() V188() set
[:(Seg C),{0}:] is INT -valued RAT -valued V35() complex-yielding V174() V175() V176() set
bool [:(Seg C),{0}:] is non empty V35() V39() set
WH is Element of the carrier of (Euclid C)
0. (TOP-REAL C) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like V62( TOP-REAL C) complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the ZeroF of (TOP-REAL C) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
Ball (WH,1) is bounded Element of bool the carrier of (Euclid C)
C is a_neighborhood of 0. (TOP-REAL C)
r is V11() real ext-real Element of REAL
r + 1 is V11() real ext-real Element of REAL
(r + 1) * C is Element of bool the carrier of (TOP-REAL C)
{ ((r + 1) * b1) where b1 is Element of the carrier of (TOP-REAL C) : b1 in C } is set
(r + 1) * 1 is V11() real ext-real Element of REAL
Ball (WH,((r + 1) * 1)) is bounded Element of bool the carrier of (Euclid C)
p12 is Element of bool the carrier of (Euclid C)
Ball (WH,(r + 1)) is bounded Element of bool the carrier of (Euclid C)
p12 is Element of bool the carrier of (Euclid C)
WH is Element of the carrier of (Euclid C)
C is V11() real ext-real Element of REAL
Ball (WH,C) is bounded Element of bool the carrier of (Euclid C)
0. (TOP-REAL C) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like V62( TOP-REAL C) complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the ZeroF of (TOP-REAL C) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
r is a_neighborhood of 0. (TOP-REAL C)
Int r is open Element of bool the carrier of (TOP-REAL C)
EX2 is V11() real ext-real set
Ball (WH,EX2) is bounded Element of bool the carrier of (Euclid C)
EX1 is V11() real ext-real Element of REAL
C / EX1 is V11() real ext-real Element of REAL
p1 is V11() real ext-real Element of REAL
EX is V11() real ext-real Element of REAL
EX * r is Element of bool the carrier of (TOP-REAL C)
{ (EX * b1) where b1 is Element of the carrier of (TOP-REAL C) : b1 in r } is set
Ball (WH,EX1) is bounded Element of bool the carrier of (Euclid C)
p1 * EX1 is V11() real ext-real Element of REAL
t2 is Element of bool the carrier of (TOP-REAL C)
p1 * t2 is Element of bool the carrier of (TOP-REAL C)
{ (p1 * b1) where b1 is Element of the carrier of (TOP-REAL C) : b1 in t2 } is set
EX * t2 is Element of bool the carrier of (TOP-REAL C)
{ (EX * b1) where b1 is Element of the carrier of (TOP-REAL C) : b1 in t2 } is set
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
bool the carrier of (TOP-REAL C) is non empty set
WH is Element of bool the carrier of (TOP-REAL C)
p is Element of bool the carrier of (TOP-REAL C)
C is ordinal natural V11() real ext-real non negative V35() cardinal set
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
bool the carrier of (TOP-REAL C) is non empty set
C is non empty MetrStruct
the carrier of C is non empty set
bool the carrier of C is non empty set
{} C is empty trivial proper ordinal natural V11() real ext-real non positive non negative Function-like functional V35() V39() cardinal {} -element FinSequence-membered bounded V183() V184() V185() V186() V187() V188() V189() Element of bool the carrier of C
p is Element of the carrier of C
WH is Element of the carrier of C
dist (p,WH) is V11() real ext-real Element of REAL
the distance of C is non empty Relation-like [: the carrier of C, the carrier of C:] -defined REAL -valued Function-like total V30([: the carrier of C, the carrier of C:], REAL ) complex-yielding V174() V175() Element of bool [:[: the carrier of C, the carrier of C:],REAL:]
[: the carrier of C, the carrier of C:] is non empty set
[:[: the carrier of C, the carrier of C:],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[: the carrier of C, the carrier of C:],REAL:] is non empty non trivial V35() set
the distance of C . (p,WH) is V11() real ext-real Element of REAL
[p,WH] is non empty set
{p,WH} is non empty V35() set
{p} is non empty trivial V35() 1 -element set
{{p,WH},{p}} is non empty V35() V39() set
the distance of C . [p,WH] is V11() real ext-real set
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
bool the carrier of (TOP-REAL C) is non empty set
Euclid C is non empty strict Reflexive discerning symmetric triangle Discerning MetrStruct
REAL C is non empty functional FinSequence-membered FinSequenceSet of REAL
C -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = C } is set
Pitag_dist C is non empty Relation-like [:(REAL C),(REAL C):] -defined REAL -valued Function-like total V30([:(REAL C),(REAL C):], REAL ) complex-yielding V174() V175() Element of bool [:[:(REAL C),(REAL C):],REAL:]
[:(REAL C),(REAL C):] is non empty set
[:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() set
MetrStruct(# (REAL C),(Pitag_dist C) #) is strict MetrStruct
the carrier of (Euclid C) is non empty set
bool the carrier of (Euclid C) is non empty set
p is Element of bool the carrier of (TOP-REAL C)
p ` is Element of bool the carrier of (TOP-REAL C)
the carrier of (TOP-REAL C) \ p is set
(TOP-REAL C) | (p `) is strict TopSpace-like SubSpace of TOP-REAL C
the carrier of ((TOP-REAL C) | (p `)) is set
bool the carrier of ((TOP-REAL C) | (p `)) is non empty set
WH is Element of bool the carrier of (TOP-REAL C)
p12 is Element of bool the carrier of ((TOP-REAL C) | (p `))
p12 is Element of bool the carrier of ((TOP-REAL C) | (p `))
p12 is Element of bool the carrier of ((TOP-REAL C) | (p `))
C is ordinal natural V11() real ext-real non negative V35() cardinal set
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
bool the carrier of (TOP-REAL C) is non empty set
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
bool the carrier of (TOP-REAL C) is non empty set
Euclid C is non empty strict Reflexive discerning symmetric triangle Discerning MetrStruct
REAL C is non empty functional FinSequence-membered FinSequenceSet of REAL
C -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = C } is set
Pitag_dist C is non empty Relation-like [:(REAL C),(REAL C):] -defined REAL -valued Function-like total V30([:(REAL C),(REAL C):], REAL ) complex-yielding V174() V175() Element of bool [:[:(REAL C),(REAL C):],REAL:]
[:(REAL C),(REAL C):] is non empty set
[:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() set
MetrStruct(# (REAL C),(Pitag_dist C) #) is strict MetrStruct
the carrier of (Euclid C) is non empty set
bool the carrier of (Euclid C) is non empty set
p is Element of bool the carrier of (TOP-REAL C)
p ` is Element of bool the carrier of (TOP-REAL C)
the carrier of (TOP-REAL C) \ p is set
(TOP-REAL C) | (p `) is strict TopSpace-like SubSpace of TOP-REAL C
the carrier of ((TOP-REAL C) | (p `)) is set
bool the carrier of ((TOP-REAL C) | (p `)) is non empty set
WH is Element of bool the carrier of (TOP-REAL C)
p12 is Element of bool the carrier of ((TOP-REAL C) | (p `))
C is Element of bool the carrier of ((TOP-REAL C) | (p `))
C is Element of bool the carrier of ((TOP-REAL C) | (p `))
p12 is Element of bool the carrier of (Euclid C)
r is Element of bool the carrier of (Euclid C)
p12 is Element of bool the carrier of ((TOP-REAL C) | (p `))
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
bool the carrier of (TOP-REAL C) is non empty set
p is Element of bool the carrier of (TOP-REAL C)
WH is Element of bool the carrier of (TOP-REAL C)
p ` is Element of bool the carrier of (TOP-REAL C)
the carrier of (TOP-REAL C) \ p is set
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
bool the carrier of (TOP-REAL C) is non empty set
p is Element of bool the carrier of (TOP-REAL C)
WH is Element of bool the carrier of (TOP-REAL C)
p ` is Element of bool the carrier of (TOP-REAL C)
the carrier of (TOP-REAL C) \ p is set
C is ordinal natural V11() real ext-real non negative V35() cardinal set
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
bool the carrier of (TOP-REAL C) is non empty set
p is Element of bool the carrier of (TOP-REAL C)
{ b1 where b1 is Element of bool the carrier of (TOP-REAL C) : (C,p,b1) } is set
union { b1 where b1 is Element of bool the carrier of (TOP-REAL C) : (C,p,b1) } is set
WH is set
p12 is set
C is Element of bool the carrier of (TOP-REAL C)
C is ordinal natural V11() real ext-real non negative V35() cardinal set
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
bool the carrier of (TOP-REAL C) is non empty set
p is Element of bool the carrier of (TOP-REAL C)
{ b1 where b1 is Element of bool the carrier of (TOP-REAL C) : (C,p,b1) } is set
union { b1 where b1 is Element of bool the carrier of (TOP-REAL C) : (C,p,b1) } is set
WH is set
p12 is set
C is Element of bool the carrier of (TOP-REAL C)
C is ordinal natural V11() real ext-real non negative V35() cardinal set
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
[#] (TOP-REAL C) is non empty non proper open closed dense non boundary Element of bool the carrier of (TOP-REAL C)
the carrier of (TOP-REAL C) is non empty set
bool the carrier of (TOP-REAL C) is non empty set
p is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
WH is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
p12 is V11() real ext-real Element of REAL
p12 * p is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
p12 * p is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
p12 multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
id REAL is non empty Relation-like REAL -defined REAL -valued Function-like one-to-one total V30( REAL , REAL ) complex-yielding V174() V175() increasing V179() Element of bool [:REAL,REAL:]
multreal [;] (p12,(id REAL)) is set
p (#) (p12 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
1 - p12 is V11() real ext-real Element of REAL
(1 - p12) * WH is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
(1 - p12) * WH is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(1 - p12) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] ((1 - p12),(id REAL)) is set
WH (#) ((1 - p12) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
K258((TOP-REAL C),(p12 * p),((1 - p12) * WH)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) is non empty Relation-like [: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):] -defined the carrier of (TOP-REAL C) -valued Function-like total V30([: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C)) Element of bool [:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):]
[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):] is non empty set
[:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):] is non empty set
bool [:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):] is non empty set
the U7 of (TOP-REAL C) . ((p12 * p),((1 - p12) * WH)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[(p12 * p),((1 - p12) * WH)] is non empty set
{(p12 * p),((1 - p12) * WH)} is non empty functional V35() V39() set
{(p12 * p)} is non empty trivial functional V35() V39() 1 -element set
{{(p12 * p),((1 - p12) * WH)},{(p12 * p)}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [(p12 * p),((1 - p12) * WH)] is set
(p12 * p) + ((1 - p12) * WH) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
addreal .: ((p12 * p),((1 - p12) * WH)) is set
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
[#] (TOP-REAL C) is 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 C)
the carrier of (TOP-REAL C) is non empty set
bool the carrier of (TOP-REAL C) is non empty set
WH is Element of bool the carrier of (TOP-REAL C)
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
bool the carrier of (TOP-REAL C) is non empty set
p is Element of bool the carrier of (TOP-REAL C)
(C,p) is Element of bool the carrier of (TOP-REAL C)
{ b1 where b1 is Element of bool the carrier of (TOP-REAL C) : (C,p,b1) } is set
union { b1 where b1 is Element of bool the carrier of (TOP-REAL C) : (C,p,b1) } is set
p ` is Element of bool the carrier of (TOP-REAL C)
the carrier of (TOP-REAL C) \ p is set
(TOP-REAL C) | (p `) is strict TopSpace-like SubSpace of TOP-REAL C
the carrier of ((TOP-REAL C) | (p `)) is set
bool the carrier of ((TOP-REAL C) | (p `)) is non empty Element of bool (bool the carrier of ((TOP-REAL C) | (p `)))
bool the carrier of ((TOP-REAL C) | (p `)) is non empty set
bool (bool the carrier of ((TOP-REAL C) | (p `))) is non empty set
WH is set
p12 is Element of bool the carrier of (TOP-REAL C)
Euclid C is non empty strict Reflexive discerning symmetric triangle Discerning MetrStruct
REAL C is non empty functional FinSequence-membered FinSequenceSet of REAL
C -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = C } is set
Pitag_dist C is non empty Relation-like [:(REAL C),(REAL C):] -defined REAL -valued Function-like total V30([:(REAL C),(REAL C):], REAL ) complex-yielding V174() V175() Element of bool [:[:(REAL C),(REAL C):],REAL:]
[:(REAL C),(REAL C):] is non empty set
[:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() set
MetrStruct(# (REAL C),(Pitag_dist C) #) is strict MetrStruct
the carrier of (Euclid C) is non empty set
bool the carrier of (Euclid C) is non empty set
C is Element of bool the carrier of ((TOP-REAL C) | (p `))
WH is Element of bool (bool the carrier of ((TOP-REAL C) | (p `)))
p12 is Element of bool (bool the carrier of ((TOP-REAL C) | (p `)))
C is Element of bool the carrier of ((TOP-REAL C) | (p `))
r is Element of bool the carrier of (TOP-REAL C)
Euclid C is non empty strict Reflexive discerning symmetric triangle Discerning MetrStruct
REAL C is non empty functional FinSequence-membered FinSequenceSet of REAL
C -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = C } is set
Pitag_dist C is non empty Relation-like [:(REAL C),(REAL C):] -defined REAL -valued Function-like total V30([:(REAL C),(REAL C):], REAL ) complex-yielding V174() V175() Element of bool [:[:(REAL C),(REAL C):],REAL:]
[:(REAL C),(REAL C):] is non empty set
[:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() set
MetrStruct(# (REAL C),(Pitag_dist C) #) is strict MetrStruct
the carrier of (Euclid C) is non empty set
bool the carrier of (Euclid C) is non empty set
EX2 is Element of bool the carrier of ((TOP-REAL C) | (p `))
union p12 is Element of bool the carrier of ((TOP-REAL C) | (p `))
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
bool the carrier of (TOP-REAL C) is non empty set
p is Element of bool the carrier of (TOP-REAL C)
(C,p) is Element of bool the carrier of (TOP-REAL C)
{ b1 where b1 is Element of bool the carrier of (TOP-REAL C) : (C,p,b1) } is set
union { b1 where b1 is Element of bool the carrier of (TOP-REAL C) : (C,p,b1) } is set
p ` is Element of bool the carrier of (TOP-REAL C)
the carrier of (TOP-REAL C) \ p is set
(TOP-REAL C) | (p `) is strict TopSpace-like SubSpace of TOP-REAL C
the carrier of ((TOP-REAL C) | (p `)) is set
bool the carrier of ((TOP-REAL C) | (p `)) is non empty Element of bool (bool the carrier of ((TOP-REAL C) | (p `)))
bool the carrier of ((TOP-REAL C) | (p `)) is non empty set
bool (bool the carrier of ((TOP-REAL C) | (p `))) is non empty set
WH is set
p12 is Element of bool the carrier of (TOP-REAL C)
Euclid C is non empty strict Reflexive discerning symmetric triangle Discerning MetrStruct
REAL C is non empty functional FinSequence-membered FinSequenceSet of REAL
C -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = C } is set
Pitag_dist C is non empty Relation-like [:(REAL C),(REAL C):] -defined REAL -valued Function-like total V30([:(REAL C),(REAL C):], REAL ) complex-yielding V174() V175() Element of bool [:[:(REAL C),(REAL C):],REAL:]
[:(REAL C),(REAL C):] is non empty set
[:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() set
MetrStruct(# (REAL C),(Pitag_dist C) #) is strict MetrStruct
the carrier of (Euclid C) is non empty set
bool the carrier of (Euclid C) is non empty set
C is Element of bool the carrier of ((TOP-REAL C) | (p `))
WH is Element of bool (bool the carrier of ((TOP-REAL C) | (p `)))
p12 is Element of bool (bool the carrier of ((TOP-REAL C) | (p `)))
C is Element of bool the carrier of ((TOP-REAL C) | (p `))
r is Element of bool the carrier of (TOP-REAL C)
Euclid C is non empty strict Reflexive discerning symmetric triangle Discerning MetrStruct
REAL C is non empty functional FinSequence-membered FinSequenceSet of REAL
C -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = C } is set
Pitag_dist C is non empty Relation-like [:(REAL C),(REAL C):] -defined REAL -valued Function-like total V30([:(REAL C),(REAL C):], REAL ) complex-yielding V174() V175() Element of bool [:[:(REAL C),(REAL C):],REAL:]
[:(REAL C),(REAL C):] is non empty set
[:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() set
MetrStruct(# (REAL C),(Pitag_dist C) #) is strict MetrStruct
the carrier of (Euclid C) is non empty set
bool the carrier of (Euclid C) is non empty set
EX2 is Element of bool the carrier of ((TOP-REAL C) | (p `))
union p12 is Element of bool the carrier of ((TOP-REAL C) | (p `))
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
bool the carrier of (TOP-REAL C) is non empty set
p is Element of bool the carrier of (TOP-REAL C)
(C,p) is Element of bool the carrier of (TOP-REAL C)
{ b1 where b1 is Element of bool the carrier of (TOP-REAL C) : (C,p,b1) } is set
union { b1 where b1 is Element of bool the carrier of (TOP-REAL C) : (C,p,b1) } is set
WH is Element of bool the carrier of (TOP-REAL C)
p12 is set
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
bool the carrier of (TOP-REAL C) is non empty set
p is Element of bool the carrier of (TOP-REAL C)
(C,p) is Element of bool the carrier of (TOP-REAL C)
{ b1 where b1 is Element of bool the carrier of (TOP-REAL C) : (C,p,b1) } is set
union { b1 where b1 is Element of bool the carrier of (TOP-REAL C) : (C,p,b1) } is set
WH is Element of bool the carrier of (TOP-REAL C)
p12 is set
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
bool the carrier of (TOP-REAL C) is non empty set
p is Element of bool the carrier of (TOP-REAL C)
(C,p) is Element of bool the carrier of (TOP-REAL C)
{ b1 where b1 is Element of bool the carrier of (TOP-REAL C) : (C,p,b1) } is set
union { b1 where b1 is Element of bool the carrier of (TOP-REAL C) : (C,p,b1) } is set
(C,p) is Element of bool the carrier of (TOP-REAL C)
{ b1 where b1 is Element of bool the carrier of (TOP-REAL C) : (C,p,b1) } is set
union { b1 where b1 is Element of bool the carrier of (TOP-REAL C) : (C,p,b1) } is set
(C,p) /\ (C,p) is Element of bool the carrier of (TOP-REAL C)
the Element of (C,p) /\ (C,p) is Element of (C,p) /\ (C,p)
p12 is set
C is set
r is Element of bool the carrier of (TOP-REAL C)
EX2 is Element of bool the carrier of (TOP-REAL C)
p ` is Element of bool the carrier of (TOP-REAL C)
the carrier of (TOP-REAL C) \ p is set
(TOP-REAL C) | (p `) is strict TopSpace-like SubSpace of TOP-REAL C
the carrier of ((TOP-REAL C) | (p `)) is set
bool the carrier of ((TOP-REAL C) | (p `)) is non empty set
Euclid C is non empty strict Reflexive discerning symmetric triangle Discerning MetrStruct
REAL C is non empty functional FinSequence-membered FinSequenceSet of REAL
C -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = C } is set
Pitag_dist C is non empty Relation-like [:(REAL C),(REAL C):] -defined REAL -valued Function-like total V30([:(REAL C),(REAL C):], REAL ) complex-yielding V174() V175() Element of bool [:[:(REAL C),(REAL C):],REAL:]
[:(REAL C),(REAL C):] is non empty set
[:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() set
MetrStruct(# (REAL C),(Pitag_dist C) #) is strict MetrStruct
the carrier of (Euclid C) is non empty set
bool the carrier of (Euclid C) is non empty set
EX1 is Element of bool the carrier of ((TOP-REAL C) | (p `))
p1 is Element of bool the carrier of ((TOP-REAL C) | (p `))
EX1 /\ p1 is Element of bool the carrier of ((TOP-REAL C) | (p `))
{} ((TOP-REAL C) | (p `)) is empty trivial ordinal natural V11() real ext-real non positive non negative Function-like functional V35() V39() cardinal {} -element FinSequence-membered open closed boundary nowhere_dense V183() V184() V185() V186() V187() V188() V189() Element of bool the carrier of ((TOP-REAL C) | (p `))
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
bool the carrier of (TOP-REAL C) is non empty set
p is Element of bool the carrier of (TOP-REAL C)
(C,p) is Element of bool the carrier of (TOP-REAL C)
{ b1 where b1 is Element of bool the carrier of (TOP-REAL C) : (C,p,b1) } is set
union { b1 where b1 is Element of bool the carrier of (TOP-REAL C) : (C,p,b1) } is set
p ` is Element of bool the carrier of (TOP-REAL C)
the carrier of (TOP-REAL C) \ p is set
(TOP-REAL C) | (p `) is strict TopSpace-like SubSpace of TOP-REAL C
the carrier of ((TOP-REAL C) | (p `)) is set
bool the carrier of ((TOP-REAL C) | (p `)) is non empty set
WH is Element of bool the carrier of ((TOP-REAL C) | (p `))
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
bool the carrier of (TOP-REAL C) is non empty set
p is Element of bool the carrier of (TOP-REAL C)
(C,p) is Element of bool the carrier of (TOP-REAL C)
{ b1 where b1 is Element of bool the carrier of (TOP-REAL C) : (C,p,b1) } is set
union { b1 where b1 is Element of bool the carrier of (TOP-REAL C) : (C,p,b1) } is set
p ` is Element of bool the carrier of (TOP-REAL C)
the carrier of (TOP-REAL C) \ p is set
(TOP-REAL C) | (p `) is strict TopSpace-like SubSpace of TOP-REAL C
the carrier of ((TOP-REAL C) | (p `)) is set
bool the carrier of ((TOP-REAL C) | (p `)) is non empty set
WH is Element of bool the carrier of ((TOP-REAL C) | (p `))
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
bool the carrier of (TOP-REAL C) is non empty set
p is Element of bool the carrier of (TOP-REAL C)
(C,p) is Element of bool the carrier of (TOP-REAL C)
{ b1 where b1 is Element of bool the carrier of (TOP-REAL C) : (C,p,b1) } is set
union { b1 where b1 is Element of bool the carrier of (TOP-REAL C) : (C,p,b1) } is set
(C,p) is Element of bool the carrier of (TOP-REAL C)
{ b1 where b1 is Element of bool the carrier of (TOP-REAL C) : (C,p,b1) } is set
union { b1 where b1 is Element of bool the carrier of (TOP-REAL C) : (C,p,b1) } is set
(C,p) \/ (C,p) is Element of bool the carrier of (TOP-REAL C)
p ` is Element of bool the carrier of (TOP-REAL C)
the carrier of (TOP-REAL C) \ p is set
WH is set
(TOP-REAL C) | (p `) is strict TopSpace-like SubSpace of TOP-REAL C
the carrier of ((TOP-REAL C) | (p `)) is set
p12 is Element of p `
r is Element of the carrier of ((TOP-REAL C) | (p `))
Component_of r is Element of bool the carrier of ((TOP-REAL C) | (p `))
bool the carrier of ((TOP-REAL C) | (p `)) is non empty set
[#] ((TOP-REAL C) | (p `)) is non proper open closed dense Element of bool the carrier of ((TOP-REAL C) | (p `))
bool ([#] ((TOP-REAL C) | (p `))) is non empty set
bool (p `) is non empty set
C is non empty Element of bool the carrier of (TOP-REAL C)
(TOP-REAL C) | C is non empty strict TopSpace-like SubSpace of TOP-REAL C
EX2 is Element of bool the carrier of (TOP-REAL C)
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
bool the carrier of (TOP-REAL C) is non empty set
REAL C is non empty functional FinSequence-membered FinSequenceSet of REAL
C -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = C } is set
p is Element of bool the carrier of (TOP-REAL C)
WH is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
p12 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
LSeg (WH,p12) is non empty closed connected compact convex Element of bool the carrier of (TOP-REAL C)
{ (((1 - b1) * WH) + (b1 * p12)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
Euclid C is non empty strict Reflexive discerning symmetric triangle Discerning MetrStruct
REAL C is non empty functional FinSequence-membered FinSequenceSet of REAL
C -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = C } is set
Pitag_dist C is non empty Relation-like [:(REAL C),(REAL C):] -defined REAL -valued Function-like total V30([:(REAL C),(REAL C):], REAL ) complex-yielding V174() V175() Element of bool [:[:(REAL C),(REAL C):],REAL:]
[:(REAL C),(REAL C):] is non empty set
[:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() set
MetrStruct(# (REAL C),(Pitag_dist C) #) is strict MetrStruct
the carrier of (Euclid C) is non empty set
bool the carrier of (Euclid C) is non empty set
p is Element of bool the carrier of (Euclid C)
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
0. (TOP-REAL C) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like V62( TOP-REAL C) complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the carrier of (TOP-REAL C) is non empty set
the ZeroF of (TOP-REAL C) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
p12 is V11() real ext-real Element of REAL
1.REAL C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
1* C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
C |-> 1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of C -tuples_on REAL
Seg C is V35() C -element V183() V184() V185() V186() V187() V188() Element of bool NAT
(Seg C) --> 1 is Relation-like Seg C -defined INT -valued RAT -valued {1} -valued Function-like total V30( Seg C,{1}) V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() V176() Element of bool [:(Seg C),{1}:]
{1} is non empty trivial V35() V39() 1 -element V183() V184() V185() V186() V187() V188() set
[:(Seg C),{1}:] is INT -valued RAT -valued V35() complex-yielding V174() V175() V176() set
bool [:(Seg C),{1}:] is non empty V35() V39() set
p12 + 1 is V11() real ext-real Element of REAL
(p12 + 1) * (1.REAL C) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
(p12 + 1) * (1.REAL C) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(p12 + 1) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
id REAL is non empty Relation-like REAL -defined REAL -valued Function-like one-to-one total V30( REAL , REAL ) complex-yielding V174() V175() increasing V179() Element of bool [:REAL,REAL:]
multreal [;] ((p12 + 1),(id REAL)) is set
(1.REAL C) (#) ((p12 + 1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
C is Element of the carrier of (Euclid C)
WH is Element of the carrier of (Euclid C)
dist (C,WH) is V11() real ext-real Element of REAL
the distance of (Euclid C) is non empty Relation-like [: the carrier of (Euclid C), the carrier of (Euclid C):] -defined REAL -valued Function-like total V30([: the carrier of (Euclid C), the carrier of (Euclid C):], REAL ) complex-yielding V174() V175() Element of bool [:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:]
[: the carrier of (Euclid C), the carrier of (Euclid C):] is non empty set
[:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:] is non empty non trivial V35() set
the distance of (Euclid C) . (C,WH) is V11() real ext-real Element of REAL
[C,WH] is non empty set
{C,WH} is non empty V35() set
{C} is non empty trivial V35() 1 -element set
{{C,WH},{C}} is non empty V35() V39() set
the distance of (Euclid C) . [C,WH] is V11() real ext-real set
((p12 + 1) * (1.REAL C)) - (0. (TOP-REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
- (0. (TOP-REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
- (0. (TOP-REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
compreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
(0. (TOP-REAL C)) (#) compreal is Relation-like Function-like V35() complex-yielding V174() V175() set
K38(1) is V11() real ext-real non positive set
K38(1) * (0. (TOP-REAL C)) is Relation-like Function-like set
K38(1) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (K38(1),(id REAL)) is set
(0. (TOP-REAL C)) (#) (K38(1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
K258((TOP-REAL C),((p12 + 1) * (1.REAL C)),(- (0. (TOP-REAL C)))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) is non empty Relation-like [: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):] -defined the carrier of (TOP-REAL C) -valued Function-like total V30([: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C)) Element of bool [:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):]
[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):] is non empty set
[:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):] is non empty set
bool [:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):] is non empty set
the U7 of (TOP-REAL C) . (((p12 + 1) * (1.REAL C)),(- (0. (TOP-REAL C)))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[((p12 + 1) * (1.REAL C)),(- (0. (TOP-REAL C)))] is non empty set
{((p12 + 1) * (1.REAL C)),(- (0. (TOP-REAL C)))} is non empty functional V35() V39() set
{((p12 + 1) * (1.REAL C))} is non empty trivial functional V35() V39() 1 -element set
{{((p12 + 1) * (1.REAL C)),(- (0. (TOP-REAL C)))},{((p12 + 1) * (1.REAL C))}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [((p12 + 1) * (1.REAL C)),(- (0. (TOP-REAL C)))] is set
((p12 + 1) * (1.REAL C)) + (- (0. (TOP-REAL C))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
addreal .: (((p12 + 1) * (1.REAL C)),(- (0. (TOP-REAL C)))) is set
((p12 + 1) * (1.REAL C)) - (0. (TOP-REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
diffreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K174(REAL,addreal,(id REAL),compreal) is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
diffreal .: (((p12 + 1) * (1.REAL C)),(0. (TOP-REAL C))) is set
K324((0. (TOP-REAL C))) is Relation-like Function-like complex-yielding set
K295(((p12 + 1) * (1.REAL C)),K324((0. (TOP-REAL C)))) is Relation-like Function-like set
|.(((p12 + 1) * (1.REAL C)) - (0. (TOP-REAL C))).| is V11() real ext-real non negative Element of REAL
sqr (((p12 + 1) * (1.REAL C)) - (0. (TOP-REAL C))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
sqrreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
(((p12 + 1) * (1.REAL C)) - (0. (TOP-REAL C))) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((((p12 + 1) * (1.REAL C)) - (0. (TOP-REAL C))),(((p12 + 1) * (1.REAL C)) - (0. (TOP-REAL C)))) is Relation-like Function-like set
multreal .: ((((p12 + 1) * (1.REAL C)) - (0. (TOP-REAL C))),(((p12 + 1) * (1.REAL C)) - (0. (TOP-REAL C)))) is set
K383((sqr (((p12 + 1) * (1.REAL C)) - (0. (TOP-REAL C))))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (((p12 + 1) * (1.REAL C)) - (0. (TOP-REAL C)))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (((p12 + 1) * (1.REAL C)) - (0. (TOP-REAL C))))) is V11() real ext-real Element of REAL
|.((p12 + 1) * (1.REAL C)).| is V11() real ext-real non negative Element of REAL
sqr ((p12 + 1) * (1.REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
((p12 + 1) * (1.REAL C)) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (((p12 + 1) * (1.REAL C)),((p12 + 1) * (1.REAL C))) is Relation-like Function-like set
multreal .: (((p12 + 1) * (1.REAL C)),((p12 + 1) * (1.REAL C))) is set
K383((sqr ((p12 + 1) * (1.REAL C)))) is V11() real ext-real Element of REAL
K195(REAL,(sqr ((p12 + 1) * (1.REAL C))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr ((p12 + 1) * (1.REAL C)))) is V11() real ext-real Element of REAL
abs (p12 + 1) is V11() real ext-real Element of REAL
|.(1.REAL C).| is V11() real ext-real non negative Element of REAL
sqr (1.REAL C) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(1.REAL C) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((1.REAL C),(1.REAL C)) is Relation-like Function-like set
multreal .: ((1.REAL C),(1.REAL C)) is set
K383((sqr (1.REAL C))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (1.REAL C)),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (1.REAL C))) is V11() real ext-real Element of REAL
(abs (p12 + 1)) * |.(1.REAL C).| is V11() real ext-real Element of REAL
sqrt C is V11() real ext-real Element of REAL
(abs (p12 + 1)) * (sqrt C) is V11() real ext-real Element of REAL
(p12 + 1) * (sqrt C) is V11() real ext-real Element of REAL
(p12 + 1) * 1 is V11() real ext-real Element of REAL
(p12 + 1) - p12 is V11() real ext-real Element of REAL
p12 - p12 is V11() real ext-real Element of REAL
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
bool the carrier of (TOP-REAL C) is non empty set
p is Element of bool the carrier of (TOP-REAL C)
Euclid C is non empty strict Reflexive discerning symmetric triangle Discerning MetrStruct
REAL C is non empty functional FinSequence-membered FinSequenceSet of REAL
C -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = C } is set
Pitag_dist C is non empty Relation-like [:(REAL C),(REAL C):] -defined REAL -valued Function-like total V30([:(REAL C),(REAL C):], REAL ) complex-yielding V174() V175() Element of bool [:[:(REAL C),(REAL C):],REAL:]
[:(REAL C),(REAL C):] is non empty set
[:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() set
MetrStruct(# (REAL C),(Pitag_dist C) #) is strict MetrStruct
the carrier of (Euclid C) is non empty set
bool the carrier of (Euclid C) is non empty set
p12 is bounded Element of bool the carrier of (Euclid C)
0. (TOP-REAL C) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like V62( TOP-REAL C) complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the ZeroF of (TOP-REAL C) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the Element of p12 is Element of p12
EX1 is V11() real ext-real Element of REAL
C is Element of the carrier of (Euclid C)
EX2 is Element of the carrier of (Euclid C)
dist (C,EX2) is V11() real ext-real Element of REAL
the distance of (Euclid C) is non empty Relation-like [: the carrier of (Euclid C), the carrier of (Euclid C):] -defined REAL -valued Function-like total V30([: the carrier of (Euclid C), the carrier of (Euclid C):], REAL ) complex-yielding V174() V175() Element of bool [:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:]
[: the carrier of (Euclid C), the carrier of (Euclid C):] is non empty set
[:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:] is non empty non trivial V35() set
the distance of (Euclid C) . (C,EX2) is V11() real ext-real Element of REAL
[C,EX2] is non empty set
{C,EX2} is non empty V35() set
{C} is non empty trivial V35() 1 -element set
{{C,EX2},{C}} is non empty V35() V39() set
the distance of (Euclid C) . [C,EX2] is V11() real ext-real set
EX1 + (dist (C,EX2)) is V11() real ext-real Element of REAL
(EX1 + (dist (C,EX2))) + 1 is V11() real ext-real Element of REAL
EX is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.EX.| is V11() real ext-real non negative Element of REAL
sqr EX is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
sqrreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
EX (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (EX,EX) is Relation-like Function-like set
multreal .: (EX,EX) is set
K383((sqr EX)) is V11() real ext-real Element of REAL
addreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K195(REAL,(sqr EX),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr EX)) is V11() real ext-real Element of REAL
EX - (0. (TOP-REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
- (0. (TOP-REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
- (0. (TOP-REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
compreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
(0. (TOP-REAL C)) (#) compreal is Relation-like Function-like V35() complex-yielding V174() V175() set
K38(1) is V11() real ext-real non positive set
K38(1) * (0. (TOP-REAL C)) is Relation-like Function-like set
K38(1) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
id REAL is non empty Relation-like REAL -defined REAL -valued Function-like one-to-one total V30( REAL , REAL ) complex-yielding V174() V175() increasing V179() Element of bool [:REAL,REAL:]
multreal [;] (K38(1),(id REAL)) is set
(0. (TOP-REAL C)) (#) (K38(1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
K258((TOP-REAL C),EX,(- (0. (TOP-REAL C)))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) is non empty Relation-like [: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):] -defined the carrier of (TOP-REAL C) -valued Function-like total V30([: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C)) Element of bool [:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):]
[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):] is non empty set
[:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):] is non empty set
bool [:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):] is non empty set
the U7 of (TOP-REAL C) . (EX,(- (0. (TOP-REAL C)))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[EX,(- (0. (TOP-REAL C)))] is non empty set
{EX,(- (0. (TOP-REAL C)))} is non empty functional V35() V39() set
{EX} is non empty trivial functional V35() V39() 1 -element set
{{EX,(- (0. (TOP-REAL C)))},{EX}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [EX,(- (0. (TOP-REAL C)))] is set
EX + (- (0. (TOP-REAL C))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (EX,(- (0. (TOP-REAL C)))) is set
EX - (0. (TOP-REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
diffreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K174(REAL,addreal,(id REAL),compreal) is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
diffreal .: (EX,(0. (TOP-REAL C))) is set
K324((0. (TOP-REAL C))) is Relation-like Function-like complex-yielding set
K295(EX,K324((0. (TOP-REAL C)))) is Relation-like Function-like set
|.(EX - (0. (TOP-REAL C))).| is V11() real ext-real non negative Element of REAL
sqr (EX - (0. (TOP-REAL C))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(EX - (0. (TOP-REAL C))) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((EX - (0. (TOP-REAL C))),(EX - (0. (TOP-REAL C)))) is Relation-like Function-like set
multreal .: ((EX - (0. (TOP-REAL C))),(EX - (0. (TOP-REAL C)))) is set
K383((sqr (EX - (0. (TOP-REAL C))))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (EX - (0. (TOP-REAL C)))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (EX - (0. (TOP-REAL C))))) is V11() real ext-real Element of REAL
t2 is Element of the carrier of (Euclid C)
dist (C,t2) is V11() real ext-real Element of REAL
the distance of (Euclid C) . (C,t2) is V11() real ext-real Element of REAL
[C,t2] is non empty set
{C,t2} is non empty V35() set
{{C,t2},{C}} is non empty V35() V39() set
the distance of (Euclid C) . [C,t2] is V11() real ext-real set
dist (EX2,t2) is V11() real ext-real Element of REAL
the distance of (Euclid C) . (EX2,t2) is V11() real ext-real Element of REAL
[EX2,t2] is non empty set
{EX2,t2} is non empty V35() set
{EX2} is non empty trivial V35() 1 -element set
{{EX2,t2},{EX2}} is non empty V35() V39() set
the distance of (Euclid C) . [EX2,t2] is V11() real ext-real set
(dist (C,EX2)) + (dist (EX2,t2)) is V11() real ext-real Element of REAL
(dist (C,EX2)) + EX1 is V11() real ext-real Element of REAL
p12 is bounded Element of bool the carrier of (Euclid C)
C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.C.| is V11() real ext-real non negative Element of REAL
sqr C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
sqrreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
C (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (C,C) is Relation-like Function-like set
multreal .: (C,C) is set
K383((sqr C)) is V11() real ext-real Element of REAL
addreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K195(REAL,(sqr C),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr C)) is V11() real ext-real Element of REAL
p12 is bounded Element of bool the carrier of (Euclid C)
p12 is V11() real ext-real Element of REAL
WH is Element of bool the carrier of (Euclid C)
the Element of WH is Element of WH
r is Element of the carrier of (Euclid C)
0. (TOP-REAL C) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like V62( TOP-REAL C) complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the ZeroF of (TOP-REAL C) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
p12 + p12 is V11() real ext-real Element of REAL
EX is Element of the carrier of (Euclid C)
t2 is Element of the carrier of (Euclid C)
dist (EX,t2) is V11() real ext-real Element of REAL
the distance of (Euclid C) is non empty Relation-like [: the carrier of (Euclid C), the carrier of (Euclid C):] -defined REAL -valued Function-like total V30([: the carrier of (Euclid C), the carrier of (Euclid C):], REAL ) complex-yielding V174() V175() Element of bool [:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:]
[: the carrier of (Euclid C), the carrier of (Euclid C):] is non empty set
[:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:] is non empty non trivial V35() set
the distance of (Euclid C) . (EX,t2) is V11() real ext-real Element of REAL
[EX,t2] is non empty set
{EX,t2} is non empty V35() set
{EX} is non empty trivial V35() 1 -element set
{{EX,t2},{EX}} is non empty V35() V39() set
the distance of (Euclid C) . [EX,t2] is V11() real ext-real set
EX1 is Element of the carrier of (Euclid C)
dist (EX1,t2) is V11() real ext-real Element of REAL
the distance of (Euclid C) . (EX1,t2) is V11() real ext-real Element of REAL
[EX1,t2] is non empty set
{EX1,t2} is non empty V35() set
{EX1} is non empty trivial V35() 1 -element set
{{EX1,t2},{EX1}} is non empty V35() V39() set
the distance of (Euclid C) . [EX1,t2] is V11() real ext-real set
qt2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
qt2 - (0. (TOP-REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
- (0. (TOP-REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
- (0. (TOP-REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
compreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
(0. (TOP-REAL C)) (#) compreal is Relation-like Function-like V35() complex-yielding V174() V175() set
K38(1) is V11() real ext-real non positive set
K38(1) * (0. (TOP-REAL C)) is Relation-like Function-like set
K38(1) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
id REAL is non empty Relation-like REAL -defined REAL -valued Function-like one-to-one total V30( REAL , REAL ) complex-yielding V174() V175() increasing V179() Element of bool [:REAL,REAL:]
multreal [;] (K38(1),(id REAL)) is set
(0. (TOP-REAL C)) (#) (K38(1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
K258((TOP-REAL C),qt2,(- (0. (TOP-REAL C)))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) is non empty Relation-like [: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):] -defined the carrier of (TOP-REAL C) -valued Function-like total V30([: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C)) Element of bool [:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):]
[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):] is non empty set
[:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):] is non empty set
bool [:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):] is non empty set
the U7 of (TOP-REAL C) . (qt2,(- (0. (TOP-REAL C)))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[qt2,(- (0. (TOP-REAL C)))] is non empty set
{qt2,(- (0. (TOP-REAL C)))} is non empty functional V35() V39() set
{qt2} is non empty trivial functional V35() V39() 1 -element set
{{qt2,(- (0. (TOP-REAL C)))},{qt2}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [qt2,(- (0. (TOP-REAL C)))] is set
qt2 + (- (0. (TOP-REAL C))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
addreal .: (qt2,(- (0. (TOP-REAL C)))) is set
qt2 - (0. (TOP-REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
diffreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K174(REAL,addreal,(id REAL),compreal) is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
diffreal .: (qt2,(0. (TOP-REAL C))) is set
K324((0. (TOP-REAL C))) is Relation-like Function-like complex-yielding set
K295(qt2,K324((0. (TOP-REAL C)))) is Relation-like Function-like set
|.(qt2 - (0. (TOP-REAL C))).| is V11() real ext-real non negative Element of REAL
sqr (qt2 - (0. (TOP-REAL C))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
sqrreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
(qt2 - (0. (TOP-REAL C))) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((qt2 - (0. (TOP-REAL C))),(qt2 - (0. (TOP-REAL C)))) is Relation-like Function-like set
multreal .: ((qt2 - (0. (TOP-REAL C))),(qt2 - (0. (TOP-REAL C)))) is set
K383((sqr (qt2 - (0. (TOP-REAL C))))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (qt2 - (0. (TOP-REAL C)))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (qt2 - (0. (TOP-REAL C))))) is V11() real ext-real Element of REAL
|.qt2.| is V11() real ext-real non negative Element of REAL
sqr qt2 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
qt2 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (qt2,qt2) is Relation-like Function-like set
multreal .: (qt2,qt2) is set
K383((sqr qt2)) is V11() real ext-real Element of REAL
K195(REAL,(sqr qt2),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr qt2)) is V11() real ext-real Element of REAL
dist (EX,EX1) is V11() real ext-real Element of REAL
the distance of (Euclid C) . (EX,EX1) is V11() real ext-real Element of REAL
[EX,EX1] is non empty set
{EX,EX1} is non empty V35() set
{{EX,EX1},{EX}} is non empty V35() V39() set
the distance of (Euclid C) . [EX,EX1] is V11() real ext-real set
r2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
r2 - (0. (TOP-REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
K258((TOP-REAL C),r2,(- (0. (TOP-REAL C)))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) . (r2,(- (0. (TOP-REAL C)))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[r2,(- (0. (TOP-REAL C)))] is non empty set
{r2,(- (0. (TOP-REAL C)))} is non empty functional V35() V39() set
{r2} is non empty trivial functional V35() V39() 1 -element set
{{r2,(- (0. (TOP-REAL C)))},{r2}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [r2,(- (0. (TOP-REAL C)))] is set
r2 + (- (0. (TOP-REAL C))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (r2,(- (0. (TOP-REAL C)))) is set
r2 - (0. (TOP-REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
diffreal .: (r2,(0. (TOP-REAL C))) is set
K295(r2,K324((0. (TOP-REAL C)))) is Relation-like Function-like set
|.(r2 - (0. (TOP-REAL C))).| is V11() real ext-real non negative Element of REAL
sqr (r2 - (0. (TOP-REAL C))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(r2 - (0. (TOP-REAL C))) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((r2 - (0. (TOP-REAL C))),(r2 - (0. (TOP-REAL C)))) is Relation-like Function-like set
multreal .: ((r2 - (0. (TOP-REAL C))),(r2 - (0. (TOP-REAL C)))) is set
K383((sqr (r2 - (0. (TOP-REAL C))))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (r2 - (0. (TOP-REAL C)))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (r2 - (0. (TOP-REAL C))))) is V11() real ext-real Element of REAL
|.r2.| is V11() real ext-real non negative Element of REAL
sqr r2 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
r2 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (r2,r2) is Relation-like Function-like set
multreal .: (r2,r2) is set
K383((sqr r2)) is V11() real ext-real Element of REAL
K195(REAL,(sqr r2),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr r2)) is V11() real ext-real Element of REAL
(dist (EX,EX1)) + (dist (EX1,t2)) is V11() real ext-real Element of REAL
EX2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.EX2.| is V11() real ext-real non negative Element of REAL
sqr EX2 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
sqrreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
EX2 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (EX2,EX2) is Relation-like Function-like set
multreal .: (EX2,EX2) is set
K383((sqr EX2)) is V11() real ext-real Element of REAL
addreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K195(REAL,(sqr EX2),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr EX2)) is V11() real ext-real Element of REAL
WH is Element of bool the carrier of (Euclid C)
WH is Element of bool the carrier of (Euclid C)
WH is Element of bool the carrier of (Euclid C)
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
[#] (TOP-REAL C) is 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 C)
the carrier of (TOP-REAL C) is non empty set
bool the carrier of (TOP-REAL C) is non empty set
Euclid C is non empty strict Reflexive discerning symmetric triangle Discerning MetrStruct
REAL C is non empty functional FinSequence-membered FinSequenceSet of REAL
C -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = C } is set
Pitag_dist C is non empty Relation-like [:(REAL C),(REAL C):] -defined REAL -valued Function-like total V30([:(REAL C),(REAL C):], REAL ) complex-yielding V174() V175() Element of bool [:[:(REAL C),(REAL C):],REAL:]
[:(REAL C),(REAL C):] is non empty set
[:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() set
MetrStruct(# (REAL C),(Pitag_dist C) #) is strict MetrStruct
the carrier of (Euclid C) is non empty set
bool the carrier of (Euclid C) is non empty set
p is bounded Element of bool the carrier of (Euclid C)
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
{} (TOP-REAL C) is empty trivial proper ordinal natural V11() real ext-real non positive non negative Function-like functional V35() V39() cardinal {} -element FinSequence-membered open closed boundary nowhere_dense V183() V184() V185() V186() V187() V188() V189() symmetric circled bounded Element of bool the carrier of (TOP-REAL C)
the carrier of (TOP-REAL C) is non empty set
bool the carrier of (TOP-REAL C) is non empty set
(C,({} (TOP-REAL C))) is Element of bool the carrier of (TOP-REAL C)
{ b1 where b1 is Element of bool the carrier of (TOP-REAL C) : (C, {} (TOP-REAL C),b1) } is set
union { b1 where b1 is Element of bool the carrier of (TOP-REAL C) : (C, {} (TOP-REAL C),b1) } is set
REAL C is non empty functional FinSequence-membered FinSequenceSet of REAL
C -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = C } is set
[#] (TOP-REAL C) is 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 C)
(TOP-REAL C) | ([#] (TOP-REAL C)) is non empty strict TopSpace-like SubSpace of TOP-REAL C
the topology of (TOP-REAL C) is non empty Element of bool (bool the carrier of (TOP-REAL C))
bool (bool the carrier of (TOP-REAL C)) is non empty set
TopStruct(# the carrier of (TOP-REAL C), the topology of (TOP-REAL C) #) is non empty strict TopSpace-like TopStruct
Euclid C is non empty strict Reflexive discerning symmetric triangle Discerning MetrStruct
Pitag_dist C is non empty Relation-like [:(REAL C),(REAL C):] -defined REAL -valued Function-like total V30([:(REAL C),(REAL C):], REAL ) complex-yielding V174() V175() Element of bool [:[:(REAL C),(REAL C):],REAL:]
[:(REAL C),(REAL C):] is non empty set
[:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() set
MetrStruct(# (REAL C),(Pitag_dist C) #) is strict MetrStruct
the carrier of (Euclid C) is non empty set
bool the carrier of (Euclid C) is non empty set
({} (TOP-REAL C)) ` is open closed dense Element of bool the carrier of (TOP-REAL C)
the carrier of (TOP-REAL C) \ ({} (TOP-REAL C)) is set
(TOP-REAL C) | (({} (TOP-REAL C)) `) is strict TopSpace-like SubSpace of TOP-REAL C
[#] ((TOP-REAL C) | (({} (TOP-REAL C)) `)) is non proper open closed dense Element of bool the carrier of ((TOP-REAL C) | (({} (TOP-REAL C)) `))
the carrier of ((TOP-REAL C) | (({} (TOP-REAL C)) `)) is set
bool the carrier of ((TOP-REAL C) | (({} (TOP-REAL C)) `)) is non empty set
WH is Element of bool the carrier of (Euclid C)
WH is Element of bool the carrier of (Euclid C)
WH is set
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
bool the carrier of (TOP-REAL C) is non empty set
p is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
WH is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
p12 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
C is non empty Element of bool the carrier of (TOP-REAL C)
(TOP-REAL C) | C is non empty strict TopSpace-like SubSpace of TOP-REAL C
the carrier of ((TOP-REAL C) | C) is non empty set
[: the carrier of I[01], the carrier of ((TOP-REAL C) | C):] is non empty set
bool [: the carrier of I[01], the carrier of ((TOP-REAL C) | C):] is non empty set
r is non empty Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL C) | C) -valued Function-like total V30( the carrier of I[01], the carrier of ((TOP-REAL C) | C)) Element of bool [: the carrier of I[01], the carrier of ((TOP-REAL C) | C):]
r . 0 is set
r . 1 is set
EX2 is non empty Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL C) | C) -valued Function-like total V30( the carrier of I[01], the carrier of ((TOP-REAL C) | C)) Element of bool [: the carrier of I[01], the carrier of ((TOP-REAL C) | C):]
EX2 . 0 is set
EX2 . 1 is set
p1 is Element of the carrier of ((TOP-REAL C) | C)
EX is Element of the carrier of ((TOP-REAL C) | C)
EX1 is Element of the carrier of ((TOP-REAL C) | C)
1 / 2 is V11() real ext-real non negative Element of REAL
qt2 is non empty Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL C) | C) -valued Function-like total V30( the carrier of I[01], the carrier of ((TOP-REAL C) | C)) Path of EX1,p1
t2 is non empty Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL C) | C) -valued Function-like total V30( the carrier of I[01], the carrier of ((TOP-REAL C) | C)) Path of p1,EX
{ b1 where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
Closed-Interval-TSpace (0,(1 / 2)) is non empty strict TopSpace-like V231() SubSpace of R^1
Closed-Interval-TSpace ((1 / 2),1) is non empty strict TopSpace-like V231() SubSpace of R^1
P[01] ((1 / 2),1,((#) (0,1)),((0,1) (#))) is non empty Relation-like the carrier of (Closed-Interval-TSpace ((1 / 2),1)) -defined the carrier of (Closed-Interval-TSpace (0,1)) -valued Function-like total V30( the carrier of (Closed-Interval-TSpace ((1 / 2),1)), the carrier of (Closed-Interval-TSpace (0,1))) complex-yielding V174() V175() Element of bool [: the carrier of (Closed-Interval-TSpace ((1 / 2),1)), the carrier of (Closed-Interval-TSpace (0,1)):]
the carrier of (Closed-Interval-TSpace ((1 / 2),1)) is non empty V183() V184() V185() set
[: the carrier of (Closed-Interval-TSpace ((1 / 2),1)), the carrier of (Closed-Interval-TSpace (0,1)):] is non empty complex-yielding V174() V175() set
bool [: the carrier of (Closed-Interval-TSpace ((1 / 2),1)), the carrier of (Closed-Interval-TSpace (0,1)):] is non empty set
P[01] (0,(1 / 2),((#) (0,1)),((0,1) (#))) is non empty Relation-like the carrier of (Closed-Interval-TSpace (0,(1 / 2))) -defined the carrier of (Closed-Interval-TSpace (0,1)) -valued Function-like total V30( the carrier of (Closed-Interval-TSpace (0,(1 / 2))), the carrier of (Closed-Interval-TSpace (0,1))) complex-yielding V174() V175() Element of bool [: the carrier of (Closed-Interval-TSpace (0,(1 / 2))), the carrier of (Closed-Interval-TSpace (0,1)):]
the carrier of (Closed-Interval-TSpace (0,(1 / 2))) is non empty V183() V184() V185() set
[: the carrier of (Closed-Interval-TSpace (0,(1 / 2))), the carrier of (Closed-Interval-TSpace (0,1)):] is non empty complex-yielding V174() V175() set
bool [: the carrier of (Closed-Interval-TSpace (0,(1 / 2))), the carrier of (Closed-Interval-TSpace (0,1)):] is non empty set
qt2 * (P[01] (0,(1 / 2),((#) (0,1)),((0,1) (#)))) is Relation-like the carrier of (Closed-Interval-TSpace (0,(1 / 2))) -defined the carrier of ((TOP-REAL C) | C) -valued Function-like Element of bool [: the carrier of (Closed-Interval-TSpace (0,(1 / 2))), the carrier of ((TOP-REAL C) | C):]
[: the carrier of (Closed-Interval-TSpace (0,(1 / 2))), the carrier of ((TOP-REAL C) | C):] is non empty set
bool [: the carrier of (Closed-Interval-TSpace (0,(1 / 2))), the carrier of ((TOP-REAL C) | C):] is non empty set
t2 * (P[01] ((1 / 2),1,((#) (0,1)),((0,1) (#)))) is Relation-like the carrier of (Closed-Interval-TSpace ((1 / 2),1)) -defined the carrier of ((TOP-REAL C) | C) -valued Function-like Element of bool [: the carrier of (Closed-Interval-TSpace ((1 / 2),1)), the carrier of ((TOP-REAL C) | C):]
[: the carrier of (Closed-Interval-TSpace ((1 / 2),1)), the carrier of ((TOP-REAL C) | C):] is non empty set
bool [: the carrier of (Closed-Interval-TSpace ((1 / 2),1)), the carrier of ((TOP-REAL C) | C):] is non empty set
(qt2 * (P[01] (0,(1 / 2),((#) (0,1)),((0,1) (#))))) +* (t2 * (P[01] ((1 / 2),1,((#) (0,1)),((0,1) (#))))) is Relation-like Function-like set
dom (P[01] (0,(1 / 2),((#) (0,1)),((0,1) (#)))) is V183() V184() V185() Element of bool the carrier of (Closed-Interval-TSpace (0,(1 / 2)))
bool the carrier of (Closed-Interval-TSpace (0,(1 / 2))) is non empty set
[.0,(1 / 2).] is V183() V184() V185() real-bounded Element of bool REAL
dom (P[01] ((1 / 2),1,((#) (0,1)),((0,1) (#)))) is V183() V184() V185() Element of bool the carrier of (Closed-Interval-TSpace ((1 / 2),1))
bool the carrier of (Closed-Interval-TSpace ((1 / 2),1)) is non empty set
[.(1 / 2),1.] is V183() V184() V185() real-bounded Element of bool REAL
r5 is TopSpace-like V231() SubSpace of I[01]
the carrier of r5 is V183() V184() V185() set
[: the carrier of r5, the carrier of ((TOP-REAL C) | C):] is set
bool [: the carrier of r5, the carrier of ((TOP-REAL C) | C):] is non empty set
q4 is TopSpace-like V231() SubSpace of I[01]
the carrier of q4 is V183() V184() V185() set
[: the carrier of q4, the carrier of ((TOP-REAL C) | C):] is set
bool [: the carrier of q4, the carrier of ((TOP-REAL C) | C):] is non empty set
{ b1 where b1 is V11() real ext-real Element of REAL : ( 1 / 2 <= b1 & b1 <= 1 ) } is set
r is V11() real ext-real Element of REAL
(t2 * (P[01] ((1 / 2),1,((#) (0,1)),((0,1) (#))))) . r is set
2 * r is V11() real ext-real Element of REAL
(2 * r) - 1 is V11() real ext-real Element of REAL
t2 . ((2 * r) - 1) is set
xr is V11() real ext-real Element of the carrier of (Closed-Interval-TSpace ((1 / 2),1))
(P[01] ((1 / 2),1,((#) (0,1)),((0,1) (#)))) . xr is V11() real ext-real Element of REAL
q is V11() real ext-real Element of REAL
z is V11() real ext-real Element of REAL
q - z is V11() real ext-real Element of REAL
1 - (1 / 2) is V11() real ext-real Element of REAL
(q - z) / (1 - (1 / 2)) is V11() real ext-real Element of REAL
((q - z) / (1 - (1 / 2))) * r is V11() real ext-real Element of REAL
1 * z is V11() real ext-real Element of REAL
(1 / 2) * q is V11() real ext-real Element of REAL
(1 * z) - ((1 / 2) * q) is V11() real ext-real Element of REAL
((1 * z) - ((1 / 2) * q)) / (1 - (1 / 2)) is V11() real ext-real Element of REAL
(((q - z) / (1 - (1 / 2))) * r) + (((1 * z) - ((1 / 2) * q)) / (1 - (1 / 2))) is V11() real ext-real Element of REAL
{ b1 where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 / 2 ) } is set
r is V11() real ext-real Element of REAL
(qt2 * (P[01] (0,(1 / 2),((#) (0,1)),((0,1) (#))))) . r is set
2 * r is V11() real ext-real Element of REAL
qt2 . (2 * r) is set
xr is V11() real ext-real Element of the carrier of (Closed-Interval-TSpace (0,(1 / 2)))
(P[01] (0,(1 / 2),((#) (0,1)),((0,1) (#)))) . xr is V11() real ext-real Element of REAL
q is V11() real ext-real Element of REAL
z is V11() real ext-real Element of REAL
q - z is V11() real ext-real Element of REAL
(1 / 2) - 0 is V11() real ext-real non negative Element of REAL
(q - z) / ((1 / 2) - 0) is V11() real ext-real Element of REAL
((q - z) / ((1 / 2) - 0)) * r is V11() real ext-real Element of REAL
(1 / 2) * z is V11() real ext-real Element of REAL
0 * q is V11() real ext-real Element of REAL
((1 / 2) * z) - (0 * q) is V11() real ext-real Element of REAL
(((1 / 2) * z) - (0 * q)) / ((1 / 2) - 0) is V11() real ext-real Element of REAL
(((q - z) / ((1 / 2) - 0)) * r) + ((((1 / 2) * z) - (0 * q)) / ((1 / 2) - 0)) is V11() real ext-real Element of REAL
W2 is Relation-like the carrier of q4 -defined the carrier of ((TOP-REAL C) | C) -valued Function-like total V30( the carrier of q4, the carrier of ((TOP-REAL C) | C)) Element of bool [: the carrier of q4, the carrier of ((TOP-REAL C) | C):]
W2 . (1 / 2) is set
2 * (1 / 2) is V11() real ext-real non negative Element of REAL
(2 * (1 / 2)) - 1 is V11() real ext-real Element of REAL
t2 . ((2 * (1 / 2)) - 1) is set
P2 is Relation-like the carrier of r5 -defined the carrier of ((TOP-REAL C) | C) -valued Function-like total V30( the carrier of r5, the carrier of ((TOP-REAL C) | C)) Element of bool [: the carrier of r5, the carrier of ((TOP-REAL C) | C):]
r2 is V11() real ext-real Element of the carrier of I[01]
P2 . r2 is set
[#] q4 is non proper open closed dense V183() V184() V185() Element of bool the carrier of q4
bool the carrier of q4 is non empty set
[#] r5 is non proper open closed dense V183() V184() V185() Element of bool the carrier of r5
bool the carrier of r5 is non empty set
([#] q4) \/ ([#] r5) is V183() V184() V185() set
[#] I[01] is non empty non proper open closed dense non boundary V183() V184() V185() Element of bool the carrier of I[01]
bool the carrier of I[01] is non empty set
([#] q4) /\ ([#] r5) is V183() V184() V185() Element of bool the carrier of r5
{r2} is non empty trivial V35() 1 -element V183() V184() V185() Element of bool REAL
rng ((qt2 * (P[01] (0,(1 / 2),((#) (0,1)),((0,1) (#))))) +* (t2 * (P[01] ((1 / 2),1,((#) (0,1)),((0,1) (#)))))) is set
rng (qt2 * (P[01] (0,(1 / 2),((#) (0,1)),((0,1) (#))))) is Element of bool the carrier of ((TOP-REAL C) | C)
bool the carrier of ((TOP-REAL C) | C) is non empty set
rng (t2 * (P[01] ((1 / 2),1,((#) (0,1)),((0,1) (#))))) is Element of bool the carrier of ((TOP-REAL C) | C)
(rng (qt2 * (P[01] (0,(1 / 2),((#) (0,1)),((0,1) (#)))))) \/ (rng (t2 * (P[01] ((1 / 2),1,((#) (0,1)),((0,1) (#)))))) is Element of bool the carrier of ((TOP-REAL C) | C)
dom qt2 is V183() V184() V185() Element of bool the carrier of I[01]
rng (P[01] (0,(1 / 2),((#) (0,1)),((0,1) (#)))) is V183() V184() V185() Element of bool the carrier of (Closed-Interval-TSpace (0,1))
bool the carrier of (Closed-Interval-TSpace (0,1)) is non empty set
dom t2 is V183() V184() V185() Element of bool the carrier of I[01]
rng (P[01] ((1 / 2),1,((#) (0,1)),((0,1) (#)))) is V183() V184() V185() Element of bool the carrier of (Closed-Interval-TSpace (0,1))
dom (t2 * (P[01] ((1 / 2),1,((#) (0,1)),((0,1) (#))))) is V183() V184() V185() Element of bool the carrier of (Closed-Interval-TSpace ((1 / 2),1))
{ b1 where b1 is V11() real ext-real Element of REAL : ( 1 / 2 <= b1 & b1 <= 1 ) } is set
z is V11() real ext-real Element of REAL
((qt2 * (P[01] (0,(1 / 2),((#) (0,1)),((0,1) (#))))) +* (t2 * (P[01] ((1 / 2),1,((#) (0,1)),((0,1) (#)))))) . 0 is set
(qt2 * (P[01] (0,(1 / 2),((#) (0,1)),((0,1) (#))))) . 0 is set
2 * 0 is empty trivial ordinal natural V11() real ext-real non positive non negative Function-like functional V35() V39() cardinal {} -element FinSequence-membered V116() V117() V183() V184() V185() V186() V187() V188() V189() Element of NAT
qt2 . (2 * 0) is set
dom ((qt2 * (P[01] (0,(1 / 2),((#) (0,1)),((0,1) (#))))) +* (t2 * (P[01] ((1 / 2),1,((#) (0,1)),((0,1) (#)))))) is set
dom (qt2 * (P[01] (0,(1 / 2),((#) (0,1)),((0,1) (#))))) is V183() V184() V185() Element of bool the carrier of (Closed-Interval-TSpace (0,(1 / 2)))
(dom (qt2 * (P[01] (0,(1 / 2),((#) (0,1)),((0,1) (#)))))) \/ (dom (t2 * (P[01] ((1 / 2),1,((#) (0,1)),((0,1) (#)))))) is V183() V184() V185() set
[.0,(1 / 2).] \/ [.(1 / 2),1.] is V183() V184() V185() Element of bool REAL
z is non empty Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL C) | C) -valued Function-like total V30( the carrier of I[01], the carrier of ((TOP-REAL C) | C)) Element of bool [: the carrier of I[01], the carrier of ((TOP-REAL C) | C):]
q is non empty Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL C) | C) -valued Function-like total V30( the carrier of I[01], the carrier of ((TOP-REAL C) | C)) continuous Element of bool [: the carrier of I[01], the carrier of ((TOP-REAL C) | C):]
q . 1 is set
(t2 * (P[01] ((1 / 2),1,((#) (0,1)),((0,1) (#))))) . 1 is set
2 * 1 is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
(2 * 1) - 1 is V11() real ext-real Element of REAL
t2 . ((2 * 1) - 1) is set
r is non empty Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL C) | C) -valued Function-like total V30( the carrier of I[01], the carrier of ((TOP-REAL C) | C)) Path of EX1,EX
xr is V11() real ext-real Element of the carrier of I[01]
r . xr is Element of the carrier of ((TOP-REAL C) | C)
t9 is V11() real ext-real Element of REAL
2 * t9 is V11() real ext-real Element of REAL
qt2 . (2 * t9) is set
(2 * t9) - 1 is V11() real ext-real Element of REAL
t2 . ((2 * t9) - 1) is set
{ b1 where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 / 2 ) } is set
[.0,(1 / 2).] /\ [.(1 / 2),1.] is V183() V184() V185() Element of bool REAL
{(1 / 2)} is non empty trivial V35() 1 -element V183() V184() V185() Element of bool REAL
(qt2 * (P[01] (0,(1 / 2),((#) (0,1)),((0,1) (#))))) . xr is set
(t2 * (P[01] ((1 / 2),1,((#) (0,1)),((0,1) (#))))) . (1 / 2) is set
(t2 * (P[01] ((1 / 2),1,((#) (0,1)),((0,1) (#))))) . xr is set
r2 is non empty Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL C) | C) -valued Function-like total V30( the carrier of I[01], the carrier of ((TOP-REAL C) | C)) Path of EX1,EX
r2 . 0 is set
r2 . 1 is set
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
bool the carrier of (TOP-REAL C) is non empty set
p is Element of bool the carrier of (TOP-REAL C)
(TOP-REAL C) | p is strict TopSpace-like SubSpace of TOP-REAL C
the carrier of ((TOP-REAL C) | p) is set
[: the carrier of I[01], the carrier of ((TOP-REAL C) | p):] is set
bool [: the carrier of I[01], the carrier of ((TOP-REAL C) | p):] is non empty set
WH is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
p12 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
LSeg (WH,p12) is non empty closed connected compact convex Element of bool the carrier of (TOP-REAL C)
{ (((1 - b1) * WH) + (b1 * p12)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
LSeg (p12,C) is non empty closed connected compact convex Element of bool the carrier of (TOP-REAL C)
{ (((1 - b1) * p12) + (b1 * C)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
(TOP-REAL C) | (LSeg (WH,p12)) is non empty strict TopSpace-like SubSpace of TOP-REAL C
the carrier of ((TOP-REAL C) | (LSeg (WH,p12))) is non empty set
[: the carrier of I[01], the carrier of ((TOP-REAL C) | (LSeg (WH,p12))):] is non empty set
bool [: the carrier of I[01], the carrier of ((TOP-REAL C) | (LSeg (WH,p12))):] is non empty set
EX2 is non empty Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL C) | (LSeg (WH,p12))) -valued Function-like total V30( the carrier of I[01], the carrier of ((TOP-REAL C) | (LSeg (WH,p12)))) Element of bool [: the carrier of I[01], the carrier of ((TOP-REAL C) | (LSeg (WH,p12))):]
EX2 . 0 is set
EX2 . 1 is set
rng EX2 is Element of bool the carrier of ((TOP-REAL C) | (LSeg (WH,p12)))
bool the carrier of ((TOP-REAL C) | (LSeg (WH,p12))) is non empty set
[#] ((TOP-REAL C) | (LSeg (WH,p12))) is non empty non proper open closed dense non boundary Element of bool the carrier of ((TOP-REAL C) | (LSeg (WH,p12)))
[#] ((TOP-REAL C) | p) is non proper open closed dense Element of bool the carrier of ((TOP-REAL C) | p)
bool the carrier of ((TOP-REAL C) | p) is non empty set
dom EX2 is V183() V184() V185() Element of bool the carrier of I[01]
bool the carrier of I[01] is non empty set
[:[.0,1.],p:] is set
bool [:[.0,1.],p:] is non empty set
r is non empty Element of bool the carrier of (TOP-REAL C)
(TOP-REAL C) | r is non empty strict TopSpace-like SubSpace of TOP-REAL C
the carrier of ((TOP-REAL C) | r) is non empty set
[: the carrier of I[01], the carrier of ((TOP-REAL C) | r):] is non empty set
bool [: the carrier of I[01], the carrier of ((TOP-REAL C) | r):] is non empty set
EX1 is Relation-like [.0,1.] -defined p -valued Function-like V30([.0,1.],p) Element of bool [:[.0,1.],p:]
(TOP-REAL C) | (LSeg (p12,C)) is non empty strict TopSpace-like SubSpace of TOP-REAL C
the carrier of ((TOP-REAL C) | (LSeg (p12,C))) is non empty set
[: the carrier of I[01], the carrier of ((TOP-REAL C) | (LSeg (p12,C))):] is non empty set
bool [: the carrier of I[01], the carrier of ((TOP-REAL C) | (LSeg (p12,C))):] is non empty set
EX is non empty Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL C) | (LSeg (p12,C))) -valued Function-like total V30( the carrier of I[01], the carrier of ((TOP-REAL C) | (LSeg (p12,C)))) Element of bool [: the carrier of I[01], the carrier of ((TOP-REAL C) | (LSeg (p12,C))):]
EX . 0 is set
EX . 1 is set
rng EX is Element of bool the carrier of ((TOP-REAL C) | (LSeg (p12,C)))
bool the carrier of ((TOP-REAL C) | (LSeg (p12,C))) is non empty set
[#] ((TOP-REAL C) | (LSeg (p12,C))) is non empty non proper open closed dense non boundary Element of bool the carrier of ((TOP-REAL C) | (LSeg (p12,C)))
p1 is non empty Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL C) | r) -valued Function-like total V30( the carrier of I[01], the carrier of ((TOP-REAL C) | r)) Element of bool [: the carrier of I[01], the carrier of ((TOP-REAL C) | r):]
qt2 is Element of the carrier of ((TOP-REAL C) | p)
p1 . 1 is set
dom EX is V183() V184() V185() Element of bool the carrier of I[01]
q4 is Relation-like [.0,1.] -defined p -valued Function-like V30([.0,1.],p) Element of bool [:[.0,1.],p:]
r5 is non empty Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL C) | r) -valued Function-like total V30( the carrier of I[01], the carrier of ((TOP-REAL C) | r)) Element of bool [: the carrier of I[01], the carrier of ((TOP-REAL C) | r):]
t2 is Element of the carrier of ((TOP-REAL C) | p)
r2 is Element of the carrier of ((TOP-REAL C) | p)
rng p1 is Element of bool the carrier of ((TOP-REAL C) | r)
bool the carrier of ((TOP-REAL C) | r) is non empty set
rng r5 is Element of bool the carrier of ((TOP-REAL C) | r)
(rng p1) \/ (rng r5) is Element of bool the carrier of ((TOP-REAL C) | r)
r0 is non empty Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL C) | r) -valued Function-like total V30( the carrier of I[01], the carrier of ((TOP-REAL C) | r)) Element of bool [: the carrier of I[01], the carrier of ((TOP-REAL C) | r):]
r0 . 0 is set
r0 . 1 is set
rng r0 is Element of bool the carrier of ((TOP-REAL C) | r)
LSeg (WH,C) is non empty closed connected compact convex Element of bool the carrier of (TOP-REAL C)
{ (((1 - b1) * WH) + (b1 * C)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
(TOP-REAL C) | (LSeg (WH,C)) is non empty strict TopSpace-like SubSpace of TOP-REAL C
the carrier of ((TOP-REAL C) | (LSeg (WH,C))) is non empty set
[: the carrier of I[01], the carrier of ((TOP-REAL C) | (LSeg (WH,C))):] is non empty set
bool [: the carrier of I[01], the carrier of ((TOP-REAL C) | (LSeg (WH,C))):] is non empty set
EX is non empty Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL C) | (LSeg (WH,C))) -valued Function-like total V30( the carrier of I[01], the carrier of ((TOP-REAL C) | (LSeg (WH,C)))) Element of bool [: the carrier of I[01], the carrier of ((TOP-REAL C) | (LSeg (WH,C))):]
EX . 0 is set
EX . 1 is set
rng EX is Element of bool the carrier of ((TOP-REAL C) | (LSeg (WH,C)))
bool the carrier of ((TOP-REAL C) | (LSeg (WH,C))) is non empty set
[#] ((TOP-REAL C) | (LSeg (WH,C))) is non empty non proper open closed dense non boundary Element of bool the carrier of ((TOP-REAL C) | (LSeg (WH,C)))
dom EX is V183() V184() V185() Element of bool the carrier of I[01]
t2 is Relation-like [.0,1.] -defined p -valued Function-like V30([.0,1.],p) Element of bool [:[.0,1.],p:]
qt2 is non empty Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL C) | r) -valued Function-like total V30( the carrier of I[01], the carrier of ((TOP-REAL C) | r)) Element of bool [: the carrier of I[01], the carrier of ((TOP-REAL C) | r):]
EX is Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL C) | p) -valued Function-like V30( the carrier of I[01], the carrier of ((TOP-REAL C) | p)) Element of bool [: the carrier of I[01], the carrier of ((TOP-REAL C) | p):]
EX . 0 is set
EX . 1 is set
LSeg (WH,C) is non empty closed connected compact convex Element of bool the carrier of (TOP-REAL C)
{ (((1 - b1) * WH) + (b1 * C)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
(TOP-REAL C) | (LSeg (WH,C)) is non empty strict TopSpace-like SubSpace of TOP-REAL C
the carrier of ((TOP-REAL C) | (LSeg (WH,C))) is non empty set
[: the carrier of I[01], the carrier of ((TOP-REAL C) | (LSeg (WH,C))):] is non empty set
bool [: the carrier of I[01], the carrier of ((TOP-REAL C) | (LSeg (WH,C))):] is non empty set
EX2 is non empty Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL C) | (LSeg (WH,C))) -valued Function-like total V30( the carrier of I[01], the carrier of ((TOP-REAL C) | (LSeg (WH,C)))) Element of bool [: the carrier of I[01], the carrier of ((TOP-REAL C) | (LSeg (WH,C))):]
EX2 . 0 is set
EX2 . 1 is set
rng EX2 is Element of bool the carrier of ((TOP-REAL C) | (LSeg (WH,C)))
bool the carrier of ((TOP-REAL C) | (LSeg (WH,C))) is non empty set
[#] ((TOP-REAL C) | (LSeg (WH,C))) is non empty non proper open closed dense non boundary Element of bool the carrier of ((TOP-REAL C) | (LSeg (WH,C)))
[#] ((TOP-REAL C) | p) is non proper open closed dense Element of bool the carrier of ((TOP-REAL C) | p)
bool the carrier of ((TOP-REAL C) | p) is non empty set
dom EX2 is V183() V184() V185() Element of bool the carrier of I[01]
bool the carrier of I[01] is non empty set
[:[.0,1.],p:] is set
bool [:[.0,1.],p:] is non empty set
r is non empty Element of bool the carrier of (TOP-REAL C)
(TOP-REAL C) | r is non empty strict TopSpace-like SubSpace of TOP-REAL C
the carrier of ((TOP-REAL C) | r) is non empty set
[: the carrier of I[01], the carrier of ((TOP-REAL C) | r):] is non empty set
bool [: the carrier of I[01], the carrier of ((TOP-REAL C) | r):] is non empty set
EX1 is Relation-like [.0,1.] -defined p -valued Function-like V30([.0,1.],p) Element of bool [:[.0,1.],p:]
p1 is non empty Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL C) | r) -valued Function-like total V30( the carrier of I[01], the carrier of ((TOP-REAL C) | r)) Element of bool [: the carrier of I[01], the carrier of ((TOP-REAL C) | r):]
[#] ((TOP-REAL C) | p) is non proper open closed dense Element of bool the carrier of ((TOP-REAL C) | p)
bool the carrier of ((TOP-REAL C) | p) is non empty set
r is non empty Element of bool the carrier of (TOP-REAL C)
(TOP-REAL C) | r is non empty strict TopSpace-like SubSpace of TOP-REAL C
the carrier of ((TOP-REAL C) | r) is non empty set
[: the carrier of I[01], the carrier of ((TOP-REAL C) | r):] is non empty set
bool [: the carrier of I[01], the carrier of ((TOP-REAL C) | r):] is non empty set
EX2 is Element of the carrier of ((TOP-REAL C) | p)
EX1 is Element of the carrier of ((TOP-REAL C) | p)
p1 is non empty Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL C) | r) -valued Function-like total V30( the carrier of I[01], the carrier of ((TOP-REAL C) | r)) Element of bool [: the carrier of I[01], the carrier of ((TOP-REAL C) | r):]
p1 . 0 is set
p1 . 1 is set
EX2 is Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL C) | p) -valued Function-like V30( the carrier of I[01], the carrier of ((TOP-REAL C) | p)) Element of bool [: the carrier of I[01], the carrier of ((TOP-REAL C) | p):]
EX2 . 0 is set
EX2 . 1 is set
EX1 is Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL C) | p) -valued Function-like V30( the carrier of I[01], the carrier of ((TOP-REAL C) | p)) Element of bool [: the carrier of I[01], the carrier of ((TOP-REAL C) | p):]
EX1 . 0 is set
EX1 . 1 is set
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
bool the carrier of (TOP-REAL C) is non empty set
p is Element of bool the carrier of (TOP-REAL C)
(TOP-REAL C) | p is strict TopSpace-like SubSpace of TOP-REAL C
the carrier of ((TOP-REAL C) | p) is set
[: the carrier of I[01], the carrier of ((TOP-REAL C) | p):] is set
bool [: the carrier of I[01], the carrier of ((TOP-REAL C) | p):] is non empty set
WH is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
p12 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
r is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
LSeg (WH,p12) is non empty closed connected compact convex Element of bool the carrier of (TOP-REAL C)
{ (((1 - b1) * WH) + (b1 * p12)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
LSeg (p12,C) is non empty closed connected compact convex Element of bool the carrier of (TOP-REAL C)
{ (((1 - b1) * p12) + (b1 * C)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
LSeg (C,r) is non empty closed connected compact convex Element of bool the carrier of (TOP-REAL C)
{ (((1 - b1) * C) + (b1 * r)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
EX1 is Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL C) | p) -valued Function-like V30( the carrier of I[01], the carrier of ((TOP-REAL C) | p)) Element of bool [: the carrier of I[01], the carrier of ((TOP-REAL C) | p):]
EX1 . 0 is set
EX1 . 1 is set
(TOP-REAL C) | (LSeg (C,r)) is non empty strict TopSpace-like SubSpace of TOP-REAL C
the carrier of ((TOP-REAL C) | (LSeg (C,r))) is non empty set
[: the carrier of I[01], the carrier of ((TOP-REAL C) | (LSeg (C,r))):] is non empty set
bool [: the carrier of I[01], the carrier of ((TOP-REAL C) | (LSeg (C,r))):] is non empty set
p1 is non empty Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL C) | (LSeg (C,r))) -valued Function-like total V30( the carrier of I[01], the carrier of ((TOP-REAL C) | (LSeg (C,r)))) Element of bool [: the carrier of I[01], the carrier of ((TOP-REAL C) | (LSeg (C,r))):]
p1 . 0 is set
p1 . 1 is set
rng p1 is Element of bool the carrier of ((TOP-REAL C) | (LSeg (C,r)))
bool the carrier of ((TOP-REAL C) | (LSeg (C,r))) is non empty set
[#] ((TOP-REAL C) | (LSeg (C,r))) is non empty non proper open closed dense non boundary Element of bool the carrier of ((TOP-REAL C) | (LSeg (C,r)))
[#] ((TOP-REAL C) | p) is non proper open closed dense Element of bool the carrier of ((TOP-REAL C) | p)
bool the carrier of ((TOP-REAL C) | p) is non empty set
t2 is Element of the carrier of ((TOP-REAL C) | p)
dom p1 is V183() V184() V185() Element of bool the carrier of I[01]
bool the carrier of I[01] is non empty set
[:[.0,1.],p:] is set
bool [:[.0,1.],p:] is non empty set
EX2 is non empty Element of bool the carrier of (TOP-REAL C)
(TOP-REAL C) | EX2 is non empty strict TopSpace-like SubSpace of TOP-REAL C
the carrier of ((TOP-REAL C) | EX2) is non empty set
[: the carrier of I[01], the carrier of ((TOP-REAL C) | EX2):] is non empty set
bool [: the carrier of I[01], the carrier of ((TOP-REAL C) | EX2):] is non empty set
r2 is Relation-like [.0,1.] -defined p -valued Function-like V30([.0,1.],p) Element of bool [:[.0,1.],p:]
q4 is non empty Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL C) | EX2) -valued Function-like total V30( the carrier of I[01], the carrier of ((TOP-REAL C) | EX2)) Element of bool [: the carrier of I[01], the carrier of ((TOP-REAL C) | EX2):]
EX is Element of the carrier of ((TOP-REAL C) | p)
qt2 is Element of the carrier of ((TOP-REAL C) | p)
rng EX1 is Element of bool the carrier of ((TOP-REAL C) | p)
rng q4 is Element of bool the carrier of ((TOP-REAL C) | EX2)
bool the carrier of ((TOP-REAL C) | EX2) is non empty set
(rng EX1) \/ (rng q4) is set
r5 is non empty Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL C) | EX2) -valued Function-like total V30( the carrier of I[01], the carrier of ((TOP-REAL C) | EX2)) Element of bool [: the carrier of I[01], the carrier of ((TOP-REAL C) | EX2):]
r5 . 0 is set
r5 . 1 is set
rng r5 is Element of bool the carrier of ((TOP-REAL C) | EX2)
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
bool the carrier of (TOP-REAL C) is non empty set
p is Element of bool the carrier of (TOP-REAL C)
(TOP-REAL C) | p is strict TopSpace-like SubSpace of TOP-REAL C
the carrier of ((TOP-REAL C) | p) is set
[: the carrier of I[01], the carrier of ((TOP-REAL C) | p):] is set
bool [: the carrier of I[01], the carrier of ((TOP-REAL C) | p):] is non empty set
WH is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
p12 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
r is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
EX2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
EX1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
p1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
LSeg (WH,p12) is non empty closed connected compact convex Element of bool the carrier of (TOP-REAL C)
{ (((1 - b1) * WH) + (b1 * p12)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
LSeg (p12,C) is non empty closed connected compact convex Element of bool the carrier of (TOP-REAL C)
{ (((1 - b1) * p12) + (b1 * C)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
LSeg (C,r) is non empty closed connected compact convex Element of bool the carrier of (TOP-REAL C)
{ (((1 - b1) * C) + (b1 * r)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
LSeg (r,EX2) is non empty closed connected compact convex Element of bool the carrier of (TOP-REAL C)
{ (((1 - b1) * r) + (b1 * EX2)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
LSeg (EX2,EX1) is non empty closed connected compact convex Element of bool the carrier of (TOP-REAL C)
{ (((1 - b1) * EX2) + (b1 * EX1)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
LSeg (EX1,p1) is non empty closed connected compact convex Element of bool the carrier of (TOP-REAL C)
{ (((1 - b1) * EX1) + (b1 * p1)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
EX is Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL C) | p) -valued Function-like V30( the carrier of I[01], the carrier of ((TOP-REAL C) | p)) Element of bool [: the carrier of I[01], the carrier of ((TOP-REAL C) | p):]
EX . 0 is set
EX . 1 is set
t2 is Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL C) | p) -valued Function-like V30( the carrier of I[01], the carrier of ((TOP-REAL C) | p)) Element of bool [: the carrier of I[01], the carrier of ((TOP-REAL C) | p):]
t2 . 0 is set
t2 . 1 is set
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
Euclid C is non empty strict Reflexive discerning symmetric triangle Discerning MetrStruct
REAL C is non empty functional FinSequence-membered FinSequenceSet of REAL
C -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = C } is set
Pitag_dist C is non empty Relation-like [:(REAL C),(REAL C):] -defined REAL -valued Function-like total V30([:(REAL C),(REAL C):], REAL ) complex-yielding V174() V175() Element of bool [:[:(REAL C),(REAL C):],REAL:]
[:(REAL C),(REAL C):] is non empty set
[:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() set
MetrStruct(# (REAL C),(Pitag_dist C) #) is strict MetrStruct
TopSpaceMetr (Euclid C) is TopStruct
the carrier of (TopSpaceMetr (Euclid C)) is set
bool the carrier of (TopSpaceMetr (Euclid C)) is non empty set
0. (TOP-REAL C) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like V62( TOP-REAL C) complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the ZeroF of (TOP-REAL C) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
p is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
WH is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
LSeg (p,WH) is non empty closed connected compact convex Element of bool the carrier of (TOP-REAL C)
bool the carrier of (TOP-REAL C) is non empty set
{ (((1 - b1) * p) + (b1 * WH)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
p12 is Element of bool the carrier of (TopSpaceMetr (Euclid C))
dist_min p12 is Relation-like the carrier of (TopSpaceMetr (Euclid C)) -defined the carrier of R^1 -valued Function-like total V30( the carrier of (TopSpaceMetr (Euclid C)), the carrier of R^1) complex-yielding V174() V175() Element of bool [: the carrier of (TopSpaceMetr (Euclid C)), the carrier of R^1:]
[: the carrier of (TopSpaceMetr (Euclid C)), the carrier of R^1:] is complex-yielding V174() V175() set
bool [: the carrier of (TopSpaceMetr (Euclid C)), the carrier of R^1:] is non empty set
(dist_min p12) . (0. (TOP-REAL C)) is V11() real ext-real Element of REAL
the topology of (TOP-REAL C) is non empty Element of bool (bool the carrier of (TOP-REAL C))
bool (bool the carrier of (TOP-REAL C)) is non empty set
TopStruct(# the carrier of (TOP-REAL C), the topology of (TOP-REAL C) #) is non empty strict TopSpace-like TopStruct
{(0. (TOP-REAL C))} is non empty trivial functional V35() V39() 1 -element compact Element of bool the carrier of (TOP-REAL C)
r is Element of bool the carrier of (TopSpaceMetr (Euclid C))
the carrier of (Euclid C) is non empty set
EX2 is Element of bool the carrier of (TopSpaceMetr (Euclid C))
min_dist_min (r,EX2) is V11() real ext-real Element of REAL
EX1 is Element of the carrier of (Euclid C)
p1 is Element of the carrier of (Euclid C)
dist (EX1,p1) is V11() real ext-real Element of REAL
the distance of (Euclid C) is non empty Relation-like [: the carrier of (Euclid C), the carrier of (Euclid C):] -defined REAL -valued Function-like total V30([: the carrier of (Euclid C), the carrier of (Euclid C):], REAL ) complex-yielding V174() V175() Element of bool [:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:]
[: the carrier of (Euclid C), the carrier of (Euclid C):] is non empty set
[:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:] is non empty non trivial V35() set
the distance of (Euclid C) . (EX1,p1) is V11() real ext-real Element of REAL
[EX1,p1] is non empty set
{EX1,p1} is non empty V35() set
{EX1} is non empty trivial V35() 1 -element set
{{EX1,p1},{EX1}} is non empty V35() V39() set
the distance of (Euclid C) . [EX1,p1] is V11() real ext-real set
dist_min r is Relation-like the carrier of (TopSpaceMetr (Euclid C)) -defined the carrier of R^1 -valued Function-like total V30( the carrier of (TopSpaceMetr (Euclid C)), the carrier of R^1) complex-yielding V174() V175() Element of bool [: the carrier of (TopSpaceMetr (Euclid C)), the carrier of R^1:]
(dist_min r) .: EX2 is V183() V184() V185() Element of bool the carrier of R^1
t2 is Element of the carrier of (Euclid C)
(dist_min r) . t2 is V11() real ext-real Element of REAL
r2 is set
dom (dist_min r) is Element of bool the carrier of (TopSpaceMetr (Euclid C))
q4 is set
(dist_min r) . q4 is V11() real ext-real Element of REAL
qt2 is Element of the carrier of (TopSpaceMetr (Euclid C))
{((dist_min r) . t2)} is non empty trivial V35() 1 -element V183() V184() V185() Element of bool REAL
[#] ((dist_min r) .: EX2) is V183() V184() V185() Element of bool REAL
lower_bound ([#] ((dist_min r) .: EX2)) is V11() real ext-real Element of REAL
lower_bound ((dist_min r) .: EX2) is V11() real ext-real Element of REAL
EX is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.EX.| is V11() real ext-real non negative Element of REAL
sqr EX is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
sqrreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
EX (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (EX,EX) is Relation-like Function-like set
multreal .: (EX,EX) is set
K383((sqr EX)) is V11() real ext-real Element of REAL
addreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K195(REAL,(sqr EX),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr EX)) is V11() real ext-real Element of REAL
EX - (0. (TOP-REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
- (0. (TOP-REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
- (0. (TOP-REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
compreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
(0. (TOP-REAL C)) (#) compreal is Relation-like Function-like V35() complex-yielding V174() V175() set
K38(1) is V11() real ext-real non positive set
K38(1) * (0. (TOP-REAL C)) is Relation-like Function-like set
K38(1) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
id REAL is non empty Relation-like REAL -defined REAL -valued Function-like one-to-one total V30( REAL , REAL ) complex-yielding V174() V175() increasing V179() Element of bool [:REAL,REAL:]
multreal [;] (K38(1),(id REAL)) is set
(0. (TOP-REAL C)) (#) (K38(1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
K258((TOP-REAL C),EX,(- (0. (TOP-REAL C)))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) is non empty Relation-like [: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):] -defined the carrier of (TOP-REAL C) -valued Function-like total V30([: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C)) Element of bool [:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):]
[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):] is non empty set
[:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):] is non empty set
bool [:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):] is non empty set
the U7 of (TOP-REAL C) . (EX,(- (0. (TOP-REAL C)))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[EX,(- (0. (TOP-REAL C)))] is non empty set
{EX,(- (0. (TOP-REAL C)))} is non empty functional V35() V39() set
{EX} is non empty trivial functional V35() V39() 1 -element set
{{EX,(- (0. (TOP-REAL C)))},{EX}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [EX,(- (0. (TOP-REAL C)))] is set
EX + (- (0. (TOP-REAL C))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (EX,(- (0. (TOP-REAL C)))) is set
EX - (0. (TOP-REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
diffreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K174(REAL,addreal,(id REAL),compreal) is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
diffreal .: (EX,(0. (TOP-REAL C))) is set
K324((0. (TOP-REAL C))) is Relation-like Function-like complex-yielding set
K295(EX,K324((0. (TOP-REAL C)))) is Relation-like Function-like set
|.(EX - (0. (TOP-REAL C))).| is V11() real ext-real non negative Element of REAL
sqr (EX - (0. (TOP-REAL C))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(EX - (0. (TOP-REAL C))) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((EX - (0. (TOP-REAL C))),(EX - (0. (TOP-REAL C)))) is Relation-like Function-like set
multreal .: ((EX - (0. (TOP-REAL C))),(EX - (0. (TOP-REAL C)))) is set
K383((sqr (EX - (0. (TOP-REAL C))))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (EX - (0. (TOP-REAL C)))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (EX - (0. (TOP-REAL C))))) is V11() real ext-real Element of REAL
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
bool the carrier of (TOP-REAL C) is non empty set
p is V11() real ext-real Element of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C) : not |.b1.| <= p } is set
WH is Element of bool the carrier of (TOP-REAL C)
p12 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the topology of (TOP-REAL C) is non empty Element of bool (bool the carrier of (TOP-REAL C))
bool (bool the carrier of (TOP-REAL C)) is non empty set
TopStruct(# the carrier of (TOP-REAL C), the topology of (TOP-REAL C) #) is non empty strict TopSpace-like TopStruct
Euclid C is non empty strict Reflexive discerning symmetric triangle Discerning MetrStruct
REAL C is non empty functional FinSequence-membered FinSequenceSet of REAL
C -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = C } is set
Pitag_dist C is non empty Relation-like [:(REAL C),(REAL C):] -defined REAL -valued Function-like total V30([:(REAL C),(REAL C):], REAL ) complex-yielding V174() V175() Element of bool [:[:(REAL C),(REAL C):],REAL:]
[:(REAL C),(REAL C):] is non empty set
[:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() set
MetrStruct(# (REAL C),(Pitag_dist C) #) is strict MetrStruct
TopSpaceMetr (Euclid C) is TopStruct
the carrier of (TopSpaceMetr (Euclid C)) is set
bool the carrier of (TopSpaceMetr (Euclid C)) is non empty set
LSeg (p12,C) is non empty closed connected compact convex Element of bool the carrier of (TOP-REAL C)
{ (((1 - b1) * p12) + (b1 * C)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
0. (TOP-REAL C) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like V62( TOP-REAL C) complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the ZeroF of (TOP-REAL C) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
r is Element of bool the carrier of (TopSpaceMetr (Euclid C))
dist_min r is Relation-like the carrier of (TopSpaceMetr (Euclid C)) -defined the carrier of R^1 -valued Function-like total V30( the carrier of (TopSpaceMetr (Euclid C)), the carrier of R^1) complex-yielding V174() V175() Element of bool [: the carrier of (TopSpaceMetr (Euclid C)), the carrier of R^1:]
[: the carrier of (TopSpaceMetr (Euclid C)), the carrier of R^1:] is complex-yielding V174() V175() set
bool [: the carrier of (TopSpaceMetr (Euclid C)), the carrier of R^1:] is non empty set
(dist_min r) . (0. (TOP-REAL C)) is V11() real ext-real Element of REAL
EX2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.EX2.| is V11() real ext-real non negative Element of REAL
sqr EX2 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
sqrreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
EX2 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (EX2,EX2) is Relation-like Function-like set
multreal .: (EX2,EX2) is set
K383((sqr EX2)) is V11() real ext-real Element of REAL
addreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K195(REAL,(sqr EX2),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr EX2)) is V11() real ext-real Element of REAL
p + 1 is V11() real ext-real Element of REAL
(p + 1) / |.EX2.| is V11() real ext-real Element of REAL
((p + 1) / |.EX2.|) * p12 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
((p + 1) / |.EX2.|) * p12 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
((p + 1) / |.EX2.|) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
id REAL is non empty Relation-like REAL -defined REAL -valued Function-like one-to-one total V30( REAL , REAL ) complex-yielding V174() V175() increasing V179() Element of bool [:REAL,REAL:]
multreal [;] (((p + 1) / |.EX2.|),(id REAL)) is set
p12 (#) (((p + 1) / |.EX2.|) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
((p + 1) / |.EX2.|) * C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
((p + 1) / |.EX2.|) * C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
C (#) (((p + 1) / |.EX2.|) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
LSeg ((((p + 1) / |.EX2.|) * p12),(((p + 1) / |.EX2.|) * C)) is non empty closed connected compact convex Element of bool the carrier of (TOP-REAL C)
{ (((1 - b1) * (((p + 1) / |.EX2.|) * p12)) + (b1 * (((p + 1) / |.EX2.|) * C))) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
the carrier of (Euclid C) is non empty set
r2 is set
abs ((p + 1) / |.EX2.|) is V11() real ext-real Element of REAL
abs (p + 1) is V11() real ext-real Element of REAL
abs |.EX2.| is V11() real ext-real Element of REAL
(abs (p + 1)) / (abs |.EX2.|) is V11() real ext-real Element of REAL
(abs (p + 1)) / |.EX2.| is V11() real ext-real Element of REAL
qt2 is Element of the carrier of (Euclid C)
dist qt2 is Relation-like the carrier of (TopSpaceMetr (Euclid C)) -defined the carrier of R^1 -valued Function-like total V30( the carrier of (TopSpaceMetr (Euclid C)), the carrier of R^1) complex-yielding V174() V175() Element of bool [: the carrier of (TopSpaceMetr (Euclid C)), the carrier of R^1:]
t2 is Element of bool the carrier of (TopSpaceMetr (Euclid C))
(dist qt2) .: t2 is V183() V184() V185() Element of bool the carrier of R^1
q4 is set
dom (dist qt2) is Element of bool the carrier of (TopSpaceMetr (Euclid C))
r5 is set
(dist qt2) . r5 is V11() real ext-real Element of REAL
r5 is V11() real ext-real Element of REAL
1 - r5 is V11() real ext-real Element of REAL
(1 - r5) * (((p + 1) / |.EX2.|) * p12) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
(1 - r5) * (((p + 1) / |.EX2.|) * p12) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(1 - r5) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] ((1 - r5),(id REAL)) is set
(((p + 1) / |.EX2.|) * p12) (#) ((1 - r5) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
r5 * (((p + 1) / |.EX2.|) * C) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
r5 * (((p + 1) / |.EX2.|) * C) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
r5 multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (r5,(id REAL)) is set
(((p + 1) / |.EX2.|) * C) (#) (r5 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
((1 - r5) * (((p + 1) / |.EX2.|) * p12)) + (r5 * (((p + 1) / |.EX2.|) * C)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) is non empty Relation-like [: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):] -defined the carrier of (TOP-REAL C) -valued Function-like total V30([: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C)) Element of bool [:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):]
[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):] is non empty set
[:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):] is non empty set
bool [:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):] is non empty set
the U7 of (TOP-REAL C) . (((1 - r5) * (((p + 1) / |.EX2.|) * p12)),(r5 * (((p + 1) / |.EX2.|) * C))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[((1 - r5) * (((p + 1) / |.EX2.|) * p12)),(r5 * (((p + 1) / |.EX2.|) * C))] is non empty set
{((1 - r5) * (((p + 1) / |.EX2.|) * p12)),(r5 * (((p + 1) / |.EX2.|) * C))} is non empty functional V35() V39() set
{((1 - r5) * (((p + 1) / |.EX2.|) * p12))} is non empty trivial functional V35() V39() 1 -element set
{{((1 - r5) * (((p + 1) / |.EX2.|) * p12)),(r5 * (((p + 1) / |.EX2.|) * C))},{((1 - r5) * (((p + 1) / |.EX2.|) * p12))}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [((1 - r5) * (((p + 1) / |.EX2.|) * p12)),(r5 * (((p + 1) / |.EX2.|) * C))] is set
((1 - r5) * (((p + 1) / |.EX2.|) * p12)) + (r5 * (((p + 1) / |.EX2.|) * C)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (((1 - r5) * (((p + 1) / |.EX2.|) * p12)),(r5 * (((p + 1) / |.EX2.|) * C))) is set
(1 - r5) * p12 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
(1 - r5) * p12 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
p12 (#) ((1 - r5) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
r5 * C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
r5 * C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
C (#) (r5 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
((1 - r5) * p12) + (r5 * C) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) . (((1 - r5) * p12),(r5 * C)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[((1 - r5) * p12),(r5 * C)] is non empty set
{((1 - r5) * p12),(r5 * C)} is non empty functional V35() V39() set
{((1 - r5) * p12)} is non empty trivial functional V35() V39() 1 -element set
{{((1 - r5) * p12),(r5 * C)},{((1 - r5) * p12)}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [((1 - r5) * p12),(r5 * C)] is set
((1 - r5) * p12) + (r5 * C) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (((1 - r5) * p12),(r5 * C)) is set
r0 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
Q is Element of the carrier of (Euclid C)
dist (Q,qt2) is V11() real ext-real Element of REAL
the distance of (Euclid C) is non empty Relation-like [: the carrier of (Euclid C), the carrier of (Euclid C):] -defined REAL -valued Function-like total V30([: the carrier of (Euclid C), the carrier of (Euclid C):], REAL ) complex-yielding V174() V175() Element of bool [:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:]
[: the carrier of (Euclid C), the carrier of (Euclid C):] is non empty set
[:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:] is non empty non trivial V35() set
the distance of (Euclid C) . (Q,qt2) is V11() real ext-real Element of REAL
[Q,qt2] is non empty set
{Q,qt2} is non empty V35() set
{Q} is non empty trivial V35() 1 -element set
{{Q,qt2},{Q}} is non empty V35() V39() set
the distance of (Euclid C) . [Q,qt2] is V11() real ext-real set
(dist qt2) . Q is V11() real ext-real Element of REAL
P3 is ext-real set
dom (dist qt2) is Element of bool the carrier of (TopSpaceMetr (Euclid C))
W3 is set
(dist qt2) . W3 is V11() real ext-real Element of REAL
Q is Element of the carrier of (Euclid C)
dist (Q,qt2) is V11() real ext-real Element of REAL
the distance of (Euclid C) . (Q,qt2) is V11() real ext-real Element of REAL
[Q,qt2] is non empty set
{Q,qt2} is non empty V35() set
{Q} is non empty trivial V35() 1 -element set
{{Q,qt2},{Q}} is non empty V35() V39() set
the distance of (Euclid C) . [Q,qt2] is V11() real ext-real set
q4 is V183() V184() V185() Element of bool REAL
dom (dist qt2) is Element of bool the carrier of (TopSpaceMetr (Euclid C))
lower_bound q4 is V11() real ext-real Element of REAL
[#] ((dist qt2) .: t2) is V183() V184() V185() Element of bool REAL
lower_bound ([#] ((dist qt2) .: t2)) is V11() real ext-real Element of REAL
lower_bound ((dist qt2) .: t2) is V11() real ext-real Element of REAL
r0 - (0. (TOP-REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
- (0. (TOP-REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
- (0. (TOP-REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
compreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
(0. (TOP-REAL C)) (#) compreal is Relation-like Function-like V35() complex-yielding V174() V175() set
K38(1) is V11() real ext-real non positive set
K38(1) * (0. (TOP-REAL C)) is Relation-like Function-like set
K38(1) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (K38(1),(id REAL)) is set
(0. (TOP-REAL C)) (#) (K38(1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
K258((TOP-REAL C),r0,(- (0. (TOP-REAL C)))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) . (r0,(- (0. (TOP-REAL C)))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[r0,(- (0. (TOP-REAL C)))] is non empty set
{r0,(- (0. (TOP-REAL C)))} is non empty functional V35() V39() set
{r0} is non empty trivial functional V35() V39() 1 -element set
{{r0,(- (0. (TOP-REAL C)))},{r0}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [r0,(- (0. (TOP-REAL C)))] is set
r0 + (- (0. (TOP-REAL C))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (r0,(- (0. (TOP-REAL C)))) is set
r0 - (0. (TOP-REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
diffreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K174(REAL,addreal,(id REAL),compreal) is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
diffreal .: (r0,(0. (TOP-REAL C))) is set
K324((0. (TOP-REAL C))) is Relation-like Function-like complex-yielding set
K295(r0,K324((0. (TOP-REAL C)))) is Relation-like Function-like set
|.(r0 - (0. (TOP-REAL C))).| is V11() real ext-real non negative Element of REAL
sqr (r0 - (0. (TOP-REAL C))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(r0 - (0. (TOP-REAL C))) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((r0 - (0. (TOP-REAL C))),(r0 - (0. (TOP-REAL C)))) is Relation-like Function-like set
multreal .: ((r0 - (0. (TOP-REAL C))),(r0 - (0. (TOP-REAL C)))) is set
K383((sqr (r0 - (0. (TOP-REAL C))))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (r0 - (0. (TOP-REAL C)))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (r0 - (0. (TOP-REAL C))))) is V11() real ext-real Element of REAL
|.r0.| is V11() real ext-real non negative Element of REAL
sqr r0 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
r0 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (r0,r0) is Relation-like Function-like set
multreal .: (r0,r0) is set
K383((sqr r0)) is V11() real ext-real Element of REAL
K195(REAL,(sqr r0),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr r0)) is V11() real ext-real Element of REAL
|.r0.| / |.EX2.| is V11() real ext-real non negative Element of REAL
(abs (p + 1)) * 1 is V11() real ext-real Element of REAL
(abs (p + 1)) * (|.r0.| / |.EX2.|) is V11() real ext-real Element of REAL
|.EX2.| " is V11() real ext-real non negative Element of REAL
(|.EX2.| ") * |.r0.| is V11() real ext-real non negative Element of REAL
(abs (p + 1)) * ((|.EX2.| ") * |.r0.|) is V11() real ext-real Element of REAL
(abs (p + 1)) * (|.EX2.| ") is V11() real ext-real Element of REAL
((abs (p + 1)) * (|.EX2.| ")) * |.r0.| is V11() real ext-real Element of REAL
((abs (p + 1)) / |.EX2.|) * |.r0.| is V11() real ext-real Element of REAL
((p + 1) / |.EX2.|) * (((1 - r5) * p12) + (r5 * C)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
((p + 1) / |.EX2.|) * (((1 - r5) * p12) + (r5 * C)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(((1 - r5) * p12) + (r5 * C)) (#) (((p + 1) / |.EX2.|) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
|.(((p + 1) / |.EX2.|) * (((1 - r5) * p12) + (r5 * C))).| is V11() real ext-real non negative Element of REAL
sqr (((p + 1) / |.EX2.|) * (((1 - r5) * p12) + (r5 * C))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(((p + 1) / |.EX2.|) * (((1 - r5) * p12) + (r5 * C))) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((((p + 1) / |.EX2.|) * (((1 - r5) * p12) + (r5 * C))),(((p + 1) / |.EX2.|) * (((1 - r5) * p12) + (r5 * C)))) is Relation-like Function-like set
multreal .: ((((p + 1) / |.EX2.|) * (((1 - r5) * p12) + (r5 * C))),(((p + 1) / |.EX2.|) * (((1 - r5) * p12) + (r5 * C)))) is set
K383((sqr (((p + 1) / |.EX2.|) * (((1 - r5) * p12) + (r5 * C))))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (((p + 1) / |.EX2.|) * (((1 - r5) * p12) + (r5 * C)))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (((p + 1) / |.EX2.|) * (((1 - r5) * p12) + (r5 * C))))) is V11() real ext-real Element of REAL
((p + 1) / |.EX2.|) * ((1 - r5) * p12) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
((p + 1) / |.EX2.|) * ((1 - r5) * p12) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
((1 - r5) * p12) (#) (((p + 1) / |.EX2.|) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
((p + 1) / |.EX2.|) * (r5 * C) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
((p + 1) / |.EX2.|) * (r5 * C) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(r5 * C) (#) (((p + 1) / |.EX2.|) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
(((p + 1) / |.EX2.|) * ((1 - r5) * p12)) + (((p + 1) / |.EX2.|) * (r5 * C)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) . ((((p + 1) / |.EX2.|) * ((1 - r5) * p12)),(((p + 1) / |.EX2.|) * (r5 * C))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[(((p + 1) / |.EX2.|) * ((1 - r5) * p12)),(((p + 1) / |.EX2.|) * (r5 * C))] is non empty set
{(((p + 1) / |.EX2.|) * ((1 - r5) * p12)),(((p + 1) / |.EX2.|) * (r5 * C))} is non empty functional V35() V39() set
{(((p + 1) / |.EX2.|) * ((1 - r5) * p12))} is non empty trivial functional V35() V39() 1 -element set
{{(((p + 1) / |.EX2.|) * ((1 - r5) * p12)),(((p + 1) / |.EX2.|) * (r5 * C))},{(((p + 1) / |.EX2.|) * ((1 - r5) * p12))}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [(((p + 1) / |.EX2.|) * ((1 - r5) * p12)),(((p + 1) / |.EX2.|) * (r5 * C))] is set
(((p + 1) / |.EX2.|) * ((1 - r5) * p12)) + (((p + 1) / |.EX2.|) * (r5 * C)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: ((((p + 1) / |.EX2.|) * ((1 - r5) * p12)),(((p + 1) / |.EX2.|) * (r5 * C))) is set
|.((((p + 1) / |.EX2.|) * ((1 - r5) * p12)) + (((p + 1) / |.EX2.|) * (r5 * C))).| is V11() real ext-real non negative Element of REAL
sqr ((((p + 1) / |.EX2.|) * ((1 - r5) * p12)) + (((p + 1) / |.EX2.|) * (r5 * C))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
((((p + 1) / |.EX2.|) * ((1 - r5) * p12)) + (((p + 1) / |.EX2.|) * (r5 * C))) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (((((p + 1) / |.EX2.|) * ((1 - r5) * p12)) + (((p + 1) / |.EX2.|) * (r5 * C))),((((p + 1) / |.EX2.|) * ((1 - r5) * p12)) + (((p + 1) / |.EX2.|) * (r5 * C)))) is Relation-like Function-like set
multreal .: (((((p + 1) / |.EX2.|) * ((1 - r5) * p12)) + (((p + 1) / |.EX2.|) * (r5 * C))),((((p + 1) / |.EX2.|) * ((1 - r5) * p12)) + (((p + 1) / |.EX2.|) * (r5 * C)))) is set
K383((sqr ((((p + 1) / |.EX2.|) * ((1 - r5) * p12)) + (((p + 1) / |.EX2.|) * (r5 * C))))) is V11() real ext-real Element of REAL
K195(REAL,(sqr ((((p + 1) / |.EX2.|) * ((1 - r5) * p12)) + (((p + 1) / |.EX2.|) * (r5 * C)))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr ((((p + 1) / |.EX2.|) * ((1 - r5) * p12)) + (((p + 1) / |.EX2.|) * (r5 * C))))) is V11() real ext-real Element of REAL
((p + 1) / |.EX2.|) * r5 is V11() real ext-real Element of REAL
(((p + 1) / |.EX2.|) * r5) * C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
(((p + 1) / |.EX2.|) * r5) * C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(((p + 1) / |.EX2.|) * r5) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] ((((p + 1) / |.EX2.|) * r5),(id REAL)) is set
C (#) ((((p + 1) / |.EX2.|) * r5) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
(((p + 1) / |.EX2.|) * ((1 - r5) * p12)) + ((((p + 1) / |.EX2.|) * r5) * C) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) . ((((p + 1) / |.EX2.|) * ((1 - r5) * p12)),((((p + 1) / |.EX2.|) * r5) * C)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[(((p + 1) / |.EX2.|) * ((1 - r5) * p12)),((((p + 1) / |.EX2.|) * r5) * C)] is non empty set
{(((p + 1) / |.EX2.|) * ((1 - r5) * p12)),((((p + 1) / |.EX2.|) * r5) * C)} is non empty functional V35() V39() set
{{(((p + 1) / |.EX2.|) * ((1 - r5) * p12)),((((p + 1) / |.EX2.|) * r5) * C)},{(((p + 1) / |.EX2.|) * ((1 - r5) * p12))}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [(((p + 1) / |.EX2.|) * ((1 - r5) * p12)),((((p + 1) / |.EX2.|) * r5) * C)] is set
(((p + 1) / |.EX2.|) * ((1 - r5) * p12)) + ((((p + 1) / |.EX2.|) * r5) * C) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: ((((p + 1) / |.EX2.|) * ((1 - r5) * p12)),((((p + 1) / |.EX2.|) * r5) * C)) is set
|.((((p + 1) / |.EX2.|) * ((1 - r5) * p12)) + ((((p + 1) / |.EX2.|) * r5) * C)).| is V11() real ext-real non negative Element of REAL
sqr ((((p + 1) / |.EX2.|) * ((1 - r5) * p12)) + ((((p + 1) / |.EX2.|) * r5) * C)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
((((p + 1) / |.EX2.|) * ((1 - r5) * p12)) + ((((p + 1) / |.EX2.|) * r5) * C)) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (((((p + 1) / |.EX2.|) * ((1 - r5) * p12)) + ((((p + 1) / |.EX2.|) * r5) * C)),((((p + 1) / |.EX2.|) * ((1 - r5) * p12)) + ((((p + 1) / |.EX2.|) * r5) * C))) is Relation-like Function-like set
multreal .: (((((p + 1) / |.EX2.|) * ((1 - r5) * p12)) + ((((p + 1) / |.EX2.|) * r5) * C)),((((p + 1) / |.EX2.|) * ((1 - r5) * p12)) + ((((p + 1) / |.EX2.|) * r5) * C))) is set
K383((sqr ((((p + 1) / |.EX2.|) * ((1 - r5) * p12)) + ((((p + 1) / |.EX2.|) * r5) * C)))) is V11() real ext-real Element of REAL
K195(REAL,(sqr ((((p + 1) / |.EX2.|) * ((1 - r5) * p12)) + ((((p + 1) / |.EX2.|) * r5) * C))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr ((((p + 1) / |.EX2.|) * ((1 - r5) * p12)) + ((((p + 1) / |.EX2.|) * r5) * C)))) is V11() real ext-real Element of REAL
((p + 1) / |.EX2.|) * (1 - r5) is V11() real ext-real Element of REAL
(((p + 1) / |.EX2.|) * (1 - r5)) * p12 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
(((p + 1) / |.EX2.|) * (1 - r5)) * p12 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(((p + 1) / |.EX2.|) * (1 - r5)) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] ((((p + 1) / |.EX2.|) * (1 - r5)),(id REAL)) is set
p12 (#) ((((p + 1) / |.EX2.|) * (1 - r5)) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
((((p + 1) / |.EX2.|) * (1 - r5)) * p12) + ((((p + 1) / |.EX2.|) * r5) * C) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) . (((((p + 1) / |.EX2.|) * (1 - r5)) * p12),((((p + 1) / |.EX2.|) * r5) * C)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[((((p + 1) / |.EX2.|) * (1 - r5)) * p12),((((p + 1) / |.EX2.|) * r5) * C)] is non empty set
{((((p + 1) / |.EX2.|) * (1 - r5)) * p12),((((p + 1) / |.EX2.|) * r5) * C)} is non empty functional V35() V39() set
{((((p + 1) / |.EX2.|) * (1 - r5)) * p12)} is non empty trivial functional V35() V39() 1 -element set
{{((((p + 1) / |.EX2.|) * (1 - r5)) * p12),((((p + 1) / |.EX2.|) * r5) * C)},{((((p + 1) / |.EX2.|) * (1 - r5)) * p12)}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [((((p + 1) / |.EX2.|) * (1 - r5)) * p12),((((p + 1) / |.EX2.|) * r5) * C)] is set
((((p + 1) / |.EX2.|) * (1 - r5)) * p12) + ((((p + 1) / |.EX2.|) * r5) * C) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (((((p + 1) / |.EX2.|) * (1 - r5)) * p12),((((p + 1) / |.EX2.|) * r5) * C)) is set
|.(((((p + 1) / |.EX2.|) * (1 - r5)) * p12) + ((((p + 1) / |.EX2.|) * r5) * C)).| is V11() real ext-real non negative Element of REAL
sqr (((((p + 1) / |.EX2.|) * (1 - r5)) * p12) + ((((p + 1) / |.EX2.|) * r5) * C)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(((((p + 1) / |.EX2.|) * (1 - r5)) * p12) + ((((p + 1) / |.EX2.|) * r5) * C)) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((((((p + 1) / |.EX2.|) * (1 - r5)) * p12) + ((((p + 1) / |.EX2.|) * r5) * C)),(((((p + 1) / |.EX2.|) * (1 - r5)) * p12) + ((((p + 1) / |.EX2.|) * r5) * C))) is Relation-like Function-like set
multreal .: ((((((p + 1) / |.EX2.|) * (1 - r5)) * p12) + ((((p + 1) / |.EX2.|) * r5) * C)),(((((p + 1) / |.EX2.|) * (1 - r5)) * p12) + ((((p + 1) / |.EX2.|) * r5) * C))) is set
K383((sqr (((((p + 1) / |.EX2.|) * (1 - r5)) * p12) + ((((p + 1) / |.EX2.|) * r5) * C)))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (((((p + 1) / |.EX2.|) * (1 - r5)) * p12) + ((((p + 1) / |.EX2.|) * r5) * C))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (((((p + 1) / |.EX2.|) * (1 - r5)) * p12) + ((((p + 1) / |.EX2.|) * r5) * C)))) is V11() real ext-real Element of REAL
(1 - r5) * ((p + 1) / |.EX2.|) is V11() real ext-real Element of REAL
((1 - r5) * ((p + 1) / |.EX2.|)) * p12 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
((1 - r5) * ((p + 1) / |.EX2.|)) * p12 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
((1 - r5) * ((p + 1) / |.EX2.|)) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (((1 - r5) * ((p + 1) / |.EX2.|)),(id REAL)) is set
p12 (#) (((1 - r5) * ((p + 1) / |.EX2.|)) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
(((1 - r5) * ((p + 1) / |.EX2.|)) * p12) + (r5 * (((p + 1) / |.EX2.|) * C)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) . ((((1 - r5) * ((p + 1) / |.EX2.|)) * p12),(r5 * (((p + 1) / |.EX2.|) * C))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[(((1 - r5) * ((p + 1) / |.EX2.|)) * p12),(r5 * (((p + 1) / |.EX2.|) * C))] is non empty set
{(((1 - r5) * ((p + 1) / |.EX2.|)) * p12),(r5 * (((p + 1) / |.EX2.|) * C))} is non empty functional V35() V39() set
{(((1 - r5) * ((p + 1) / |.EX2.|)) * p12)} is non empty trivial functional V35() V39() 1 -element set
{{(((1 - r5) * ((p + 1) / |.EX2.|)) * p12),(r5 * (((p + 1) / |.EX2.|) * C))},{(((1 - r5) * ((p + 1) / |.EX2.|)) * p12)}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [(((1 - r5) * ((p + 1) / |.EX2.|)) * p12),(r5 * (((p + 1) / |.EX2.|) * C))] is set
(((1 - r5) * ((p + 1) / |.EX2.|)) * p12) + (r5 * (((p + 1) / |.EX2.|) * C)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: ((((1 - r5) * ((p + 1) / |.EX2.|)) * p12),(r5 * (((p + 1) / |.EX2.|) * C))) is set
|.((((1 - r5) * ((p + 1) / |.EX2.|)) * p12) + (r5 * (((p + 1) / |.EX2.|) * C))).| is V11() real ext-real non negative Element of REAL
sqr ((((1 - r5) * ((p + 1) / |.EX2.|)) * p12) + (r5 * (((p + 1) / |.EX2.|) * C))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
((((1 - r5) * ((p + 1) / |.EX2.|)) * p12) + (r5 * (((p + 1) / |.EX2.|) * C))) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (((((1 - r5) * ((p + 1) / |.EX2.|)) * p12) + (r5 * (((p + 1) / |.EX2.|) * C))),((((1 - r5) * ((p + 1) / |.EX2.|)) * p12) + (r5 * (((p + 1) / |.EX2.|) * C)))) is Relation-like Function-like set
multreal .: (((((1 - r5) * ((p + 1) / |.EX2.|)) * p12) + (r5 * (((p + 1) / |.EX2.|) * C))),((((1 - r5) * ((p + 1) / |.EX2.|)) * p12) + (r5 * (((p + 1) / |.EX2.|) * C)))) is set
K383((sqr ((((1 - r5) * ((p + 1) / |.EX2.|)) * p12) + (r5 * (((p + 1) / |.EX2.|) * C))))) is V11() real ext-real Element of REAL
K195(REAL,(sqr ((((1 - r5) * ((p + 1) / |.EX2.|)) * p12) + (r5 * (((p + 1) / |.EX2.|) * C)))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr ((((1 - r5) * ((p + 1) / |.EX2.|)) * p12) + (r5 * (((p + 1) / |.EX2.|) * C))))) is V11() real ext-real Element of REAL
|.(((1 - r5) * (((p + 1) / |.EX2.|) * p12)) + (r5 * (((p + 1) / |.EX2.|) * C))).| is V11() real ext-real non negative Element of REAL
sqr (((1 - r5) * (((p + 1) / |.EX2.|) * p12)) + (r5 * (((p + 1) / |.EX2.|) * C))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(((1 - r5) * (((p + 1) / |.EX2.|) * p12)) + (r5 * (((p + 1) / |.EX2.|) * C))) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((((1 - r5) * (((p + 1) / |.EX2.|) * p12)) + (r5 * (((p + 1) / |.EX2.|) * C))),(((1 - r5) * (((p + 1) / |.EX2.|) * p12)) + (r5 * (((p + 1) / |.EX2.|) * C)))) is Relation-like Function-like set
multreal .: ((((1 - r5) * (((p + 1) / |.EX2.|) * p12)) + (r5 * (((p + 1) / |.EX2.|) * C))),(((1 - r5) * (((p + 1) / |.EX2.|) * p12)) + (r5 * (((p + 1) / |.EX2.|) * C)))) is set
K383((sqr (((1 - r5) * (((p + 1) / |.EX2.|) * p12)) + (r5 * (((p + 1) / |.EX2.|) * C))))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (((1 - r5) * (((p + 1) / |.EX2.|) * p12)) + (r5 * (((p + 1) / |.EX2.|) * C)))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (((1 - r5) * (((p + 1) / |.EX2.|) * p12)) + (r5 * (((p + 1) / |.EX2.|) * C))))) is V11() real ext-real Element of REAL
LSeg (C,(((p + 1) / |.EX2.|) * C)) is non empty closed connected compact convex Element of bool the carrier of (TOP-REAL C)
{ (((1 - b1) * C) + (b1 * (((p + 1) / |.EX2.|) * C))) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
t2 is set
qt2 is V11() real ext-real Element of REAL
1 - qt2 is V11() real ext-real Element of REAL
(1 - qt2) * C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
(1 - qt2) * C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(1 - qt2) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] ((1 - qt2),(id REAL)) is set
C (#) ((1 - qt2) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
qt2 * (((p + 1) / |.EX2.|) * C) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
qt2 * (((p + 1) / |.EX2.|) * C) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
qt2 multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (qt2,(id REAL)) is set
(((p + 1) / |.EX2.|) * C) (#) (qt2 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) is non empty Relation-like [: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):] -defined the carrier of (TOP-REAL C) -valued Function-like total V30([: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C)) Element of bool [:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):]
[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):] is non empty set
[:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):] is non empty set
bool [:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):] is non empty set
the U7 of (TOP-REAL C) . (((1 - qt2) * C),(qt2 * (((p + 1) / |.EX2.|) * C))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[((1 - qt2) * C),(qt2 * (((p + 1) / |.EX2.|) * C))] is non empty set
{((1 - qt2) * C),(qt2 * (((p + 1) / |.EX2.|) * C))} is non empty functional V35() V39() set
{((1 - qt2) * C)} is non empty trivial functional V35() V39() 1 -element set
{{((1 - qt2) * C),(qt2 * (((p + 1) / |.EX2.|) * C))},{((1 - qt2) * C)}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [((1 - qt2) * C),(qt2 * (((p + 1) / |.EX2.|) * C))] is set
((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (((1 - qt2) * C),(qt2 * (((p + 1) / |.EX2.|) * C))) is set
LSeg (C,p12) is non empty closed connected compact convex Element of bool the carrier of (TOP-REAL C)
{ (((1 - b1) * C) + (b1 * p12)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
the carrier of (Euclid C) is non empty set
1 - 0 is non empty V11() real ext-real positive non negative Element of REAL
(1 - 0) * C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
(1 - 0) * C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(1 - 0) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] ((1 - 0),(id REAL)) is set
C (#) ((1 - 0) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
0 * p12 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
0 * p12 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
0 multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (0,(id REAL)) is set
p12 (#) (0 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
((1 - 0) * C) + (0 * p12) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) . (((1 - 0) * C),(0 * p12)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[((1 - 0) * C),(0 * p12)] is non empty set
{((1 - 0) * C),(0 * p12)} is non empty functional V35() V39() set
{((1 - 0) * C)} is non empty trivial functional V35() V39() 1 -element set
{{((1 - 0) * C),(0 * p12)},{((1 - 0) * C)}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [((1 - 0) * C),(0 * p12)] is set
((1 - 0) * C) + (0 * p12) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (((1 - 0) * C),(0 * p12)) is set
((1 - 0) * C) + (0. (TOP-REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) . (((1 - 0) * C),(0. (TOP-REAL C))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[((1 - 0) * C),(0. (TOP-REAL C))] is non empty set
{((1 - 0) * C),(0. (TOP-REAL C))} is non empty functional V35() V39() set
{{((1 - 0) * C),(0. (TOP-REAL C))},{((1 - 0) * C)}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [((1 - 0) * C),(0. (TOP-REAL C))] is set
((1 - 0) * C) + (0. (TOP-REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (((1 - 0) * C),(0. (TOP-REAL C))) is set
q4 is Element of the carrier of (Euclid C)
dist q4 is Relation-like the carrier of (TopSpaceMetr (Euclid C)) -defined the carrier of R^1 -valued Function-like total V30( the carrier of (TopSpaceMetr (Euclid C)), the carrier of R^1) complex-yielding V174() V175() Element of bool [: the carrier of (TopSpaceMetr (Euclid C)), the carrier of R^1:]
r2 is Element of bool the carrier of (TopSpaceMetr (Euclid C))
(dist q4) .: r2 is V183() V184() V185() Element of bool the carrier of R^1
r0 is set
dom (dist q4) is Element of bool the carrier of (TopSpaceMetr (Euclid C))
Q is set
(dist q4) . Q is V11() real ext-real Element of REAL
r5 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
Q is Element of the carrier of (Euclid C)
dist (Q,q4) is V11() real ext-real Element of REAL
the distance of (Euclid C) is non empty Relation-like [: the carrier of (Euclid C), the carrier of (Euclid C):] -defined REAL -valued Function-like total V30([: the carrier of (Euclid C), the carrier of (Euclid C):], REAL ) complex-yielding V174() V175() Element of bool [:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:]
[: the carrier of (Euclid C), the carrier of (Euclid C):] is non empty set
[:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:] is non empty non trivial V35() set
the distance of (Euclid C) . (Q,q4) is V11() real ext-real Element of REAL
[Q,q4] is non empty set
{Q,q4} is non empty V35() set
{Q} is non empty trivial V35() 1 -element set
{{Q,q4},{Q}} is non empty V35() V39() set
the distance of (Euclid C) . [Q,q4] is V11() real ext-real set
(dist q4) . Q is V11() real ext-real Element of REAL
P3 is ext-real set
dom (dist q4) is Element of bool the carrier of (TopSpaceMetr (Euclid C))
W3 is set
(dist q4) . W3 is V11() real ext-real Element of REAL
Q is Element of the carrier of (Euclid C)
dist (Q,q4) is V11() real ext-real Element of REAL
the distance of (Euclid C) . (Q,q4) is V11() real ext-real Element of REAL
[Q,q4] is non empty set
{Q,q4} is non empty V35() set
{Q} is non empty trivial V35() 1 -element set
{{Q,q4},{Q}} is non empty V35() V39() set
the distance of (Euclid C) . [Q,q4] is V11() real ext-real set
r0 is V183() V184() V185() Element of bool REAL
dom (dist q4) is Element of bool the carrier of (TopSpaceMetr (Euclid C))
lower_bound r0 is V11() real ext-real Element of REAL
[#] ((dist q4) .: r2) is V183() V184() V185() Element of bool REAL
lower_bound ([#] ((dist q4) .: r2)) is V11() real ext-real Element of REAL
lower_bound ((dist q4) .: r2) is V11() real ext-real Element of REAL
r5 - (0. (TOP-REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
- (0. (TOP-REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
- (0. (TOP-REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
compreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
(0. (TOP-REAL C)) (#) compreal is Relation-like Function-like V35() complex-yielding V174() V175() set
K38(1) is V11() real ext-real non positive set
K38(1) * (0. (TOP-REAL C)) is Relation-like Function-like set
K38(1) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (K38(1),(id REAL)) is set
(0. (TOP-REAL C)) (#) (K38(1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
K258((TOP-REAL C),r5,(- (0. (TOP-REAL C)))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) . (r5,(- (0. (TOP-REAL C)))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[r5,(- (0. (TOP-REAL C)))] is non empty set
{r5,(- (0. (TOP-REAL C)))} is non empty functional V35() V39() set
{r5} is non empty trivial functional V35() V39() 1 -element set
{{r5,(- (0. (TOP-REAL C)))},{r5}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [r5,(- (0. (TOP-REAL C)))] is set
r5 + (- (0. (TOP-REAL C))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (r5,(- (0. (TOP-REAL C)))) is set
r5 - (0. (TOP-REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
diffreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K174(REAL,addreal,(id REAL),compreal) is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
diffreal .: (r5,(0. (TOP-REAL C))) is set
K324((0. (TOP-REAL C))) is Relation-like Function-like complex-yielding set
K295(r5,K324((0. (TOP-REAL C)))) is Relation-like Function-like set
|.(r5 - (0. (TOP-REAL C))).| is V11() real ext-real non negative Element of REAL
sqr (r5 - (0. (TOP-REAL C))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(r5 - (0. (TOP-REAL C))) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((r5 - (0. (TOP-REAL C))),(r5 - (0. (TOP-REAL C)))) is Relation-like Function-like set
multreal .: ((r5 - (0. (TOP-REAL C))),(r5 - (0. (TOP-REAL C)))) is set
K383((sqr (r5 - (0. (TOP-REAL C))))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (r5 - (0. (TOP-REAL C)))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (r5 - (0. (TOP-REAL C))))) is V11() real ext-real Element of REAL
|.r5.| is V11() real ext-real non negative Element of REAL
sqr r5 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
r5 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (r5,r5) is Relation-like Function-like set
multreal .: (r5,r5) is set
K383((sqr r5)) is V11() real ext-real Element of REAL
K195(REAL,(sqr r5),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr r5)) is V11() real ext-real Element of REAL
qt2 * ((p + 1) / |.EX2.|) is V11() real ext-real Element of REAL
(qt2 * ((p + 1) / |.EX2.|)) * |.EX2.| is V11() real ext-real Element of REAL
qt2 * (p + 1) is V11() real ext-real Element of REAL
(qt2 * (p + 1)) / |.EX2.| is V11() real ext-real Element of REAL
((qt2 * (p + 1)) / |.EX2.|) * |.EX2.| is V11() real ext-real Element of REAL
|.C.| is V11() real ext-real non negative Element of REAL
sqr C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
C (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (C,C) is Relation-like Function-like set
multreal .: (C,C) is set
K383((sqr C)) is V11() real ext-real Element of REAL
K195(REAL,(sqr C),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr C)) is V11() real ext-real Element of REAL
(qt2 * ((p + 1) / |.EX2.|)) * |.C.| is V11() real ext-real Element of REAL
p + 0 is V11() real ext-real Element of REAL
p + qt2 is V11() real ext-real Element of REAL
(1 - qt2) * |.C.| is V11() real ext-real Element of REAL
(1 - qt2) * p is V11() real ext-real Element of REAL
P3 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.P3.| is V11() real ext-real non negative Element of REAL
sqr P3 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
P3 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (P3,P3) is Relation-like Function-like set
multreal .: (P3,P3) is set
K383((sqr P3)) is V11() real ext-real Element of REAL
K195(REAL,(sqr P3),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr P3)) is V11() real ext-real Element of REAL
(1 - qt2) + (qt2 * ((p + 1) / |.EX2.|)) is V11() real ext-real Element of REAL
abs ((1 - qt2) + (qt2 * ((p + 1) / |.EX2.|))) is V11() real ext-real Element of REAL
(abs ((1 - qt2) + (qt2 * ((p + 1) / |.EX2.|)))) * |.C.| is V11() real ext-real Element of REAL
((1 - qt2) + (qt2 * ((p + 1) / |.EX2.|))) * |.C.| is V11() real ext-real Element of REAL
((1 - qt2) * |.C.|) + ((qt2 * ((p + 1) / |.EX2.|)) * |.C.|) is V11() real ext-real Element of REAL
(qt2 * (p + 1)) + ((1 - qt2) * p) is V11() real ext-real Element of REAL
((1 - qt2) + (qt2 * ((p + 1) / |.EX2.|))) * C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
((1 - qt2) + (qt2 * ((p + 1) / |.EX2.|))) * C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
((1 - qt2) + (qt2 * ((p + 1) / |.EX2.|))) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (((1 - qt2) + (qt2 * ((p + 1) / |.EX2.|))),(id REAL)) is set
C (#) (((1 - qt2) + (qt2 * ((p + 1) / |.EX2.|))) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
|.(((1 - qt2) + (qt2 * ((p + 1) / |.EX2.|))) * C).| is V11() real ext-real non negative Element of REAL
sqr (((1 - qt2) + (qt2 * ((p + 1) / |.EX2.|))) * C) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(((1 - qt2) + (qt2 * ((p + 1) / |.EX2.|))) * C) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((((1 - qt2) + (qt2 * ((p + 1) / |.EX2.|))) * C),(((1 - qt2) + (qt2 * ((p + 1) / |.EX2.|))) * C)) is Relation-like Function-like set
multreal .: ((((1 - qt2) + (qt2 * ((p + 1) / |.EX2.|))) * C),(((1 - qt2) + (qt2 * ((p + 1) / |.EX2.|))) * C)) is set
K383((sqr (((1 - qt2) + (qt2 * ((p + 1) / |.EX2.|))) * C))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (((1 - qt2) + (qt2 * ((p + 1) / |.EX2.|))) * C)),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (((1 - qt2) + (qt2 * ((p + 1) / |.EX2.|))) * C))) is V11() real ext-real Element of REAL
(qt2 * ((p + 1) / |.EX2.|)) * C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
(qt2 * ((p + 1) / |.EX2.|)) * C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(qt2 * ((p + 1) / |.EX2.|)) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] ((qt2 * ((p + 1) / |.EX2.|)),(id REAL)) is set
C (#) ((qt2 * ((p + 1) / |.EX2.|)) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
((1 - qt2) * C) + ((qt2 * ((p + 1) / |.EX2.|)) * C) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) . (((1 - qt2) * C),((qt2 * ((p + 1) / |.EX2.|)) * C)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[((1 - qt2) * C),((qt2 * ((p + 1) / |.EX2.|)) * C)] is non empty set
{((1 - qt2) * C),((qt2 * ((p + 1) / |.EX2.|)) * C)} is non empty functional V35() V39() set
{{((1 - qt2) * C),((qt2 * ((p + 1) / |.EX2.|)) * C)},{((1 - qt2) * C)}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [((1 - qt2) * C),((qt2 * ((p + 1) / |.EX2.|)) * C)] is set
((1 - qt2) * C) + ((qt2 * ((p + 1) / |.EX2.|)) * C) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (((1 - qt2) * C),((qt2 * ((p + 1) / |.EX2.|)) * C)) is set
|.(((1 - qt2) * C) + ((qt2 * ((p + 1) / |.EX2.|)) * C)).| is V11() real ext-real non negative Element of REAL
sqr (((1 - qt2) * C) + ((qt2 * ((p + 1) / |.EX2.|)) * C)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(((1 - qt2) * C) + ((qt2 * ((p + 1) / |.EX2.|)) * C)) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((((1 - qt2) * C) + ((qt2 * ((p + 1) / |.EX2.|)) * C)),(((1 - qt2) * C) + ((qt2 * ((p + 1) / |.EX2.|)) * C))) is Relation-like Function-like set
multreal .: ((((1 - qt2) * C) + ((qt2 * ((p + 1) / |.EX2.|)) * C)),(((1 - qt2) * C) + ((qt2 * ((p + 1) / |.EX2.|)) * C))) is set
K383((sqr (((1 - qt2) * C) + ((qt2 * ((p + 1) / |.EX2.|)) * C)))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (((1 - qt2) * C) + ((qt2 * ((p + 1) / |.EX2.|)) * C))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (((1 - qt2) * C) + ((qt2 * ((p + 1) / |.EX2.|)) * C)))) is V11() real ext-real Element of REAL
|.(((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C))).| is V11() real ext-real non negative Element of REAL
sqr (((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C))) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C))),(((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C)))) is Relation-like Function-like set
multreal .: ((((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C))),(((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C)))) is set
K383((sqr (((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C))))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C)))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C))))) is V11() real ext-real Element of REAL
(1 - qt2) + qt2 is V11() real ext-real Element of REAL
0 + qt2 is V11() real ext-real Element of REAL
1 * (((p + 1) / |.EX2.|) * C) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
1 * (((p + 1) / |.EX2.|) * C) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
1 multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (1,(id REAL)) is set
(((p + 1) / |.EX2.|) * C) (#) (1 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
(0. (TOP-REAL C)) + (1 * (((p + 1) / |.EX2.|) * C)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) . ((0. (TOP-REAL C)),(1 * (((p + 1) / |.EX2.|) * C))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[(0. (TOP-REAL C)),(1 * (((p + 1) / |.EX2.|) * C))] is non empty set
{(0. (TOP-REAL C)),(1 * (((p + 1) / |.EX2.|) * C))} is non empty functional V35() V39() set
{(0. (TOP-REAL C))} is non empty trivial functional V35() V39() 1 -element set
{{(0. (TOP-REAL C)),(1 * (((p + 1) / |.EX2.|) * C))},{(0. (TOP-REAL C))}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [(0. (TOP-REAL C)),(1 * (((p + 1) / |.EX2.|) * C))] is set
(0. (TOP-REAL C)) + (1 * (((p + 1) / |.EX2.|) * C)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: ((0. (TOP-REAL C)),(1 * (((p + 1) / |.EX2.|) * C))) is set
(0. (TOP-REAL C)) + (((p + 1) / |.EX2.|) * C) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) . ((0. (TOP-REAL C)),(((p + 1) / |.EX2.|) * C)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[(0. (TOP-REAL C)),(((p + 1) / |.EX2.|) * C)] is non empty set
{(0. (TOP-REAL C)),(((p + 1) / |.EX2.|) * C)} is non empty functional V35() V39() set
{{(0. (TOP-REAL C)),(((p + 1) / |.EX2.|) * C)},{(0. (TOP-REAL C))}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [(0. (TOP-REAL C)),(((p + 1) / |.EX2.|) * C)] is set
(0. (TOP-REAL C)) + (((p + 1) / |.EX2.|) * C) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: ((0. (TOP-REAL C)),(((p + 1) / |.EX2.|) * C)) is set
|.(((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C))).| is V11() real ext-real non negative Element of REAL
sqr (((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C))) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C))),(((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C)))) is Relation-like Function-like set
multreal .: ((((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C))),(((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C)))) is set
K383((sqr (((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C))))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C)))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C))))) is V11() real ext-real Element of REAL
P3 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.P3.| is V11() real ext-real non negative Element of REAL
sqr P3 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
P3 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (P3,P3) is Relation-like Function-like set
multreal .: (P3,P3) is set
K383((sqr P3)) is V11() real ext-real Element of REAL
K195(REAL,(sqr P3),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr P3)) is V11() real ext-real Element of REAL
|.(((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C))).| is V11() real ext-real non negative Element of REAL
sqr (((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C))) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C))),(((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C)))) is Relation-like Function-like set
multreal .: ((((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C))),(((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C)))) is set
K383((sqr (((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C))))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C)))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C))))) is V11() real ext-real Element of REAL
|.(((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C))).| is V11() real ext-real non negative Element of REAL
sqr (((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C))) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C))),(((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C)))) is Relation-like Function-like set
multreal .: ((((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C))),(((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C)))) is set
K383((sqr (((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C))))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C)))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C))))) is V11() real ext-real Element of REAL
|.(((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C))).| is V11() real ext-real non negative Element of REAL
sqr (((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C))) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C))),(((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C)))) is Relation-like Function-like set
multreal .: ((((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C))),(((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C)))) is set
K383((sqr (((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C))))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C)))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C))))) is V11() real ext-real Element of REAL
|.(((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C))).| is V11() real ext-real non negative Element of REAL
sqr (((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C))) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C))),(((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C)))) is Relation-like Function-like set
multreal .: ((((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C))),(((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C)))) is set
K383((sqr (((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C))))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C)))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C))))) is V11() real ext-real Element of REAL
|.(((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C))).| is V11() real ext-real non negative Element of REAL
sqr (((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C))) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C))),(((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C)))) is Relation-like Function-like set
multreal .: ((((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C))),(((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C)))) is set
K383((sqr (((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C))))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C)))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (((1 - qt2) * C) + (qt2 * (((p + 1) / |.EX2.|) * C))))) is V11() real ext-real Element of REAL
LSeg (p12,(((p + 1) / |.EX2.|) * p12)) is non empty closed connected compact convex Element of bool the carrier of (TOP-REAL C)
{ (((1 - b1) * p12) + (b1 * (((p + 1) / |.EX2.|) * p12))) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
t2 is set
qt2 is V11() real ext-real Element of REAL
1 - qt2 is V11() real ext-real Element of REAL
(1 - qt2) * p12 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
(1 - qt2) * p12 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(1 - qt2) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] ((1 - qt2),(id REAL)) is set
p12 (#) ((1 - qt2) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
qt2 * (((p + 1) / |.EX2.|) * p12) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
qt2 * (((p + 1) / |.EX2.|) * p12) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
qt2 multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (qt2,(id REAL)) is set
(((p + 1) / |.EX2.|) * p12) (#) (qt2 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) is non empty Relation-like [: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):] -defined the carrier of (TOP-REAL C) -valued Function-like total V30([: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C)) Element of bool [:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):]
[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):] is non empty set
[:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):] is non empty set
bool [:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):] is non empty set
the U7 of (TOP-REAL C) . (((1 - qt2) * p12),(qt2 * (((p + 1) / |.EX2.|) * p12))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[((1 - qt2) * p12),(qt2 * (((p + 1) / |.EX2.|) * p12))] is non empty set
{((1 - qt2) * p12),(qt2 * (((p + 1) / |.EX2.|) * p12))} is non empty functional V35() V39() set
{((1 - qt2) * p12)} is non empty trivial functional V35() V39() 1 -element set
{{((1 - qt2) * p12),(qt2 * (((p + 1) / |.EX2.|) * p12))},{((1 - qt2) * p12)}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [((1 - qt2) * p12),(qt2 * (((p + 1) / |.EX2.|) * p12))] is set
((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (((1 - qt2) * p12),(qt2 * (((p + 1) / |.EX2.|) * p12))) is set
the carrier of (Euclid C) is non empty set
1 - 0 is non empty V11() real ext-real positive non negative Element of REAL
(1 - 0) * p12 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
(1 - 0) * p12 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(1 - 0) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] ((1 - 0),(id REAL)) is set
p12 (#) ((1 - 0) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
0 * C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
0 * C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
0 multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (0,(id REAL)) is set
C (#) (0 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
((1 - 0) * p12) + (0 * C) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) . (((1 - 0) * p12),(0 * C)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[((1 - 0) * p12),(0 * C)] is non empty set
{((1 - 0) * p12),(0 * C)} is non empty functional V35() V39() set
{((1 - 0) * p12)} is non empty trivial functional V35() V39() 1 -element set
{{((1 - 0) * p12),(0 * C)},{((1 - 0) * p12)}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [((1 - 0) * p12),(0 * C)] is set
((1 - 0) * p12) + (0 * C) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (((1 - 0) * p12),(0 * C)) is set
((1 - 0) * p12) + (0. (TOP-REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) . (((1 - 0) * p12),(0. (TOP-REAL C))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[((1 - 0) * p12),(0. (TOP-REAL C))] is non empty set
{((1 - 0) * p12),(0. (TOP-REAL C))} is non empty functional V35() V39() set
{{((1 - 0) * p12),(0. (TOP-REAL C))},{((1 - 0) * p12)}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [((1 - 0) * p12),(0. (TOP-REAL C))] is set
((1 - 0) * p12) + (0. (TOP-REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (((1 - 0) * p12),(0. (TOP-REAL C))) is set
q4 is Element of the carrier of (Euclid C)
dist q4 is Relation-like the carrier of (TopSpaceMetr (Euclid C)) -defined the carrier of R^1 -valued Function-like total V30( the carrier of (TopSpaceMetr (Euclid C)), the carrier of R^1) complex-yielding V174() V175() Element of bool [: the carrier of (TopSpaceMetr (Euclid C)), the carrier of R^1:]
r2 is Element of bool the carrier of (TopSpaceMetr (Euclid C))
(dist q4) .: r2 is V183() V184() V185() Element of bool the carrier of R^1
r0 is set
dom (dist q4) is Element of bool the carrier of (TopSpaceMetr (Euclid C))
Q is set
(dist q4) . Q is V11() real ext-real Element of REAL
r5 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
P3 is ext-real set
dom (dist q4) is Element of bool the carrier of (TopSpaceMetr (Euclid C))
W3 is set
(dist q4) . W3 is V11() real ext-real Element of REAL
Q is Element of the carrier of (Euclid C)
dist (Q,q4) is V11() real ext-real Element of REAL
the distance of (Euclid C) is non empty Relation-like [: the carrier of (Euclid C), the carrier of (Euclid C):] -defined REAL -valued Function-like total V30([: the carrier of (Euclid C), the carrier of (Euclid C):], REAL ) complex-yielding V174() V175() Element of bool [:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:]
[: the carrier of (Euclid C), the carrier of (Euclid C):] is non empty set
[:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:] is non empty non trivial V35() set
the distance of (Euclid C) . (Q,q4) is V11() real ext-real Element of REAL
[Q,q4] is non empty set
{Q,q4} is non empty V35() set
{Q} is non empty trivial V35() 1 -element set
{{Q,q4},{Q}} is non empty V35() V39() set
the distance of (Euclid C) . [Q,q4] is V11() real ext-real set
r0 is V183() V184() V185() Element of bool REAL
Q is Element of the carrier of (Euclid C)
dom (dist q4) is Element of bool the carrier of (TopSpaceMetr (Euclid C))
dist (Q,q4) is V11() real ext-real Element of REAL
the distance of (Euclid C) is non empty Relation-like [: the carrier of (Euclid C), the carrier of (Euclid C):] -defined REAL -valued Function-like total V30([: the carrier of (Euclid C), the carrier of (Euclid C):], REAL ) complex-yielding V174() V175() Element of bool [:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:]
[: the carrier of (Euclid C), the carrier of (Euclid C):] is non empty set
[:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:] is non empty non trivial V35() set
the distance of (Euclid C) . (Q,q4) is V11() real ext-real Element of REAL
[Q,q4] is non empty set
{Q,q4} is non empty V35() set
{Q} is non empty trivial V35() 1 -element set
{{Q,q4},{Q}} is non empty V35() V39() set
the distance of (Euclid C) . [Q,q4] is V11() real ext-real set
(dist q4) . Q is V11() real ext-real Element of REAL
lower_bound r0 is V11() real ext-real Element of REAL
[#] ((dist q4) .: r2) is V183() V184() V185() Element of bool REAL
lower_bound ([#] ((dist q4) .: r2)) is V11() real ext-real Element of REAL
lower_bound ((dist q4) .: r2) is V11() real ext-real Element of REAL
r5 - (0. (TOP-REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
- (0. (TOP-REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
- (0. (TOP-REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
compreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
(0. (TOP-REAL C)) (#) compreal is Relation-like Function-like V35() complex-yielding V174() V175() set
K38(1) is V11() real ext-real non positive set
K38(1) * (0. (TOP-REAL C)) is Relation-like Function-like set
K38(1) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (K38(1),(id REAL)) is set
(0. (TOP-REAL C)) (#) (K38(1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
K258((TOP-REAL C),r5,(- (0. (TOP-REAL C)))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) . (r5,(- (0. (TOP-REAL C)))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[r5,(- (0. (TOP-REAL C)))] is non empty set
{r5,(- (0. (TOP-REAL C)))} is non empty functional V35() V39() set
{r5} is non empty trivial functional V35() V39() 1 -element set
{{r5,(- (0. (TOP-REAL C)))},{r5}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [r5,(- (0. (TOP-REAL C)))] is set
r5 + (- (0. (TOP-REAL C))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (r5,(- (0. (TOP-REAL C)))) is set
r5 - (0. (TOP-REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
diffreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K174(REAL,addreal,(id REAL),compreal) is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
diffreal .: (r5,(0. (TOP-REAL C))) is set
K324((0. (TOP-REAL C))) is Relation-like Function-like complex-yielding set
K295(r5,K324((0. (TOP-REAL C)))) is Relation-like Function-like set
|.(r5 - (0. (TOP-REAL C))).| is V11() real ext-real non negative Element of REAL
sqr (r5 - (0. (TOP-REAL C))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(r5 - (0. (TOP-REAL C))) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((r5 - (0. (TOP-REAL C))),(r5 - (0. (TOP-REAL C)))) is Relation-like Function-like set
multreal .: ((r5 - (0. (TOP-REAL C))),(r5 - (0. (TOP-REAL C)))) is set
K383((sqr (r5 - (0. (TOP-REAL C))))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (r5 - (0. (TOP-REAL C)))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (r5 - (0. (TOP-REAL C))))) is V11() real ext-real Element of REAL
|.r5.| is V11() real ext-real non negative Element of REAL
sqr r5 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
r5 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (r5,r5) is Relation-like Function-like set
multreal .: (r5,r5) is set
K383((sqr r5)) is V11() real ext-real Element of REAL
K195(REAL,(sqr r5),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr r5)) is V11() real ext-real Element of REAL
qt2 * ((p + 1) / |.EX2.|) is V11() real ext-real Element of REAL
(qt2 * ((p + 1) / |.EX2.|)) * |.EX2.| is V11() real ext-real Element of REAL
qt2 * (p + 1) is V11() real ext-real Element of REAL
(qt2 * (p + 1)) / |.EX2.| is V11() real ext-real Element of REAL
((qt2 * (p + 1)) / |.EX2.|) * |.EX2.| is V11() real ext-real Element of REAL
|.p12.| is V11() real ext-real non negative Element of REAL
sqr p12 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
p12 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (p12,p12) is Relation-like Function-like set
multreal .: (p12,p12) is set
K383((sqr p12)) is V11() real ext-real Element of REAL
K195(REAL,(sqr p12),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr p12)) is V11() real ext-real Element of REAL
(qt2 * ((p + 1) / |.EX2.|)) * |.p12.| is V11() real ext-real Element of REAL
p + 0 is V11() real ext-real Element of REAL
p + qt2 is V11() real ext-real Element of REAL
(1 - qt2) * |.p12.| is V11() real ext-real Element of REAL
(1 - qt2) * p is V11() real ext-real Element of REAL
P3 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.P3.| is V11() real ext-real non negative Element of REAL
sqr P3 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
P3 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (P3,P3) is Relation-like Function-like set
multreal .: (P3,P3) is set
K383((sqr P3)) is V11() real ext-real Element of REAL
K195(REAL,(sqr P3),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr P3)) is V11() real ext-real Element of REAL
(1 - qt2) + (qt2 * ((p + 1) / |.EX2.|)) is V11() real ext-real Element of REAL
abs ((1 - qt2) + (qt2 * ((p + 1) / |.EX2.|))) is V11() real ext-real Element of REAL
(abs ((1 - qt2) + (qt2 * ((p + 1) / |.EX2.|)))) * |.p12.| is V11() real ext-real Element of REAL
((1 - qt2) + (qt2 * ((p + 1) / |.EX2.|))) * |.p12.| is V11() real ext-real Element of REAL
((1 - qt2) * |.p12.|) + ((qt2 * ((p + 1) / |.EX2.|)) * |.p12.|) is V11() real ext-real Element of REAL
(qt2 * (p + 1)) + ((1 - qt2) * p) is V11() real ext-real Element of REAL
((1 - qt2) + (qt2 * ((p + 1) / |.EX2.|))) * p12 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
((1 - qt2) + (qt2 * ((p + 1) / |.EX2.|))) * p12 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
((1 - qt2) + (qt2 * ((p + 1) / |.EX2.|))) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (((1 - qt2) + (qt2 * ((p + 1) / |.EX2.|))),(id REAL)) is set
p12 (#) (((1 - qt2) + (qt2 * ((p + 1) / |.EX2.|))) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
|.(((1 - qt2) + (qt2 * ((p + 1) / |.EX2.|))) * p12).| is V11() real ext-real non negative Element of REAL
sqr (((1 - qt2) + (qt2 * ((p + 1) / |.EX2.|))) * p12) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(((1 - qt2) + (qt2 * ((p + 1) / |.EX2.|))) * p12) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((((1 - qt2) + (qt2 * ((p + 1) / |.EX2.|))) * p12),(((1 - qt2) + (qt2 * ((p + 1) / |.EX2.|))) * p12)) is Relation-like Function-like set
multreal .: ((((1 - qt2) + (qt2 * ((p + 1) / |.EX2.|))) * p12),(((1 - qt2) + (qt2 * ((p + 1) / |.EX2.|))) * p12)) is set
K383((sqr (((1 - qt2) + (qt2 * ((p + 1) / |.EX2.|))) * p12))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (((1 - qt2) + (qt2 * ((p + 1) / |.EX2.|))) * p12)),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (((1 - qt2) + (qt2 * ((p + 1) / |.EX2.|))) * p12))) is V11() real ext-real Element of REAL
(qt2 * ((p + 1) / |.EX2.|)) * p12 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
(qt2 * ((p + 1) / |.EX2.|)) * p12 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(qt2 * ((p + 1) / |.EX2.|)) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] ((qt2 * ((p + 1) / |.EX2.|)),(id REAL)) is set
p12 (#) ((qt2 * ((p + 1) / |.EX2.|)) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
((1 - qt2) * p12) + ((qt2 * ((p + 1) / |.EX2.|)) * p12) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) . (((1 - qt2) * p12),((qt2 * ((p + 1) / |.EX2.|)) * p12)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[((1 - qt2) * p12),((qt2 * ((p + 1) / |.EX2.|)) * p12)] is non empty set
{((1 - qt2) * p12),((qt2 * ((p + 1) / |.EX2.|)) * p12)} is non empty functional V35() V39() set
{{((1 - qt2) * p12),((qt2 * ((p + 1) / |.EX2.|)) * p12)},{((1 - qt2) * p12)}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [((1 - qt2) * p12),((qt2 * ((p + 1) / |.EX2.|)) * p12)] is set
((1 - qt2) * p12) + ((qt2 * ((p + 1) / |.EX2.|)) * p12) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (((1 - qt2) * p12),((qt2 * ((p + 1) / |.EX2.|)) * p12)) is set
|.(((1 - qt2) * p12) + ((qt2 * ((p + 1) / |.EX2.|)) * p12)).| is V11() real ext-real non negative Element of REAL
sqr (((1 - qt2) * p12) + ((qt2 * ((p + 1) / |.EX2.|)) * p12)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(((1 - qt2) * p12) + ((qt2 * ((p + 1) / |.EX2.|)) * p12)) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((((1 - qt2) * p12) + ((qt2 * ((p + 1) / |.EX2.|)) * p12)),(((1 - qt2) * p12) + ((qt2 * ((p + 1) / |.EX2.|)) * p12))) is Relation-like Function-like set
multreal .: ((((1 - qt2) * p12) + ((qt2 * ((p + 1) / |.EX2.|)) * p12)),(((1 - qt2) * p12) + ((qt2 * ((p + 1) / |.EX2.|)) * p12))) is set
K383((sqr (((1 - qt2) * p12) + ((qt2 * ((p + 1) / |.EX2.|)) * p12)))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (((1 - qt2) * p12) + ((qt2 * ((p + 1) / |.EX2.|)) * p12))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (((1 - qt2) * p12) + ((qt2 * ((p + 1) / |.EX2.|)) * p12)))) is V11() real ext-real Element of REAL
|.(((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12))).| is V11() real ext-real non negative Element of REAL
sqr (((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12))) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12))),(((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12)))) is Relation-like Function-like set
multreal .: ((((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12))),(((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12)))) is set
K383((sqr (((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12))))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12)))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12))))) is V11() real ext-real Element of REAL
(1 - qt2) + qt2 is V11() real ext-real Element of REAL
0 + qt2 is V11() real ext-real Element of REAL
1 * (((p + 1) / |.EX2.|) * p12) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
1 * (((p + 1) / |.EX2.|) * p12) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
1 multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (1,(id REAL)) is set
(((p + 1) / |.EX2.|) * p12) (#) (1 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
(0. (TOP-REAL C)) + (1 * (((p + 1) / |.EX2.|) * p12)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) . ((0. (TOP-REAL C)),(1 * (((p + 1) / |.EX2.|) * p12))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[(0. (TOP-REAL C)),(1 * (((p + 1) / |.EX2.|) * p12))] is non empty set
{(0. (TOP-REAL C)),(1 * (((p + 1) / |.EX2.|) * p12))} is non empty functional V35() V39() set
{(0. (TOP-REAL C))} is non empty trivial functional V35() V39() 1 -element set
{{(0. (TOP-REAL C)),(1 * (((p + 1) / |.EX2.|) * p12))},{(0. (TOP-REAL C))}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [(0. (TOP-REAL C)),(1 * (((p + 1) / |.EX2.|) * p12))] is set
(0. (TOP-REAL C)) + (1 * (((p + 1) / |.EX2.|) * p12)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: ((0. (TOP-REAL C)),(1 * (((p + 1) / |.EX2.|) * p12))) is set
(0. (TOP-REAL C)) + (((p + 1) / |.EX2.|) * p12) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) . ((0. (TOP-REAL C)),(((p + 1) / |.EX2.|) * p12)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[(0. (TOP-REAL C)),(((p + 1) / |.EX2.|) * p12)] is non empty set
{(0. (TOP-REAL C)),(((p + 1) / |.EX2.|) * p12)} is non empty functional V35() V39() set
{{(0. (TOP-REAL C)),(((p + 1) / |.EX2.|) * p12)},{(0. (TOP-REAL C))}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [(0. (TOP-REAL C)),(((p + 1) / |.EX2.|) * p12)] is set
(0. (TOP-REAL C)) + (((p + 1) / |.EX2.|) * p12) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: ((0. (TOP-REAL C)),(((p + 1) / |.EX2.|) * p12)) is set
|.(((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12))).| is V11() real ext-real non negative Element of REAL
sqr (((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12))) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12))),(((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12)))) is Relation-like Function-like set
multreal .: ((((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12))),(((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12)))) is set
K383((sqr (((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12))))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12)))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12))))) is V11() real ext-real Element of REAL
P3 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.P3.| is V11() real ext-real non negative Element of REAL
sqr P3 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
P3 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (P3,P3) is Relation-like Function-like set
multreal .: (P3,P3) is set
K383((sqr P3)) is V11() real ext-real Element of REAL
K195(REAL,(sqr P3),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr P3)) is V11() real ext-real Element of REAL
|.(((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12))).| is V11() real ext-real non negative Element of REAL
sqr (((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12))) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12))),(((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12)))) is Relation-like Function-like set
multreal .: ((((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12))),(((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12)))) is set
K383((sqr (((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12))))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12)))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12))))) is V11() real ext-real Element of REAL
|.(((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12))).| is V11() real ext-real non negative Element of REAL
sqr (((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12))) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12))),(((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12)))) is Relation-like Function-like set
multreal .: ((((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12))),(((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12)))) is set
K383((sqr (((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12))))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12)))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12))))) is V11() real ext-real Element of REAL
|.(((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12))).| is V11() real ext-real non negative Element of REAL
sqr (((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12))) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12))),(((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12)))) is Relation-like Function-like set
multreal .: ((((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12))),(((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12)))) is set
K383((sqr (((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12))))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12)))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12))))) is V11() real ext-real Element of REAL
|.(((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12))).| is V11() real ext-real non negative Element of REAL
sqr (((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12))) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12))),(((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12)))) is Relation-like Function-like set
multreal .: ((((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12))),(((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12)))) is set
K383((sqr (((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12))))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12)))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12))))) is V11() real ext-real Element of REAL
|.(((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12))).| is V11() real ext-real non negative Element of REAL
sqr (((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12))) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12))),(((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12)))) is Relation-like Function-like set
multreal .: ((((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12))),(((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12)))) is set
K383((sqr (((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12))))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12)))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (((1 - qt2) * p12) + (qt2 * (((p + 1) / |.EX2.|) * p12))))) is V11() real ext-real Element of REAL
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
bool the carrier of (TOP-REAL C) is non empty set
REAL C is non empty functional FinSequence-membered FinSequenceSet of REAL
C -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = C } is set
p is V11() real ext-real Element of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C) : not p <= |.b1.| } is set
(REAL C) \ { b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C) : not p <= |.b1.| } is functional FinSequence-membered Element of bool (REAL C)
bool (REAL C) is non empty set
WH is Element of bool the carrier of (TOP-REAL C)
p12 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the topology of (TOP-REAL C) is non empty Element of bool (bool the carrier of (TOP-REAL C))
bool (bool the carrier of (TOP-REAL C)) is non empty set
TopStruct(# the carrier of (TOP-REAL C), the topology of (TOP-REAL C) #) is non empty strict TopSpace-like TopStruct
Euclid C is non empty strict Reflexive discerning symmetric triangle Discerning MetrStruct
Pitag_dist C is non empty Relation-like [:(REAL C),(REAL C):] -defined REAL -valued Function-like total V30([:(REAL C),(REAL C):], REAL ) complex-yielding V174() V175() Element of bool [:[:(REAL C),(REAL C):],REAL:]
[:(REAL C),(REAL C):] is non empty set
[:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() set
MetrStruct(# (REAL C),(Pitag_dist C) #) is strict MetrStruct
TopSpaceMetr (Euclid C) is TopStruct
the carrier of (TopSpaceMetr (Euclid C)) is set
bool the carrier of (TopSpaceMetr (Euclid C)) is non empty set
LSeg (p12,C) is non empty closed connected compact convex Element of bool the carrier of (TOP-REAL C)
{ (((1 - b1) * p12) + (b1 * C)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
0. (TOP-REAL C) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like V62( TOP-REAL C) complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the ZeroF of (TOP-REAL C) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
r is Element of bool the carrier of (TopSpaceMetr (Euclid C))
dist_min r is Relation-like the carrier of (TopSpaceMetr (Euclid C)) -defined the carrier of R^1 -valued Function-like total V30( the carrier of (TopSpaceMetr (Euclid C)), the carrier of R^1) complex-yielding V174() V175() Element of bool [: the carrier of (TopSpaceMetr (Euclid C)), the carrier of R^1:]
[: the carrier of (TopSpaceMetr (Euclid C)), the carrier of R^1:] is complex-yielding V174() V175() set
bool [: the carrier of (TopSpaceMetr (Euclid C)), the carrier of R^1:] is non empty set
(dist_min r) . (0. (TOP-REAL C)) is V11() real ext-real Element of REAL
EX2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.EX2.| is V11() real ext-real non negative Element of REAL
sqr EX2 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
sqrreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
EX2 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (EX2,EX2) is Relation-like Function-like set
multreal .: (EX2,EX2) is set
K383((sqr EX2)) is V11() real ext-real Element of REAL
addreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K195(REAL,(sqr EX2),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr EX2)) is V11() real ext-real Element of REAL
p / |.EX2.| is V11() real ext-real Element of REAL
(p / |.EX2.|) * p12 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
(p / |.EX2.|) * p12 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(p / |.EX2.|) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
id REAL is non empty Relation-like REAL -defined REAL -valued Function-like one-to-one total V30( REAL , REAL ) complex-yielding V174() V175() increasing V179() Element of bool [:REAL,REAL:]
multreal [;] ((p / |.EX2.|),(id REAL)) is set
p12 (#) ((p / |.EX2.|) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
(p / |.EX2.|) * C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
(p / |.EX2.|) * C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
C (#) ((p / |.EX2.|) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C) : p <= |.b1.| } is set
t2 is set
qt2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.qt2.| is V11() real ext-real non negative Element of REAL
sqr qt2 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
qt2 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (qt2,qt2) is Relation-like Function-like set
multreal .: (qt2,qt2) is set
K383((sqr qt2)) is V11() real ext-real Element of REAL
K195(REAL,(sqr qt2),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr qt2)) is V11() real ext-real Element of REAL
t2 is set
qt2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.qt2.| is V11() real ext-real non negative Element of REAL
sqr qt2 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
qt2 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (qt2,qt2) is Relation-like Function-like set
multreal .: (qt2,qt2) is set
K383((sqr qt2)) is V11() real ext-real Element of REAL
K195(REAL,(sqr qt2),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr qt2)) is V11() real ext-real Element of REAL
r2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.r2.| is V11() real ext-real non negative Element of REAL
sqr r2 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
r2 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (r2,r2) is Relation-like Function-like set
multreal .: (r2,r2) is set
K383((sqr r2)) is V11() real ext-real Element of REAL
K195(REAL,(sqr r2),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr r2)) is V11() real ext-real Element of REAL
LSeg (p12,((p / |.EX2.|) * p12)) is non empty closed connected compact convex Element of bool the carrier of (TOP-REAL C)
{ (((1 - b1) * p12) + (b1 * ((p / |.EX2.|) * p12))) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
t2 is set
qt2 is V11() real ext-real Element of REAL
1 - qt2 is V11() real ext-real Element of REAL
(1 - qt2) * p12 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
(1 - qt2) * p12 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(1 - qt2) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] ((1 - qt2),(id REAL)) is set
p12 (#) ((1 - qt2) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
qt2 * ((p / |.EX2.|) * p12) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
qt2 * ((p / |.EX2.|) * p12) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
qt2 multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (qt2,(id REAL)) is set
((p / |.EX2.|) * p12) (#) (qt2 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
((1 - qt2) * p12) + (qt2 * ((p / |.EX2.|) * p12)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) is non empty Relation-like [: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):] -defined the carrier of (TOP-REAL C) -valued Function-like total V30([: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C)) Element of bool [:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):]
[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):] is non empty set
[:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):] is non empty set
bool [:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):] is non empty set
the U7 of (TOP-REAL C) . (((1 - qt2) * p12),(qt2 * ((p / |.EX2.|) * p12))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[((1 - qt2) * p12),(qt2 * ((p / |.EX2.|) * p12))] is non empty set
{((1 - qt2) * p12),(qt2 * ((p / |.EX2.|) * p12))} is non empty functional V35() V39() set
{((1 - qt2) * p12)} is non empty trivial functional V35() V39() 1 -element set
{{((1 - qt2) * p12),(qt2 * ((p / |.EX2.|) * p12))},{((1 - qt2) * p12)}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [((1 - qt2) * p12),(qt2 * ((p / |.EX2.|) * p12))] is set
((1 - qt2) * p12) + (qt2 * ((p / |.EX2.|) * p12)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (((1 - qt2) * p12),(qt2 * ((p / |.EX2.|) * p12))) is set
the carrier of (Euclid C) is non empty set
1 - 0 is non empty V11() real ext-real positive non negative Element of REAL
(1 - 0) * p12 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
(1 - 0) * p12 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(1 - 0) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] ((1 - 0),(id REAL)) is set
p12 (#) ((1 - 0) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
0 * C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
0 * C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
0 multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (0,(id REAL)) is set
C (#) (0 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
((1 - 0) * p12) + (0 * C) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) . (((1 - 0) * p12),(0 * C)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[((1 - 0) * p12),(0 * C)] is non empty set
{((1 - 0) * p12),(0 * C)} is non empty functional V35() V39() set
{((1 - 0) * p12)} is non empty trivial functional V35() V39() 1 -element set
{{((1 - 0) * p12),(0 * C)},{((1 - 0) * p12)}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [((1 - 0) * p12),(0 * C)] is set
((1 - 0) * p12) + (0 * C) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (((1 - 0) * p12),(0 * C)) is set
((1 - 0) * p12) + (0. (TOP-REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) . (((1 - 0) * p12),(0. (TOP-REAL C))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[((1 - 0) * p12),(0. (TOP-REAL C))] is non empty set
{((1 - 0) * p12),(0. (TOP-REAL C))} is non empty functional V35() V39() set
{{((1 - 0) * p12),(0. (TOP-REAL C))},{((1 - 0) * p12)}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [((1 - 0) * p12),(0. (TOP-REAL C))] is set
((1 - 0) * p12) + (0. (TOP-REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (((1 - 0) * p12),(0. (TOP-REAL C))) is set
q4 is Element of the carrier of (Euclid C)
dist q4 is Relation-like the carrier of (TopSpaceMetr (Euclid C)) -defined the carrier of R^1 -valued Function-like total V30( the carrier of (TopSpaceMetr (Euclid C)), the carrier of R^1) complex-yielding V174() V175() Element of bool [: the carrier of (TopSpaceMetr (Euclid C)), the carrier of R^1:]
r2 is Element of bool the carrier of (TopSpaceMetr (Euclid C))
(dist q4) .: r2 is V183() V184() V185() Element of bool the carrier of R^1
r0 is set
dom (dist q4) is Element of bool the carrier of (TopSpaceMetr (Euclid C))
Q is set
(dist q4) . Q is V11() real ext-real Element of REAL
r5 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
P3 is ext-real set
dom (dist q4) is Element of bool the carrier of (TopSpaceMetr (Euclid C))
W3 is set
(dist q4) . W3 is V11() real ext-real Element of REAL
Q is Element of the carrier of (Euclid C)
dist (Q,q4) is V11() real ext-real Element of REAL
the distance of (Euclid C) is non empty Relation-like [: the carrier of (Euclid C), the carrier of (Euclid C):] -defined REAL -valued Function-like total V30([: the carrier of (Euclid C), the carrier of (Euclid C):], REAL ) complex-yielding V174() V175() Element of bool [:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:]
[: the carrier of (Euclid C), the carrier of (Euclid C):] is non empty set
[:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:] is non empty non trivial V35() set
the distance of (Euclid C) . (Q,q4) is V11() real ext-real Element of REAL
[Q,q4] is non empty set
{Q,q4} is non empty V35() set
{Q} is non empty trivial V35() 1 -element set
{{Q,q4},{Q}} is non empty V35() V39() set
the distance of (Euclid C) . [Q,q4] is V11() real ext-real set
r0 is V183() V184() V185() Element of bool REAL
Q is Element of the carrier of (Euclid C)
dom (dist q4) is Element of bool the carrier of (TopSpaceMetr (Euclid C))
dist (Q,q4) is V11() real ext-real Element of REAL
the distance of (Euclid C) is non empty Relation-like [: the carrier of (Euclid C), the carrier of (Euclid C):] -defined REAL -valued Function-like total V30([: the carrier of (Euclid C), the carrier of (Euclid C):], REAL ) complex-yielding V174() V175() Element of bool [:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:]
[: the carrier of (Euclid C), the carrier of (Euclid C):] is non empty set
[:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:] is non empty non trivial V35() set
the distance of (Euclid C) . (Q,q4) is V11() real ext-real Element of REAL
[Q,q4] is non empty set
{Q,q4} is non empty V35() set
{Q} is non empty trivial V35() 1 -element set
{{Q,q4},{Q}} is non empty V35() V39() set
the distance of (Euclid C) . [Q,q4] is V11() real ext-real set
(dist q4) . Q is V11() real ext-real Element of REAL
lower_bound r0 is V11() real ext-real Element of REAL
[#] ((dist q4) .: r2) is V183() V184() V185() Element of bool REAL
lower_bound ([#] ((dist q4) .: r2)) is V11() real ext-real Element of REAL
lower_bound ((dist q4) .: r2) is V11() real ext-real Element of REAL
r5 - (0. (TOP-REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
- (0. (TOP-REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
- (0. (TOP-REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
compreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
(0. (TOP-REAL C)) (#) compreal is Relation-like Function-like V35() complex-yielding V174() V175() set
K38(1) is V11() real ext-real non positive set
K38(1) * (0. (TOP-REAL C)) is Relation-like Function-like set
K38(1) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (K38(1),(id REAL)) is set
(0. (TOP-REAL C)) (#) (K38(1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
K258((TOP-REAL C),r5,(- (0. (TOP-REAL C)))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) . (r5,(- (0. (TOP-REAL C)))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[r5,(- (0. (TOP-REAL C)))] is non empty set
{r5,(- (0. (TOP-REAL C)))} is non empty functional V35() V39() set
{r5} is non empty trivial functional V35() V39() 1 -element set
{{r5,(- (0. (TOP-REAL C)))},{r5}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [r5,(- (0. (TOP-REAL C)))] is set
r5 + (- (0. (TOP-REAL C))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (r5,(- (0. (TOP-REAL C)))) is set
r5 - (0. (TOP-REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
diffreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K174(REAL,addreal,(id REAL),compreal) is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
diffreal .: (r5,(0. (TOP-REAL C))) is set
K324((0. (TOP-REAL C))) is Relation-like Function-like complex-yielding set
K295(r5,K324((0. (TOP-REAL C)))) is Relation-like Function-like set
|.(r5 - (0. (TOP-REAL C))).| is V11() real ext-real non negative Element of REAL
sqr (r5 - (0. (TOP-REAL C))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(r5 - (0. (TOP-REAL C))) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((r5 - (0. (TOP-REAL C))),(r5 - (0. (TOP-REAL C)))) is Relation-like Function-like set
multreal .: ((r5 - (0. (TOP-REAL C))),(r5 - (0. (TOP-REAL C)))) is set
K383((sqr (r5 - (0. (TOP-REAL C))))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (r5 - (0. (TOP-REAL C)))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (r5 - (0. (TOP-REAL C))))) is V11() real ext-real Element of REAL
|.r5.| is V11() real ext-real non negative Element of REAL
sqr r5 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
r5 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (r5,r5) is Relation-like Function-like set
multreal .: (r5,r5) is set
K383((sqr r5)) is V11() real ext-real Element of REAL
K195(REAL,(sqr r5),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr r5)) is V11() real ext-real Element of REAL
qt2 * (p / |.EX2.|) is V11() real ext-real Element of REAL
(1 - qt2) + (qt2 * (p / |.EX2.|)) is V11() real ext-real Element of REAL
abs ((1 - qt2) + (qt2 * (p / |.EX2.|))) is V11() real ext-real Element of REAL
|.p12.| is V11() real ext-real non negative Element of REAL
sqr p12 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
p12 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (p12,p12) is Relation-like Function-like set
multreal .: (p12,p12) is set
K383((sqr p12)) is V11() real ext-real Element of REAL
K195(REAL,(sqr p12),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr p12)) is V11() real ext-real Element of REAL
(abs ((1 - qt2) + (qt2 * (p / |.EX2.|)))) * |.p12.| is V11() real ext-real Element of REAL
((1 - qt2) + (qt2 * (p / |.EX2.|))) * |.p12.| is V11() real ext-real Element of REAL
(1 - qt2) * |.p12.| is V11() real ext-real Element of REAL
(qt2 * (p / |.EX2.|)) * |.p12.| is V11() real ext-real Element of REAL
((1 - qt2) * |.p12.|) + ((qt2 * (p / |.EX2.|)) * |.p12.|) is V11() real ext-real Element of REAL
(1 - qt2) * p is V11() real ext-real Element of REAL
P3 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.P3.| is V11() real ext-real non negative Element of REAL
sqr P3 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
P3 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (P3,P3) is Relation-like Function-like set
multreal .: (P3,P3) is set
K383((sqr P3)) is V11() real ext-real Element of REAL
K195(REAL,(sqr P3),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr P3)) is V11() real ext-real Element of REAL
(qt2 * (p / |.EX2.|)) * |.EX2.| is V11() real ext-real Element of REAL
qt2 * p is V11() real ext-real Element of REAL
(qt2 * p) / |.EX2.| is V11() real ext-real Element of REAL
((qt2 * p) / |.EX2.|) * |.EX2.| is V11() real ext-real Element of REAL
(qt2 * p) + ((1 - qt2) * p) is V11() real ext-real Element of REAL
((1 - qt2) + (qt2 * (p / |.EX2.|))) * p12 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
((1 - qt2) + (qt2 * (p / |.EX2.|))) * p12 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
((1 - qt2) + (qt2 * (p / |.EX2.|))) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (((1 - qt2) + (qt2 * (p / |.EX2.|))),(id REAL)) is set
p12 (#) (((1 - qt2) + (qt2 * (p / |.EX2.|))) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
|.(((1 - qt2) + (qt2 * (p / |.EX2.|))) * p12).| is V11() real ext-real non negative Element of REAL
sqr (((1 - qt2) + (qt2 * (p / |.EX2.|))) * p12) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(((1 - qt2) + (qt2 * (p / |.EX2.|))) * p12) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((((1 - qt2) + (qt2 * (p / |.EX2.|))) * p12),(((1 - qt2) + (qt2 * (p / |.EX2.|))) * p12)) is Relation-like Function-like set
multreal .: ((((1 - qt2) + (qt2 * (p / |.EX2.|))) * p12),(((1 - qt2) + (qt2 * (p / |.EX2.|))) * p12)) is set
K383((sqr (((1 - qt2) + (qt2 * (p / |.EX2.|))) * p12))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (((1 - qt2) + (qt2 * (p / |.EX2.|))) * p12)),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (((1 - qt2) + (qt2 * (p / |.EX2.|))) * p12))) is V11() real ext-real Element of REAL
(qt2 * (p / |.EX2.|)) * p12 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
(qt2 * (p / |.EX2.|)) * p12 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(qt2 * (p / |.EX2.|)) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] ((qt2 * (p / |.EX2.|)),(id REAL)) is set
p12 (#) ((qt2 * (p / |.EX2.|)) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
((1 - qt2) * p12) + ((qt2 * (p / |.EX2.|)) * p12) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) . (((1 - qt2) * p12),((qt2 * (p / |.EX2.|)) * p12)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[((1 - qt2) * p12),((qt2 * (p / |.EX2.|)) * p12)] is non empty set
{((1 - qt2) * p12),((qt2 * (p / |.EX2.|)) * p12)} is non empty functional V35() V39() set
{{((1 - qt2) * p12),((qt2 * (p / |.EX2.|)) * p12)},{((1 - qt2) * p12)}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [((1 - qt2) * p12),((qt2 * (p / |.EX2.|)) * p12)] is set
((1 - qt2) * p12) + ((qt2 * (p / |.EX2.|)) * p12) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (((1 - qt2) * p12),((qt2 * (p / |.EX2.|)) * p12)) is set
|.(((1 - qt2) * p12) + ((qt2 * (p / |.EX2.|)) * p12)).| is V11() real ext-real non negative Element of REAL
sqr (((1 - qt2) * p12) + ((qt2 * (p / |.EX2.|)) * p12)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(((1 - qt2) * p12) + ((qt2 * (p / |.EX2.|)) * p12)) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((((1 - qt2) * p12) + ((qt2 * (p / |.EX2.|)) * p12)),(((1 - qt2) * p12) + ((qt2 * (p / |.EX2.|)) * p12))) is Relation-like Function-like set
multreal .: ((((1 - qt2) * p12) + ((qt2 * (p / |.EX2.|)) * p12)),(((1 - qt2) * p12) + ((qt2 * (p / |.EX2.|)) * p12))) is set
K383((sqr (((1 - qt2) * p12) + ((qt2 * (p / |.EX2.|)) * p12)))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (((1 - qt2) * p12) + ((qt2 * (p / |.EX2.|)) * p12))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (((1 - qt2) * p12) + ((qt2 * (p / |.EX2.|)) * p12)))) is V11() real ext-real Element of REAL
|.(((1 - qt2) * p12) + (qt2 * ((p / |.EX2.|) * p12))).| is V11() real ext-real non negative Element of REAL
sqr (((1 - qt2) * p12) + (qt2 * ((p / |.EX2.|) * p12))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(((1 - qt2) * p12) + (qt2 * ((p / |.EX2.|) * p12))) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((((1 - qt2) * p12) + (qt2 * ((p / |.EX2.|) * p12))),(((1 - qt2) * p12) + (qt2 * ((p / |.EX2.|) * p12)))) is Relation-like Function-like set
multreal .: ((((1 - qt2) * p12) + (qt2 * ((p / |.EX2.|) * p12))),(((1 - qt2) * p12) + (qt2 * ((p / |.EX2.|) * p12)))) is set
K383((sqr (((1 - qt2) * p12) + (qt2 * ((p / |.EX2.|) * p12))))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (((1 - qt2) * p12) + (qt2 * ((p / |.EX2.|) * p12)))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (((1 - qt2) * p12) + (qt2 * ((p / |.EX2.|) * p12))))) is V11() real ext-real Element of REAL
|.(((1 - qt2) * p12) + (qt2 * ((p / |.EX2.|) * p12))).| is V11() real ext-real non negative Element of REAL
sqr (((1 - qt2) * p12) + (qt2 * ((p / |.EX2.|) * p12))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(((1 - qt2) * p12) + (qt2 * ((p / |.EX2.|) * p12))) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((((1 - qt2) * p12) + (qt2 * ((p / |.EX2.|) * p12))),(((1 - qt2) * p12) + (qt2 * ((p / |.EX2.|) * p12)))) is Relation-like Function-like set
multreal .: ((((1 - qt2) * p12) + (qt2 * ((p / |.EX2.|) * p12))),(((1 - qt2) * p12) + (qt2 * ((p / |.EX2.|) * p12)))) is set
K383((sqr (((1 - qt2) * p12) + (qt2 * ((p / |.EX2.|) * p12))))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (((1 - qt2) * p12) + (qt2 * ((p / |.EX2.|) * p12)))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (((1 - qt2) * p12) + (qt2 * ((p / |.EX2.|) * p12))))) is V11() real ext-real Element of REAL
|.(((1 - qt2) * p12) + (qt2 * ((p / |.EX2.|) * p12))).| is V11() real ext-real non negative Element of REAL
sqr (((1 - qt2) * p12) + (qt2 * ((p / |.EX2.|) * p12))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(((1 - qt2) * p12) + (qt2 * ((p / |.EX2.|) * p12))) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((((1 - qt2) * p12) + (qt2 * ((p / |.EX2.|) * p12))),(((1 - qt2) * p12) + (qt2 * ((p / |.EX2.|) * p12)))) is Relation-like Function-like set
multreal .: ((((1 - qt2) * p12) + (qt2 * ((p / |.EX2.|) * p12))),(((1 - qt2) * p12) + (qt2 * ((p / |.EX2.|) * p12)))) is set
K383((sqr (((1 - qt2) * p12) + (qt2 * ((p / |.EX2.|) * p12))))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (((1 - qt2) * p12) + (qt2 * ((p / |.EX2.|) * p12)))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (((1 - qt2) * p12) + (qt2 * ((p / |.EX2.|) * p12))))) is V11() real ext-real Element of REAL
|.(((1 - qt2) * p12) + (qt2 * ((p / |.EX2.|) * p12))).| is V11() real ext-real non negative Element of REAL
sqr (((1 - qt2) * p12) + (qt2 * ((p / |.EX2.|) * p12))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(((1 - qt2) * p12) + (qt2 * ((p / |.EX2.|) * p12))) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((((1 - qt2) * p12) + (qt2 * ((p / |.EX2.|) * p12))),(((1 - qt2) * p12) + (qt2 * ((p / |.EX2.|) * p12)))) is Relation-like Function-like set
multreal .: ((((1 - qt2) * p12) + (qt2 * ((p / |.EX2.|) * p12))),(((1 - qt2) * p12) + (qt2 * ((p / |.EX2.|) * p12)))) is set
K383((sqr (((1 - qt2) * p12) + (qt2 * ((p / |.EX2.|) * p12))))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (((1 - qt2) * p12) + (qt2 * ((p / |.EX2.|) * p12)))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (((1 - qt2) * p12) + (qt2 * ((p / |.EX2.|) * p12))))) is V11() real ext-real Element of REAL
LSeg (C,((p / |.EX2.|) * C)) is non empty closed connected compact convex Element of bool the carrier of (TOP-REAL C)
{ (((1 - b1) * C) + (b1 * ((p / |.EX2.|) * C))) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
t2 is set
qt2 is V11() real ext-real Element of REAL
1 - qt2 is V11() real ext-real Element of REAL
(1 - qt2) * C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
(1 - qt2) * C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(1 - qt2) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] ((1 - qt2),(id REAL)) is set
C (#) ((1 - qt2) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
qt2 * ((p / |.EX2.|) * C) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
qt2 * ((p / |.EX2.|) * C) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
qt2 multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (qt2,(id REAL)) is set
((p / |.EX2.|) * C) (#) (qt2 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
((1 - qt2) * C) + (qt2 * ((p / |.EX2.|) * C)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) is non empty Relation-like [: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):] -defined the carrier of (TOP-REAL C) -valued Function-like total V30([: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C)) Element of bool [:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):]
[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):] is non empty set
[:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):] is non empty set
bool [:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):] is non empty set
the U7 of (TOP-REAL C) . (((1 - qt2) * C),(qt2 * ((p / |.EX2.|) * C))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[((1 - qt2) * C),(qt2 * ((p / |.EX2.|) * C))] is non empty set
{((1 - qt2) * C),(qt2 * ((p / |.EX2.|) * C))} is non empty functional V35() V39() set
{((1 - qt2) * C)} is non empty trivial functional V35() V39() 1 -element set
{{((1 - qt2) * C),(qt2 * ((p / |.EX2.|) * C))},{((1 - qt2) * C)}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [((1 - qt2) * C),(qt2 * ((p / |.EX2.|) * C))] is set
((1 - qt2) * C) + (qt2 * ((p / |.EX2.|) * C)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (((1 - qt2) * C),(qt2 * ((p / |.EX2.|) * C))) is set
LSeg (C,p12) is non empty closed connected compact convex Element of bool the carrier of (TOP-REAL C)
{ (((1 - b1) * C) + (b1 * p12)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
the carrier of (Euclid C) is non empty set
1 - 0 is non empty V11() real ext-real positive non negative Element of REAL
(1 - 0) * C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
(1 - 0) * C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(1 - 0) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] ((1 - 0),(id REAL)) is set
C (#) ((1 - 0) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
0 * p12 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
0 * p12 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
0 multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (0,(id REAL)) is set
p12 (#) (0 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
((1 - 0) * C) + (0 * p12) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) . (((1 - 0) * C),(0 * p12)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[((1 - 0) * C),(0 * p12)] is non empty set
{((1 - 0) * C),(0 * p12)} is non empty functional V35() V39() set
{((1 - 0) * C)} is non empty trivial functional V35() V39() 1 -element set
{{((1 - 0) * C),(0 * p12)},{((1 - 0) * C)}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [((1 - 0) * C),(0 * p12)] is set
((1 - 0) * C) + (0 * p12) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (((1 - 0) * C),(0 * p12)) is set
((1 - 0) * C) + (0. (TOP-REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) . (((1 - 0) * C),(0. (TOP-REAL C))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[((1 - 0) * C),(0. (TOP-REAL C))] is non empty set
{((1 - 0) * C),(0. (TOP-REAL C))} is non empty functional V35() V39() set
{{((1 - 0) * C),(0. (TOP-REAL C))},{((1 - 0) * C)}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [((1 - 0) * C),(0. (TOP-REAL C))] is set
((1 - 0) * C) + (0. (TOP-REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (((1 - 0) * C),(0. (TOP-REAL C))) is set
q4 is Element of the carrier of (Euclid C)
dist q4 is Relation-like the carrier of (TopSpaceMetr (Euclid C)) -defined the carrier of R^1 -valued Function-like total V30( the carrier of (TopSpaceMetr (Euclid C)), the carrier of R^1) complex-yielding V174() V175() Element of bool [: the carrier of (TopSpaceMetr (Euclid C)), the carrier of R^1:]
r2 is Element of bool the carrier of (TopSpaceMetr (Euclid C))
(dist q4) .: r2 is V183() V184() V185() Element of bool the carrier of R^1
r0 is set
dom (dist q4) is Element of bool the carrier of (TopSpaceMetr (Euclid C))
Q is set
(dist q4) . Q is V11() real ext-real Element of REAL
r5 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
Q is Element of the carrier of (Euclid C)
dist (Q,q4) is V11() real ext-real Element of REAL
the distance of (Euclid C) is non empty Relation-like [: the carrier of (Euclid C), the carrier of (Euclid C):] -defined REAL -valued Function-like total V30([: the carrier of (Euclid C), the carrier of (Euclid C):], REAL ) complex-yielding V174() V175() Element of bool [:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:]
[: the carrier of (Euclid C), the carrier of (Euclid C):] is non empty set
[:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:] is non empty non trivial V35() set
the distance of (Euclid C) . (Q,q4) is V11() real ext-real Element of REAL
[Q,q4] is non empty set
{Q,q4} is non empty V35() set
{Q} is non empty trivial V35() 1 -element set
{{Q,q4},{Q}} is non empty V35() V39() set
the distance of (Euclid C) . [Q,q4] is V11() real ext-real set
(dist q4) . Q is V11() real ext-real Element of REAL
P3 is ext-real set
dom (dist q4) is Element of bool the carrier of (TopSpaceMetr (Euclid C))
W3 is set
(dist q4) . W3 is V11() real ext-real Element of REAL
Q is Element of the carrier of (Euclid C)
dist (Q,q4) is V11() real ext-real Element of REAL
the distance of (Euclid C) . (Q,q4) is V11() real ext-real Element of REAL
[Q,q4] is non empty set
{Q,q4} is non empty V35() set
{Q} is non empty trivial V35() 1 -element set
{{Q,q4},{Q}} is non empty V35() V39() set
the distance of (Euclid C) . [Q,q4] is V11() real ext-real set
r0 is V183() V184() V185() Element of bool REAL
dom (dist q4) is Element of bool the carrier of (TopSpaceMetr (Euclid C))
lower_bound r0 is V11() real ext-real Element of REAL
[#] ((dist q4) .: r2) is V183() V184() V185() Element of bool REAL
lower_bound ([#] ((dist q4) .: r2)) is V11() real ext-real Element of REAL
lower_bound ((dist q4) .: r2) is V11() real ext-real Element of REAL
r5 - (0. (TOP-REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
- (0. (TOP-REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
- (0. (TOP-REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
compreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
(0. (TOP-REAL C)) (#) compreal is Relation-like Function-like V35() complex-yielding V174() V175() set
K38(1) is V11() real ext-real non positive set
K38(1) * (0. (TOP-REAL C)) is Relation-like Function-like set
K38(1) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (K38(1),(id REAL)) is set
(0. (TOP-REAL C)) (#) (K38(1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
K258((TOP-REAL C),r5,(- (0. (TOP-REAL C)))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) . (r5,(- (0. (TOP-REAL C)))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[r5,(- (0. (TOP-REAL C)))] is non empty set
{r5,(- (0. (TOP-REAL C)))} is non empty functional V35() V39() set
{r5} is non empty trivial functional V35() V39() 1 -element set
{{r5,(- (0. (TOP-REAL C)))},{r5}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [r5,(- (0. (TOP-REAL C)))] is set
r5 + (- (0. (TOP-REAL C))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (r5,(- (0. (TOP-REAL C)))) is set
r5 - (0. (TOP-REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
diffreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K174(REAL,addreal,(id REAL),compreal) is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
diffreal .: (r5,(0. (TOP-REAL C))) is set
K324((0. (TOP-REAL C))) is Relation-like Function-like complex-yielding set
K295(r5,K324((0. (TOP-REAL C)))) is Relation-like Function-like set
|.(r5 - (0. (TOP-REAL C))).| is V11() real ext-real non negative Element of REAL
sqr (r5 - (0. (TOP-REAL C))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(r5 - (0. (TOP-REAL C))) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((r5 - (0. (TOP-REAL C))),(r5 - (0. (TOP-REAL C)))) is Relation-like Function-like set
multreal .: ((r5 - (0. (TOP-REAL C))),(r5 - (0. (TOP-REAL C)))) is set
K383((sqr (r5 - (0. (TOP-REAL C))))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (r5 - (0. (TOP-REAL C)))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (r5 - (0. (TOP-REAL C))))) is V11() real ext-real Element of REAL
|.r5.| is V11() real ext-real non negative Element of REAL
sqr r5 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
r5 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (r5,r5) is Relation-like Function-like set
multreal .: (r5,r5) is set
K383((sqr r5)) is V11() real ext-real Element of REAL
K195(REAL,(sqr r5),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr r5)) is V11() real ext-real Element of REAL
qt2 * (p / |.EX2.|) is V11() real ext-real Element of REAL
(1 - qt2) + (qt2 * (p / |.EX2.|)) is V11() real ext-real Element of REAL
abs ((1 - qt2) + (qt2 * (p / |.EX2.|))) is V11() real ext-real Element of REAL
|.C.| is V11() real ext-real non negative Element of REAL
sqr C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
C (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (C,C) is Relation-like Function-like set
multreal .: (C,C) is set
K383((sqr C)) is V11() real ext-real Element of REAL
K195(REAL,(sqr C),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr C)) is V11() real ext-real Element of REAL
(abs ((1 - qt2) + (qt2 * (p / |.EX2.|)))) * |.C.| is V11() real ext-real Element of REAL
((1 - qt2) + (qt2 * (p / |.EX2.|))) * |.C.| is V11() real ext-real Element of REAL
(1 - qt2) * |.C.| is V11() real ext-real Element of REAL
(qt2 * (p / |.EX2.|)) * |.C.| is V11() real ext-real Element of REAL
((1 - qt2) * |.C.|) + ((qt2 * (p / |.EX2.|)) * |.C.|) is V11() real ext-real Element of REAL
(1 - qt2) * p is V11() real ext-real Element of REAL
P3 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.P3.| is V11() real ext-real non negative Element of REAL
sqr P3 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
P3 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (P3,P3) is Relation-like Function-like set
multreal .: (P3,P3) is set
K383((sqr P3)) is V11() real ext-real Element of REAL
K195(REAL,(sqr P3),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr P3)) is V11() real ext-real Element of REAL
(qt2 * (p / |.EX2.|)) * |.EX2.| is V11() real ext-real Element of REAL
qt2 * p is V11() real ext-real Element of REAL
(qt2 * p) / |.EX2.| is V11() real ext-real Element of REAL
((qt2 * p) / |.EX2.|) * |.EX2.| is V11() real ext-real Element of REAL
(qt2 * p) + ((1 - qt2) * p) is V11() real ext-real Element of REAL
((1 - qt2) + (qt2 * (p / |.EX2.|))) * C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
((1 - qt2) + (qt2 * (p / |.EX2.|))) * C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
((1 - qt2) + (qt2 * (p / |.EX2.|))) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (((1 - qt2) + (qt2 * (p / |.EX2.|))),(id REAL)) is set
C (#) (((1 - qt2) + (qt2 * (p / |.EX2.|))) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
|.(((1 - qt2) + (qt2 * (p / |.EX2.|))) * C).| is V11() real ext-real non negative Element of REAL
sqr (((1 - qt2) + (qt2 * (p / |.EX2.|))) * C) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(((1 - qt2) + (qt2 * (p / |.EX2.|))) * C) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((((1 - qt2) + (qt2 * (p / |.EX2.|))) * C),(((1 - qt2) + (qt2 * (p / |.EX2.|))) * C)) is Relation-like Function-like set
multreal .: ((((1 - qt2) + (qt2 * (p / |.EX2.|))) * C),(((1 - qt2) + (qt2 * (p / |.EX2.|))) * C)) is set
K383((sqr (((1 - qt2) + (qt2 * (p / |.EX2.|))) * C))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (((1 - qt2) + (qt2 * (p / |.EX2.|))) * C)),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (((1 - qt2) + (qt2 * (p / |.EX2.|))) * C))) is V11() real ext-real Element of REAL
(qt2 * (p / |.EX2.|)) * C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
(qt2 * (p / |.EX2.|)) * C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(qt2 * (p / |.EX2.|)) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] ((qt2 * (p / |.EX2.|)),(id REAL)) is set
C (#) ((qt2 * (p / |.EX2.|)) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
((1 - qt2) * C) + ((qt2 * (p / |.EX2.|)) * C) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) . (((1 - qt2) * C),((qt2 * (p / |.EX2.|)) * C)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[((1 - qt2) * C),((qt2 * (p / |.EX2.|)) * C)] is non empty set
{((1 - qt2) * C),((qt2 * (p / |.EX2.|)) * C)} is non empty functional V35() V39() set
{{((1 - qt2) * C),((qt2 * (p / |.EX2.|)) * C)},{((1 - qt2) * C)}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [((1 - qt2) * C),((qt2 * (p / |.EX2.|)) * C)] is set
((1 - qt2) * C) + ((qt2 * (p / |.EX2.|)) * C) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (((1 - qt2) * C),((qt2 * (p / |.EX2.|)) * C)) is set
|.(((1 - qt2) * C) + ((qt2 * (p / |.EX2.|)) * C)).| is V11() real ext-real non negative Element of REAL
sqr (((1 - qt2) * C) + ((qt2 * (p / |.EX2.|)) * C)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(((1 - qt2) * C) + ((qt2 * (p / |.EX2.|)) * C)) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((((1 - qt2) * C) + ((qt2 * (p / |.EX2.|)) * C)),(((1 - qt2) * C) + ((qt2 * (p / |.EX2.|)) * C))) is Relation-like Function-like set
multreal .: ((((1 - qt2) * C) + ((qt2 * (p / |.EX2.|)) * C)),(((1 - qt2) * C) + ((qt2 * (p / |.EX2.|)) * C))) is set
K383((sqr (((1 - qt2) * C) + ((qt2 * (p / |.EX2.|)) * C)))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (((1 - qt2) * C) + ((qt2 * (p / |.EX2.|)) * C))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (((1 - qt2) * C) + ((qt2 * (p / |.EX2.|)) * C)))) is V11() real ext-real Element of REAL
|.(((1 - qt2) * C) + (qt2 * ((p / |.EX2.|) * C))).| is V11() real ext-real non negative Element of REAL
sqr (((1 - qt2) * C) + (qt2 * ((p / |.EX2.|) * C))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(((1 - qt2) * C) + (qt2 * ((p / |.EX2.|) * C))) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((((1 - qt2) * C) + (qt2 * ((p / |.EX2.|) * C))),(((1 - qt2) * C) + (qt2 * ((p / |.EX2.|) * C)))) is Relation-like Function-like set
multreal .: ((((1 - qt2) * C) + (qt2 * ((p / |.EX2.|) * C))),(((1 - qt2) * C) + (qt2 * ((p / |.EX2.|) * C)))) is set
K383((sqr (((1 - qt2) * C) + (qt2 * ((p / |.EX2.|) * C))))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (((1 - qt2) * C) + (qt2 * ((p / |.EX2.|) * C)))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (((1 - qt2) * C) + (qt2 * ((p / |.EX2.|) * C))))) is V11() real ext-real Element of REAL
|.(((1 - qt2) * C) + (qt2 * ((p / |.EX2.|) * C))).| is V11() real ext-real non negative Element of REAL
sqr (((1 - qt2) * C) + (qt2 * ((p / |.EX2.|) * C))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(((1 - qt2) * C) + (qt2 * ((p / |.EX2.|) * C))) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((((1 - qt2) * C) + (qt2 * ((p / |.EX2.|) * C))),(((1 - qt2) * C) + (qt2 * ((p / |.EX2.|) * C)))) is Relation-like Function-like set
multreal .: ((((1 - qt2) * C) + (qt2 * ((p / |.EX2.|) * C))),(((1 - qt2) * C) + (qt2 * ((p / |.EX2.|) * C)))) is set
K383((sqr (((1 - qt2) * C) + (qt2 * ((p / |.EX2.|) * C))))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (((1 - qt2) * C) + (qt2 * ((p / |.EX2.|) * C)))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (((1 - qt2) * C) + (qt2 * ((p / |.EX2.|) * C))))) is V11() real ext-real Element of REAL
|.(((1 - qt2) * C) + (qt2 * ((p / |.EX2.|) * C))).| is V11() real ext-real non negative Element of REAL
sqr (((1 - qt2) * C) + (qt2 * ((p / |.EX2.|) * C))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(((1 - qt2) * C) + (qt2 * ((p / |.EX2.|) * C))) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((((1 - qt2) * C) + (qt2 * ((p / |.EX2.|) * C))),(((1 - qt2) * C) + (qt2 * ((p / |.EX2.|) * C)))) is Relation-like Function-like set
multreal .: ((((1 - qt2) * C) + (qt2 * ((p / |.EX2.|) * C))),(((1 - qt2) * C) + (qt2 * ((p / |.EX2.|) * C)))) is set
K383((sqr (((1 - qt2) * C) + (qt2 * ((p / |.EX2.|) * C))))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (((1 - qt2) * C) + (qt2 * ((p / |.EX2.|) * C)))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (((1 - qt2) * C) + (qt2 * ((p / |.EX2.|) * C))))) is V11() real ext-real Element of REAL
|.(((1 - qt2) * C) + (qt2 * ((p / |.EX2.|) * C))).| is V11() real ext-real non negative Element of REAL
sqr (((1 - qt2) * C) + (qt2 * ((p / |.EX2.|) * C))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(((1 - qt2) * C) + (qt2 * ((p / |.EX2.|) * C))) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((((1 - qt2) * C) + (qt2 * ((p / |.EX2.|) * C))),(((1 - qt2) * C) + (qt2 * ((p / |.EX2.|) * C)))) is Relation-like Function-like set
multreal .: ((((1 - qt2) * C) + (qt2 * ((p / |.EX2.|) * C))),(((1 - qt2) * C) + (qt2 * ((p / |.EX2.|) * C)))) is set
K383((sqr (((1 - qt2) * C) + (qt2 * ((p / |.EX2.|) * C))))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (((1 - qt2) * C) + (qt2 * ((p / |.EX2.|) * C)))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (((1 - qt2) * C) + (qt2 * ((p / |.EX2.|) * C))))) is V11() real ext-real Element of REAL
LSeg (((p / |.EX2.|) * p12),((p / |.EX2.|) * C)) is non empty closed connected compact convex Element of bool the carrier of (TOP-REAL C)
{ (((1 - b1) * ((p / |.EX2.|) * p12)) + (b1 * ((p / |.EX2.|) * C))) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
the carrier of (Euclid C) is non empty set
r2 is set
abs (p / |.EX2.|) is V11() real ext-real Element of REAL
abs p is V11() real ext-real Element of REAL
abs |.EX2.| is V11() real ext-real Element of REAL
(abs p) / (abs |.EX2.|) is V11() real ext-real Element of REAL
(abs p) / |.EX2.| is V11() real ext-real Element of REAL
qt2 is Element of the carrier of (Euclid C)
dist qt2 is Relation-like the carrier of (TopSpaceMetr (Euclid C)) -defined the carrier of R^1 -valued Function-like total V30( the carrier of (TopSpaceMetr (Euclid C)), the carrier of R^1) complex-yielding V174() V175() Element of bool [: the carrier of (TopSpaceMetr (Euclid C)), the carrier of R^1:]
t2 is Element of bool the carrier of (TopSpaceMetr (Euclid C))
(dist qt2) .: t2 is V183() V184() V185() Element of bool the carrier of R^1
q4 is set
dom (dist qt2) is Element of bool the carrier of (TopSpaceMetr (Euclid C))
r5 is set
(dist qt2) . r5 is V11() real ext-real Element of REAL
r5 is V11() real ext-real Element of REAL
1 - r5 is V11() real ext-real Element of REAL
(1 - r5) * ((p / |.EX2.|) * p12) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
(1 - r5) * ((p / |.EX2.|) * p12) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(1 - r5) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] ((1 - r5),(id REAL)) is set
((p / |.EX2.|) * p12) (#) ((1 - r5) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
r5 * ((p / |.EX2.|) * C) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
r5 * ((p / |.EX2.|) * C) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
r5 multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (r5,(id REAL)) is set
((p / |.EX2.|) * C) (#) (r5 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
((1 - r5) * ((p / |.EX2.|) * p12)) + (r5 * ((p / |.EX2.|) * C)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) is non empty Relation-like [: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):] -defined the carrier of (TOP-REAL C) -valued Function-like total V30([: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C)) Element of bool [:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):]
[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):] is non empty set
[:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):] is non empty set
bool [:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):] is non empty set
the U7 of (TOP-REAL C) . (((1 - r5) * ((p / |.EX2.|) * p12)),(r5 * ((p / |.EX2.|) * C))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[((1 - r5) * ((p / |.EX2.|) * p12)),(r5 * ((p / |.EX2.|) * C))] is non empty set
{((1 - r5) * ((p / |.EX2.|) * p12)),(r5 * ((p / |.EX2.|) * C))} is non empty functional V35() V39() set
{((1 - r5) * ((p / |.EX2.|) * p12))} is non empty trivial functional V35() V39() 1 -element set
{{((1 - r5) * ((p / |.EX2.|) * p12)),(r5 * ((p / |.EX2.|) * C))},{((1 - r5) * ((p / |.EX2.|) * p12))}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [((1 - r5) * ((p / |.EX2.|) * p12)),(r5 * ((p / |.EX2.|) * C))] is set
((1 - r5) * ((p / |.EX2.|) * p12)) + (r5 * ((p / |.EX2.|) * C)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (((1 - r5) * ((p / |.EX2.|) * p12)),(r5 * ((p / |.EX2.|) * C))) is set
(1 - r5) * p12 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
(1 - r5) * p12 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
p12 (#) ((1 - r5) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
r5 * C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
r5 * C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
C (#) (r5 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
((1 - r5) * p12) + (r5 * C) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) . (((1 - r5) * p12),(r5 * C)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[((1 - r5) * p12),(r5 * C)] is non empty set
{((1 - r5) * p12),(r5 * C)} is non empty functional V35() V39() set
{((1 - r5) * p12)} is non empty trivial functional V35() V39() 1 -element set
{{((1 - r5) * p12),(r5 * C)},{((1 - r5) * p12)}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [((1 - r5) * p12),(r5 * C)] is set
((1 - r5) * p12) + (r5 * C) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (((1 - r5) * p12),(r5 * C)) is set
r0 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
Q is Element of the carrier of (Euclid C)
dist (Q,qt2) is V11() real ext-real Element of REAL
the distance of (Euclid C) is non empty Relation-like [: the carrier of (Euclid C), the carrier of (Euclid C):] -defined REAL -valued Function-like total V30([: the carrier of (Euclid C), the carrier of (Euclid C):], REAL ) complex-yielding V174() V175() Element of bool [:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:]
[: the carrier of (Euclid C), the carrier of (Euclid C):] is non empty set
[:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:] is non empty non trivial V35() set
the distance of (Euclid C) . (Q,qt2) is V11() real ext-real Element of REAL
[Q,qt2] is non empty set
{Q,qt2} is non empty V35() set
{Q} is non empty trivial V35() 1 -element set
{{Q,qt2},{Q}} is non empty V35() V39() set
the distance of (Euclid C) . [Q,qt2] is V11() real ext-real set
(dist qt2) . Q is V11() real ext-real Element of REAL
P3 is ext-real set
dom (dist qt2) is Element of bool the carrier of (TopSpaceMetr (Euclid C))
W3 is set
(dist qt2) . W3 is V11() real ext-real Element of REAL
Q is Element of the carrier of (Euclid C)
dist (Q,qt2) is V11() real ext-real Element of REAL
the distance of (Euclid C) . (Q,qt2) is V11() real ext-real Element of REAL
[Q,qt2] is non empty set
{Q,qt2} is non empty V35() set
{Q} is non empty trivial V35() 1 -element set
{{Q,qt2},{Q}} is non empty V35() V39() set
the distance of (Euclid C) . [Q,qt2] is V11() real ext-real set
q4 is V183() V184() V185() Element of bool REAL
dom (dist qt2) is Element of bool the carrier of (TopSpaceMetr (Euclid C))
lower_bound q4 is V11() real ext-real Element of REAL
[#] ((dist qt2) .: t2) is V183() V184() V185() Element of bool REAL
lower_bound ([#] ((dist qt2) .: t2)) is V11() real ext-real Element of REAL
lower_bound ((dist qt2) .: t2) is V11() real ext-real Element of REAL
r0 - (0. (TOP-REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
- (0. (TOP-REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
- (0. (TOP-REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
compreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
(0. (TOP-REAL C)) (#) compreal is Relation-like Function-like V35() complex-yielding V174() V175() set
K38(1) is V11() real ext-real non positive set
K38(1) * (0. (TOP-REAL C)) is Relation-like Function-like set
K38(1) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (K38(1),(id REAL)) is set
(0. (TOP-REAL C)) (#) (K38(1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
K258((TOP-REAL C),r0,(- (0. (TOP-REAL C)))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) . (r0,(- (0. (TOP-REAL C)))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[r0,(- (0. (TOP-REAL C)))] is non empty set
{r0,(- (0. (TOP-REAL C)))} is non empty functional V35() V39() set
{r0} is non empty trivial functional V35() V39() 1 -element set
{{r0,(- (0. (TOP-REAL C)))},{r0}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [r0,(- (0. (TOP-REAL C)))] is set
r0 + (- (0. (TOP-REAL C))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (r0,(- (0. (TOP-REAL C)))) is set
r0 - (0. (TOP-REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
diffreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K174(REAL,addreal,(id REAL),compreal) is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
diffreal .: (r0,(0. (TOP-REAL C))) is set
K324((0. (TOP-REAL C))) is Relation-like Function-like complex-yielding set
K295(r0,K324((0. (TOP-REAL C)))) is Relation-like Function-like set
|.(r0 - (0. (TOP-REAL C))).| is V11() real ext-real non negative Element of REAL
sqr (r0 - (0. (TOP-REAL C))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(r0 - (0. (TOP-REAL C))) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((r0 - (0. (TOP-REAL C))),(r0 - (0. (TOP-REAL C)))) is Relation-like Function-like set
multreal .: ((r0 - (0. (TOP-REAL C))),(r0 - (0. (TOP-REAL C)))) is set
K383((sqr (r0 - (0. (TOP-REAL C))))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (r0 - (0. (TOP-REAL C)))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (r0 - (0. (TOP-REAL C))))) is V11() real ext-real Element of REAL
|.r0.| is V11() real ext-real non negative Element of REAL
sqr r0 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
r0 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (r0,r0) is Relation-like Function-like set
multreal .: (r0,r0) is set
K383((sqr r0)) is V11() real ext-real Element of REAL
K195(REAL,(sqr r0),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr r0)) is V11() real ext-real Element of REAL
|.r0.| / |.EX2.| is V11() real ext-real non negative Element of REAL
(abs p) * 1 is V11() real ext-real Element of REAL
(abs p) * (|.r0.| / |.EX2.|) is V11() real ext-real Element of REAL
|.EX2.| " is V11() real ext-real non negative Element of REAL
|.r0.| * (|.EX2.| ") is V11() real ext-real non negative Element of REAL
(abs p) * (|.r0.| * (|.EX2.| ")) is V11() real ext-real Element of REAL
(abs p) * (|.EX2.| ") is V11() real ext-real Element of REAL
((abs p) * (|.EX2.| ")) * |.r0.| is V11() real ext-real Element of REAL
((abs p) / |.EX2.|) * |.r0.| is V11() real ext-real Element of REAL
(p / |.EX2.|) * (((1 - r5) * p12) + (r5 * C)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
(p / |.EX2.|) * (((1 - r5) * p12) + (r5 * C)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(((1 - r5) * p12) + (r5 * C)) (#) ((p / |.EX2.|) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
|.((p / |.EX2.|) * (((1 - r5) * p12) + (r5 * C))).| is V11() real ext-real non negative Element of REAL
sqr ((p / |.EX2.|) * (((1 - r5) * p12) + (r5 * C))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
((p / |.EX2.|) * (((1 - r5) * p12) + (r5 * C))) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (((p / |.EX2.|) * (((1 - r5) * p12) + (r5 * C))),((p / |.EX2.|) * (((1 - r5) * p12) + (r5 * C)))) is Relation-like Function-like set
multreal .: (((p / |.EX2.|) * (((1 - r5) * p12) + (r5 * C))),((p / |.EX2.|) * (((1 - r5) * p12) + (r5 * C)))) is set
K383((sqr ((p / |.EX2.|) * (((1 - r5) * p12) + (r5 * C))))) is V11() real ext-real Element of REAL
K195(REAL,(sqr ((p / |.EX2.|) * (((1 - r5) * p12) + (r5 * C)))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr ((p / |.EX2.|) * (((1 - r5) * p12) + (r5 * C))))) is V11() real ext-real Element of REAL
(p / |.EX2.|) * ((1 - r5) * p12) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
(p / |.EX2.|) * ((1 - r5) * p12) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
((1 - r5) * p12) (#) ((p / |.EX2.|) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
(p / |.EX2.|) * (r5 * C) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
(p / |.EX2.|) * (r5 * C) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(r5 * C) (#) ((p / |.EX2.|) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
((p / |.EX2.|) * ((1 - r5) * p12)) + ((p / |.EX2.|) * (r5 * C)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) . (((p / |.EX2.|) * ((1 - r5) * p12)),((p / |.EX2.|) * (r5 * C))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[((p / |.EX2.|) * ((1 - r5) * p12)),((p / |.EX2.|) * (r5 * C))] is non empty set
{((p / |.EX2.|) * ((1 - r5) * p12)),((p / |.EX2.|) * (r5 * C))} is non empty functional V35() V39() set
{((p / |.EX2.|) * ((1 - r5) * p12))} is non empty trivial functional V35() V39() 1 -element set
{{((p / |.EX2.|) * ((1 - r5) * p12)),((p / |.EX2.|) * (r5 * C))},{((p / |.EX2.|) * ((1 - r5) * p12))}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [((p / |.EX2.|) * ((1 - r5) * p12)),((p / |.EX2.|) * (r5 * C))] is set
((p / |.EX2.|) * ((1 - r5) * p12)) + ((p / |.EX2.|) * (r5 * C)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (((p / |.EX2.|) * ((1 - r5) * p12)),((p / |.EX2.|) * (r5 * C))) is set
|.(((p / |.EX2.|) * ((1 - r5) * p12)) + ((p / |.EX2.|) * (r5 * C))).| is V11() real ext-real non negative Element of REAL
sqr (((p / |.EX2.|) * ((1 - r5) * p12)) + ((p / |.EX2.|) * (r5 * C))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(((p / |.EX2.|) * ((1 - r5) * p12)) + ((p / |.EX2.|) * (r5 * C))) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((((p / |.EX2.|) * ((1 - r5) * p12)) + ((p / |.EX2.|) * (r5 * C))),(((p / |.EX2.|) * ((1 - r5) * p12)) + ((p / |.EX2.|) * (r5 * C)))) is Relation-like Function-like set
multreal .: ((((p / |.EX2.|) * ((1 - r5) * p12)) + ((p / |.EX2.|) * (r5 * C))),(((p / |.EX2.|) * ((1 - r5) * p12)) + ((p / |.EX2.|) * (r5 * C)))) is set
K383((sqr (((p / |.EX2.|) * ((1 - r5) * p12)) + ((p / |.EX2.|) * (r5 * C))))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (((p / |.EX2.|) * ((1 - r5) * p12)) + ((p / |.EX2.|) * (r5 * C)))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (((p / |.EX2.|) * ((1 - r5) * p12)) + ((p / |.EX2.|) * (r5 * C))))) is V11() real ext-real Element of REAL
(p / |.EX2.|) * r5 is V11() real ext-real Element of REAL
((p / |.EX2.|) * r5) * C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
((p / |.EX2.|) * r5) * C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
((p / |.EX2.|) * r5) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (((p / |.EX2.|) * r5),(id REAL)) is set
C (#) (((p / |.EX2.|) * r5) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
((p / |.EX2.|) * ((1 - r5) * p12)) + (((p / |.EX2.|) * r5) * C) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) . (((p / |.EX2.|) * ((1 - r5) * p12)),(((p / |.EX2.|) * r5) * C)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[((p / |.EX2.|) * ((1 - r5) * p12)),(((p / |.EX2.|) * r5) * C)] is non empty set
{((p / |.EX2.|) * ((1 - r5) * p12)),(((p / |.EX2.|) * r5) * C)} is non empty functional V35() V39() set
{{((p / |.EX2.|) * ((1 - r5) * p12)),(((p / |.EX2.|) * r5) * C)},{((p / |.EX2.|) * ((1 - r5) * p12))}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [((p / |.EX2.|) * ((1 - r5) * p12)),(((p / |.EX2.|) * r5) * C)] is set
((p / |.EX2.|) * ((1 - r5) * p12)) + (((p / |.EX2.|) * r5) * C) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (((p / |.EX2.|) * ((1 - r5) * p12)),(((p / |.EX2.|) * r5) * C)) is set
|.(((p / |.EX2.|) * ((1 - r5) * p12)) + (((p / |.EX2.|) * r5) * C)).| is V11() real ext-real non negative Element of REAL
sqr (((p / |.EX2.|) * ((1 - r5) * p12)) + (((p / |.EX2.|) * r5) * C)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(((p / |.EX2.|) * ((1 - r5) * p12)) + (((p / |.EX2.|) * r5) * C)) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((((p / |.EX2.|) * ((1 - r5) * p12)) + (((p / |.EX2.|) * r5) * C)),(((p / |.EX2.|) * ((1 - r5) * p12)) + (((p / |.EX2.|) * r5) * C))) is Relation-like Function-like set
multreal .: ((((p / |.EX2.|) * ((1 - r5) * p12)) + (((p / |.EX2.|) * r5) * C)),(((p / |.EX2.|) * ((1 - r5) * p12)) + (((p / |.EX2.|) * r5) * C))) is set
K383((sqr (((p / |.EX2.|) * ((1 - r5) * p12)) + (((p / |.EX2.|) * r5) * C)))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (((p / |.EX2.|) * ((1 - r5) * p12)) + (((p / |.EX2.|) * r5) * C))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (((p / |.EX2.|) * ((1 - r5) * p12)) + (((p / |.EX2.|) * r5) * C)))) is V11() real ext-real Element of REAL
(p / |.EX2.|) * (1 - r5) is V11() real ext-real Element of REAL
((p / |.EX2.|) * (1 - r5)) * p12 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
((p / |.EX2.|) * (1 - r5)) * p12 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
((p / |.EX2.|) * (1 - r5)) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (((p / |.EX2.|) * (1 - r5)),(id REAL)) is set
p12 (#) (((p / |.EX2.|) * (1 - r5)) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
(((p / |.EX2.|) * (1 - r5)) * p12) + (((p / |.EX2.|) * r5) * C) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) . ((((p / |.EX2.|) * (1 - r5)) * p12),(((p / |.EX2.|) * r5) * C)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[(((p / |.EX2.|) * (1 - r5)) * p12),(((p / |.EX2.|) * r5) * C)] is non empty set
{(((p / |.EX2.|) * (1 - r5)) * p12),(((p / |.EX2.|) * r5) * C)} is non empty functional V35() V39() set
{(((p / |.EX2.|) * (1 - r5)) * p12)} is non empty trivial functional V35() V39() 1 -element set
{{(((p / |.EX2.|) * (1 - r5)) * p12),(((p / |.EX2.|) * r5) * C)},{(((p / |.EX2.|) * (1 - r5)) * p12)}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [(((p / |.EX2.|) * (1 - r5)) * p12),(((p / |.EX2.|) * r5) * C)] is set
(((p / |.EX2.|) * (1 - r5)) * p12) + (((p / |.EX2.|) * r5) * C) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: ((((p / |.EX2.|) * (1 - r5)) * p12),(((p / |.EX2.|) * r5) * C)) is set
|.((((p / |.EX2.|) * (1 - r5)) * p12) + (((p / |.EX2.|) * r5) * C)).| is V11() real ext-real non negative Element of REAL
sqr ((((p / |.EX2.|) * (1 - r5)) * p12) + (((p / |.EX2.|) * r5) * C)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
((((p / |.EX2.|) * (1 - r5)) * p12) + (((p / |.EX2.|) * r5) * C)) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (((((p / |.EX2.|) * (1 - r5)) * p12) + (((p / |.EX2.|) * r5) * C)),((((p / |.EX2.|) * (1 - r5)) * p12) + (((p / |.EX2.|) * r5) * C))) is Relation-like Function-like set
multreal .: (((((p / |.EX2.|) * (1 - r5)) * p12) + (((p / |.EX2.|) * r5) * C)),((((p / |.EX2.|) * (1 - r5)) * p12) + (((p / |.EX2.|) * r5) * C))) is set
K383((sqr ((((p / |.EX2.|) * (1 - r5)) * p12) + (((p / |.EX2.|) * r5) * C)))) is V11() real ext-real Element of REAL
K195(REAL,(sqr ((((p / |.EX2.|) * (1 - r5)) * p12) + (((p / |.EX2.|) * r5) * C))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr ((((p / |.EX2.|) * (1 - r5)) * p12) + (((p / |.EX2.|) * r5) * C)))) is V11() real ext-real Element of REAL
(1 - r5) * (p / |.EX2.|) is V11() real ext-real Element of REAL
((1 - r5) * (p / |.EX2.|)) * p12 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
((1 - r5) * (p / |.EX2.|)) * p12 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
((1 - r5) * (p / |.EX2.|)) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (((1 - r5) * (p / |.EX2.|)),(id REAL)) is set
p12 (#) (((1 - r5) * (p / |.EX2.|)) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
(((1 - r5) * (p / |.EX2.|)) * p12) + (r5 * ((p / |.EX2.|) * C)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) . ((((1 - r5) * (p / |.EX2.|)) * p12),(r5 * ((p / |.EX2.|) * C))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[(((1 - r5) * (p / |.EX2.|)) * p12),(r5 * ((p / |.EX2.|) * C))] is non empty set
{(((1 - r5) * (p / |.EX2.|)) * p12),(r5 * ((p / |.EX2.|) * C))} is non empty functional V35() V39() set
{(((1 - r5) * (p / |.EX2.|)) * p12)} is non empty trivial functional V35() V39() 1 -element set
{{(((1 - r5) * (p / |.EX2.|)) * p12),(r5 * ((p / |.EX2.|) * C))},{(((1 - r5) * (p / |.EX2.|)) * p12)}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [(((1 - r5) * (p / |.EX2.|)) * p12),(r5 * ((p / |.EX2.|) * C))] is set
(((1 - r5) * (p / |.EX2.|)) * p12) + (r5 * ((p / |.EX2.|) * C)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: ((((1 - r5) * (p / |.EX2.|)) * p12),(r5 * ((p / |.EX2.|) * C))) is set
|.((((1 - r5) * (p / |.EX2.|)) * p12) + (r5 * ((p / |.EX2.|) * C))).| is V11() real ext-real non negative Element of REAL
sqr ((((1 - r5) * (p / |.EX2.|)) * p12) + (r5 * ((p / |.EX2.|) * C))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
((((1 - r5) * (p / |.EX2.|)) * p12) + (r5 * ((p / |.EX2.|) * C))) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (((((1 - r5) * (p / |.EX2.|)) * p12) + (r5 * ((p / |.EX2.|) * C))),((((1 - r5) * (p / |.EX2.|)) * p12) + (r5 * ((p / |.EX2.|) * C)))) is Relation-like Function-like set
multreal .: (((((1 - r5) * (p / |.EX2.|)) * p12) + (r5 * ((p / |.EX2.|) * C))),((((1 - r5) * (p / |.EX2.|)) * p12) + (r5 * ((p / |.EX2.|) * C)))) is set
K383((sqr ((((1 - r5) * (p / |.EX2.|)) * p12) + (r5 * ((p / |.EX2.|) * C))))) is V11() real ext-real Element of REAL
K195(REAL,(sqr ((((1 - r5) * (p / |.EX2.|)) * p12) + (r5 * ((p / |.EX2.|) * C)))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr ((((1 - r5) * (p / |.EX2.|)) * p12) + (r5 * ((p / |.EX2.|) * C))))) is V11() real ext-real Element of REAL
|.(((1 - r5) * ((p / |.EX2.|) * p12)) + (r5 * ((p / |.EX2.|) * C))).| is V11() real ext-real non negative Element of REAL
sqr (((1 - r5) * ((p / |.EX2.|) * p12)) + (r5 * ((p / |.EX2.|) * C))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(((1 - r5) * ((p / |.EX2.|) * p12)) + (r5 * ((p / |.EX2.|) * C))) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((((1 - r5) * ((p / |.EX2.|) * p12)) + (r5 * ((p / |.EX2.|) * C))),(((1 - r5) * ((p / |.EX2.|) * p12)) + (r5 * ((p / |.EX2.|) * C)))) is Relation-like Function-like set
multreal .: ((((1 - r5) * ((p / |.EX2.|) * p12)) + (r5 * ((p / |.EX2.|) * C))),(((1 - r5) * ((p / |.EX2.|) * p12)) + (r5 * ((p / |.EX2.|) * C)))) is set
K383((sqr (((1 - r5) * ((p / |.EX2.|) * p12)) + (r5 * ((p / |.EX2.|) * C))))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (((1 - r5) * ((p / |.EX2.|) * p12)) + (r5 * ((p / |.EX2.|) * C)))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (((1 - r5) * ((p / |.EX2.|) * p12)) + (r5 * ((p / |.EX2.|) * C))))) is V11() real ext-real Element of REAL
C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
len C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
REAL (len C) is non empty functional FinSequence-membered FinSequenceSet of REAL
(len C) -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = len C } is set
p is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
len p is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
TOP-REAL (len p) is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL (len p)) is non empty set
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
REAL C is non empty functional FinSequence-membered FinSequenceSet of REAL
C -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = C } is set
id REAL is non empty Relation-like REAL -defined REAL -valued Function-like one-to-one total V30( REAL , REAL ) complex-yielding V174() V175() increasing V179() Element of bool [:REAL,REAL:]
WH is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
p12 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
len p12 is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
len C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
r is V11() real ext-real Element of REAL
r * WH is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
r multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (r,(id REAL)) is set
WH (#) (r multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
dom (id REAL) is V183() V184() V185() Element of bool REAL
(dom (id REAL)) --> r is Relation-like dom (id REAL) -defined REAL -valued Function-like total V30( dom (id REAL), REAL ) complex-yielding V174() V175() Element of bool [:(dom (id REAL)),REAL:]
[:(dom (id REAL)),REAL:] is complex-yielding V174() V175() set
bool [:(dom (id REAL)),REAL:] is non empty set
p is Relation-like Function-like set
<:((dom (id REAL)) --> r),p:> is Relation-like Function-like set
dom <:((dom (id REAL)) --> r),p:> is set
dom ((dom (id REAL)) --> r) is V183() V184() V185() Element of bool (dom (id REAL))
bool (dom (id REAL)) is non empty set
(dom ((dom (id REAL)) --> r)) /\ (dom (id REAL)) is V183() V184() V185() Element of bool REAL
<:((dom (id REAL)) --> r),p:> (#) multreal is Relation-like Function-like complex-yielding V174() V175() set
WH (#) (<:((dom (id REAL)) --> r),p:> (#) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
EX1 is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
C /. EX1 is V11() real ext-real Element of REAL
p12 /. EX1 is V11() real ext-real Element of REAL
r * (p12 /. EX1) is V11() real ext-real Element of REAL
dom p is set
WH . EX1 is V11() real ext-real Element of REAL
((dom (id REAL)) --> r) . (WH . EX1) is V11() real ext-real Element of REAL
p . (WH . EX1) is set
p12 . EX1 is V11() real ext-real Element of REAL
Seg (len p12) is V35() len p12 -element V183() V184() V185() V186() V187() V188() Element of bool NAT
dom C is V35() V183() V184() V185() V186() V187() V188() Element of bool NAT
C . EX1 is V11() real ext-real Element of REAL
(<:((dom (id REAL)) --> r),p:> (#) multreal) . (WH . EX1) is V11() real ext-real Element of REAL
(dom ((dom (id REAL)) --> r)) /\ REAL is V183() V184() V185() Element of bool (dom (id REAL))
<:((dom (id REAL)) --> r),p:> . (WH . EX1) is set
[(((dom (id REAL)) --> r) . (WH . EX1)),(p . (WH . EX1))] is non empty set
{(((dom (id REAL)) --> r) . (WH . EX1)),(p . (WH . EX1))} is non empty V35() set
{(((dom (id REAL)) --> r) . (WH . EX1))} is non empty trivial V35() 1 -element V183() V184() V185() set
{{(((dom (id REAL)) --> r) . (WH . EX1)),(p . (WH . EX1))},{(((dom (id REAL)) --> r) . (WH . EX1))}} is non empty V35() V39() set
multreal . (r,(p12 . EX1)) is V11() real ext-real Element of REAL
[r,(p12 . EX1)] is non empty set
{r,(p12 . EX1)} is non empty V35() V183() V184() V185() set
{r} is non empty trivial V35() 1 -element V183() V184() V185() set
{{r,(p12 . EX1)},{r}} is non empty V35() V39() set
multreal . [r,(p12 . EX1)] is V11() real ext-real set
EX1 is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
C /. EX1 is V11() real ext-real Element of REAL
p12 /. EX1 is V11() real ext-real Element of REAL
r * (p12 /. EX1) is V11() real ext-real Element of REAL
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
REAL C is non empty functional FinSequence-membered FinSequenceSet of REAL
C -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = C } is set
0* C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
C |-> 0 is Relation-like empty-yielding NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of C -tuples_on REAL
Seg C is V35() C -element V183() V184() V185() V186() V187() V188() Element of bool NAT
(Seg C) --> 0 is Relation-like Seg C -defined INT -valued RAT -valued {0} -valued Function-like total V30( Seg C,{0}) V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() V176() Element of bool [:(Seg C),{0}:]
{0} is non empty trivial V35() V39() 1 -element V183() V184() V185() V186() V187() V188() set
[:(Seg C),{0}:] is INT -valued RAT -valued V35() complex-yielding V174() V175() V176() set
bool [:(Seg C),{0}:] is non empty V35() V39() set
p is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
WH is Relation-like NAT -defined Function-like V35() FinSequence-like FinSubsequence-like set
len WH is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
{0} is non empty trivial V35() V39() 1 -element V183() V184() V185() V186() V187() V188() Element of bool REAL
p12 is set
C is set
r is set
[C,r] is non empty set
{C,r} is non empty V35() set
{C} is non empty trivial V35() 1 -element set
{{C,r},{C}} is non empty V35() V39() set
WH . C is set
dom WH is V35() V183() V184() V185() V186() V187() V188() Element of bool NAT
Seg (len WH) is V35() len WH -element V183() V184() V185() V186() V187() V188() Element of bool NAT
EX2 is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
WH . EX2 is set
C is set
r is set
[C,r] is non empty set
{C,r} is non empty V35() set
{C} is non empty trivial V35() 1 -element set
{{C,r},{C}} is non empty V35() V39() set
EX2 is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
WH . C is set
[:(Seg C),{0}:] is INT -valued RAT -valued V35() complex-yielding V174() V175() V176() set
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
REAL C is non empty functional FinSequence-membered FinSequenceSet of REAL
C -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = C } is set
0* C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
C |-> 0 is Relation-like empty-yielding NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of C -tuples_on REAL
Seg C is V35() C -element V183() V184() V185() V186() V187() V188() Element of bool NAT
(Seg C) --> 0 is Relation-like Seg C -defined INT -valued RAT -valued {0} -valued Function-like total V30( Seg C,{0}) V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() V176() Element of bool [:(Seg C),{0}:]
{0} is non empty trivial V35() V39() 1 -element V183() V184() V185() V186() V187() V188() set
[:(Seg C),{0}:] is INT -valued RAT -valued V35() complex-yielding V174() V175() V176() set
bool [:(Seg C),{0}:] is non empty V35() V39() set
p is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
WH is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
p12 is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
WH . p12 is V11() real ext-real Element of REAL
len WH is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
WH /. 1 is V11() real ext-real Element of REAL
(WH /. 1) + 1 is V11() real ext-real Element of REAL
<*((WH /. 1) + 1)*> is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() FinSequence of REAL
mid (WH,2,(len WH)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
<*((WH /. 1) + 1)*> ^ (mid (WH,2,(len WH))) is non empty Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
len (mid (WH,2,(len WH))) is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
(len WH) -' 2 is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
((len WH) -' 2) + 1 is non empty ordinal natural V11() real ext-real positive non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
(len WH) - 2 is V11() real ext-real Element of REAL
((len WH) - 2) + 1 is V11() real ext-real Element of REAL
C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
len C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
len <*((WH /. 1) + 1)*> is non empty ordinal natural V11() real ext-real positive non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
(len <*((WH /. 1) + 1)*>) + (len (mid (WH,2,(len WH)))) is non empty ordinal natural V11() real ext-real positive non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
1 + (((len WH) - 2) + 1) is V11() real ext-real Element of REAL
r is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
EX2 is V11() real ext-real Element of REAL
EX2 * p is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
EX2 multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
id REAL is non empty Relation-like REAL -defined REAL -valued Function-like one-to-one total V30( REAL , REAL ) complex-yielding V174() V175() increasing V179() Element of bool [:REAL,REAL:]
multreal [;] (EX2,(id REAL)) is set
p (#) (EX2 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
EX2 * r is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
r (#) (EX2 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
1 + 1 is non empty ordinal natural V11() real ext-real positive non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
(len WH) - (1 + 1) is V11() real ext-real Element of REAL
((len WH) - (1 + 1)) + (1 + 1) is V11() real ext-real Element of REAL
p12 - 1 is V11() real ext-real Element of REAL
((len WH) - (1 + 1)) + 1 is V11() real ext-real Element of REAL
(((len WH) - (1 + 1)) + 1) + 1 is V11() real ext-real Element of REAL
((((len WH) - (1 + 1)) + 1) + 1) - 1 is V11() real ext-real Element of REAL
p12 -' 1 is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
C /. 1 is V11() real ext-real Element of REAL
C . 1 is V11() real ext-real Element of REAL
C /. p12 is V11() real ext-real Element of REAL
C . p12 is V11() real ext-real Element of REAL
(p12 -' 1) + 2 is non empty ordinal natural V11() real ext-real positive non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
((p12 -' 1) + 2) -' 1 is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
(p12 -' 1) + 1 is non empty ordinal natural V11() real ext-real positive non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
((p12 -' 1) + 1) + 1 is non empty ordinal natural V11() real ext-real positive non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
(((p12 -' 1) + 1) + 1) -' 1 is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
(p12 - 1) + 1 is V11() real ext-real Element of REAL
WH /. p12 is V11() real ext-real Element of REAL
1 + (len (mid (WH,2,(len WH)))) is non empty ordinal natural V11() real ext-real positive non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
(mid (WH,2,(len WH))) . (p12 - 1) is V11() real ext-real Element of REAL
1 * (WH /. p12) is V11() real ext-real Element of REAL
EX2 * (WH /. p12) is V11() real ext-real Element of REAL
EX2 * (WH /. 1) is V11() real ext-real Element of REAL
1 * (WH /. 1) is V11() real ext-real Element of REAL
1 + 1 is non empty ordinal natural V11() real ext-real positive non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
(len WH) - (1 + 1) is V11() real ext-real Element of REAL
((len WH) - (1 + 1)) + (1 + 1) is V11() real ext-real Element of REAL
p12 - 1 is V11() real ext-real Element of REAL
((len WH) - (1 + 1)) + 1 is V11() real ext-real Element of REAL
(((len WH) - (1 + 1)) + 1) + 1 is V11() real ext-real Element of REAL
((((len WH) - (1 + 1)) + 1) + 1) - 1 is V11() real ext-real Element of REAL
p12 -' 1 is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
C /. 1 is V11() real ext-real Element of REAL
C . 1 is V11() real ext-real Element of REAL
C /. p12 is V11() real ext-real Element of REAL
C . p12 is V11() real ext-real Element of REAL
(p12 -' 1) + 2 is non empty ordinal natural V11() real ext-real positive non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
((p12 -' 1) + 2) -' 1 is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
(p12 -' 1) + 1 is non empty ordinal natural V11() real ext-real positive non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
((p12 -' 1) + 1) + 1 is non empty ordinal natural V11() real ext-real positive non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
(((p12 -' 1) + 1) + 1) -' 1 is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
(p12 - 1) + 1 is V11() real ext-real Element of REAL
WH /. p12 is V11() real ext-real Element of REAL
1 + (len (mid (WH,2,(len WH)))) is non empty ordinal natural V11() real ext-real positive non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
(mid (WH,2,(len WH))) . (p12 - 1) is V11() real ext-real Element of REAL
1 * (WH /. p12) is V11() real ext-real Element of REAL
EX2 * (WH /. p12) is V11() real ext-real Element of REAL
EX2 * (C /. 1) is V11() real ext-real Element of REAL
1 * (WH /. 1) is V11() real ext-real Element of REAL
(len WH) -' 1 is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
mid (WH,1,((len WH) -' 1)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
WH /. (len WH) is V11() real ext-real Element of REAL
(WH /. (len WH)) + 1 is V11() real ext-real Element of REAL
<*((WH /. (len WH)) + 1)*> is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() FinSequence of REAL
(mid (WH,1,((len WH) -' 1))) ^ <*((WH /. (len WH)) + 1)*> is non empty Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
1 + 1 is non empty ordinal natural V11() real ext-real positive non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
(1 + 1) - 1 is V11() real ext-real Element of REAL
(len WH) - 1 is V11() real ext-real Element of REAL
((len WH) -' 1) -' 1 is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
(((len WH) -' 1) -' 1) + 1 is non empty ordinal natural V11() real ext-real positive non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
((len WH) - 1) - 1 is V11() real ext-real Element of REAL
(((len WH) - 1) - 1) + 1 is V11() real ext-real Element of REAL
(len WH) - (1 + 1) is V11() real ext-real Element of REAL
((len WH) - (1 + 1)) + 1 is V11() real ext-real Element of REAL
len (mid (WH,1,((len WH) -' 1))) is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
len <*((WH /. (len WH)) + 1)*> is non empty ordinal natural V11() real ext-real positive non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
(len WH) - 2 is V11() real ext-real Element of REAL
((len WH) - 2) + 1 is V11() real ext-real Element of REAL
C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
len C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
(((len WH) - 2) + 1) + 1 is V11() real ext-real Element of REAL
r is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
EX2 is V11() real ext-real Element of REAL
EX2 * p is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
EX2 multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
id REAL is non empty Relation-like REAL -defined REAL -valued Function-like one-to-one total V30( REAL , REAL ) complex-yielding V174() V175() increasing V179() Element of bool [:REAL,REAL:]
multreal [;] (EX2,(id REAL)) is set
p (#) (EX2 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
EX2 * r is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
r (#) (EX2 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
C /. p12 is V11() real ext-real Element of REAL
C . p12 is V11() real ext-real Element of REAL
WH /. p12 is V11() real ext-real Element of REAL
(mid (WH,1,((len WH) -' 1))) . p12 is V11() real ext-real Element of REAL
1 * (WH /. p12) is V11() real ext-real Element of REAL
EX2 * (WH /. p12) is V11() real ext-real Element of REAL
C . (len WH) is V11() real ext-real Element of REAL
((len WH) - 1) + 1 is V11() real ext-real Element of REAL
C . (((len WH) - 1) + 1) is V11() real ext-real Element of REAL
C /. (len WH) is V11() real ext-real Element of REAL
EX2 * (WH /. (len WH)) is V11() real ext-real Element of REAL
C /. p12 is V11() real ext-real Element of REAL
C . p12 is V11() real ext-real Element of REAL
WH /. p12 is V11() real ext-real Element of REAL
(mid (WH,1,((len WH) -' 1))) . p12 is V11() real ext-real Element of REAL
1 * (WH /. p12) is V11() real ext-real Element of REAL
EX2 * (WH /. p12) is V11() real ext-real Element of REAL
C . (len WH) is V11() real ext-real Element of REAL
((len WH) - 1) + 1 is V11() real ext-real Element of REAL
C . (((len WH) - 1) + 1) is V11() real ext-real Element of REAL
C /. (len WH) is V11() real ext-real Element of REAL
EX2 * (C /. (len WH)) is V11() real ext-real Element of REAL
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
bool the carrier of (TOP-REAL C) is non empty set
p is V11() real ext-real Element of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C) : not |.b1.| <= p } is set
WH is Element of bool the carrier of (TOP-REAL C)
p12 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
REAL C is non empty functional FinSequence-membered FinSequenceSet of REAL
C -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = C } is set
EX2 is V11() real ext-real Element of REAL
EX2 * C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
EX2 * C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
EX2 multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
id REAL is non empty Relation-like REAL -defined REAL -valued Function-like one-to-one total V30( REAL , REAL ) complex-yielding V174() V175() increasing V179() Element of bool [:REAL,REAL:]
multreal [;] (EX2,(id REAL)) is set
C (#) (EX2 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
EX2 * p12 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
EX2 * p12 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
p12 (#) (EX2 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
0. (TOP-REAL C) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like V62( TOP-REAL C) complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the ZeroF of (TOP-REAL C) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
EX1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.EX1.| is V11() real ext-real non negative Element of REAL
sqr EX1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
sqrreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
EX1 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (EX1,EX1) is Relation-like Function-like set
multreal .: (EX1,EX1) is set
K383((sqr EX1)) is V11() real ext-real Element of REAL
addreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K195(REAL,(sqr EX1),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr EX1)) is V11() real ext-real Element of REAL
0* C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
C |-> 0 is Relation-like empty-yielding NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of C -tuples_on REAL
Seg C is V35() C -element V183() V184() V185() V186() V187() V188() Element of bool NAT
(Seg C) --> 0 is Relation-like Seg C -defined INT -valued RAT -valued {0} -valued Function-like total V30( Seg C,{0}) V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() V176() Element of bool [:(Seg C),{0}:]
{0} is non empty trivial V35() V39() 1 -element V183() V184() V185() V186() V187() V188() set
[:(Seg C),{0}:] is INT -valued RAT -valued V35() complex-yielding V174() V175() V176() set
bool [:(Seg C),{0}:] is non empty V35() V39() set
r is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
EX1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
p + 1 is V11() real ext-real Element of REAL
|.EX1.| is V11() real ext-real non negative Element of REAL
sqr EX1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
sqrreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
EX1 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (EX1,EX1) is Relation-like Function-like set
multreal .: (EX1,EX1) is set
K383((sqr EX1)) is V11() real ext-real Element of REAL
addreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K195(REAL,(sqr EX1),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr EX1)) is V11() real ext-real Element of REAL
(p + 1) / |.EX1.| is V11() real ext-real Element of REAL
((p + 1) / |.EX1.|) * EX1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
((p + 1) / |.EX1.|) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (((p + 1) / |.EX1.|),(id REAL)) is set
EX1 (#) (((p + 1) / |.EX1.|) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
0 * r is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
0 multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (0,(id REAL)) is set
r (#) (0 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
0 * p12 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
0 * p12 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
p12 (#) (0 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
EX is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
r2 is V11() real ext-real Element of REAL
r2 * EX is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
r2 * EX is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
r2 multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (r2,(id REAL)) is set
EX (#) (r2 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
r2 * p12 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
r2 * p12 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
p12 (#) (r2 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
r2 * ((p + 1) / |.EX1.|) is V11() real ext-real Element of REAL
(r2 * ((p + 1) / |.EX1.|)) * EX1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
(r2 * ((p + 1) / |.EX1.|)) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] ((r2 * ((p + 1) / |.EX1.|)),(id REAL)) is set
EX1 (#) ((r2 * ((p + 1) / |.EX1.|)) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
t2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of C -tuples_on REAL
((p + 1) / |.EX1.|) " is V11() real ext-real Element of REAL
(((p + 1) / |.EX1.|) ") * ((p + 1) / |.EX1.|) is V11() real ext-real Element of REAL
((((p + 1) / |.EX1.|) ") * ((p + 1) / |.EX1.|)) * t2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of C -tuples_on REAL
((((p + 1) / |.EX1.|) ") * ((p + 1) / |.EX1.|)) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (((((p + 1) / |.EX1.|) ") * ((p + 1) / |.EX1.|)),(id REAL)) is set
t2 (#) (((((p + 1) / |.EX1.|) ") * ((p + 1) / |.EX1.|)) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
r2 * r is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
r (#) (r2 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
(((p + 1) / |.EX1.|) ") * (r2 * r) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
(((p + 1) / |.EX1.|) ") multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] ((((p + 1) / |.EX1.|) "),(id REAL)) is set
(r2 * r) (#) ((((p + 1) / |.EX1.|) ") multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
((((p + 1) / |.EX1.|) ") * ((p + 1) / |.EX1.|)) * EX1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
EX1 (#) (((((p + 1) / |.EX1.|) ") * ((p + 1) / |.EX1.|)) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
qt2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of C -tuples_on REAL
(((p + 1) / |.EX1.|) ") * r2 is V11() real ext-real Element of REAL
((((p + 1) / |.EX1.|) ") * r2) * qt2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of C -tuples_on REAL
((((p + 1) / |.EX1.|) ") * r2) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (((((p + 1) / |.EX1.|) ") * r2),(id REAL)) is set
qt2 (#) (((((p + 1) / |.EX1.|) ") * r2) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
1 * EX1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
1 multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (1,(id REAL)) is set
EX1 (#) (1 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
((((p + 1) / |.EX1.|) ") * r2) * r is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
r (#) (((((p + 1) / |.EX1.|) ") * r2) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
|.EX.| is V11() real ext-real non negative Element of REAL
sqr EX is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
EX (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (EX,EX) is Relation-like Function-like set
multreal .: (EX,EX) is set
K383((sqr EX)) is V11() real ext-real Element of REAL
K195(REAL,(sqr EX),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr EX)) is V11() real ext-real Element of REAL
abs ((p + 1) / |.EX1.|) is V11() real ext-real Element of REAL
(abs ((p + 1) / |.EX1.|)) * |.EX1.| is V11() real ext-real Element of REAL
((p + 1) / |.EX1.|) * |.EX1.| is V11() real ext-real Element of REAL
t2 is V11() real ext-real Element of REAL
t2 * C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
t2 * C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
t2 multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (t2,(id REAL)) is set
C (#) (t2 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
t2 * EX is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
t2 * EX is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
EX (#) (t2 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
qt2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.qt2.| is V11() real ext-real non negative Element of REAL
sqr qt2 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
qt2 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (qt2,qt2) is Relation-like Function-like set
multreal .: (qt2,qt2) is set
K383((sqr qt2)) is V11() real ext-real Element of REAL
K195(REAL,(sqr qt2),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr qt2)) is V11() real ext-real Element of REAL
t2 " is V11() real ext-real Element of REAL
(t2 ") * EX is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
(t2 ") * EX is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(t2 ") multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] ((t2 "),(id REAL)) is set
EX (#) ((t2 ") multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
(t2 ") * t2 is V11() real ext-real Element of REAL
((t2 ") * t2) * C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
((t2 ") * t2) * C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
((t2 ") * t2) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (((t2 ") * t2),(id REAL)) is set
C (#) (((t2 ") * t2) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
1 * C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
1 * C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
1 multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (1,(id REAL)) is set
C (#) (1 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
EX2 * (t2 ") is V11() real ext-real Element of REAL
(EX2 * (t2 ")) * EX is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
(EX2 * (t2 ")) * EX is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(EX2 * (t2 ")) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] ((EX2 * (t2 ")),(id REAL)) is set
EX (#) ((EX2 * (t2 ")) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
t2 " is V11() real ext-real Element of REAL
(t2 ") * C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
(t2 ") * C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(t2 ") multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] ((t2 "),(id REAL)) is set
C (#) ((t2 ") multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
(t2 ") * t2 is V11() real ext-real Element of REAL
((t2 ") * t2) * EX is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
((t2 ") * t2) * EX is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
((t2 ") * t2) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (((t2 ") * t2),(id REAL)) is set
EX (#) (((t2 ") * t2) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
1 * EX is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
1 * EX is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
1 multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (1,(id REAL)) is set
EX (#) (1 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
(t2 ") " is V11() real ext-real Element of REAL
((t2 ") ") * EX is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
((t2 ") ") * EX is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
((t2 ") ") multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (((t2 ") "),(id REAL)) is set
EX (#) (((t2 ") ") multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
((t2 ") ") * (t2 ") is V11() real ext-real Element of REAL
(((t2 ") ") * (t2 ")) * C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
(((t2 ") ") * (t2 ")) * C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(((t2 ") ") * (t2 ")) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] ((((t2 ") ") * (t2 ")),(id REAL)) is set
C (#) ((((t2 ") ") * (t2 ")) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
1 * C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
1 * C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
C (#) (1 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
EX2 * ((t2 ") ") is V11() real ext-real Element of REAL
(EX2 * ((t2 ") ")) * EX is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
(EX2 * ((t2 ") ")) * EX is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(EX2 * ((t2 ") ")) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] ((EX2 * ((t2 ") ")),(id REAL)) is set
EX (#) ((EX2 * ((t2 ") ")) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
qt2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.qt2.| is V11() real ext-real non negative Element of REAL
sqr qt2 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
qt2 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (qt2,qt2) is Relation-like Function-like set
multreal .: (qt2,qt2) is set
K383((sqr qt2)) is V11() real ext-real Element of REAL
K195(REAL,(sqr qt2),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr qt2)) is V11() real ext-real Element of REAL
EX2 " is V11() real ext-real Element of REAL
(EX2 ") * C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
(EX2 ") * C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(EX2 ") multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] ((EX2 "),(id REAL)) is set
C (#) ((EX2 ") multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
(EX2 ") * EX2 is V11() real ext-real Element of REAL
((EX2 ") * EX2) * p12 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
((EX2 ") * EX2) * p12 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
((EX2 ") * EX2) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (((EX2 ") * EX2),(id REAL)) is set
p12 (#) (((EX2 ") * EX2) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
1 * p12 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
1 * p12 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
1 multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (1,(id REAL)) is set
p12 (#) (1 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
t2 " is V11() real ext-real Element of REAL
(t2 ") * EX is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
(t2 ") * EX is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(t2 ") multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] ((t2 "),(id REAL)) is set
EX (#) ((t2 ") multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
(t2 ") * t2 is V11() real ext-real Element of REAL
((t2 ") * t2) * C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
((t2 ") * t2) * C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
((t2 ") * t2) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (((t2 ") * t2),(id REAL)) is set
C (#) (((t2 ") * t2) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
1 * C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
1 * C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
C (#) (1 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
(EX2 ") * (t2 ") is V11() real ext-real Element of REAL
((EX2 ") * (t2 ")) * EX is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
((EX2 ") * (t2 ")) * EX is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
((EX2 ") * (t2 ")) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (((EX2 ") * (t2 ")),(id REAL)) is set
EX (#) (((EX2 ") * (t2 ")) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
t2 " is V11() real ext-real Element of REAL
(t2 ") * C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
(t2 ") * C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(t2 ") multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] ((t2 "),(id REAL)) is set
C (#) ((t2 ") multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
(t2 ") * t2 is V11() real ext-real Element of REAL
((t2 ") * t2) * EX is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
((t2 ") * t2) * EX is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
((t2 ") * t2) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (((t2 ") * t2),(id REAL)) is set
EX (#) (((t2 ") * t2) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
1 * EX is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
1 * EX is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
EX (#) (1 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
(t2 ") " is V11() real ext-real Element of REAL
((t2 ") ") * EX is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
((t2 ") ") * EX is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
((t2 ") ") multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (((t2 ") "),(id REAL)) is set
EX (#) (((t2 ") ") multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
((t2 ") ") * (t2 ") is V11() real ext-real Element of REAL
(((t2 ") ") * (t2 ")) * C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
(((t2 ") ") * (t2 ")) * C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(((t2 ") ") * (t2 ")) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] ((((t2 ") ") * (t2 ")),(id REAL)) is set
C (#) ((((t2 ") ") * (t2 ")) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
1 * C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
1 * C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
C (#) (1 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
(EX2 ") * ((t2 ") ") is V11() real ext-real Element of REAL
((EX2 ") * ((t2 ") ")) * EX is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
((EX2 ") * ((t2 ") ")) * EX is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
((EX2 ") * ((t2 ") ")) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (((EX2 ") * ((t2 ") ")),(id REAL)) is set
EX (#) (((EX2 ") * ((t2 ") ")) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
t2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
qt2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
LSeg (p12,t2) is non empty closed connected compact convex Element of bool the carrier of (TOP-REAL C)
{ (((1 - b1) * p12) + (b1 * t2)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
LSeg (t2,qt2) is non empty closed connected compact convex Element of bool the carrier of (TOP-REAL C)
{ (((1 - b1) * t2) + (b1 * qt2)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
LSeg (qt2,EX) is non empty closed connected compact convex Element of bool the carrier of (TOP-REAL C)
{ (((1 - b1) * qt2) + (b1 * EX)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
r2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
q4 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
LSeg (EX,r2) is non empty closed connected compact convex Element of bool the carrier of (TOP-REAL C)
{ (((1 - b1) * EX) + (b1 * r2)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
LSeg (r2,q4) is non empty closed connected compact convex Element of bool the carrier of (TOP-REAL C)
{ (((1 - b1) * r2) + (b1 * q4)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
LSeg (q4,C) is non empty closed connected compact convex Element of bool the carrier of (TOP-REAL C)
{ (((1 - b1) * q4) + (b1 * C)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
0. (TOP-REAL C) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like V62( TOP-REAL C) complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the ZeroF of (TOP-REAL C) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
p1 is set
EX is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.EX.| is V11() real ext-real non negative Element of REAL
sqr EX is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
sqrreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
EX (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (EX,EX) is Relation-like Function-like set
multreal .: (EX,EX) is set
K383((sqr EX)) is V11() real ext-real Element of REAL
addreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K195(REAL,(sqr EX),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr EX)) is V11() real ext-real Element of REAL
LSeg (p12,(0. (TOP-REAL C))) is non empty closed connected compact convex Element of bool the carrier of (TOP-REAL C)
{ (((1 - b1) * p12) + (b1 * (0. (TOP-REAL C)))) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
LSeg ((0. (TOP-REAL C)),C) is non empty closed connected compact convex Element of bool the carrier of (TOP-REAL C)
{ (((1 - b1) * (0. (TOP-REAL C))) + (b1 * C)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
bool the carrier of (TOP-REAL C) is non empty set
REAL C is non empty functional FinSequence-membered FinSequenceSet of REAL
C -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = C } is set
p is V11() real ext-real Element of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C) : not p <= |.b1.| } is set
(REAL C) \ { b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C) : not p <= |.b1.| } is functional FinSequence-membered Element of bool (REAL C)
bool (REAL C) is non empty set
WH is Element of bool the carrier of (TOP-REAL C)
p12 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
EX2 is V11() real ext-real Element of REAL
EX2 * C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
EX2 * C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
EX2 multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
id REAL is non empty Relation-like REAL -defined REAL -valued Function-like one-to-one total V30( REAL , REAL ) complex-yielding V174() V175() increasing V179() Element of bool [:REAL,REAL:]
multreal [;] (EX2,(id REAL)) is set
C (#) (EX2 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
EX1 is V11() real ext-real Element of REAL
EX1 * p12 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
EX1 * p12 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
EX1 multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (EX1,(id REAL)) is set
p12 (#) (EX1 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
EX2 is V11() real ext-real Element of REAL
EX2 * C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
EX2 * C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
EX2 multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
id REAL is non empty Relation-like REAL -defined REAL -valued Function-like one-to-one total V30( REAL , REAL ) complex-yielding V174() V175() increasing V179() Element of bool [:REAL,REAL:]
multreal [;] (EX2,(id REAL)) is set
C (#) (EX2 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
EX2 * p12 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
EX2 * p12 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
p12 (#) (EX2 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
0. (TOP-REAL C) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like V62( TOP-REAL C) complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the ZeroF of (TOP-REAL C) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.p12.| is V11() real ext-real non negative Element of REAL
sqr p12 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
sqrreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
p12 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (p12,p12) is Relation-like Function-like set
multreal .: (p12,p12) is set
K383((sqr p12)) is V11() real ext-real Element of REAL
addreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K195(REAL,(sqr p12),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr p12)) is V11() real ext-real Element of REAL
EX1 is V11() real ext-real Element of REAL
EX1 * C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
EX1 * C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
EX1 multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (EX1,(id REAL)) is set
C (#) (EX1 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
p1 is V11() real ext-real Element of REAL
p1 * p12 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
p1 * p12 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
p1 multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (p1,(id REAL)) is set
p12 (#) (p1 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
0* C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
C |-> 0 is Relation-like empty-yielding NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of C -tuples_on REAL
Seg C is V35() C -element V183() V184() V185() V186() V187() V188() Element of bool NAT
(Seg C) --> 0 is Relation-like Seg C -defined INT -valued RAT -valued {0} -valued Function-like total V30( Seg C,{0}) V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() V176() Element of bool [:(Seg C),{0}:]
{0} is non empty trivial V35() V39() 1 -element V183() V184() V185() V186() V187() V188() set
[:(Seg C),{0}:] is INT -valued RAT -valued V35() complex-yielding V174() V175() V176() set
bool [:(Seg C),{0}:] is non empty V35() V39() set
r is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
EX1 is V11() real ext-real Element of REAL
EX1 * C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
EX1 * C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
EX1 multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (EX1,(id REAL)) is set
C (#) (EX1 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
p1 is V11() real ext-real Element of REAL
p1 * p12 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
p1 * p12 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
p1 multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (p1,(id REAL)) is set
p12 (#) (p1 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
EX1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
|.EX1.| is V11() real ext-real non negative Element of REAL
sqr EX1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
EX1 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (EX1,EX1) is Relation-like Function-like set
multreal .: (EX1,EX1) is set
K383((sqr EX1)) is V11() real ext-real Element of REAL
K195(REAL,(sqr EX1),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr EX1)) is V11() real ext-real Element of REAL
p / |.EX1.| is V11() real ext-real Element of REAL
(p / |.EX1.|) * EX1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
(p / |.EX1.|) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] ((p / |.EX1.|),(id REAL)) is set
EX1 (#) ((p / |.EX1.|) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
0 * r is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
0 multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (0,(id REAL)) is set
r (#) (0 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
0 * p12 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
0 * p12 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
p12 (#) (0 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
EX is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
r2 is V11() real ext-real Element of REAL
r2 * EX is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
r2 * EX is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
r2 multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (r2,(id REAL)) is set
EX (#) (r2 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
r2 * p12 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
r2 * p12 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
p12 (#) (r2 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
r2 * (p / |.EX1.|) is V11() real ext-real Element of REAL
(r2 * (p / |.EX1.|)) * EX1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
(r2 * (p / |.EX1.|)) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] ((r2 * (p / |.EX1.|)),(id REAL)) is set
EX1 (#) ((r2 * (p / |.EX1.|)) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
t2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of C -tuples_on REAL
(p / |.EX1.|) " is V11() real ext-real Element of REAL
((p / |.EX1.|) ") * (p / |.EX1.|) is V11() real ext-real Element of REAL
(((p / |.EX1.|) ") * (p / |.EX1.|)) * t2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of C -tuples_on REAL
(((p / |.EX1.|) ") * (p / |.EX1.|)) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] ((((p / |.EX1.|) ") * (p / |.EX1.|)),(id REAL)) is set
t2 (#) ((((p / |.EX1.|) ") * (p / |.EX1.|)) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
r2 * r is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
r (#) (r2 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
((p / |.EX1.|) ") * (r2 * r) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
((p / |.EX1.|) ") multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (((p / |.EX1.|) "),(id REAL)) is set
(r2 * r) (#) (((p / |.EX1.|) ") multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
(((p / |.EX1.|) ") * (p / |.EX1.|)) * EX1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
EX1 (#) ((((p / |.EX1.|) ") * (p / |.EX1.|)) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
qt2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of C -tuples_on REAL
((p / |.EX1.|) ") * r2 is V11() real ext-real Element of REAL
(((p / |.EX1.|) ") * r2) * qt2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of C -tuples_on REAL
(((p / |.EX1.|) ") * r2) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] ((((p / |.EX1.|) ") * r2),(id REAL)) is set
qt2 (#) ((((p / |.EX1.|) ") * r2) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
(r2 * (p / |.EX1.|)) * t2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of C -tuples_on REAL
t2 (#) ((r2 * (p / |.EX1.|)) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
1 * EX1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
1 multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (1,(id REAL)) is set
EX1 (#) (1 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
(((p / |.EX1.|) ") * r2) * r is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
r (#) ((((p / |.EX1.|) ") * r2) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
|.EX.| is V11() real ext-real non negative Element of REAL
sqr EX is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
EX (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (EX,EX) is Relation-like Function-like set
multreal .: (EX,EX) is set
K383((sqr EX)) is V11() real ext-real Element of REAL
K195(REAL,(sqr EX),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr EX)) is V11() real ext-real Element of REAL
abs (p / |.EX1.|) is V11() real ext-real Element of REAL
(abs (p / |.EX1.|)) * |.EX1.| is V11() real ext-real Element of REAL
(p / |.EX1.|) * |.EX1.| is V11() real ext-real Element of REAL
t2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.t2.| is V11() real ext-real non negative Element of REAL
sqr t2 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
t2 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (t2,t2) is Relation-like Function-like set
multreal .: (t2,t2) is set
K383((sqr t2)) is V11() real ext-real Element of REAL
K195(REAL,(sqr t2),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr t2)) is V11() real ext-real Element of REAL
t2 is V11() real ext-real Element of REAL
t2 * C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
t2 * C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
t2 multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (t2,(id REAL)) is set
C (#) (t2 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
qt2 is V11() real ext-real Element of REAL
qt2 * p12 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
qt2 * p12 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
qt2 multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (qt2,(id REAL)) is set
p12 (#) (qt2 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
t2 is V11() real ext-real Element of REAL
t2 * C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
t2 * C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
t2 multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (t2,(id REAL)) is set
C (#) (t2 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
t2 * EX is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
t2 * EX is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
EX (#) (t2 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
|.C.| is V11() real ext-real non negative Element of REAL
sqr C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
C (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (C,C) is Relation-like Function-like set
multreal .: (C,C) is set
K383((sqr C)) is V11() real ext-real Element of REAL
K195(REAL,(sqr C),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr C)) is V11() real ext-real Element of REAL
qt2 is V11() real ext-real Element of REAL
qt2 * C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
qt2 * C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
qt2 multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (qt2,(id REAL)) is set
C (#) (qt2 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
r2 is V11() real ext-real Element of REAL
r2 * p12 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
r2 * p12 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
r2 multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (r2,(id REAL)) is set
p12 (#) (r2 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
t2 " is V11() real ext-real Element of REAL
(t2 ") * EX is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
(t2 ") * EX is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(t2 ") multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] ((t2 "),(id REAL)) is set
EX (#) ((t2 ") multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
(t2 ") * t2 is V11() real ext-real Element of REAL
((t2 ") * t2) * C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
((t2 ") * t2) * C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
((t2 ") * t2) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (((t2 ") * t2),(id REAL)) is set
C (#) (((t2 ") * t2) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
1 * C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
1 * C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
C (#) (1 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
EX2 * (t2 ") is V11() real ext-real Element of REAL
(EX2 * (t2 ")) * EX is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
(EX2 * (t2 ")) * EX is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(EX2 * (t2 ")) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] ((EX2 * (t2 ")),(id REAL)) is set
EX (#) ((EX2 * (t2 ")) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
t2 " is V11() real ext-real Element of REAL
(t2 ") * C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
(t2 ") * C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(t2 ") multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] ((t2 "),(id REAL)) is set
C (#) ((t2 ") multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
(t2 ") * t2 is V11() real ext-real Element of REAL
((t2 ") * t2) * EX is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
((t2 ") * t2) * EX is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
((t2 ") * t2) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (((t2 ") * t2),(id REAL)) is set
EX (#) (((t2 ") * t2) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
1 * EX is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
1 * EX is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
EX (#) (1 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
(t2 ") " is V11() real ext-real Element of REAL
((t2 ") ") * EX is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
((t2 ") ") * EX is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
((t2 ") ") multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (((t2 ") "),(id REAL)) is set
EX (#) (((t2 ") ") multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
((t2 ") ") * (t2 ") is V11() real ext-real Element of REAL
(((t2 ") ") * (t2 ")) * C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
(((t2 ") ") * (t2 ")) * C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(((t2 ") ") * (t2 ")) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] ((((t2 ") ") * (t2 ")),(id REAL)) is set
C (#) ((((t2 ") ") * (t2 ")) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
1 * C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
1 * C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
C (#) (1 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
EX2 * ((t2 ") ") is V11() real ext-real Element of REAL
(EX2 * ((t2 ") ")) * EX is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
(EX2 * ((t2 ") ")) * EX is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(EX2 * ((t2 ") ")) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] ((EX2 * ((t2 ") ")),(id REAL)) is set
EX (#) ((EX2 * ((t2 ") ")) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
qt2 is V11() real ext-real Element of REAL
qt2 * C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
qt2 * C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
qt2 multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (qt2,(id REAL)) is set
C (#) (qt2 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
r2 is V11() real ext-real Element of REAL
r2 * p12 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
r2 * p12 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
r2 multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (r2,(id REAL)) is set
p12 (#) (r2 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
EX2 " is V11() real ext-real Element of REAL
(EX2 ") * C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
(EX2 ") * C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(EX2 ") multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] ((EX2 "),(id REAL)) is set
C (#) ((EX2 ") multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
(EX2 ") * EX2 is V11() real ext-real Element of REAL
((EX2 ") * EX2) * p12 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
((EX2 ") * EX2) * p12 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
((EX2 ") * EX2) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (((EX2 ") * EX2),(id REAL)) is set
p12 (#) (((EX2 ") * EX2) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
1 * p12 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
1 * p12 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
p12 (#) (1 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
t2 " is V11() real ext-real Element of REAL
(t2 ") * EX is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
(t2 ") * EX is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(t2 ") multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] ((t2 "),(id REAL)) is set
EX (#) ((t2 ") multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
(t2 ") * t2 is V11() real ext-real Element of REAL
((t2 ") * t2) * C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
((t2 ") * t2) * C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
((t2 ") * t2) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (((t2 ") * t2),(id REAL)) is set
C (#) (((t2 ") * t2) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
1 * C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
1 * C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
C (#) (1 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
(EX2 ") * (t2 ") is V11() real ext-real Element of REAL
((EX2 ") * (t2 ")) * EX is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
((EX2 ") * (t2 ")) * EX is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
((EX2 ") * (t2 ")) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (((EX2 ") * (t2 ")),(id REAL)) is set
EX (#) (((EX2 ") * (t2 ")) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
t2 " is V11() real ext-real Element of REAL
(t2 ") * C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
(t2 ") * C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(t2 ") multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] ((t2 "),(id REAL)) is set
C (#) ((t2 ") multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
(t2 ") * t2 is V11() real ext-real Element of REAL
((t2 ") * t2) * EX is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
((t2 ") * t2) * EX is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
((t2 ") * t2) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (((t2 ") * t2),(id REAL)) is set
EX (#) (((t2 ") * t2) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
1 * EX is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
1 * EX is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
EX (#) (1 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
(t2 ") " is V11() real ext-real Element of REAL
((t2 ") ") * EX is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
((t2 ") ") * EX is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
((t2 ") ") multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (((t2 ") "),(id REAL)) is set
EX (#) (((t2 ") ") multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
((t2 ") ") * (t2 ") is V11() real ext-real Element of REAL
(((t2 ") ") * (t2 ")) * C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
(((t2 ") ") * (t2 ")) * C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(((t2 ") ") * (t2 ")) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] ((((t2 ") ") * (t2 ")),(id REAL)) is set
C (#) ((((t2 ") ") * (t2 ")) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
1 * C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
1 * C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
C (#) (1 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
(EX2 ") * ((t2 ") ") is V11() real ext-real Element of REAL
((EX2 ") * ((t2 ") ")) * EX is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
((EX2 ") * ((t2 ") ")) * EX is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
((EX2 ") * ((t2 ") ")) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (((EX2 ") * ((t2 ") ")),(id REAL)) is set
EX (#) (((EX2 ") * ((t2 ") ")) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
t2 is V11() real ext-real Element of REAL
t2 * C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
t2 * C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
t2 multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (t2,(id REAL)) is set
C (#) (t2 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
qt2 is V11() real ext-real Element of REAL
qt2 * p12 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
qt2 * p12 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
qt2 multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (qt2,(id REAL)) is set
p12 (#) (qt2 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
t2 is V11() real ext-real Element of REAL
t2 * C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
t2 * C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
t2 multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (t2,(id REAL)) is set
C (#) (t2 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
qt2 is V11() real ext-real Element of REAL
qt2 * p12 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
qt2 * p12 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
qt2 multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (qt2,(id REAL)) is set
p12 (#) (qt2 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
t2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
qt2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
LSeg (p12,t2) is non empty closed connected compact convex Element of bool the carrier of (TOP-REAL C)
{ (((1 - b1) * p12) + (b1 * t2)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
LSeg (t2,qt2) is non empty closed connected compact convex Element of bool the carrier of (TOP-REAL C)
{ (((1 - b1) * t2) + (b1 * qt2)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
LSeg (qt2,EX) is non empty closed connected compact convex Element of bool the carrier of (TOP-REAL C)
{ (((1 - b1) * qt2) + (b1 * EX)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
r2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
q4 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
LSeg (EX,r2) is non empty closed connected compact convex Element of bool the carrier of (TOP-REAL C)
{ (((1 - b1) * EX) + (b1 * r2)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
LSeg (r2,q4) is non empty closed connected compact convex Element of bool the carrier of (TOP-REAL C)
{ (((1 - b1) * r2) + (b1 * q4)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
LSeg (q4,C) is non empty closed connected compact convex Element of bool the carrier of (TOP-REAL C)
{ (((1 - b1) * q4) + (b1 * C)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
0. (TOP-REAL C) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like V62( TOP-REAL C) complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the ZeroF of (TOP-REAL C) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
p1 is set
EX is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.EX.| is V11() real ext-real non negative Element of REAL
sqr EX is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
sqrreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
EX (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (EX,EX) is Relation-like Function-like set
multreal .: (EX,EX) is set
K383((sqr EX)) is V11() real ext-real Element of REAL
addreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K195(REAL,(sqr EX),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr EX)) is V11() real ext-real Element of REAL
EX is V11() real ext-real Element of REAL
EX * C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
EX * C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
EX multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (EX,(id REAL)) is set
C (#) (EX multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
t2 is V11() real ext-real Element of REAL
t2 * p12 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
t2 * p12 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
t2 multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (t2,(id REAL)) is set
p12 (#) (t2 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
LSeg (p12,(0. (TOP-REAL C))) is non empty closed connected compact convex Element of bool the carrier of (TOP-REAL C)
{ (((1 - b1) * p12) + (b1 * (0. (TOP-REAL C)))) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
LSeg ((0. (TOP-REAL C)),C) is non empty closed connected compact convex Element of bool the carrier of (TOP-REAL C)
{ (((1 - b1) * (0. (TOP-REAL C))) + (b1 * C)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
p is V11() real ext-real Element of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C) : not |.b1.| <= p } is set
p + 1 is V11() real ext-real Element of REAL
abs (p + 1) is V11() real ext-real Element of REAL
sqrt C is V11() real ext-real Element of REAL
(abs (p + 1)) * 1 is V11() real ext-real Element of REAL
(abs (p + 1)) * (sqrt C) is V11() real ext-real Element of REAL
1.REAL C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
1* C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
REAL C is non empty functional FinSequence-membered FinSequenceSet of REAL
C -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = C } is set
C |-> 1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of C -tuples_on REAL
Seg C is V35() C -element V183() V184() V185() V186() V187() V188() Element of bool NAT
(Seg C) --> 1 is Relation-like Seg C -defined INT -valued RAT -valued {1} -valued Function-like total V30( Seg C,{1}) V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() V176() Element of bool [:(Seg C),{1}:]
{1} is non empty trivial V35() V39() 1 -element V183() V184() V185() V186() V187() V188() set
[:(Seg C),{1}:] is INT -valued RAT -valued V35() complex-yielding V174() V175() V176() set
bool [:(Seg C),{1}:] is non empty V35() V39() set
(p + 1) * (1.REAL C) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
(p + 1) * (1.REAL C) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(p + 1) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
id REAL is non empty Relation-like REAL -defined REAL -valued Function-like one-to-one total V30( REAL , REAL ) complex-yielding V174() V175() increasing V179() Element of bool [:REAL,REAL:]
multreal [;] ((p + 1),(id REAL)) is set
(1.REAL C) (#) ((p + 1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
|.((p + 1) * (1.REAL C)).| is V11() real ext-real non negative Element of REAL
sqr ((p + 1) * (1.REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
sqrreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
((p + 1) * (1.REAL C)) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (((p + 1) * (1.REAL C)),((p + 1) * (1.REAL C))) is Relation-like Function-like set
multreal .: (((p + 1) * (1.REAL C)),((p + 1) * (1.REAL C))) is set
K383((sqr ((p + 1) * (1.REAL C)))) is V11() real ext-real Element of REAL
addreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K195(REAL,(sqr ((p + 1) * (1.REAL C))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr ((p + 1) * (1.REAL C)))) is V11() real ext-real Element of REAL
|.(1.REAL C).| is V11() real ext-real non negative Element of REAL
sqr (1.REAL C) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(1.REAL C) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((1.REAL C),(1.REAL C)) is Relation-like Function-like set
multreal .: ((1.REAL C),(1.REAL C)) is set
K383((sqr (1.REAL C))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (1.REAL C)),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (1.REAL C))) is V11() real ext-real Element of REAL
(abs (p + 1)) * |.(1.REAL C).| is V11() real ext-real Element of REAL
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
bool the carrier of (TOP-REAL C) is non empty set
p is V11() real ext-real Element of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C) : not |.b1.| <= p } is set
WH is Element of bool the carrier of (TOP-REAL C)
p12 is non empty Element of bool the carrier of (TOP-REAL C)
(TOP-REAL C) | p12 is non empty strict TopSpace-like SubSpace of TOP-REAL C
the carrier of ((TOP-REAL C) | p12) is non empty set
[: the carrier of I[01], the carrier of ((TOP-REAL C) | p12):] is non empty set
bool [: the carrier of I[01], the carrier of ((TOP-REAL C) | p12):] is non empty set
C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
r is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
EX2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
EX1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
LSeg (C,EX2) is non empty closed connected compact convex Element of bool the carrier of (TOP-REAL C)
{ (((1 - b1) * C) + (b1 * EX2)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
LSeg (EX2,EX1) is non empty closed connected compact convex Element of bool the carrier of (TOP-REAL C)
{ (((1 - b1) * EX2) + (b1 * EX1)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
LSeg (EX1,r) is non empty closed connected compact convex Element of bool the carrier of (TOP-REAL C)
{ (((1 - b1) * EX1) + (b1 * r)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
EX2 is V11() real ext-real Element of REAL
EX2 * r is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
EX2 * r is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
EX2 multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
id REAL is non empty Relation-like REAL -defined REAL -valued Function-like one-to-one total V30( REAL , REAL ) complex-yielding V174() V175() increasing V179() Element of bool [:REAL,REAL:]
multreal [;] (EX2,(id REAL)) is set
r (#) (EX2 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
EX1 is V11() real ext-real Element of REAL
EX1 * C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
EX1 * C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
EX1 multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (EX1,(id REAL)) is set
C (#) (EX1 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
EX2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
EX1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
p1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
EX is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
t2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
LSeg (C,EX2) is non empty closed connected compact convex Element of bool the carrier of (TOP-REAL C)
{ (((1 - b1) * C) + (b1 * EX2)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
LSeg (EX2,EX1) is non empty closed connected compact convex Element of bool the carrier of (TOP-REAL C)
{ (((1 - b1) * EX2) + (b1 * EX1)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
LSeg (EX1,p1) is non empty closed connected compact convex Element of bool the carrier of (TOP-REAL C)
{ (((1 - b1) * EX1) + (b1 * p1)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
LSeg (p1,EX) is non empty closed connected compact convex Element of bool the carrier of (TOP-REAL C)
{ (((1 - b1) * p1) + (b1 * EX)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
LSeg (EX,t2) is non empty closed connected compact convex Element of bool the carrier of (TOP-REAL C)
{ (((1 - b1) * EX) + (b1 * t2)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
LSeg (t2,r) is non empty closed connected compact convex Element of bool the carrier of (TOP-REAL C)
{ (((1 - b1) * t2) + (b1 * r)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
EX2 is V11() real ext-real Element of REAL
EX2 * r is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
EX2 * r is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
EX2 multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
id REAL is non empty Relation-like REAL -defined REAL -valued Function-like one-to-one total V30( REAL , REAL ) complex-yielding V174() V175() increasing V179() Element of bool [:REAL,REAL:]
multreal [;] (EX2,(id REAL)) is set
r (#) (EX2 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
EX1 is V11() real ext-real Element of REAL
EX1 * C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
EX1 * C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
EX1 multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (EX1,(id REAL)) is set
C (#) (EX1 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
REAL C is non empty functional FinSequence-membered FinSequenceSet of REAL
C -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = C } is set
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
p is V11() real ext-real Element of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C) : not p <= |.b1.| } is set
(REAL C) \ { b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C) : not p <= |.b1.| } is functional FinSequence-membered Element of bool (REAL C)
bool (REAL C) is non empty set
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C) : not |.b1.| <= p } is set
WH is set
p12 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.p12.| is V11() real ext-real non negative Element of REAL
sqr p12 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
sqrreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
p12 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (p12,p12) is Relation-like Function-like set
multreal .: (p12,p12) is set
K383((sqr p12)) is V11() real ext-real Element of REAL
addreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K195(REAL,(sqr p12),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr p12)) is V11() real ext-real Element of REAL
C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.C.| is V11() real ext-real non negative Element of REAL
sqr C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
C (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (C,C) is Relation-like Function-like set
multreal .: (C,C) is set
K383((sqr C)) is V11() real ext-real Element of REAL
K195(REAL,(sqr C),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr C)) is V11() real ext-real Element of REAL
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
bool the carrier of (TOP-REAL C) is non empty set
REAL C is non empty functional FinSequence-membered FinSequenceSet of REAL
C -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = C } is set
p is V11() real ext-real Element of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C) : not p <= |.b1.| } is set
(REAL C) \ { b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C) : not p <= |.b1.| } is functional FinSequence-membered Element of bool (REAL C)
bool (REAL C) is non empty set
WH is Element of bool the carrier of (TOP-REAL C)
p12 is non empty Element of bool the carrier of (TOP-REAL C)
(TOP-REAL C) | p12 is non empty strict TopSpace-like SubSpace of TOP-REAL C
the carrier of ((TOP-REAL C) | p12) is non empty set
[: the carrier of I[01], the carrier of ((TOP-REAL C) | p12):] is non empty set
bool [: the carrier of I[01], the carrier of ((TOP-REAL C) | p12):] is non empty set
C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
r is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
EX2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
EX1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
LSeg (C,EX2) is non empty closed connected compact convex Element of bool the carrier of (TOP-REAL C)
{ (((1 - b1) * C) + (b1 * EX2)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
LSeg (EX2,EX1) is non empty closed connected compact convex Element of bool the carrier of (TOP-REAL C)
{ (((1 - b1) * EX2) + (b1 * EX1)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
LSeg (EX1,r) is non empty closed connected compact convex Element of bool the carrier of (TOP-REAL C)
{ (((1 - b1) * EX1) + (b1 * r)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
EX2 is V11() real ext-real Element of REAL
EX2 * r is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
EX2 * r is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
EX2 multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
id REAL is non empty Relation-like REAL -defined REAL -valued Function-like one-to-one total V30( REAL , REAL ) complex-yielding V174() V175() increasing V179() Element of bool [:REAL,REAL:]
multreal [;] (EX2,(id REAL)) is set
r (#) (EX2 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
EX1 is V11() real ext-real Element of REAL
EX1 * C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
EX1 * C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
EX1 multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (EX1,(id REAL)) is set
C (#) (EX1 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
EX2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
EX1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
p1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
EX is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
t2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
LSeg (C,EX2) is non empty closed connected compact convex Element of bool the carrier of (TOP-REAL C)
{ (((1 - b1) * C) + (b1 * EX2)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
LSeg (EX2,EX1) is non empty closed connected compact convex Element of bool the carrier of (TOP-REAL C)
{ (((1 - b1) * EX2) + (b1 * EX1)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
LSeg (EX1,p1) is non empty closed connected compact convex Element of bool the carrier of (TOP-REAL C)
{ (((1 - b1) * EX1) + (b1 * p1)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
LSeg (p1,EX) is non empty closed connected compact convex Element of bool the carrier of (TOP-REAL C)
{ (((1 - b1) * p1) + (b1 * EX)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
LSeg (EX,t2) is non empty closed connected compact convex Element of bool the carrier of (TOP-REAL C)
{ (((1 - b1) * EX) + (b1 * t2)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
LSeg (t2,r) is non empty closed connected compact convex Element of bool the carrier of (TOP-REAL C)
{ (((1 - b1) * t2) + (b1 * r)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
EX2 is V11() real ext-real Element of REAL
EX2 * r is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
EX2 * r is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
EX2 multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
id REAL is non empty Relation-like REAL -defined REAL -valued Function-like one-to-one total V30( REAL , REAL ) complex-yielding V174() V175() increasing V179() Element of bool [:REAL,REAL:]
multreal [;] (EX2,(id REAL)) is set
r (#) (EX2 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
EX1 is V11() real ext-real Element of REAL
EX1 * C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
EX1 * C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
EX1 multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (EX1,(id REAL)) is set
C (#) (EX1 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
C is V11() real ext-real Element of REAL
p is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
TOP-REAL p is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL p) is non empty set
bool the carrier of (TOP-REAL p) is non empty set
REAL p is non empty functional FinSequence-membered FinSequenceSet of REAL
p -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = p } is set
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() p -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL p) : not C <= |.b1.| } is set
(REAL p) \ { b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() p -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL p) : not C <= |.b1.| } is functional FinSequence-membered Element of bool (REAL p)
bool (REAL p) is non empty set
WH is Element of bool the carrier of (TOP-REAL p)
the Element of WH is Element of WH
C is V11() real ext-real Element of REAL
r is Relation-like NAT -defined REAL -valued Function-like V35() p -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL p)
|.r.| is V11() real ext-real non negative Element of REAL
sqr r is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
sqrreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
r (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (r,r) is Relation-like Function-like set
multreal .: (r,r) is set
K383((sqr r)) is V11() real ext-real Element of REAL
addreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K195(REAL,(sqr r),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr r)) is V11() real ext-real Element of REAL
1.REAL p is Relation-like NAT -defined REAL -valued Function-like V35() p -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL p)
1* p is Relation-like NAT -defined REAL -valued Function-like V35() p -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL p
p |-> 1 is Relation-like NAT -defined REAL -valued Function-like V35() p -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of p -tuples_on REAL
Seg p is V35() p -element V183() V184() V185() V186() V187() V188() Element of bool NAT
(Seg p) --> 1 is Relation-like Seg p -defined INT -valued RAT -valued {1} -valued Function-like total V30( Seg p,{1}) V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() V176() Element of bool [:(Seg p),{1}:]
{1} is non empty trivial V35() V39() 1 -element V183() V184() V185() V186() V187() V188() set
[:(Seg p),{1}:] is INT -valued RAT -valued V35() complex-yielding V174() V175() V176() set
bool [:(Seg p),{1}:] is non empty V35() V39() set
C + C is V11() real ext-real Element of REAL
(C + C) + 1 is V11() real ext-real Element of REAL
((C + C) + 1) * (1.REAL p) is Relation-like NAT -defined REAL -valued Function-like V35() p -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL p)
((C + C) + 1) * (1.REAL p) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
((C + C) + 1) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
id REAL is non empty Relation-like REAL -defined REAL -valued Function-like one-to-one total V30( REAL , REAL ) complex-yielding V174() V175() increasing V179() Element of bool [:REAL,REAL:]
multreal [;] (((C + C) + 1),(id REAL)) is set
(1.REAL p) (#) (((C + C) + 1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
abs ((C + C) + 1) is V11() real ext-real Element of REAL
sqrt p is V11() real ext-real Element of REAL
(abs ((C + C) + 1)) * 1 is V11() real ext-real Element of REAL
(abs ((C + C) + 1)) * (sqrt p) is V11() real ext-real Element of REAL
|.(((C + C) + 1) * (1.REAL p)).| is V11() real ext-real non negative Element of REAL
sqr (((C + C) + 1) * (1.REAL p)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(((C + C) + 1) * (1.REAL p)) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((((C + C) + 1) * (1.REAL p)),(((C + C) + 1) * (1.REAL p))) is Relation-like Function-like set
multreal .: ((((C + C) + 1) * (1.REAL p)),(((C + C) + 1) * (1.REAL p))) is set
K383((sqr (((C + C) + 1) * (1.REAL p)))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (((C + C) + 1) * (1.REAL p))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (((C + C) + 1) * (1.REAL p)))) is V11() real ext-real Element of REAL
|.(1.REAL p).| is V11() real ext-real non negative Element of REAL
sqr (1.REAL p) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(1.REAL p) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((1.REAL p),(1.REAL p)) is Relation-like Function-like set
multreal .: ((1.REAL p),(1.REAL p)) is set
K383((sqr (1.REAL p))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (1.REAL p)),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (1.REAL p))) is V11() real ext-real Element of REAL
(abs ((C + C) + 1)) * |.(1.REAL p).| is V11() real ext-real Element of REAL
EX2 is Relation-like NAT -defined REAL -valued Function-like V35() p -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL p)
|.EX2.| is V11() real ext-real non negative Element of REAL
sqr EX2 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
EX2 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (EX2,EX2) is Relation-like Function-like set
multreal .: (EX2,EX2) is set
K383((sqr EX2)) is V11() real ext-real Element of REAL
K195(REAL,(sqr EX2),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr EX2)) is V11() real ext-real Element of REAL
C + C is V11() real ext-real Element of REAL
p12 is set
C is Relation-like NAT -defined REAL -valued Function-like V35() p -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL p)
|.C.| is V11() real ext-real non negative Element of REAL
sqr C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
sqrreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
C (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (C,C) is Relation-like Function-like set
multreal .: (C,C) is set
K383((sqr C)) is V11() real ext-real Element of REAL
addreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K195(REAL,(sqr C),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr C)) is V11() real ext-real Element of REAL
p12 is Element of bool the carrier of (TOP-REAL p)
the Element of p12 is Element of p12
r is Relation-like NAT -defined REAL -valued Function-like V35() p -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL p)
|.r.| is V11() real ext-real non negative Element of REAL
sqr r is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
sqrreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
r (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (r,r) is Relation-like Function-like set
multreal .: (r,r) is set
K383((sqr r)) is V11() real ext-real Element of REAL
addreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K195(REAL,(sqr r),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr r)) is V11() real ext-real Element of REAL
[#] (TOP-REAL p) is 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 p)
bool the carrier of (TOP-REAL 1) is non empty set
C is V11() real ext-real Element of REAL
{ b1 where b1 is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1) : ex b2 being V11() real ext-real Element of REAL st
( b1 = <*b2*> & not b2 <= C ) } is set
p is Element of bool the carrier of (TOP-REAL 1)
WH is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
p12 is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
LSeg (WH,p12) is non empty closed connected compact convex Element of bool the carrier of (TOP-REAL 1)
{ (((1 - b1) * WH) + (b1 * p12)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
C is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
r is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
EX2 is V11() real ext-real Element of REAL
<*EX2*> is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() FinSequence of REAL
EX2 is V11() real ext-real Element of REAL
<*EX2*> is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() FinSequence of REAL
EX1 is V11() real ext-real Element of REAL
<*EX1*> is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() FinSequence of REAL
EX1 is V11() real ext-real Element of REAL
<*EX1*> is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() FinSequence of REAL
p1 is set
EX is V11() real ext-real Element of REAL
1 - EX is V11() real ext-real Element of REAL
(1 - EX) * WH is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
(1 - EX) * WH is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(1 - EX) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
id REAL is non empty Relation-like REAL -defined REAL -valued Function-like one-to-one total V30( REAL , REAL ) complex-yielding V174() V175() increasing V179() Element of bool [:REAL,REAL:]
multreal [;] ((1 - EX),(id REAL)) is set
WH (#) ((1 - EX) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
EX * p12 is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
EX * p12 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
EX multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (EX,(id REAL)) is set
p12 (#) (EX multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
((1 - EX) * WH) + (EX * p12) is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
the U7 of (TOP-REAL 1) is non empty Relation-like [: the carrier of (TOP-REAL 1), the carrier of (TOP-REAL 1):] -defined the carrier of (TOP-REAL 1) -valued Function-like total V30([: the carrier of (TOP-REAL 1), the carrier of (TOP-REAL 1):], the carrier of (TOP-REAL 1)) Element of bool [:[: the carrier of (TOP-REAL 1), the carrier of (TOP-REAL 1):], the carrier of (TOP-REAL 1):]
[: the carrier of (TOP-REAL 1), the carrier of (TOP-REAL 1):] is non empty set
[:[: the carrier of (TOP-REAL 1), the carrier of (TOP-REAL 1):], the carrier of (TOP-REAL 1):] is non empty set
bool [:[: the carrier of (TOP-REAL 1), the carrier of (TOP-REAL 1):], the carrier of (TOP-REAL 1):] is non empty set
the U7 of (TOP-REAL 1) . (((1 - EX) * WH),(EX * p12)) is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
[((1 - EX) * WH),(EX * p12)] is non empty set
{((1 - EX) * WH),(EX * p12)} is non empty functional V35() V39() set
{((1 - EX) * WH)} is non empty trivial functional V35() V39() 1 -element set
{{((1 - EX) * WH),(EX * p12)},{((1 - EX) * WH)}} is non empty V35() V39() set
the U7 of (TOP-REAL 1) . [((1 - EX) * WH),(EX * p12)] is set
((1 - EX) * WH) + (EX * p12) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
addreal .: (((1 - EX) * WH),(EX * p12)) is set
(1 - EX) * C is V11() real ext-real Element of REAL
(1 - EX) * EX1 is V11() real ext-real Element of REAL
EX * C is V11() real ext-real Element of REAL
((1 - EX) * C) + (EX * C) is V11() real ext-real Element of REAL
EX * EX2 is V11() real ext-real Element of REAL
((1 - EX) * EX1) + (EX * EX2) is V11() real ext-real Element of REAL
<*(((1 - EX) * EX1) + (EX * EX2))*> is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() FinSequence of REAL
|[((1 - EX) * EX1)]| is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
|[(EX * EX2)]| is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
|[((1 - EX) * EX1)]| + |[(EX * EX2)]| is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
the U7 of (TOP-REAL 1) . (|[((1 - EX) * EX1)]|,|[(EX * EX2)]|) is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
[|[((1 - EX) * EX1)]|,|[(EX * EX2)]|] is non empty set
{|[((1 - EX) * EX1)]|,|[(EX * EX2)]|} is non empty functional V35() V39() set
{|[((1 - EX) * EX1)]|} is non empty trivial functional V35() V39() 1 -element set
{{|[((1 - EX) * EX1)]|,|[(EX * EX2)]|},{|[((1 - EX) * EX1)]|}} is non empty V35() V39() set
the U7 of (TOP-REAL 1) . [|[((1 - EX) * EX1)]|,|[(EX * EX2)]|] is set
|[((1 - EX) * EX1)]| + |[(EX * EX2)]| is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (|[((1 - EX) * EX1)]|,|[(EX * EX2)]|) is set
|[EX1]| is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
(1 - EX) * |[EX1]| is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
(1 - EX) * |[EX1]| is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
|[EX1]| (#) ((1 - EX) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
((1 - EX) * |[EX1]|) + |[(EX * EX2)]| is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
the U7 of (TOP-REAL 1) . (((1 - EX) * |[EX1]|),|[(EX * EX2)]|) is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
[((1 - EX) * |[EX1]|),|[(EX * EX2)]|] is non empty set
{((1 - EX) * |[EX1]|),|[(EX * EX2)]|} is non empty functional V35() V39() set
{((1 - EX) * |[EX1]|)} is non empty trivial functional V35() V39() 1 -element set
{{((1 - EX) * |[EX1]|),|[(EX * EX2)]|},{((1 - EX) * |[EX1]|)}} is non empty V35() V39() set
the U7 of (TOP-REAL 1) . [((1 - EX) * |[EX1]|),|[(EX * EX2)]|] is set
((1 - EX) * |[EX1]|) + |[(EX * EX2)]| is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (((1 - EX) * |[EX1]|),|[(EX * EX2)]|) is set
|[EX2]| is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
EX * |[EX2]| is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
EX * |[EX2]| is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
|[EX2]| (#) (EX multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
((1 - EX) * |[EX1]|) + (EX * |[EX2]|) is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
the U7 of (TOP-REAL 1) . (((1 - EX) * |[EX1]|),(EX * |[EX2]|)) is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
[((1 - EX) * |[EX1]|),(EX * |[EX2]|)] is non empty set
{((1 - EX) * |[EX1]|),(EX * |[EX2]|)} is non empty functional V35() V39() set
{{((1 - EX) * |[EX1]|),(EX * |[EX2]|)},{((1 - EX) * |[EX1]|)}} is non empty V35() V39() set
the U7 of (TOP-REAL 1) . [((1 - EX) * |[EX1]|),(EX * |[EX2]|)] is set
((1 - EX) * |[EX1]|) + (EX * |[EX2]|) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (((1 - EX) * |[EX1]|),(EX * |[EX2]|)) is set
0 * p12 is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
0 * p12 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
0 multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (0,(id REAL)) is set
p12 (#) (0 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
WH + (0 * p12) is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
the U7 of (TOP-REAL 1) . (WH,(0 * p12)) is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
[WH,(0 * p12)] is non empty set
{WH,(0 * p12)} is non empty functional V35() V39() set
{WH} is non empty trivial functional V35() V39() 1 -element set
{{WH,(0 * p12)},{WH}} is non empty V35() V39() set
the U7 of (TOP-REAL 1) . [WH,(0 * p12)] is set
WH + (0 * p12) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (WH,(0 * p12)) is set
0. (TOP-REAL 1) is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like V62( TOP-REAL 1) complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
the ZeroF of (TOP-REAL 1) is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
WH + (0. (TOP-REAL 1)) is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
the U7 of (TOP-REAL 1) . (WH,(0. (TOP-REAL 1))) is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
[WH,(0. (TOP-REAL 1))] is non empty set
{WH,(0. (TOP-REAL 1))} is non empty functional V35() V39() set
{{WH,(0. (TOP-REAL 1))},{WH}} is non empty V35() V39() set
the U7 of (TOP-REAL 1) . [WH,(0. (TOP-REAL 1))] is set
WH + (0. (TOP-REAL 1)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (WH,(0. (TOP-REAL 1))) is set
C is V11() real ext-real Element of REAL
- C is V11() real ext-real Element of REAL
{ b1 where b1 is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1) : ex b2 being V11() real ext-real Element of REAL st
( b1 = <*b2*> & not - C <= b2 ) } is set
p is Element of bool the carrier of (TOP-REAL 1)
WH is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
p12 is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
LSeg (WH,p12) is non empty closed connected compact convex Element of bool the carrier of (TOP-REAL 1)
{ (((1 - b1) * WH) + (b1 * p12)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
C is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
r is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
EX2 is V11() real ext-real Element of REAL
<*EX2*> is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() FinSequence of REAL
EX2 is V11() real ext-real Element of REAL
<*EX2*> is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() FinSequence of REAL
EX1 is V11() real ext-real Element of REAL
<*EX1*> is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() FinSequence of REAL
EX1 is V11() real ext-real Element of REAL
<*EX1*> is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() FinSequence of REAL
p1 is set
EX is V11() real ext-real Element of REAL
1 - EX is V11() real ext-real Element of REAL
(1 - EX) * WH is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
(1 - EX) * WH is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(1 - EX) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
id REAL is non empty Relation-like REAL -defined REAL -valued Function-like one-to-one total V30( REAL , REAL ) complex-yielding V174() V175() increasing V179() Element of bool [:REAL,REAL:]
multreal [;] ((1 - EX),(id REAL)) is set
WH (#) ((1 - EX) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
EX * p12 is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
EX * p12 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
EX multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (EX,(id REAL)) is set
p12 (#) (EX multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
((1 - EX) * WH) + (EX * p12) is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
the U7 of (TOP-REAL 1) is non empty Relation-like [: the carrier of (TOP-REAL 1), the carrier of (TOP-REAL 1):] -defined the carrier of (TOP-REAL 1) -valued Function-like total V30([: the carrier of (TOP-REAL 1), the carrier of (TOP-REAL 1):], the carrier of (TOP-REAL 1)) Element of bool [:[: the carrier of (TOP-REAL 1), the carrier of (TOP-REAL 1):], the carrier of (TOP-REAL 1):]
[: the carrier of (TOP-REAL 1), the carrier of (TOP-REAL 1):] is non empty set
[:[: the carrier of (TOP-REAL 1), the carrier of (TOP-REAL 1):], the carrier of (TOP-REAL 1):] is non empty set
bool [:[: the carrier of (TOP-REAL 1), the carrier of (TOP-REAL 1):], the carrier of (TOP-REAL 1):] is non empty set
the U7 of (TOP-REAL 1) . (((1 - EX) * WH),(EX * p12)) is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
[((1 - EX) * WH),(EX * p12)] is non empty set
{((1 - EX) * WH),(EX * p12)} is non empty functional V35() V39() set
{((1 - EX) * WH)} is non empty trivial functional V35() V39() 1 -element set
{{((1 - EX) * WH),(EX * p12)},{((1 - EX) * WH)}} is non empty V35() V39() set
the U7 of (TOP-REAL 1) . [((1 - EX) * WH),(EX * p12)] is set
((1 - EX) * WH) + (EX * p12) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
addreal .: (((1 - EX) * WH),(EX * p12)) is set
(1 - EX) * EX1 is V11() real ext-real Element of REAL
(1 - EX) * (- C) is V11() real ext-real Element of REAL
EX * (- C) is V11() real ext-real Element of REAL
((1 - EX) * (- C)) + (EX * (- C)) is V11() real ext-real Element of REAL
EX * EX2 is V11() real ext-real Element of REAL
((1 - EX) * EX1) + (EX * EX2) is V11() real ext-real Element of REAL
<*(((1 - EX) * EX1) + (EX * EX2))*> is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() FinSequence of REAL
|[((1 - EX) * EX1)]| is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
|[(EX * EX2)]| is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
|[((1 - EX) * EX1)]| + |[(EX * EX2)]| is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
the U7 of (TOP-REAL 1) . (|[((1 - EX) * EX1)]|,|[(EX * EX2)]|) is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
[|[((1 - EX) * EX1)]|,|[(EX * EX2)]|] is non empty set
{|[((1 - EX) * EX1)]|,|[(EX * EX2)]|} is non empty functional V35() V39() set
{|[((1 - EX) * EX1)]|} is non empty trivial functional V35() V39() 1 -element set
{{|[((1 - EX) * EX1)]|,|[(EX * EX2)]|},{|[((1 - EX) * EX1)]|}} is non empty V35() V39() set
the U7 of (TOP-REAL 1) . [|[((1 - EX) * EX1)]|,|[(EX * EX2)]|] is set
|[((1 - EX) * EX1)]| + |[(EX * EX2)]| is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (|[((1 - EX) * EX1)]|,|[(EX * EX2)]|) is set
|[EX1]| is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
(1 - EX) * |[EX1]| is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
(1 - EX) * |[EX1]| is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
|[EX1]| (#) ((1 - EX) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
((1 - EX) * |[EX1]|) + |[(EX * EX2)]| is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
the U7 of (TOP-REAL 1) . (((1 - EX) * |[EX1]|),|[(EX * EX2)]|) is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
[((1 - EX) * |[EX1]|),|[(EX * EX2)]|] is non empty set
{((1 - EX) * |[EX1]|),|[(EX * EX2)]|} is non empty functional V35() V39() set
{((1 - EX) * |[EX1]|)} is non empty trivial functional V35() V39() 1 -element set
{{((1 - EX) * |[EX1]|),|[(EX * EX2)]|},{((1 - EX) * |[EX1]|)}} is non empty V35() V39() set
the U7 of (TOP-REAL 1) . [((1 - EX) * |[EX1]|),|[(EX * EX2)]|] is set
((1 - EX) * |[EX1]|) + |[(EX * EX2)]| is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (((1 - EX) * |[EX1]|),|[(EX * EX2)]|) is set
|[EX2]| is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
EX * |[EX2]| is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
EX * |[EX2]| is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
|[EX2]| (#) (EX multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
((1 - EX) * |[EX1]|) + (EX * |[EX2]|) is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
the U7 of (TOP-REAL 1) . (((1 - EX) * |[EX1]|),(EX * |[EX2]|)) is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
[((1 - EX) * |[EX1]|),(EX * |[EX2]|)] is non empty set
{((1 - EX) * |[EX1]|),(EX * |[EX2]|)} is non empty functional V35() V39() set
{{((1 - EX) * |[EX1]|),(EX * |[EX2]|)},{((1 - EX) * |[EX1]|)}} is non empty V35() V39() set
the U7 of (TOP-REAL 1) . [((1 - EX) * |[EX1]|),(EX * |[EX2]|)] is set
((1 - EX) * |[EX1]|) + (EX * |[EX2]|) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (((1 - EX) * |[EX1]|),(EX * |[EX2]|)) is set
0 * p12 is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
0 * p12 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
0 multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (0,(id REAL)) is set
p12 (#) (0 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
WH + (0 * p12) is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
the U7 of (TOP-REAL 1) . (WH,(0 * p12)) is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
[WH,(0 * p12)] is non empty set
{WH,(0 * p12)} is non empty functional V35() V39() set
{WH} is non empty trivial functional V35() V39() 1 -element set
{{WH,(0 * p12)},{WH}} is non empty V35() V39() set
the U7 of (TOP-REAL 1) . [WH,(0 * p12)] is set
WH + (0 * p12) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (WH,(0 * p12)) is set
0. (TOP-REAL 1) is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like V62( TOP-REAL 1) complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
the ZeroF of (TOP-REAL 1) is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
WH + (0. (TOP-REAL 1)) is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
the U7 of (TOP-REAL 1) . (WH,(0. (TOP-REAL 1))) is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
[WH,(0. (TOP-REAL 1))] is non empty set
{WH,(0. (TOP-REAL 1))} is non empty functional V35() V39() set
{{WH,(0. (TOP-REAL 1))},{WH}} is non empty V35() V39() set
the U7 of (TOP-REAL 1) . [WH,(0. (TOP-REAL 1))] is set
WH + (0. (TOP-REAL 1)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (WH,(0. (TOP-REAL 1))) is set
Euclid 1 is non empty strict Reflexive discerning symmetric triangle Discerning MetrStruct
REAL 1 is non empty functional FinSequence-membered FinSequenceSet of REAL
1 -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = 1 } is set
Pitag_dist 1 is non empty Relation-like [:(REAL 1),(REAL 1):] -defined REAL -valued Function-like total V30([:(REAL 1),(REAL 1):], REAL ) complex-yielding V174() V175() Element of bool [:[:(REAL 1),(REAL 1):],REAL:]
[:(REAL 1),(REAL 1):] is non empty set
[:[:(REAL 1),(REAL 1):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[:(REAL 1),(REAL 1):],REAL:] is non empty non trivial V35() set
MetrStruct(# (REAL 1),(Pitag_dist 1) #) is strict MetrStruct
the carrier of (Euclid 1) is non empty set
bool the carrier of (Euclid 1) is non empty set
C is Element of bool the carrier of (Euclid 1)
p is V11() real ext-real Element of REAL
{ b1 where b1 is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1) : ex b2 being V11() real ext-real Element of REAL st
( b1 = <*b2*> & not b2 <= p ) } is set
abs p is V11() real ext-real Element of REAL
0 + (abs p) is V11() real ext-real Element of REAL
(abs p) + (abs p) is V11() real ext-real Element of REAL
((abs p) + (abs p)) + (abs p) is V11() real ext-real Element of REAL
WH is V11() real ext-real Element of REAL
1.REAL 1 is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
1* 1 is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of REAL 1
1 |-> 1 is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of 1 -tuples_on REAL
Seg 1 is non empty trivial V35() 1 -element V183() V184() V185() V186() V187() V188() Element of bool NAT
(Seg 1) --> 1 is non empty Relation-like Seg 1 -defined INT -valued RAT -valued {1} -valued Function-like total V30( Seg 1,{1}) V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() V176() Element of bool [:(Seg 1),{1}:]
{1} is non empty trivial V35() V39() 1 -element V183() V184() V185() V186() V187() V188() set
[:(Seg 1),{1}:] is non empty INT -valued RAT -valued V35() complex-yielding V174() V175() V176() set
bool [:(Seg 1),{1}:] is non empty V35() V39() set
WH + (abs p) is V11() real ext-real Element of REAL
(WH + (abs p)) * (1.REAL 1) is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
(WH + (abs p)) * (1.REAL 1) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(WH + (abs p)) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
id REAL is non empty Relation-like REAL -defined REAL -valued Function-like one-to-one total V30( REAL , REAL ) complex-yielding V174() V175() increasing V179() Element of bool [:REAL,REAL:]
multreal [;] ((WH + (abs p)),(id REAL)) is set
(1.REAL 1) (#) ((WH + (abs p)) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
<*1*> is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() FinSequence of REAL
(WH + (abs p)) * <*1*> is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
<*1*> (#) ((WH + (abs p)) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
(WH + (abs p)) * 1 is V11() real ext-real Element of REAL
<*((WH + (abs p)) * 1)*> is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() FinSequence of REAL
3 * (WH + (abs p)) is V11() real ext-real Element of REAL
(3 * (WH + (abs p))) * (1.REAL 1) is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
(3 * (WH + (abs p))) * (1.REAL 1) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(3 * (WH + (abs p))) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] ((3 * (WH + (abs p))),(id REAL)) is set
(1.REAL 1) (#) ((3 * (WH + (abs p))) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
(3 * (WH + (abs p))) * <*1*> is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
<*1*> (#) ((3 * (WH + (abs p))) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
(3 * (WH + (abs p))) * 1 is V11() real ext-real Element of REAL
<*((3 * (WH + (abs p))) * 1)*> is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() FinSequence of REAL
C is Element of the carrier of (Euclid 1)
p12 is Element of the carrier of (Euclid 1)
dist (C,p12) is V11() real ext-real Element of REAL
the distance of (Euclid 1) is non empty Relation-like [: the carrier of (Euclid 1), the carrier of (Euclid 1):] -defined REAL -valued Function-like total V30([: the carrier of (Euclid 1), the carrier of (Euclid 1):], REAL ) complex-yielding V174() V175() Element of bool [:[: the carrier of (Euclid 1), the carrier of (Euclid 1):],REAL:]
[: the carrier of (Euclid 1), the carrier of (Euclid 1):] is non empty set
[:[: the carrier of (Euclid 1), the carrier of (Euclid 1):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[: the carrier of (Euclid 1), the carrier of (Euclid 1):],REAL:] is non empty non trivial V35() set
the distance of (Euclid 1) . (C,p12) is V11() real ext-real Element of REAL
[C,p12] is non empty set
{C,p12} is non empty V35() set
{C} is non empty trivial V35() 1 -element set
{{C,p12},{C}} is non empty V35() V39() set
the distance of (Euclid 1) . [C,p12] is V11() real ext-real set
((3 * (WH + (abs p))) * (1.REAL 1)) - ((WH + (abs p)) * (1.REAL 1)) is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
- ((WH + (abs p)) * (1.REAL 1)) is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
- ((WH + (abs p)) * (1.REAL 1)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
compreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
((WH + (abs p)) * (1.REAL 1)) (#) compreal is Relation-like Function-like V35() complex-yielding V174() V175() set
K38(1) is V11() real ext-real non positive set
K38(1) * ((WH + (abs p)) * (1.REAL 1)) is Relation-like Function-like set
K38(1) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (K38(1),(id REAL)) is set
((WH + (abs p)) * (1.REAL 1)) (#) (K38(1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
K258((TOP-REAL 1),((3 * (WH + (abs p))) * (1.REAL 1)),(- ((WH + (abs p)) * (1.REAL 1)))) is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
the U7 of (TOP-REAL 1) is non empty Relation-like [: the carrier of (TOP-REAL 1), the carrier of (TOP-REAL 1):] -defined the carrier of (TOP-REAL 1) -valued Function-like total V30([: the carrier of (TOP-REAL 1), the carrier of (TOP-REAL 1):], the carrier of (TOP-REAL 1)) Element of bool [:[: the carrier of (TOP-REAL 1), the carrier of (TOP-REAL 1):], the carrier of (TOP-REAL 1):]
[: the carrier of (TOP-REAL 1), the carrier of (TOP-REAL 1):] is non empty set
[:[: the carrier of (TOP-REAL 1), the carrier of (TOP-REAL 1):], the carrier of (TOP-REAL 1):] is non empty set
bool [:[: the carrier of (TOP-REAL 1), the carrier of (TOP-REAL 1):], the carrier of (TOP-REAL 1):] is non empty set
the U7 of (TOP-REAL 1) . (((3 * (WH + (abs p))) * (1.REAL 1)),(- ((WH + (abs p)) * (1.REAL 1)))) is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
[((3 * (WH + (abs p))) * (1.REAL 1)),(- ((WH + (abs p)) * (1.REAL 1)))] is non empty set
{((3 * (WH + (abs p))) * (1.REAL 1)),(- ((WH + (abs p)) * (1.REAL 1)))} is non empty functional V35() V39() set
{((3 * (WH + (abs p))) * (1.REAL 1))} is non empty trivial functional V35() V39() 1 -element set
{{((3 * (WH + (abs p))) * (1.REAL 1)),(- ((WH + (abs p)) * (1.REAL 1)))},{((3 * (WH + (abs p))) * (1.REAL 1))}} is non empty V35() V39() set
the U7 of (TOP-REAL 1) . [((3 * (WH + (abs p))) * (1.REAL 1)),(- ((WH + (abs p)) * (1.REAL 1)))] is set
((3 * (WH + (abs p))) * (1.REAL 1)) + (- ((WH + (abs p)) * (1.REAL 1))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
addreal .: (((3 * (WH + (abs p))) * (1.REAL 1)),(- ((WH + (abs p)) * (1.REAL 1)))) is set
((3 * (WH + (abs p))) * (1.REAL 1)) - ((WH + (abs p)) * (1.REAL 1)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
diffreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K174(REAL,addreal,(id REAL),compreal) is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
diffreal .: (((3 * (WH + (abs p))) * (1.REAL 1)),((WH + (abs p)) * (1.REAL 1))) is set
K324(((WH + (abs p)) * (1.REAL 1))) is Relation-like Function-like complex-yielding set
K295(((3 * (WH + (abs p))) * (1.REAL 1)),K324(((WH + (abs p)) * (1.REAL 1)))) is Relation-like Function-like set
|.(((3 * (WH + (abs p))) * (1.REAL 1)) - ((WH + (abs p)) * (1.REAL 1))).| is V11() real ext-real non negative Element of REAL
sqr (((3 * (WH + (abs p))) * (1.REAL 1)) - ((WH + (abs p)) * (1.REAL 1))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
sqrreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
(((3 * (WH + (abs p))) * (1.REAL 1)) - ((WH + (abs p)) * (1.REAL 1))) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((((3 * (WH + (abs p))) * (1.REAL 1)) - ((WH + (abs p)) * (1.REAL 1))),(((3 * (WH + (abs p))) * (1.REAL 1)) - ((WH + (abs p)) * (1.REAL 1)))) is Relation-like Function-like set
multreal .: ((((3 * (WH + (abs p))) * (1.REAL 1)) - ((WH + (abs p)) * (1.REAL 1))),(((3 * (WH + (abs p))) * (1.REAL 1)) - ((WH + (abs p)) * (1.REAL 1)))) is set
K383((sqr (((3 * (WH + (abs p))) * (1.REAL 1)) - ((WH + (abs p)) * (1.REAL 1))))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (((3 * (WH + (abs p))) * (1.REAL 1)) - ((WH + (abs p)) * (1.REAL 1)))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (((3 * (WH + (abs p))) * (1.REAL 1)) - ((WH + (abs p)) * (1.REAL 1))))) is V11() real ext-real Element of REAL
(WH + (abs p)) + (WH + (abs p)) is V11() real ext-real Element of REAL
((WH + (abs p)) + (WH + (abs p))) + (WH + (abs p)) is V11() real ext-real Element of REAL
(((WH + (abs p)) + (WH + (abs p))) + (WH + (abs p))) - (WH + (abs p)) is V11() real ext-real Element of REAL
((((WH + (abs p)) + (WH + (abs p))) + (WH + (abs p))) - (WH + (abs p))) * (1.REAL 1) is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
((((WH + (abs p)) + (WH + (abs p))) + (WH + (abs p))) - (WH + (abs p))) * (1.REAL 1) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
((((WH + (abs p)) + (WH + (abs p))) + (WH + (abs p))) - (WH + (abs p))) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (((((WH + (abs p)) + (WH + (abs p))) + (WH + (abs p))) - (WH + (abs p))),(id REAL)) is set
(1.REAL 1) (#) (((((WH + (abs p)) + (WH + (abs p))) + (WH + (abs p))) - (WH + (abs p))) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
|.(((((WH + (abs p)) + (WH + (abs p))) + (WH + (abs p))) - (WH + (abs p))) * (1.REAL 1)).| is V11() real ext-real non negative Element of REAL
sqr (((((WH + (abs p)) + (WH + (abs p))) + (WH + (abs p))) - (WH + (abs p))) * (1.REAL 1)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(((((WH + (abs p)) + (WH + (abs p))) + (WH + (abs p))) - (WH + (abs p))) * (1.REAL 1)) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((((((WH + (abs p)) + (WH + (abs p))) + (WH + (abs p))) - (WH + (abs p))) * (1.REAL 1)),(((((WH + (abs p)) + (WH + (abs p))) + (WH + (abs p))) - (WH + (abs p))) * (1.REAL 1))) is Relation-like Function-like set
multreal .: ((((((WH + (abs p)) + (WH + (abs p))) + (WH + (abs p))) - (WH + (abs p))) * (1.REAL 1)),(((((WH + (abs p)) + (WH + (abs p))) + (WH + (abs p))) - (WH + (abs p))) * (1.REAL 1))) is set
K383((sqr (((((WH + (abs p)) + (WH + (abs p))) + (WH + (abs p))) - (WH + (abs p))) * (1.REAL 1)))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (((((WH + (abs p)) + (WH + (abs p))) + (WH + (abs p))) - (WH + (abs p))) * (1.REAL 1))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (((((WH + (abs p)) + (WH + (abs p))) + (WH + (abs p))) - (WH + (abs p))) * (1.REAL 1)))) is V11() real ext-real Element of REAL
abs ((WH + (abs p)) + (WH + (abs p))) is V11() real ext-real Element of REAL
|.(1.REAL 1).| is V11() real ext-real non negative Element of REAL
sqr (1.REAL 1) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(1.REAL 1) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((1.REAL 1),(1.REAL 1)) is Relation-like Function-like set
multreal .: ((1.REAL 1),(1.REAL 1)) is set
K383((sqr (1.REAL 1))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (1.REAL 1)),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (1.REAL 1))) is V11() real ext-real Element of REAL
(abs ((WH + (abs p)) + (WH + (abs p)))) * |.(1.REAL 1).| is V11() real ext-real Element of REAL
(abs ((WH + (abs p)) + (WH + (abs p)))) * (sqrt 1) is V11() real ext-real Element of REAL
(WH + (abs p)) + 0 is V11() real ext-real Element of REAL
WH + 0 is V11() real ext-real Element of REAL
3 * WH is V11() real ext-real Element of REAL
3 * (abs p) is V11() real ext-real Element of REAL
(3 * WH) + (3 * (abs p)) is V11() real ext-real Element of REAL
C is Element of bool the carrier of (Euclid 1)
p is V11() real ext-real Element of REAL
- p is V11() real ext-real Element of REAL
{ b1 where b1 is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1) : ex b2 being V11() real ext-real Element of REAL st
( b1 = <*b2*> & not - p <= b2 ) } is set
abs p is V11() real ext-real Element of REAL
0 + (abs p) is V11() real ext-real Element of REAL
(abs p) + (abs p) is V11() real ext-real Element of REAL
((abs p) + (abs p)) + (abs p) is V11() real ext-real Element of REAL
WH is V11() real ext-real Element of REAL
1.REAL 1 is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
1* 1 is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of REAL 1
1 |-> 1 is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of 1 -tuples_on REAL
Seg 1 is non empty trivial V35() 1 -element V183() V184() V185() V186() V187() V188() Element of bool NAT
(Seg 1) --> 1 is non empty Relation-like Seg 1 -defined INT -valued RAT -valued {1} -valued Function-like total V30( Seg 1,{1}) V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() V176() Element of bool [:(Seg 1),{1}:]
{1} is non empty trivial V35() V39() 1 -element V183() V184() V185() V186() V187() V188() set
[:(Seg 1),{1}:] is non empty INT -valued RAT -valued V35() complex-yielding V174() V175() V176() set
bool [:(Seg 1),{1}:] is non empty V35() V39() set
WH + (abs p) is V11() real ext-real Element of REAL
3 * (WH + (abs p)) is V11() real ext-real Element of REAL
- (3 * (WH + (abs p))) is V11() real ext-real Element of REAL
(- (3 * (WH + (abs p)))) * (1.REAL 1) is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
(- (3 * (WH + (abs p)))) * (1.REAL 1) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(- (3 * (WH + (abs p)))) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
id REAL is non empty Relation-like REAL -defined REAL -valued Function-like one-to-one total V30( REAL , REAL ) complex-yielding V174() V175() increasing V179() Element of bool [:REAL,REAL:]
multreal [;] ((- (3 * (WH + (abs p)))),(id REAL)) is set
(1.REAL 1) (#) ((- (3 * (WH + (abs p)))) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
<*1*> is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() FinSequence of REAL
(- (3 * (WH + (abs p)))) * <*1*> is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
<*1*> (#) ((- (3 * (WH + (abs p)))) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
(- (3 * (WH + (abs p)))) * 1 is V11() real ext-real Element of REAL
<*((- (3 * (WH + (abs p)))) * 1)*> is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() FinSequence of REAL
3 * WH is V11() real ext-real Element of REAL
3 * (abs p) is V11() real ext-real Element of REAL
(3 * WH) + (3 * (abs p)) is V11() real ext-real Element of REAL
- (WH + (abs p)) is V11() real ext-real Element of REAL
(- (WH + (abs p))) * (1.REAL 1) is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
(- (WH + (abs p))) * (1.REAL 1) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(- (WH + (abs p))) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] ((- (WH + (abs p))),(id REAL)) is set
(1.REAL 1) (#) ((- (WH + (abs p))) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
(- (WH + (abs p))) * <*1*> is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
<*1*> (#) ((- (WH + (abs p))) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
(- (WH + (abs p))) * 1 is V11() real ext-real Element of REAL
<*((- (WH + (abs p))) * 1)*> is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() FinSequence of REAL
p12 is Element of the carrier of (Euclid 1)
C is Element of the carrier of (Euclid 1)
dist (p12,C) is V11() real ext-real Element of REAL
the distance of (Euclid 1) is non empty Relation-like [: the carrier of (Euclid 1), the carrier of (Euclid 1):] -defined REAL -valued Function-like total V30([: the carrier of (Euclid 1), the carrier of (Euclid 1):], REAL ) complex-yielding V174() V175() Element of bool [:[: the carrier of (Euclid 1), the carrier of (Euclid 1):],REAL:]
[: the carrier of (Euclid 1), the carrier of (Euclid 1):] is non empty set
[:[: the carrier of (Euclid 1), the carrier of (Euclid 1):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[: the carrier of (Euclid 1), the carrier of (Euclid 1):],REAL:] is non empty non trivial V35() set
the distance of (Euclid 1) . (p12,C) is V11() real ext-real Element of REAL
[p12,C] is non empty set
{p12,C} is non empty V35() set
{p12} is non empty trivial V35() 1 -element set
{{p12,C},{p12}} is non empty V35() V39() set
the distance of (Euclid 1) . [p12,C] is V11() real ext-real set
((- (3 * (WH + (abs p)))) * (1.REAL 1)) - ((- (WH + (abs p))) * (1.REAL 1)) is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
- ((- (WH + (abs p))) * (1.REAL 1)) is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
- ((- (WH + (abs p))) * (1.REAL 1)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
compreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
((- (WH + (abs p))) * (1.REAL 1)) (#) compreal is Relation-like Function-like V35() complex-yielding V174() V175() set
K38(1) is V11() real ext-real non positive set
K38(1) * ((- (WH + (abs p))) * (1.REAL 1)) is Relation-like Function-like set
K38(1) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (K38(1),(id REAL)) is set
((- (WH + (abs p))) * (1.REAL 1)) (#) (K38(1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
K258((TOP-REAL 1),((- (3 * (WH + (abs p)))) * (1.REAL 1)),(- ((- (WH + (abs p))) * (1.REAL 1)))) is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
the U7 of (TOP-REAL 1) is non empty Relation-like [: the carrier of (TOP-REAL 1), the carrier of (TOP-REAL 1):] -defined the carrier of (TOP-REAL 1) -valued Function-like total V30([: the carrier of (TOP-REAL 1), the carrier of (TOP-REAL 1):], the carrier of (TOP-REAL 1)) Element of bool [:[: the carrier of (TOP-REAL 1), the carrier of (TOP-REAL 1):], the carrier of (TOP-REAL 1):]
[: the carrier of (TOP-REAL 1), the carrier of (TOP-REAL 1):] is non empty set
[:[: the carrier of (TOP-REAL 1), the carrier of (TOP-REAL 1):], the carrier of (TOP-REAL 1):] is non empty set
bool [:[: the carrier of (TOP-REAL 1), the carrier of (TOP-REAL 1):], the carrier of (TOP-REAL 1):] is non empty set
the U7 of (TOP-REAL 1) . (((- (3 * (WH + (abs p)))) * (1.REAL 1)),(- ((- (WH + (abs p))) * (1.REAL 1)))) is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
[((- (3 * (WH + (abs p)))) * (1.REAL 1)),(- ((- (WH + (abs p))) * (1.REAL 1)))] is non empty set
{((- (3 * (WH + (abs p)))) * (1.REAL 1)),(- ((- (WH + (abs p))) * (1.REAL 1)))} is non empty functional V35() V39() set
{((- (3 * (WH + (abs p)))) * (1.REAL 1))} is non empty trivial functional V35() V39() 1 -element set
{{((- (3 * (WH + (abs p)))) * (1.REAL 1)),(- ((- (WH + (abs p))) * (1.REAL 1)))},{((- (3 * (WH + (abs p)))) * (1.REAL 1))}} is non empty V35() V39() set
the U7 of (TOP-REAL 1) . [((- (3 * (WH + (abs p)))) * (1.REAL 1)),(- ((- (WH + (abs p))) * (1.REAL 1)))] is set
((- (3 * (WH + (abs p)))) * (1.REAL 1)) + (- ((- (WH + (abs p))) * (1.REAL 1))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
addreal .: (((- (3 * (WH + (abs p)))) * (1.REAL 1)),(- ((- (WH + (abs p))) * (1.REAL 1)))) is set
((- (3 * (WH + (abs p)))) * (1.REAL 1)) - ((- (WH + (abs p))) * (1.REAL 1)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
diffreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K174(REAL,addreal,(id REAL),compreal) is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
diffreal .: (((- (3 * (WH + (abs p)))) * (1.REAL 1)),((- (WH + (abs p))) * (1.REAL 1))) is set
K324(((- (WH + (abs p))) * (1.REAL 1))) is Relation-like Function-like complex-yielding set
K295(((- (3 * (WH + (abs p)))) * (1.REAL 1)),K324(((- (WH + (abs p))) * (1.REAL 1)))) is Relation-like Function-like set
|.(((- (3 * (WH + (abs p)))) * (1.REAL 1)) - ((- (WH + (abs p))) * (1.REAL 1))).| is V11() real ext-real non negative Element of REAL
sqr (((- (3 * (WH + (abs p)))) * (1.REAL 1)) - ((- (WH + (abs p))) * (1.REAL 1))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
sqrreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
(((- (3 * (WH + (abs p)))) * (1.REAL 1)) - ((- (WH + (abs p))) * (1.REAL 1))) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((((- (3 * (WH + (abs p)))) * (1.REAL 1)) - ((- (WH + (abs p))) * (1.REAL 1))),(((- (3 * (WH + (abs p)))) * (1.REAL 1)) - ((- (WH + (abs p))) * (1.REAL 1)))) is Relation-like Function-like set
multreal .: ((((- (3 * (WH + (abs p)))) * (1.REAL 1)) - ((- (WH + (abs p))) * (1.REAL 1))),(((- (3 * (WH + (abs p)))) * (1.REAL 1)) - ((- (WH + (abs p))) * (1.REAL 1)))) is set
K383((sqr (((- (3 * (WH + (abs p)))) * (1.REAL 1)) - ((- (WH + (abs p))) * (1.REAL 1))))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (((- (3 * (WH + (abs p)))) * (1.REAL 1)) - ((- (WH + (abs p))) * (1.REAL 1)))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (((- (3 * (WH + (abs p)))) * (1.REAL 1)) - ((- (WH + (abs p))) * (1.REAL 1))))) is V11() real ext-real Element of REAL
(- (3 * (WH + (abs p)))) - (- (WH + (abs p))) is V11() real ext-real Element of REAL
((- (3 * (WH + (abs p)))) - (- (WH + (abs p)))) * (1.REAL 1) is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
((- (3 * (WH + (abs p)))) - (- (WH + (abs p)))) * (1.REAL 1) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
((- (3 * (WH + (abs p)))) - (- (WH + (abs p)))) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (((- (3 * (WH + (abs p)))) - (- (WH + (abs p)))),(id REAL)) is set
(1.REAL 1) (#) (((- (3 * (WH + (abs p)))) - (- (WH + (abs p)))) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
|.(((- (3 * (WH + (abs p)))) - (- (WH + (abs p)))) * (1.REAL 1)).| is V11() real ext-real non negative Element of REAL
sqr (((- (3 * (WH + (abs p)))) - (- (WH + (abs p)))) * (1.REAL 1)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(((- (3 * (WH + (abs p)))) - (- (WH + (abs p)))) * (1.REAL 1)) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((((- (3 * (WH + (abs p)))) - (- (WH + (abs p)))) * (1.REAL 1)),(((- (3 * (WH + (abs p)))) - (- (WH + (abs p)))) * (1.REAL 1))) is Relation-like Function-like set
multreal .: ((((- (3 * (WH + (abs p)))) - (- (WH + (abs p)))) * (1.REAL 1)),(((- (3 * (WH + (abs p)))) - (- (WH + (abs p)))) * (1.REAL 1))) is set
K383((sqr (((- (3 * (WH + (abs p)))) - (- (WH + (abs p)))) * (1.REAL 1)))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (((- (3 * (WH + (abs p)))) - (- (WH + (abs p)))) * (1.REAL 1))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (((- (3 * (WH + (abs p)))) - (- (WH + (abs p)))) * (1.REAL 1)))) is V11() real ext-real Element of REAL
- (((- (3 * (WH + (abs p)))) - (- (WH + (abs p)))) * (1.REAL 1)) is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
- (((- (3 * (WH + (abs p)))) - (- (WH + (abs p)))) * (1.REAL 1)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(((- (3 * (WH + (abs p)))) - (- (WH + (abs p)))) * (1.REAL 1)) (#) compreal is Relation-like Function-like V35() complex-yielding V174() V175() set
K38(1) * (((- (3 * (WH + (abs p)))) - (- (WH + (abs p)))) * (1.REAL 1)) is Relation-like Function-like set
(((- (3 * (WH + (abs p)))) - (- (WH + (abs p)))) * (1.REAL 1)) (#) (K38(1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
|.(- (((- (3 * (WH + (abs p)))) - (- (WH + (abs p)))) * (1.REAL 1))).| is V11() real ext-real non negative Element of REAL
sqr (- (((- (3 * (WH + (abs p)))) - (- (WH + (abs p)))) * (1.REAL 1))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(- (((- (3 * (WH + (abs p)))) - (- (WH + (abs p)))) * (1.REAL 1))) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((- (((- (3 * (WH + (abs p)))) - (- (WH + (abs p)))) * (1.REAL 1))),(- (((- (3 * (WH + (abs p)))) - (- (WH + (abs p)))) * (1.REAL 1)))) is Relation-like Function-like set
multreal .: ((- (((- (3 * (WH + (abs p)))) - (- (WH + (abs p)))) * (1.REAL 1))),(- (((- (3 * (WH + (abs p)))) - (- (WH + (abs p)))) * (1.REAL 1)))) is set
K383((sqr (- (((- (3 * (WH + (abs p)))) - (- (WH + (abs p)))) * (1.REAL 1))))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (- (((- (3 * (WH + (abs p)))) - (- (WH + (abs p)))) * (1.REAL 1)))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (- (((- (3 * (WH + (abs p)))) - (- (WH + (abs p)))) * (1.REAL 1))))) is V11() real ext-real Element of REAL
- (- (WH + (abs p))) is V11() real ext-real Element of REAL
(- (3 * (WH + (abs p)))) + (- (- (WH + (abs p)))) is V11() real ext-real Element of REAL
- ((- (3 * (WH + (abs p)))) + (- (- (WH + (abs p))))) is V11() real ext-real Element of REAL
(- ((- (3 * (WH + (abs p)))) + (- (- (WH + (abs p)))))) * (1.REAL 1) is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
(- ((- (3 * (WH + (abs p)))) + (- (- (WH + (abs p)))))) * (1.REAL 1) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(- ((- (3 * (WH + (abs p)))) + (- (- (WH + (abs p)))))) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] ((- ((- (3 * (WH + (abs p)))) + (- (- (WH + (abs p)))))),(id REAL)) is set
(1.REAL 1) (#) ((- ((- (3 * (WH + (abs p)))) + (- (- (WH + (abs p)))))) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
|.((- ((- (3 * (WH + (abs p)))) + (- (- (WH + (abs p)))))) * (1.REAL 1)).| is V11() real ext-real non negative Element of REAL
sqr ((- ((- (3 * (WH + (abs p)))) + (- (- (WH + (abs p)))))) * (1.REAL 1)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
((- ((- (3 * (WH + (abs p)))) + (- (- (WH + (abs p)))))) * (1.REAL 1)) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (((- ((- (3 * (WH + (abs p)))) + (- (- (WH + (abs p)))))) * (1.REAL 1)),((- ((- (3 * (WH + (abs p)))) + (- (- (WH + (abs p)))))) * (1.REAL 1))) is Relation-like Function-like set
multreal .: (((- ((- (3 * (WH + (abs p)))) + (- (- (WH + (abs p)))))) * (1.REAL 1)),((- ((- (3 * (WH + (abs p)))) + (- (- (WH + (abs p)))))) * (1.REAL 1))) is set
K383((sqr ((- ((- (3 * (WH + (abs p)))) + (- (- (WH + (abs p)))))) * (1.REAL 1)))) is V11() real ext-real Element of REAL
K195(REAL,(sqr ((- ((- (3 * (WH + (abs p)))) + (- (- (WH + (abs p)))))) * (1.REAL 1))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr ((- ((- (3 * (WH + (abs p)))) + (- (- (WH + (abs p)))))) * (1.REAL 1)))) is V11() real ext-real Element of REAL
(WH + (abs p)) + (WH + (abs p)) is V11() real ext-real Element of REAL
abs ((WH + (abs p)) + (WH + (abs p))) is V11() real ext-real Element of REAL
|.(1.REAL 1).| is V11() real ext-real non negative Element of REAL
sqr (1.REAL 1) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(1.REAL 1) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((1.REAL 1),(1.REAL 1)) is Relation-like Function-like set
multreal .: ((1.REAL 1),(1.REAL 1)) is set
K383((sqr (1.REAL 1))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (1.REAL 1)),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (1.REAL 1))) is V11() real ext-real Element of REAL
(abs ((WH + (abs p)) + (WH + (abs p)))) * |.(1.REAL 1).| is V11() real ext-real Element of REAL
(abs ((WH + (abs p)) + (WH + (abs p)))) * (sqrt 1) is V11() real ext-real Element of REAL
(WH + (abs p)) + 0 is V11() real ext-real Element of REAL
WH + 0 is V11() real ext-real Element of REAL
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
Euclid C is non empty strict Reflexive discerning symmetric triangle Discerning MetrStruct
REAL C is non empty functional FinSequence-membered FinSequenceSet of REAL
C -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = C } is set
Pitag_dist C is non empty Relation-like [:(REAL C),(REAL C):] -defined REAL -valued Function-like total V30([:(REAL C),(REAL C):], REAL ) complex-yielding V174() V175() Element of bool [:[:(REAL C),(REAL C):],REAL:]
[:(REAL C),(REAL C):] is non empty set
[:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() set
MetrStruct(# (REAL C),(Pitag_dist C) #) is strict MetrStruct
the carrier of (Euclid C) is non empty set
bool the carrier of (Euclid C) is non empty set
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
p is Element of bool the carrier of (Euclid C)
WH is V11() real ext-real Element of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C) : not |.b1.| <= WH } is set
sqrt C is V11() real ext-real Element of REAL
p12 is V11() real ext-real Element of REAL
abs WH is V11() real ext-real Element of REAL
p12 + (abs WH) is V11() real ext-real Element of REAL
abs (p12 + (abs WH)) is V11() real ext-real Element of REAL
(abs (p12 + (abs WH))) * 1 is V11() real ext-real Element of REAL
(abs (p12 + (abs WH))) * (sqrt C) is V11() real ext-real Element of REAL
1.REAL C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
1* C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
C |-> 1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of C -tuples_on REAL
Seg C is V35() C -element V183() V184() V185() V186() V187() V188() Element of bool NAT
(Seg C) --> 1 is Relation-like Seg C -defined INT -valued RAT -valued {1} -valued Function-like total V30( Seg C,{1}) V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() V176() Element of bool [:(Seg C),{1}:]
{1} is non empty trivial V35() V39() 1 -element V183() V184() V185() V186() V187() V188() set
[:(Seg C),{1}:] is INT -valued RAT -valued V35() complex-yielding V174() V175() V176() set
bool [:(Seg C),{1}:] is non empty V35() V39() set
(p12 + (abs WH)) * (1.REAL C) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
(p12 + (abs WH)) * (1.REAL C) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(p12 + (abs WH)) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
id REAL is non empty Relation-like REAL -defined REAL -valued Function-like one-to-one total V30( REAL , REAL ) complex-yielding V174() V175() increasing V179() Element of bool [:REAL,REAL:]
multreal [;] ((p12 + (abs WH)),(id REAL)) is set
(1.REAL C) (#) ((p12 + (abs WH)) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
- ((p12 + (abs WH)) * (1.REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
- ((p12 + (abs WH)) * (1.REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
compreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
((p12 + (abs WH)) * (1.REAL C)) (#) compreal is Relation-like Function-like V35() complex-yielding V174() V175() set
K38(1) is V11() real ext-real non positive set
K38(1) * ((p12 + (abs WH)) * (1.REAL C)) is Relation-like Function-like set
K38(1) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (K38(1),(id REAL)) is set
((p12 + (abs WH)) * (1.REAL C)) (#) (K38(1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
|.(- ((p12 + (abs WH)) * (1.REAL C))).| is V11() real ext-real non negative Element of REAL
sqr (- ((p12 + (abs WH)) * (1.REAL C))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
sqrreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
(- ((p12 + (abs WH)) * (1.REAL C))) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((- ((p12 + (abs WH)) * (1.REAL C))),(- ((p12 + (abs WH)) * (1.REAL C)))) is Relation-like Function-like set
multreal .: ((- ((p12 + (abs WH)) * (1.REAL C))),(- ((p12 + (abs WH)) * (1.REAL C)))) is set
K383((sqr (- ((p12 + (abs WH)) * (1.REAL C))))) is V11() real ext-real Element of REAL
addreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K195(REAL,(sqr (- ((p12 + (abs WH)) * (1.REAL C)))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (- ((p12 + (abs WH)) * (1.REAL C))))) is V11() real ext-real Element of REAL
|.((p12 + (abs WH)) * (1.REAL C)).| is V11() real ext-real non negative Element of REAL
sqr ((p12 + (abs WH)) * (1.REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
((p12 + (abs WH)) * (1.REAL C)) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (((p12 + (abs WH)) * (1.REAL C)),((p12 + (abs WH)) * (1.REAL C))) is Relation-like Function-like set
multreal .: (((p12 + (abs WH)) * (1.REAL C)),((p12 + (abs WH)) * (1.REAL C))) is set
K383((sqr ((p12 + (abs WH)) * (1.REAL C)))) is V11() real ext-real Element of REAL
K195(REAL,(sqr ((p12 + (abs WH)) * (1.REAL C))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr ((p12 + (abs WH)) * (1.REAL C)))) is V11() real ext-real Element of REAL
|.(1.REAL C).| is V11() real ext-real non negative Element of REAL
sqr (1.REAL C) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(1.REAL C) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((1.REAL C),(1.REAL C)) is Relation-like Function-like set
multreal .: ((1.REAL C),(1.REAL C)) is set
K383((sqr (1.REAL C))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (1.REAL C)),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (1.REAL C))) is V11() real ext-real Element of REAL
(abs (p12 + (abs WH))) * |.(1.REAL C).| is V11() real ext-real Element of REAL
(p12 + (abs WH)) + (p12 + (abs WH)) is V11() real ext-real Element of REAL
abs ((p12 + (abs WH)) + (p12 + (abs WH))) is V11() real ext-real Element of REAL
(abs ((p12 + (abs WH)) + (p12 + (abs WH)))) * 1 is V11() real ext-real Element of REAL
(abs ((p12 + (abs WH)) + (p12 + (abs WH)))) * (sqrt C) is V11() real ext-real Element of REAL
p12 + 0 is V11() real ext-real Element of REAL
(p12 + (abs WH)) + 0 is V11() real ext-real Element of REAL
r is Element of the carrier of (Euclid C)
C is Element of the carrier of (Euclid C)
dist (r,C) is V11() real ext-real Element of REAL
the distance of (Euclid C) is non empty Relation-like [: the carrier of (Euclid C), the carrier of (Euclid C):] -defined REAL -valued Function-like total V30([: the carrier of (Euclid C), the carrier of (Euclid C):], REAL ) complex-yielding V174() V175() Element of bool [:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:]
[: the carrier of (Euclid C), the carrier of (Euclid C):] is non empty set
[:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:] is non empty non trivial V35() set
the distance of (Euclid C) . (r,C) is V11() real ext-real Element of REAL
[r,C] is non empty set
{r,C} is non empty V35() set
{r} is non empty trivial V35() 1 -element set
{{r,C},{r}} is non empty V35() V39() set
the distance of (Euclid C) . [r,C] is V11() real ext-real set
((p12 + (abs WH)) * (1.REAL C)) - (- ((p12 + (abs WH)) * (1.REAL C))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
- (- ((p12 + (abs WH)) * (1.REAL C))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
- (- ((p12 + (abs WH)) * (1.REAL C))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(- ((p12 + (abs WH)) * (1.REAL C))) (#) compreal is Relation-like Function-like V35() complex-yielding V174() V175() set
K38(1) * (- ((p12 + (abs WH)) * (1.REAL C))) is Relation-like Function-like set
(- ((p12 + (abs WH)) * (1.REAL C))) (#) (K38(1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
K258((TOP-REAL C),((p12 + (abs WH)) * (1.REAL C)),(- (- ((p12 + (abs WH)) * (1.REAL C))))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) is non empty Relation-like [: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):] -defined the carrier of (TOP-REAL C) -valued Function-like total V30([: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C)) Element of bool [:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):]
[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):] is non empty set
[:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):] is non empty set
bool [:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):] is non empty set
the U7 of (TOP-REAL C) . (((p12 + (abs WH)) * (1.REAL C)),(- (- ((p12 + (abs WH)) * (1.REAL C))))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[((p12 + (abs WH)) * (1.REAL C)),(- (- ((p12 + (abs WH)) * (1.REAL C))))] is non empty set
{((p12 + (abs WH)) * (1.REAL C)),(- (- ((p12 + (abs WH)) * (1.REAL C))))} is non empty functional V35() V39() set
{((p12 + (abs WH)) * (1.REAL C))} is non empty trivial functional V35() V39() 1 -element set
{{((p12 + (abs WH)) * (1.REAL C)),(- (- ((p12 + (abs WH)) * (1.REAL C))))},{((p12 + (abs WH)) * (1.REAL C))}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [((p12 + (abs WH)) * (1.REAL C)),(- (- ((p12 + (abs WH)) * (1.REAL C))))] is set
((p12 + (abs WH)) * (1.REAL C)) + (- (- ((p12 + (abs WH)) * (1.REAL C)))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (((p12 + (abs WH)) * (1.REAL C)),(- (- ((p12 + (abs WH)) * (1.REAL C))))) is set
((p12 + (abs WH)) * (1.REAL C)) - (- ((p12 + (abs WH)) * (1.REAL C))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
diffreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K174(REAL,addreal,(id REAL),compreal) is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
diffreal .: (((p12 + (abs WH)) * (1.REAL C)),(- ((p12 + (abs WH)) * (1.REAL C)))) is set
K324((- ((p12 + (abs WH)) * (1.REAL C)))) is Relation-like Function-like complex-yielding set
K295(((p12 + (abs WH)) * (1.REAL C)),K324((- ((p12 + (abs WH)) * (1.REAL C))))) is Relation-like Function-like set
|.(((p12 + (abs WH)) * (1.REAL C)) - (- ((p12 + (abs WH)) * (1.REAL C)))).| is V11() real ext-real non negative Element of REAL
sqr (((p12 + (abs WH)) * (1.REAL C)) - (- ((p12 + (abs WH)) * (1.REAL C)))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(((p12 + (abs WH)) * (1.REAL C)) - (- ((p12 + (abs WH)) * (1.REAL C)))) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((((p12 + (abs WH)) * (1.REAL C)) - (- ((p12 + (abs WH)) * (1.REAL C)))),(((p12 + (abs WH)) * (1.REAL C)) - (- ((p12 + (abs WH)) * (1.REAL C))))) is Relation-like Function-like set
multreal .: ((((p12 + (abs WH)) * (1.REAL C)) - (- ((p12 + (abs WH)) * (1.REAL C)))),(((p12 + (abs WH)) * (1.REAL C)) - (- ((p12 + (abs WH)) * (1.REAL C))))) is set
K383((sqr (((p12 + (abs WH)) * (1.REAL C)) - (- ((p12 + (abs WH)) * (1.REAL C)))))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (((p12 + (abs WH)) * (1.REAL C)) - (- ((p12 + (abs WH)) * (1.REAL C))))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (((p12 + (abs WH)) * (1.REAL C)) - (- ((p12 + (abs WH)) * (1.REAL C)))))) is V11() real ext-real Element of REAL
((p12 + (abs WH)) * (1.REAL C)) + ((p12 + (abs WH)) * (1.REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) . (((p12 + (abs WH)) * (1.REAL C)),((p12 + (abs WH)) * (1.REAL C))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[((p12 + (abs WH)) * (1.REAL C)),((p12 + (abs WH)) * (1.REAL C))] is non empty set
{((p12 + (abs WH)) * (1.REAL C)),((p12 + (abs WH)) * (1.REAL C))} is non empty functional V35() V39() set
{{((p12 + (abs WH)) * (1.REAL C)),((p12 + (abs WH)) * (1.REAL C))},{((p12 + (abs WH)) * (1.REAL C))}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [((p12 + (abs WH)) * (1.REAL C)),((p12 + (abs WH)) * (1.REAL C))] is set
((p12 + (abs WH)) * (1.REAL C)) + ((p12 + (abs WH)) * (1.REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (((p12 + (abs WH)) * (1.REAL C)),((p12 + (abs WH)) * (1.REAL C))) is set
|.(((p12 + (abs WH)) * (1.REAL C)) + ((p12 + (abs WH)) * (1.REAL C))).| is V11() real ext-real non negative Element of REAL
sqr (((p12 + (abs WH)) * (1.REAL C)) + ((p12 + (abs WH)) * (1.REAL C))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(((p12 + (abs WH)) * (1.REAL C)) + ((p12 + (abs WH)) * (1.REAL C))) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((((p12 + (abs WH)) * (1.REAL C)) + ((p12 + (abs WH)) * (1.REAL C))),(((p12 + (abs WH)) * (1.REAL C)) + ((p12 + (abs WH)) * (1.REAL C)))) is Relation-like Function-like set
multreal .: ((((p12 + (abs WH)) * (1.REAL C)) + ((p12 + (abs WH)) * (1.REAL C))),(((p12 + (abs WH)) * (1.REAL C)) + ((p12 + (abs WH)) * (1.REAL C)))) is set
K383((sqr (((p12 + (abs WH)) * (1.REAL C)) + ((p12 + (abs WH)) * (1.REAL C))))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (((p12 + (abs WH)) * (1.REAL C)) + ((p12 + (abs WH)) * (1.REAL C)))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (((p12 + (abs WH)) * (1.REAL C)) + ((p12 + (abs WH)) * (1.REAL C))))) is V11() real ext-real Element of REAL
((p12 + (abs WH)) + (p12 + (abs WH))) * (1.REAL C) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
((p12 + (abs WH)) + (p12 + (abs WH))) * (1.REAL C) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
((p12 + (abs WH)) + (p12 + (abs WH))) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (((p12 + (abs WH)) + (p12 + (abs WH))),(id REAL)) is set
(1.REAL C) (#) (((p12 + (abs WH)) + (p12 + (abs WH))) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
|.(((p12 + (abs WH)) + (p12 + (abs WH))) * (1.REAL C)).| is V11() real ext-real non negative Element of REAL
sqr (((p12 + (abs WH)) + (p12 + (abs WH))) * (1.REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(((p12 + (abs WH)) + (p12 + (abs WH))) * (1.REAL C)) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((((p12 + (abs WH)) + (p12 + (abs WH))) * (1.REAL C)),(((p12 + (abs WH)) + (p12 + (abs WH))) * (1.REAL C))) is Relation-like Function-like set
multreal .: ((((p12 + (abs WH)) + (p12 + (abs WH))) * (1.REAL C)),(((p12 + (abs WH)) + (p12 + (abs WH))) * (1.REAL C))) is set
K383((sqr (((p12 + (abs WH)) + (p12 + (abs WH))) * (1.REAL C)))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (((p12 + (abs WH)) + (p12 + (abs WH))) * (1.REAL C))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (((p12 + (abs WH)) + (p12 + (abs WH))) * (1.REAL C)))) is V11() real ext-real Element of REAL
(abs ((p12 + (abs WH)) + (p12 + (abs WH)))) * |.(1.REAL C).| is V11() real ext-real Element of REAL
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
Euclid C is non empty strict Reflexive discerning symmetric triangle Discerning MetrStruct
REAL C is non empty functional FinSequence-membered FinSequenceSet of REAL
C -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = C } is set
Pitag_dist C is non empty Relation-like [:(REAL C),(REAL C):] -defined REAL -valued Function-like total V30([:(REAL C),(REAL C):], REAL ) complex-yielding V174() V175() Element of bool [:[:(REAL C),(REAL C):],REAL:]
[:(REAL C),(REAL C):] is non empty set
[:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() set
MetrStruct(# (REAL C),(Pitag_dist C) #) is strict MetrStruct
the carrier of (Euclid C) is non empty set
bool the carrier of (Euclid C) is non empty set
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
p is Element of bool the carrier of (Euclid C)
WH is V11() real ext-real Element of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C) : not WH <= |.b1.| } is set
(REAL C) \ { b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C) : not WH <= |.b1.| } is functional FinSequence-membered Element of bool (REAL C)
bool (REAL C) is non empty set
1.REAL C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
1* C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
C |-> 1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of C -tuples_on REAL
Seg C is V35() C -element V183() V184() V185() V186() V187() V188() Element of bool NAT
(Seg C) --> 1 is Relation-like Seg C -defined INT -valued RAT -valued {1} -valued Function-like total V30( Seg C,{1}) V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() V176() Element of bool [:(Seg C),{1}:]
{1} is non empty trivial V35() V39() 1 -element V183() V184() V185() V186() V187() V188() set
[:(Seg C),{1}:] is INT -valued RAT -valued V35() complex-yielding V174() V175() V176() set
bool [:(Seg C),{1}:] is non empty V35() V39() set
C is V11() real ext-real Element of REAL
abs WH is V11() real ext-real Element of REAL
C + (abs WH) is V11() real ext-real Element of REAL
(C + (abs WH)) + (C + (abs WH)) is V11() real ext-real Element of REAL
(C + (abs WH)) + 0 is V11() real ext-real Element of REAL
sqrt C is V11() real ext-real Element of REAL
(C + (abs WH)) * (1.REAL C) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
(C + (abs WH)) * (1.REAL C) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(C + (abs WH)) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
id REAL is non empty Relation-like REAL -defined REAL -valued Function-like one-to-one total V30( REAL , REAL ) complex-yielding V174() V175() increasing V179() Element of bool [:REAL,REAL:]
multreal [;] ((C + (abs WH)),(id REAL)) is set
(1.REAL C) (#) ((C + (abs WH)) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
- ((C + (abs WH)) * (1.REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
- ((C + (abs WH)) * (1.REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
compreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
((C + (abs WH)) * (1.REAL C)) (#) compreal is Relation-like Function-like V35() complex-yielding V174() V175() set
K38(1) is V11() real ext-real non positive set
K38(1) * ((C + (abs WH)) * (1.REAL C)) is Relation-like Function-like set
K38(1) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (K38(1),(id REAL)) is set
((C + (abs WH)) * (1.REAL C)) (#) (K38(1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
abs (C + (abs WH)) is V11() real ext-real Element of REAL
(abs (C + (abs WH))) * 1 is V11() real ext-real Element of REAL
(abs (C + (abs WH))) * (sqrt C) is V11() real ext-real Element of REAL
|.(- ((C + (abs WH)) * (1.REAL C))).| is V11() real ext-real non negative Element of REAL
sqr (- ((C + (abs WH)) * (1.REAL C))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
sqrreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
(- ((C + (abs WH)) * (1.REAL C))) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((- ((C + (abs WH)) * (1.REAL C))),(- ((C + (abs WH)) * (1.REAL C)))) is Relation-like Function-like set
multreal .: ((- ((C + (abs WH)) * (1.REAL C))),(- ((C + (abs WH)) * (1.REAL C)))) is set
K383((sqr (- ((C + (abs WH)) * (1.REAL C))))) is V11() real ext-real Element of REAL
addreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K195(REAL,(sqr (- ((C + (abs WH)) * (1.REAL C)))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (- ((C + (abs WH)) * (1.REAL C))))) is V11() real ext-real Element of REAL
|.((C + (abs WH)) * (1.REAL C)).| is V11() real ext-real non negative Element of REAL
sqr ((C + (abs WH)) * (1.REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
((C + (abs WH)) * (1.REAL C)) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (((C + (abs WH)) * (1.REAL C)),((C + (abs WH)) * (1.REAL C))) is Relation-like Function-like set
multreal .: (((C + (abs WH)) * (1.REAL C)),((C + (abs WH)) * (1.REAL C))) is set
K383((sqr ((C + (abs WH)) * (1.REAL C)))) is V11() real ext-real Element of REAL
K195(REAL,(sqr ((C + (abs WH)) * (1.REAL C))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr ((C + (abs WH)) * (1.REAL C)))) is V11() real ext-real Element of REAL
|.(1.REAL C).| is V11() real ext-real non negative Element of REAL
sqr (1.REAL C) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(1.REAL C) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((1.REAL C),(1.REAL C)) is Relation-like Function-like set
multreal .: ((1.REAL C),(1.REAL C)) is set
K383((sqr (1.REAL C))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (1.REAL C)),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (1.REAL C))) is V11() real ext-real Element of REAL
(abs (C + (abs WH))) * |.(1.REAL C).| is V11() real ext-real Element of REAL
r is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.r.| is V11() real ext-real non negative Element of REAL
sqr r is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
r (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (r,r) is Relation-like Function-like set
multreal .: (r,r) is set
K383((sqr r)) is V11() real ext-real Element of REAL
K195(REAL,(sqr r),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr r)) is V11() real ext-real Element of REAL
r is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.r.| is V11() real ext-real non negative Element of REAL
sqr r is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
r (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (r,r) is Relation-like Function-like set
multreal .: (r,r) is set
K383((sqr r)) is V11() real ext-real Element of REAL
K195(REAL,(sqr r),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr r)) is V11() real ext-real Element of REAL
abs ((C + (abs WH)) + (C + (abs WH))) is V11() real ext-real Element of REAL
(abs ((C + (abs WH)) + (C + (abs WH)))) * 1 is V11() real ext-real Element of REAL
(abs ((C + (abs WH)) + (C + (abs WH)))) * (sqrt C) is V11() real ext-real Element of REAL
EX2 is Element of the carrier of (Euclid C)
r is Element of the carrier of (Euclid C)
dist (EX2,r) is V11() real ext-real Element of REAL
the distance of (Euclid C) is non empty Relation-like [: the carrier of (Euclid C), the carrier of (Euclid C):] -defined REAL -valued Function-like total V30([: the carrier of (Euclid C), the carrier of (Euclid C):], REAL ) complex-yielding V174() V175() Element of bool [:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:]
[: the carrier of (Euclid C), the carrier of (Euclid C):] is non empty set
[:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:] is non empty non trivial V35() set
the distance of (Euclid C) . (EX2,r) is V11() real ext-real Element of REAL
[EX2,r] is non empty set
{EX2,r} is non empty V35() set
{EX2} is non empty trivial V35() 1 -element set
{{EX2,r},{EX2}} is non empty V35() V39() set
the distance of (Euclid C) . [EX2,r] is V11() real ext-real set
((C + (abs WH)) * (1.REAL C)) - (- ((C + (abs WH)) * (1.REAL C))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
- (- ((C + (abs WH)) * (1.REAL C))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
- (- ((C + (abs WH)) * (1.REAL C))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(- ((C + (abs WH)) * (1.REAL C))) (#) compreal is Relation-like Function-like V35() complex-yielding V174() V175() set
K38(1) * (- ((C + (abs WH)) * (1.REAL C))) is Relation-like Function-like set
(- ((C + (abs WH)) * (1.REAL C))) (#) (K38(1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
K258((TOP-REAL C),((C + (abs WH)) * (1.REAL C)),(- (- ((C + (abs WH)) * (1.REAL C))))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) is non empty Relation-like [: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):] -defined the carrier of (TOP-REAL C) -valued Function-like total V30([: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C)) Element of bool [:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):]
[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):] is non empty set
[:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):] is non empty set
bool [:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):] is non empty set
the U7 of (TOP-REAL C) . (((C + (abs WH)) * (1.REAL C)),(- (- ((C + (abs WH)) * (1.REAL C))))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[((C + (abs WH)) * (1.REAL C)),(- (- ((C + (abs WH)) * (1.REAL C))))] is non empty set
{((C + (abs WH)) * (1.REAL C)),(- (- ((C + (abs WH)) * (1.REAL C))))} is non empty functional V35() V39() set
{((C + (abs WH)) * (1.REAL C))} is non empty trivial functional V35() V39() 1 -element set
{{((C + (abs WH)) * (1.REAL C)),(- (- ((C + (abs WH)) * (1.REAL C))))},{((C + (abs WH)) * (1.REAL C))}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [((C + (abs WH)) * (1.REAL C)),(- (- ((C + (abs WH)) * (1.REAL C))))] is set
((C + (abs WH)) * (1.REAL C)) + (- (- ((C + (abs WH)) * (1.REAL C)))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (((C + (abs WH)) * (1.REAL C)),(- (- ((C + (abs WH)) * (1.REAL C))))) is set
((C + (abs WH)) * (1.REAL C)) - (- ((C + (abs WH)) * (1.REAL C))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
diffreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K174(REAL,addreal,(id REAL),compreal) is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
diffreal .: (((C + (abs WH)) * (1.REAL C)),(- ((C + (abs WH)) * (1.REAL C)))) is set
K324((- ((C + (abs WH)) * (1.REAL C)))) is Relation-like Function-like complex-yielding set
K295(((C + (abs WH)) * (1.REAL C)),K324((- ((C + (abs WH)) * (1.REAL C))))) is Relation-like Function-like set
|.(((C + (abs WH)) * (1.REAL C)) - (- ((C + (abs WH)) * (1.REAL C)))).| is V11() real ext-real non negative Element of REAL
sqr (((C + (abs WH)) * (1.REAL C)) - (- ((C + (abs WH)) * (1.REAL C)))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(((C + (abs WH)) * (1.REAL C)) - (- ((C + (abs WH)) * (1.REAL C)))) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((((C + (abs WH)) * (1.REAL C)) - (- ((C + (abs WH)) * (1.REAL C)))),(((C + (abs WH)) * (1.REAL C)) - (- ((C + (abs WH)) * (1.REAL C))))) is Relation-like Function-like set
multreal .: ((((C + (abs WH)) * (1.REAL C)) - (- ((C + (abs WH)) * (1.REAL C)))),(((C + (abs WH)) * (1.REAL C)) - (- ((C + (abs WH)) * (1.REAL C))))) is set
K383((sqr (((C + (abs WH)) * (1.REAL C)) - (- ((C + (abs WH)) * (1.REAL C)))))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (((C + (abs WH)) * (1.REAL C)) - (- ((C + (abs WH)) * (1.REAL C))))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (((C + (abs WH)) * (1.REAL C)) - (- ((C + (abs WH)) * (1.REAL C)))))) is V11() real ext-real Element of REAL
p12 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
(C + (abs WH)) * p12 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
(C + (abs WH)) * p12 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
p12 (#) ((C + (abs WH)) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
- ((C + (abs WH)) * p12) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
- ((C + (abs WH)) * p12) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
((C + (abs WH)) * p12) (#) compreal is Relation-like Function-like V35() complex-yielding V174() V175() set
K38(1) * ((C + (abs WH)) * p12) is Relation-like Function-like set
((C + (abs WH)) * p12) (#) (K38(1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
- (- ((C + (abs WH)) * p12)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
- (- ((C + (abs WH)) * p12)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(- ((C + (abs WH)) * p12)) (#) compreal is Relation-like Function-like V35() complex-yielding V174() V175() set
K38(1) * (- ((C + (abs WH)) * p12)) is Relation-like Function-like set
(- ((C + (abs WH)) * p12)) (#) (K38(1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
((C + (abs WH)) * p12) + (- (- ((C + (abs WH)) * p12))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) . (((C + (abs WH)) * p12),(- (- ((C + (abs WH)) * p12)))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[((C + (abs WH)) * p12),(- (- ((C + (abs WH)) * p12)))] is non empty set
{((C + (abs WH)) * p12),(- (- ((C + (abs WH)) * p12)))} is non empty functional V35() V39() set
{((C + (abs WH)) * p12)} is non empty trivial functional V35() V39() 1 -element set
{{((C + (abs WH)) * p12),(- (- ((C + (abs WH)) * p12)))},{((C + (abs WH)) * p12)}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [((C + (abs WH)) * p12),(- (- ((C + (abs WH)) * p12)))] is set
((C + (abs WH)) * p12) + (- (- ((C + (abs WH)) * p12))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (((C + (abs WH)) * p12),(- (- ((C + (abs WH)) * p12)))) is set
|.(((C + (abs WH)) * p12) + (- (- ((C + (abs WH)) * p12)))).| is V11() real ext-real non negative Element of REAL
sqr (((C + (abs WH)) * p12) + (- (- ((C + (abs WH)) * p12)))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(((C + (abs WH)) * p12) + (- (- ((C + (abs WH)) * p12)))) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((((C + (abs WH)) * p12) + (- (- ((C + (abs WH)) * p12)))),(((C + (abs WH)) * p12) + (- (- ((C + (abs WH)) * p12))))) is Relation-like Function-like set
multreal .: ((((C + (abs WH)) * p12) + (- (- ((C + (abs WH)) * p12)))),(((C + (abs WH)) * p12) + (- (- ((C + (abs WH)) * p12))))) is set
K383((sqr (((C + (abs WH)) * p12) + (- (- ((C + (abs WH)) * p12)))))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (((C + (abs WH)) * p12) + (- (- ((C + (abs WH)) * p12))))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (((C + (abs WH)) * p12) + (- (- ((C + (abs WH)) * p12)))))) is V11() real ext-real Element of REAL
((C + (abs WH)) * p12) + ((C + (abs WH)) * p12) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) . (((C + (abs WH)) * p12),((C + (abs WH)) * p12)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[((C + (abs WH)) * p12),((C + (abs WH)) * p12)] is non empty set
{((C + (abs WH)) * p12),((C + (abs WH)) * p12)} is non empty functional V35() V39() set
{{((C + (abs WH)) * p12),((C + (abs WH)) * p12)},{((C + (abs WH)) * p12)}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [((C + (abs WH)) * p12),((C + (abs WH)) * p12)] is set
((C + (abs WH)) * p12) + ((C + (abs WH)) * p12) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (((C + (abs WH)) * p12),((C + (abs WH)) * p12)) is set
|.(((C + (abs WH)) * p12) + ((C + (abs WH)) * p12)).| is V11() real ext-real non negative Element of REAL
sqr (((C + (abs WH)) * p12) + ((C + (abs WH)) * p12)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(((C + (abs WH)) * p12) + ((C + (abs WH)) * p12)) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((((C + (abs WH)) * p12) + ((C + (abs WH)) * p12)),(((C + (abs WH)) * p12) + ((C + (abs WH)) * p12))) is Relation-like Function-like set
multreal .: ((((C + (abs WH)) * p12) + ((C + (abs WH)) * p12)),(((C + (abs WH)) * p12) + ((C + (abs WH)) * p12))) is set
K383((sqr (((C + (abs WH)) * p12) + ((C + (abs WH)) * p12)))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (((C + (abs WH)) * p12) + ((C + (abs WH)) * p12))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (((C + (abs WH)) * p12) + ((C + (abs WH)) * p12)))) is V11() real ext-real Element of REAL
((C + (abs WH)) + (C + (abs WH))) * p12 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
((C + (abs WH)) + (C + (abs WH))) * p12 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
((C + (abs WH)) + (C + (abs WH))) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (((C + (abs WH)) + (C + (abs WH))),(id REAL)) is set
p12 (#) (((C + (abs WH)) + (C + (abs WH))) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
|.(((C + (abs WH)) + (C + (abs WH))) * p12).| is V11() real ext-real non negative Element of REAL
sqr (((C + (abs WH)) + (C + (abs WH))) * p12) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(((C + (abs WH)) + (C + (abs WH))) * p12) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((((C + (abs WH)) + (C + (abs WH))) * p12),(((C + (abs WH)) + (C + (abs WH))) * p12)) is Relation-like Function-like set
multreal .: ((((C + (abs WH)) + (C + (abs WH))) * p12),(((C + (abs WH)) + (C + (abs WH))) * p12)) is set
K383((sqr (((C + (abs WH)) + (C + (abs WH))) * p12))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (((C + (abs WH)) + (C + (abs WH))) * p12)),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (((C + (abs WH)) + (C + (abs WH))) * p12))) is V11() real ext-real Element of REAL
((C + (abs WH)) + (C + (abs WH))) * (1.REAL C) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
((C + (abs WH)) + (C + (abs WH))) * (1.REAL C) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(1.REAL C) (#) (((C + (abs WH)) + (C + (abs WH))) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
|.(((C + (abs WH)) + (C + (abs WH))) * (1.REAL C)).| is V11() real ext-real non negative Element of REAL
sqr (((C + (abs WH)) + (C + (abs WH))) * (1.REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(((C + (abs WH)) + (C + (abs WH))) * (1.REAL C)) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((((C + (abs WH)) + (C + (abs WH))) * (1.REAL C)),(((C + (abs WH)) + (C + (abs WH))) * (1.REAL C))) is Relation-like Function-like set
multreal .: ((((C + (abs WH)) + (C + (abs WH))) * (1.REAL C)),(((C + (abs WH)) + (C + (abs WH))) * (1.REAL C))) is set
K383((sqr (((C + (abs WH)) + (C + (abs WH))) * (1.REAL C)))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (((C + (abs WH)) + (C + (abs WH))) * (1.REAL C))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (((C + (abs WH)) + (C + (abs WH))) * (1.REAL C)))) is V11() real ext-real Element of REAL
(abs ((C + (abs WH)) + (C + (abs WH)))) * |.(1.REAL C).| is V11() real ext-real Element of REAL
C + 0 is V11() real ext-real Element of REAL
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
bool the carrier of (TOP-REAL C) is non empty set
Euclid C is non empty strict Reflexive discerning symmetric triangle Discerning MetrStruct
REAL C is non empty functional FinSequence-membered FinSequenceSet of REAL
C -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = C } is set
Pitag_dist C is non empty Relation-like [:(REAL C),(REAL C):] -defined REAL -valued Function-like total V30([:(REAL C),(REAL C):], REAL ) complex-yielding V174() V175() Element of bool [:[:(REAL C),(REAL C):],REAL:]
[:(REAL C),(REAL C):] is non empty set
[:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() set
MetrStruct(# (REAL C),(Pitag_dist C) #) is strict MetrStruct
the carrier of (Euclid C) is non empty set
bool the carrier of (Euclid C) is non empty set
p is Element of bool the carrier of (TOP-REAL C)
WH is Element of bool the carrier of (TOP-REAL C)
p12 is Element of bool the carrier of (TOP-REAL C)
p12 ` is Element of bool the carrier of (TOP-REAL C)
the carrier of (TOP-REAL C) \ p12 is set
(TOP-REAL C) | (p12 `) is strict TopSpace-like SubSpace of TOP-REAL C
Down (p,(p12 `)) is Element of bool the carrier of ((TOP-REAL C) | (p12 `))
the carrier of ((TOP-REAL C) | (p12 `)) is set
bool the carrier of ((TOP-REAL C) | (p12 `)) is non empty set
p /\ (p12 `) is Element of bool the carrier of (TOP-REAL C)
Component_of (Down (p,(p12 `))) is Element of bool the carrier of ((TOP-REAL C) | (p12 `))
C is Element of bool the carrier of (Euclid C)
(TOP-REAL C) | p is strict TopSpace-like SubSpace of TOP-REAL C
p \ p12 is Element of bool the carrier of (TOP-REAL C)
r is Element of bool the carrier of ((TOP-REAL C) | (p12 `))
Component_of r is Element of bool the carrier of ((TOP-REAL C) | (p12 `))
((TOP-REAL C) | (p12 `)) | r is strict TopSpace-like SubSpace of (TOP-REAL C) | (p12 `)
EX2 is Element of bool the carrier of (Euclid C)
{} (Euclid C) is empty trivial proper ordinal natural V11() real ext-real non positive non negative Function-like functional V35() V39() cardinal {} -element FinSequence-membered bounded V183() V184() V185() V186() V187() V188() V189() Element of bool the carrier of (Euclid C)
C /\ p12 is Element of bool the carrier of (TOP-REAL C)
{} the carrier of (TOP-REAL C) is empty trivial proper ordinal natural V11() real ext-real non positive non negative Function-like functional V35() V39() cardinal {} -element FinSequence-membered open closed boundary nowhere_dense V183() V184() V185() V186() V187() V188() V189() symmetric circled bounded Element of bool the carrier of (TOP-REAL C)
({} the carrier of (TOP-REAL C)) ` is open closed dense Element of bool the carrier of (TOP-REAL C)
the carrier of (TOP-REAL C) \ ({} the carrier of (TOP-REAL C)) is set
EX1 is non empty Element of bool the carrier of (TOP-REAL C)
(TOP-REAL C) | EX1 is non empty strict TopSpace-like SubSpace of TOP-REAL C
p1 is Element of bool the carrier of (Euclid C)
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
Euclid C is non empty strict Reflexive discerning symmetric triangle Discerning MetrStruct
REAL C is non empty functional FinSequence-membered FinSequenceSet of REAL
C -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = C } is set
Pitag_dist C is non empty Relation-like [:(REAL C),(REAL C):] -defined REAL -valued Function-like total V30([:(REAL C),(REAL C):], REAL ) complex-yielding V174() V175() Element of bool [:[:(REAL C),(REAL C):],REAL:]
[:(REAL C),(REAL C):] is non empty set
[:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() set
MetrStruct(# (REAL C),(Pitag_dist C) #) is strict MetrStruct
the carrier of (Euclid C) is non empty set
bool the carrier of (Euclid C) is non empty set
p is Element of bool the carrier of (Euclid C)
WH is non empty Element of bool the carrier of (Euclid C)
(Euclid C) | WH is non empty strict Reflexive discerning symmetric triangle Discerning SubSpace of Euclid C
the carrier of ((Euclid C) | WH) is non empty set
bool the carrier of ((Euclid C) | WH) is non empty set
p12 is Element of bool the carrier of ((Euclid C) | WH)
C is V11() real ext-real Element of REAL
r is Element of the carrier of (Euclid C)
EX2 is Element of the carrier of (Euclid C)
dist (r,EX2) is V11() real ext-real Element of REAL
the distance of (Euclid C) is non empty Relation-like [: the carrier of (Euclid C), the carrier of (Euclid C):] -defined REAL -valued Function-like total V30([: the carrier of (Euclid C), the carrier of (Euclid C):], REAL ) complex-yielding V174() V175() Element of bool [:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:]
[: the carrier of (Euclid C), the carrier of (Euclid C):] is non empty set
[:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:] is non empty non trivial V35() set
the distance of (Euclid C) . (r,EX2) is V11() real ext-real Element of REAL
[r,EX2] is non empty set
{r,EX2} is non empty V35() set
{r} is non empty trivial V35() 1 -element set
{{r,EX2},{r}} is non empty V35() V39() set
the distance of (Euclid C) . [r,EX2] is V11() real ext-real set
the distance of ((Euclid C) | WH) is non empty Relation-like [: the carrier of ((Euclid C) | WH), the carrier of ((Euclid C) | WH):] -defined REAL -valued Function-like total V30([: the carrier of ((Euclid C) | WH), the carrier of ((Euclid C) | WH):], REAL ) complex-yielding V174() V175() Element of bool [:[: the carrier of ((Euclid C) | WH), the carrier of ((Euclid C) | WH):],REAL:]
[: the carrier of ((Euclid C) | WH), the carrier of ((Euclid C) | WH):] is non empty set
[:[: the carrier of ((Euclid C) | WH), the carrier of ((Euclid C) | WH):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[: the carrier of ((Euclid C) | WH), the carrier of ((Euclid C) | WH):],REAL:] is non empty non trivial V35() set
EX1 is Element of the carrier of ((Euclid C) | WH)
p1 is Element of the carrier of ((Euclid C) | WH)
the distance of ((Euclid C) | WH) . (EX1,p1) is V11() real ext-real Element of REAL
[EX1,p1] is non empty set
{EX1,p1} is non empty V35() set
{EX1} is non empty trivial V35() 1 -element set
{{EX1,p1},{EX1}} is non empty V35() V39() set
the distance of ((Euclid C) | WH) . [EX1,p1] is V11() real ext-real set
dist (EX1,p1) is V11() real ext-real Element of REAL
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
bool the carrier of (TOP-REAL C) is non empty set
p is Element of bool the carrier of (TOP-REAL C)
(TOP-REAL C) | p is strict TopSpace-like SubSpace of TOP-REAL C
the carrier of ((TOP-REAL C) | p) is set
bool the carrier of ((TOP-REAL C) | p) is non empty set
Euclid C is non empty strict Reflexive discerning symmetric triangle Discerning MetrStruct
REAL C is non empty functional FinSequence-membered FinSequenceSet of REAL
C -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = C } is set
Pitag_dist C is non empty Relation-like [:(REAL C),(REAL C):] -defined REAL -valued Function-like total V30([:(REAL C),(REAL C):], REAL ) complex-yielding V174() V175() Element of bool [:[:(REAL C),(REAL C):],REAL:]
[:(REAL C),(REAL C):] is non empty set
[:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() set
MetrStruct(# (REAL C),(Pitag_dist C) #) is strict MetrStruct
the carrier of (Euclid C) is non empty set
bool the carrier of (Euclid C) is non empty set
[#] ((TOP-REAL C) | p) is non proper open closed dense Element of bool the carrier of ((TOP-REAL C) | p)
WH is Element of bool the carrier of ((TOP-REAL C) | p)
p12 is non empty Element of bool the carrier of (Euclid C)
(Euclid C) | p12 is non empty strict Reflexive discerning symmetric triangle Discerning SubSpace of Euclid C
TopSpaceMetr ((Euclid C) | p12) is TopStruct
[#] ((Euclid C) | p12) is non empty non proper Element of bool the carrier of ((Euclid C) | p12)
the carrier of ((Euclid C) | p12) is non empty set
bool the carrier of ((Euclid C) | p12) is non empty set
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
bool the carrier of (TOP-REAL C) is non empty set
p is Element of bool the carrier of (TOP-REAL C)
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
bool the carrier of (TOP-REAL C) is non empty set
p is Element of bool the carrier of (TOP-REAL C)
p ` is Element of bool the carrier of (TOP-REAL C)
the carrier of (TOP-REAL C) \ p is set
WH is V11() real ext-real Element of REAL
abs WH is V11() real ext-real Element of REAL
(abs WH) * 1 is V11() real ext-real Element of REAL
1.REAL C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
1* C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
REAL C is non empty functional FinSequence-membered FinSequenceSet of REAL
C -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = C } is set
C |-> 1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of C -tuples_on REAL
Seg C is V35() C -element V183() V184() V185() V186() V187() V188() Element of bool NAT
(Seg C) --> 1 is Relation-like Seg C -defined INT -valued RAT -valued {1} -valued Function-like total V30( Seg C,{1}) V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() V176() Element of bool [:(Seg C),{1}:]
{1} is non empty trivial V35() V39() 1 -element V183() V184() V185() V186() V187() V188() set
[:(Seg C),{1}:] is INT -valued RAT -valued V35() complex-yielding V174() V175() V176() set
bool [:(Seg C),{1}:] is non empty V35() V39() set
|.(1.REAL C).| is V11() real ext-real non negative Element of REAL
sqr (1.REAL C) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
sqrreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
(1.REAL C) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((1.REAL C),(1.REAL C)) is Relation-like Function-like set
multreal .: ((1.REAL C),(1.REAL C)) is set
K383((sqr (1.REAL C))) is V11() real ext-real Element of REAL
addreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K195(REAL,(sqr (1.REAL C)),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (1.REAL C))) is V11() real ext-real Element of REAL
(abs WH) * |.(1.REAL C).| is V11() real ext-real Element of REAL
WH * (1.REAL C) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
WH * (1.REAL C) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
WH multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
id REAL is non empty Relation-like REAL -defined REAL -valued Function-like one-to-one total V30( REAL , REAL ) complex-yielding V174() V175() increasing V179() Element of bool [:REAL,REAL:]
multreal [;] (WH,(id REAL)) is set
(1.REAL C) (#) (WH multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
|.(WH * (1.REAL C)).| is V11() real ext-real non negative Element of REAL
sqr (WH * (1.REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(WH * (1.REAL C)) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((WH * (1.REAL C)),(WH * (1.REAL C))) is Relation-like Function-like set
multreal .: ((WH * (1.REAL C)),(WH * (1.REAL C))) is set
K383((sqr (WH * (1.REAL C)))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (WH * (1.REAL C))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (WH * (1.REAL C)))) is V11() real ext-real Element of REAL
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
Euclid C is non empty strict Reflexive discerning symmetric triangle Discerning MetrStruct
REAL C is non empty functional FinSequence-membered FinSequenceSet of REAL
C -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = C } is set
Pitag_dist C is non empty Relation-like [:(REAL C),(REAL C):] -defined REAL -valued Function-like total V30([:(REAL C),(REAL C):], REAL ) complex-yielding V174() V175() Element of bool [:[:(REAL C),(REAL C):],REAL:]
[:(REAL C),(REAL C):] is non empty set
[:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() set
MetrStruct(# (REAL C),(Pitag_dist C) #) is strict MetrStruct
the carrier of (Euclid C) is non empty set
bool the carrier of (Euclid C) is non empty set
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
p is V11() real ext-real Element of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C) : not p <= |.b1.| } is set
WH is set
p12 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.p12.| is V11() real ext-real non negative Element of REAL
sqr p12 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
sqrreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
p12 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (p12,p12) is Relation-like Function-like set
multreal .: (p12,p12) is set
K383((sqr p12)) is V11() real ext-real Element of REAL
addreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K195(REAL,(sqr p12),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr p12)) is V11() real ext-real Element of REAL
bool the carrier of (TOP-REAL C) is non empty set
p12 is Element of bool the carrier of (Euclid C)
WH is Element of bool the carrier of (TOP-REAL C)
C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.C.| is V11() real ext-real non negative Element of REAL
sqr C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
sqrreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
C (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (C,C) is Relation-like Function-like set
multreal .: (C,C) is set
K383((sqr C)) is V11() real ext-real Element of REAL
addreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K195(REAL,(sqr C),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr C)) is V11() real ext-real Element of REAL
r is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.r.| is V11() real ext-real non negative Element of REAL
sqr r is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
r (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (r,r) is Relation-like Function-like set
multreal .: (r,r) is set
K383((sqr r)) is V11() real ext-real Element of REAL
K195(REAL,(sqr r),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr r)) is V11() real ext-real Element of REAL
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
bool the carrier of (TOP-REAL C) is non empty set
p is Element of bool the carrier of (TOP-REAL C)
(C,p) is Element of bool the carrier of (TOP-REAL C)
{ b1 where b1 is Element of bool the carrier of (TOP-REAL C) : (C,p,b1) } is set
union { b1 where b1 is Element of bool the carrier of (TOP-REAL C) : (C,p,b1) } is set
Euclid C is non empty strict Reflexive discerning symmetric triangle Discerning MetrStruct
REAL C is non empty functional FinSequence-membered FinSequenceSet of REAL
C -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = C } is set
Pitag_dist C is non empty Relation-like [:(REAL C),(REAL C):] -defined REAL -valued Function-like total V30([:(REAL C),(REAL C):], REAL ) complex-yielding V174() V175() Element of bool [:[:(REAL C),(REAL C):],REAL:]
[:(REAL C),(REAL C):] is non empty set
[:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() set
MetrStruct(# (REAL C),(Pitag_dist C) #) is strict MetrStruct
the carrier of (Euclid C) is non empty set
bool the carrier of (Euclid C) is non empty set
WH is bounded Element of bool the carrier of (Euclid C)
the Element of WH is Element of WH
0. (TOP-REAL C) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like V62( TOP-REAL C) complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the ZeroF of (TOP-REAL C) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
EX1 is V11() real ext-real Element of REAL
r is Element of the carrier of (Euclid C)
EX2 is Element of the carrier of (Euclid C)
dist (r,EX2) is V11() real ext-real Element of REAL
the distance of (Euclid C) is non empty Relation-like [: the carrier of (Euclid C), the carrier of (Euclid C):] -defined REAL -valued Function-like total V30([: the carrier of (Euclid C), the carrier of (Euclid C):], REAL ) complex-yielding V174() V175() Element of bool [:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:]
[: the carrier of (Euclid C), the carrier of (Euclid C):] is non empty set
[:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:] is non empty non trivial V35() set
the distance of (Euclid C) . (r,EX2) is V11() real ext-real Element of REAL
[r,EX2] is non empty set
{r,EX2} is non empty V35() set
{r} is non empty trivial V35() 1 -element set
{{r,EX2},{r}} is non empty V35() V39() set
the distance of (Euclid C) . [r,EX2] is V11() real ext-real set
EX1 + (dist (r,EX2)) is V11() real ext-real Element of REAL
(EX1 + (dist (r,EX2))) + 1 is V11() real ext-real Element of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C) : not (EX1 + (dist (r,EX2))) + 1 <= |.b1.| } is set
(REAL C) \ { b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C) : not (EX1 + (dist (r,EX2))) + 1 <= |.b1.| } is functional FinSequence-membered Element of bool (REAL C)
bool (REAL C) is non empty set
EX is Element of bool the carrier of (Euclid C)
t2 is set
qt2 is Element of the carrier of (Euclid C)
dist (EX2,qt2) is V11() real ext-real Element of REAL
the distance of (Euclid C) . (EX2,qt2) is V11() real ext-real Element of REAL
[EX2,qt2] is non empty set
{EX2,qt2} is non empty V35() set
{EX2} is non empty trivial V35() 1 -element set
{{EX2,qt2},{EX2}} is non empty V35() V39() set
the distance of (Euclid C) . [EX2,qt2] is V11() real ext-real set
dist (r,qt2) is V11() real ext-real Element of REAL
the distance of (Euclid C) . (r,qt2) is V11() real ext-real Element of REAL
[r,qt2] is non empty set
{r,qt2} is non empty V35() set
{{r,qt2},{r}} is non empty V35() V39() set
the distance of (Euclid C) . [r,qt2] is V11() real ext-real set
(dist (r,EX2)) + (dist (EX2,qt2)) is V11() real ext-real Element of REAL
(dist (r,EX2)) + EX1 is V11() real ext-real Element of REAL
r2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
r2 - (0. (TOP-REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
- (0. (TOP-REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
- (0. (TOP-REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
compreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
(0. (TOP-REAL C)) (#) compreal is Relation-like Function-like V35() complex-yielding V174() V175() set
K38(1) is V11() real ext-real non positive set
K38(1) * (0. (TOP-REAL C)) is Relation-like Function-like set
K38(1) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
id REAL is non empty Relation-like REAL -defined REAL -valued Function-like one-to-one total V30( REAL , REAL ) complex-yielding V174() V175() increasing V179() Element of bool [:REAL,REAL:]
multreal [;] (K38(1),(id REAL)) is set
(0. (TOP-REAL C)) (#) (K38(1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
K258((TOP-REAL C),r2,(- (0. (TOP-REAL C)))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) is non empty Relation-like [: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):] -defined the carrier of (TOP-REAL C) -valued Function-like total V30([: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C)) Element of bool [:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):]
[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):] is non empty set
[:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):] is non empty set
bool [:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):] is non empty set
the U7 of (TOP-REAL C) . (r2,(- (0. (TOP-REAL C)))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[r2,(- (0. (TOP-REAL C)))] is non empty set
{r2,(- (0. (TOP-REAL C)))} is non empty functional V35() V39() set
{r2} is non empty trivial functional V35() V39() 1 -element set
{{r2,(- (0. (TOP-REAL C)))},{r2}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [r2,(- (0. (TOP-REAL C)))] is set
r2 + (- (0. (TOP-REAL C))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
addreal .: (r2,(- (0. (TOP-REAL C)))) is set
r2 - (0. (TOP-REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
diffreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K174(REAL,addreal,(id REAL),compreal) is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
diffreal .: (r2,(0. (TOP-REAL C))) is set
K324((0. (TOP-REAL C))) is Relation-like Function-like complex-yielding set
K295(r2,K324((0. (TOP-REAL C)))) is Relation-like Function-like set
|.(r2 - (0. (TOP-REAL C))).| is V11() real ext-real non negative Element of REAL
sqr (r2 - (0. (TOP-REAL C))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
sqrreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
(r2 - (0. (TOP-REAL C))) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((r2 - (0. (TOP-REAL C))),(r2 - (0. (TOP-REAL C)))) is Relation-like Function-like set
multreal .: ((r2 - (0. (TOP-REAL C))),(r2 - (0. (TOP-REAL C)))) is set
K383((sqr (r2 - (0. (TOP-REAL C))))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (r2 - (0. (TOP-REAL C)))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (r2 - (0. (TOP-REAL C))))) is V11() real ext-real Element of REAL
|.r2.| is V11() real ext-real non negative Element of REAL
sqr r2 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
r2 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (r2,r2) is Relation-like Function-like set
multreal .: (r2,r2) is set
K383((sqr r2)) is V11() real ext-real Element of REAL
K195(REAL,(sqr r2),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr r2)) is V11() real ext-real Element of REAL
(dist (r,EX2)) + 1 is V11() real ext-real Element of REAL
EX1 + ((dist (r,EX2)) + 1) is V11() real ext-real Element of REAL
(dist (r,EX2)) + 0 is V11() real ext-real Element of REAL
t2 is Element of bool the carrier of (TOP-REAL C)
p ` is Element of bool the carrier of (TOP-REAL C)
the carrier of (TOP-REAL C) \ p is set
(TOP-REAL C) | (p `) is strict TopSpace-like SubSpace of TOP-REAL C
the carrier of ((TOP-REAL C) | (p `)) is set
qt2 is Element of bool the carrier of (TOP-REAL C)
Down (qt2,(p `)) is Element of bool the carrier of ((TOP-REAL C) | (p `))
bool the carrier of ((TOP-REAL C) | (p `)) is non empty set
qt2 /\ (p `) is Element of bool the carrier of (TOP-REAL C)
Component_of (Down (qt2,(p `))) is Element of bool the carrier of ((TOP-REAL C) | (p `))
r2 is Element of bool the carrier of (TOP-REAL C)
(TOP-REAL C) | qt2 is strict TopSpace-like SubSpace of TOP-REAL C
((TOP-REAL C) | (p `)) | (Down (qt2,(p `))) is strict TopSpace-like SubSpace of (TOP-REAL C) | (p `)
r5 is set
q4 is non empty Element of bool the carrier of (TOP-REAL C)
(TOP-REAL C) | q4 is non empty strict TopSpace-like SubSpace of TOP-REAL C
r0 is set
Q is Element of bool the carrier of (TOP-REAL C)
P3 is Element of bool the carrier of ((TOP-REAL C) | (p `))
W3 is Element of bool the carrier of (Euclid C)
Q is Element of bool the carrier of (Euclid C)
P2 is set
C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.C.| is V11() real ext-real non negative Element of REAL
sqr C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
C (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (C,C) is Relation-like Function-like set
multreal .: (C,C) is set
K383((sqr C)) is V11() real ext-real Element of REAL
K195(REAL,(sqr C),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr C)) is V11() real ext-real Element of REAL
C - (0. (TOP-REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
K258((TOP-REAL C),C,(- (0. (TOP-REAL C)))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) . (C,(- (0. (TOP-REAL C)))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[C,(- (0. (TOP-REAL C)))] is non empty set
{C,(- (0. (TOP-REAL C)))} is non empty functional V35() V39() set
{C} is non empty trivial functional V35() V39() 1 -element set
{{C,(- (0. (TOP-REAL C)))},{C}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [C,(- (0. (TOP-REAL C)))] is set
C + (- (0. (TOP-REAL C))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (C,(- (0. (TOP-REAL C)))) is set
C - (0. (TOP-REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
diffreal .: (C,(0. (TOP-REAL C))) is set
K295(C,K324((0. (TOP-REAL C)))) is Relation-like Function-like set
|.(C - (0. (TOP-REAL C))).| is V11() real ext-real non negative Element of REAL
sqr (C - (0. (TOP-REAL C))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(C - (0. (TOP-REAL C))) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((C - (0. (TOP-REAL C))),(C - (0. (TOP-REAL C)))) is Relation-like Function-like set
multreal .: ((C - (0. (TOP-REAL C))),(C - (0. (TOP-REAL C)))) is set
K383((sqr (C - (0. (TOP-REAL C))))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (C - (0. (TOP-REAL C)))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (C - (0. (TOP-REAL C))))) is V11() real ext-real Element of REAL
dist (EX2,r) is V11() real ext-real Element of REAL
the distance of (Euclid C) . (EX2,r) is V11() real ext-real Element of REAL
[EX2,r] is non empty set
{EX2,r} is non empty V35() set
{{EX2,r},{EX2}} is non empty V35() V39() set
the distance of (Euclid C) . [EX2,r] is V11() real ext-real set
W2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
W2 - C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
- C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
- C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
C (#) compreal is Relation-like Function-like V35() complex-yielding V174() V175() set
K38(1) * C is Relation-like Function-like set
C (#) (K38(1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
K258((TOP-REAL C),W2,(- C)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) . (W2,(- C)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[W2,(- C)] is non empty set
{W2,(- C)} is non empty functional V35() V39() set
{W2} is non empty trivial functional V35() V39() 1 -element set
{{W2,(- C)},{W2}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [W2,(- C)] is set
W2 + (- C) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (W2,(- C)) is set
W2 - C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
diffreal .: (W2,C) is set
K324(C) is Relation-like Function-like complex-yielding set
K295(W2,K324(C)) is Relation-like Function-like set
|.(W2 - C).| is V11() real ext-real non negative Element of REAL
sqr (W2 - C) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(W2 - C) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((W2 - C),(W2 - C)) is Relation-like Function-like set
multreal .: ((W2 - C),(W2 - C)) is set
K383((sqr (W2 - C))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (W2 - C)),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (W2 - C))) is V11() real ext-real Element of REAL
z is Element of the carrier of (Euclid C)
dist (z,EX2) is V11() real ext-real Element of REAL
the distance of (Euclid C) . (z,EX2) is V11() real ext-real Element of REAL
[z,EX2] is non empty set
{z,EX2} is non empty V35() set
{z} is non empty trivial V35() 1 -element set
{{z,EX2},{z}} is non empty V35() V39() set
the distance of (Euclid C) . [z,EX2] is V11() real ext-real set
|.(W2 - C).| + |.C.| is V11() real ext-real non negative Element of REAL
|.W2.| is V11() real ext-real non negative Element of REAL
sqr W2 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
W2 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (W2,W2) is Relation-like Function-like set
multreal .: (W2,W2) is set
K383((sqr W2)) is V11() real ext-real Element of REAL
K195(REAL,(sqr W2),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr W2)) is V11() real ext-real Element of REAL
(W2 - C) + C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) . ((W2 - C),C) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[(W2 - C),C] is non empty set
{(W2 - C),C} is non empty functional V35() V39() set
{(W2 - C)} is non empty trivial functional V35() V39() 1 -element set
{{(W2 - C),C},{(W2 - C)}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [(W2 - C),C] is set
(W2 - C) + C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: ((W2 - C),C) is set
|.((W2 - C) + C).| is V11() real ext-real non negative Element of REAL
sqr ((W2 - C) + C) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
((W2 - C) + C) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (((W2 - C) + C),((W2 - C) + C)) is Relation-like Function-like set
multreal .: (((W2 - C) + C),((W2 - C) + C)) is set
K383((sqr ((W2 - C) + C))) is V11() real ext-real Element of REAL
K195(REAL,(sqr ((W2 - C) + C)),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr ((W2 - C) + C))) is V11() real ext-real Element of REAL
Q ` is Element of bool the carrier of (Euclid C)
the carrier of (Euclid C) \ Q is set
the carrier of (TOP-REAL C) \ p is Element of bool the carrier of (TOP-REAL C)
qt2 /\ (Q `) is Element of bool the carrier of (Euclid C)
EX /\ P3 is Element of bool the carrier of ((TOP-REAL C) | (p `))
W2 is set
P2 is Element of bool the carrier of (Euclid C)
(Down (qt2,(p `))) /\ P3 is Element of bool the carrier of ((TOP-REAL C) | (p `))
WH is bounded Element of bool the carrier of (Euclid C)
p12 is Element of bool the carrier of (Euclid C)
p12 /\ p is Element of bool the carrier of (TOP-REAL C)
C is Element of bool the carrier of (TOP-REAL C)
p ` is Element of bool the carrier of (TOP-REAL C)
the carrier of (TOP-REAL C) \ p is set
(TOP-REAL C) | (p `) is strict TopSpace-like SubSpace of TOP-REAL C
the carrier of ((TOP-REAL C) | (p `)) is set
r is Element of bool the carrier of (TOP-REAL C)
Down (r,(p `)) is Element of bool the carrier of ((TOP-REAL C) | (p `))
bool the carrier of ((TOP-REAL C) | (p `)) is non empty set
r /\ (p `) is Element of bool the carrier of (TOP-REAL C)
Component_of (Down (r,(p `))) is Element of bool the carrier of ((TOP-REAL C) | (p `))
[#] (TOP-REAL C) is 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 C)
the topology of (TOP-REAL C) is non empty Element of bool (bool the carrier of (TOP-REAL C))
bool (bool the carrier of (TOP-REAL C)) is non empty set
TopStruct(# the carrier of (TOP-REAL C), the topology of (TOP-REAL C) #) is non empty strict TopSpace-like TopStruct
[#] TopStruct(# the carrier of (TOP-REAL C), the topology of (TOP-REAL C) #) is non empty non proper open closed dense non boundary Element of bool the carrier of TopStruct(# the carrier of (TOP-REAL C), the topology of (TOP-REAL C) #)
the carrier of TopStruct(# the carrier of (TOP-REAL C), the topology of (TOP-REAL C) #) is non empty set
bool the carrier of TopStruct(# the carrier of (TOP-REAL C), the topology of (TOP-REAL C) #) is non empty set
EX2 is Element of bool the carrier of (TOP-REAL C)
{} (TOP-REAL C) is empty trivial proper ordinal natural V11() real ext-real non positive non negative Function-like functional V35() V39() cardinal {} -element FinSequence-membered open closed boundary nowhere_dense V183() V184() V185() V186() V187() V188() V189() symmetric circled bounded Element of bool the carrier of (TOP-REAL C)
(TOP-REAL C) | ([#] (TOP-REAL C)) is non empty strict TopSpace-like SubSpace of TOP-REAL C
WH is bounded Element of bool the carrier of (Euclid C)
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
bool the carrier of (TOP-REAL C) is non empty set
p is V11() real ext-real Element of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C) : not p <= |.b1.| } is set
WH is Element of bool the carrier of (TOP-REAL C)
p12 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
LSeg (p12,C) is non empty closed connected compact bounded convex Element of bool the carrier of (TOP-REAL C)
{ (((1 - b1) * p12) + (b1 * C)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
r is set
EX2 is V11() real ext-real Element of REAL
1 - EX2 is V11() real ext-real Element of REAL
(1 - EX2) * p12 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
(1 - EX2) * p12 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(1 - EX2) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
id REAL is non empty Relation-like REAL -defined REAL -valued Function-like one-to-one total V30( REAL , REAL ) complex-yielding V174() V175() increasing V179() Element of bool [:REAL,REAL:]
multreal [;] ((1 - EX2),(id REAL)) is set
p12 (#) ((1 - EX2) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
EX2 * C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
EX2 * C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
EX2 multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (EX2,(id REAL)) is set
C (#) (EX2 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
((1 - EX2) * p12) + (EX2 * C) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) is non empty Relation-like [: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):] -defined the carrier of (TOP-REAL C) -valued Function-like total V30([: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C)) Element of bool [:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):]
[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):] is non empty set
[:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):] is non empty set
bool [:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):] is non empty set
the U7 of (TOP-REAL C) . (((1 - EX2) * p12),(EX2 * C)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[((1 - EX2) * p12),(EX2 * C)] is non empty set
{((1 - EX2) * p12),(EX2 * C)} is non empty functional V35() V39() set
{((1 - EX2) * p12)} is non empty trivial functional V35() V39() 1 -element set
{{((1 - EX2) * p12),(EX2 * C)},{((1 - EX2) * p12)}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [((1 - EX2) * p12),(EX2 * C)] is set
((1 - EX2) * p12) + (EX2 * C) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
addreal .: (((1 - EX2) * p12),(EX2 * C)) is set
|.((1 - EX2) * p12).| is V11() real ext-real non negative Element of REAL
sqr ((1 - EX2) * p12) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
sqrreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
((1 - EX2) * p12) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (((1 - EX2) * p12),((1 - EX2) * p12)) is Relation-like Function-like set
multreal .: (((1 - EX2) * p12),((1 - EX2) * p12)) is set
K383((sqr ((1 - EX2) * p12))) is V11() real ext-real Element of REAL
K195(REAL,(sqr ((1 - EX2) * p12)),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr ((1 - EX2) * p12))) is V11() real ext-real Element of REAL
abs (1 - EX2) is V11() real ext-real Element of REAL
|.p12.| is V11() real ext-real non negative Element of REAL
sqr p12 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
p12 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (p12,p12) is Relation-like Function-like set
multreal .: (p12,p12) is set
K383((sqr p12)) is V11() real ext-real Element of REAL
K195(REAL,(sqr p12),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr p12)) is V11() real ext-real Element of REAL
(abs (1 - EX2)) * |.p12.| is V11() real ext-real Element of REAL
|.(((1 - EX2) * p12) + (EX2 * C)).| is V11() real ext-real non negative Element of REAL
sqr (((1 - EX2) * p12) + (EX2 * C)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(((1 - EX2) * p12) + (EX2 * C)) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((((1 - EX2) * p12) + (EX2 * C)),(((1 - EX2) * p12) + (EX2 * C))) is Relation-like Function-like set
multreal .: ((((1 - EX2) * p12) + (EX2 * C)),(((1 - EX2) * p12) + (EX2 * C))) is set
K383((sqr (((1 - EX2) * p12) + (EX2 * C)))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (((1 - EX2) * p12) + (EX2 * C))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (((1 - EX2) * p12) + (EX2 * C)))) is V11() real ext-real Element of REAL
|.(EX2 * C).| is V11() real ext-real non negative Element of REAL
sqr (EX2 * C) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(EX2 * C) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((EX2 * C),(EX2 * C)) is Relation-like Function-like set
multreal .: ((EX2 * C),(EX2 * C)) is set
K383((sqr (EX2 * C))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (EX2 * C)),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (EX2 * C))) is V11() real ext-real Element of REAL
|.((1 - EX2) * p12).| + |.(EX2 * C).| is V11() real ext-real non negative Element of REAL
abs EX2 is V11() real ext-real Element of REAL
|.C.| is V11() real ext-real non negative Element of REAL
sqr C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
C (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (C,C) is Relation-like Function-like set
multreal .: (C,C) is set
K383((sqr C)) is V11() real ext-real Element of REAL
K195(REAL,(sqr C),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr C)) is V11() real ext-real Element of REAL
(abs EX2) * |.C.| is V11() real ext-real Element of REAL
(abs EX2) * p is V11() real ext-real Element of REAL
p1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.p1.| is V11() real ext-real non negative Element of REAL
sqr p1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
p1 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (p1,p1) is Relation-like Function-like set
multreal .: (p1,p1) is set
K383((sqr p1)) is V11() real ext-real Element of REAL
K195(REAL,(sqr p1),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr p1)) is V11() real ext-real Element of REAL
(abs (1 - EX2)) * p is V11() real ext-real Element of REAL
p1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.p1.| is V11() real ext-real non negative Element of REAL
sqr p1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
p1 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (p1,p1) is Relation-like Function-like set
multreal .: (p1,p1) is set
K383((sqr p1)) is V11() real ext-real Element of REAL
K195(REAL,(sqr p1),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr p1)) is V11() real ext-real Element of REAL
(1 - EX2) * p is V11() real ext-real Element of REAL
EX2 * p is V11() real ext-real Element of REAL
((1 - EX2) * p) + (EX2 * p) is V11() real ext-real Element of REAL
EX1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.EX1.| is V11() real ext-real non negative Element of REAL
sqr EX1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
EX1 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (EX1,EX1) is Relation-like Function-like set
multreal .: (EX1,EX1) is set
K383((sqr EX1)) is V11() real ext-real Element of REAL
K195(REAL,(sqr EX1),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr EX1)) is V11() real ext-real Element of REAL
(1 - EX2) + EX2 is V11() real ext-real Element of REAL
0 + EX2 is V11() real ext-real Element of REAL
abs EX2 is V11() real ext-real Element of REAL
(abs EX2) * p is V11() real ext-real Element of REAL
|.C.| is V11() real ext-real non negative Element of REAL
sqr C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
C (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (C,C) is Relation-like Function-like set
multreal .: (C,C) is set
K383((sqr C)) is V11() real ext-real Element of REAL
K195(REAL,(sqr C),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr C)) is V11() real ext-real Element of REAL
(abs EX2) * |.C.| is V11() real ext-real Element of REAL
p1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.p1.| is V11() real ext-real non negative Element of REAL
sqr p1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
p1 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (p1,p1) is Relation-like Function-like set
multreal .: (p1,p1) is set
K383((sqr p1)) is V11() real ext-real Element of REAL
K195(REAL,(sqr p1),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr p1)) is V11() real ext-real Element of REAL
(abs (1 - EX2)) * p is V11() real ext-real Element of REAL
p1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.p1.| is V11() real ext-real non negative Element of REAL
sqr p1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
p1 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (p1,p1) is Relation-like Function-like set
multreal .: (p1,p1) is set
K383((sqr p1)) is V11() real ext-real Element of REAL
K195(REAL,(sqr p1),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr p1)) is V11() real ext-real Element of REAL
(1 - EX2) * p is V11() real ext-real Element of REAL
EX2 * p is V11() real ext-real Element of REAL
((1 - EX2) * p) + (EX2 * p) is V11() real ext-real Element of REAL
EX1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.EX1.| is V11() real ext-real non negative Element of REAL
sqr EX1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
EX1 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (EX1,EX1) is Relation-like Function-like set
multreal .: (EX1,EX1) is set
K383((sqr EX1)) is V11() real ext-real Element of REAL
K195(REAL,(sqr EX1),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr EX1)) is V11() real ext-real Element of REAL
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
Euclid C is non empty strict Reflexive discerning symmetric triangle Discerning MetrStruct
REAL C is non empty functional FinSequence-membered FinSequenceSet of REAL
C -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = C } is set
Pitag_dist C is non empty Relation-like [:(REAL C),(REAL C):] -defined REAL -valued Function-like total V30([:(REAL C),(REAL C):], REAL ) complex-yielding V174() V175() Element of bool [:[:(REAL C),(REAL C):],REAL:]
[:(REAL C),(REAL C):] is non empty set
[:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() set
MetrStruct(# (REAL C),(Pitag_dist C) #) is strict MetrStruct
the carrier of (Euclid C) is non empty set
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
bool the carrier of (TOP-REAL C) is non empty set
p is Element of the carrier of (Euclid C)
WH is V11() real ext-real Element of REAL
Ball (p,WH) is bounded Element of bool the carrier of (Euclid C)
bool the carrier of (Euclid C) is non empty set
p12 is Element of bool the carrier of (TOP-REAL C)
r is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
EX2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
LSeg (r,EX2) is non empty closed connected compact bounded convex Element of bool the carrier of (TOP-REAL C)
{ (((1 - b1) * r) + (b1 * EX2)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
{ b1 where b1 is Element of the carrier of (Euclid C) : not WH <= dist (p,b1) } is set
C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
C - EX2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
- EX2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
- EX2 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
compreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
EX2 (#) compreal is Relation-like Function-like V35() complex-yielding V174() V175() set
K38(1) is V11() real ext-real non positive set
K38(1) * EX2 is Relation-like Function-like set
K38(1) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
id REAL is non empty Relation-like REAL -defined REAL -valued Function-like one-to-one total V30( REAL , REAL ) complex-yielding V174() V175() increasing V179() Element of bool [:REAL,REAL:]
multreal [;] (K38(1),(id REAL)) is set
EX2 (#) (K38(1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
K258((TOP-REAL C),C,(- EX2)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) is non empty Relation-like [: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):] -defined the carrier of (TOP-REAL C) -valued Function-like total V30([: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C)) Element of bool [:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):]
[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):] is non empty set
[:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):] is non empty set
bool [:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):] is non empty set
the U7 of (TOP-REAL C) . (C,(- EX2)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[C,(- EX2)] is non empty set
{C,(- EX2)} is non empty functional V35() V39() set
{C} is non empty trivial functional V35() V39() 1 -element set
{{C,(- EX2)},{C}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [C,(- EX2)] is set
C + (- EX2) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
addreal .: (C,(- EX2)) is set
C - EX2 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
diffreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K174(REAL,addreal,(id REAL),compreal) is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
diffreal .: (C,EX2) is set
K324(EX2) is Relation-like Function-like complex-yielding set
K295(C,K324(EX2)) is Relation-like Function-like set
|.(C - EX2).| is V11() real ext-real non negative Element of REAL
sqr (C - EX2) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
sqrreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
(C - EX2) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((C - EX2),(C - EX2)) is Relation-like Function-like set
multreal .: ((C - EX2),(C - EX2)) is set
K383((sqr (C - EX2))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (C - EX2)),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (C - EX2))) is V11() real ext-real Element of REAL
EX1 is Element of the carrier of (Euclid C)
dist (p,EX1) is V11() real ext-real Element of REAL
the distance of (Euclid C) is non empty Relation-like [: the carrier of (Euclid C), the carrier of (Euclid C):] -defined REAL -valued Function-like total V30([: the carrier of (Euclid C), the carrier of (Euclid C):], REAL ) complex-yielding V174() V175() Element of bool [:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:]
[: the carrier of (Euclid C), the carrier of (Euclid C):] is non empty set
[:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:] is non empty non trivial V35() set
the distance of (Euclid C) . (p,EX1) is V11() real ext-real Element of REAL
[p,EX1] is non empty set
{p,EX1} is non empty V35() set
{p} is non empty trivial V35() 1 -element set
{{p,EX1},{p}} is non empty V35() V39() set
the distance of (Euclid C) . [p,EX1] is V11() real ext-real set
EX1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
C - EX1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
- EX1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
- EX1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
EX1 (#) compreal is Relation-like Function-like V35() complex-yielding V174() V175() set
K38(1) * EX1 is Relation-like Function-like set
EX1 (#) (K38(1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
K258((TOP-REAL C),C,(- EX1)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) . (C,(- EX1)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[C,(- EX1)] is non empty set
{C,(- EX1)} is non empty functional V35() V39() set
{{C,(- EX1)},{C}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [C,(- EX1)] is set
C + (- EX1) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (C,(- EX1)) is set
C - EX1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
diffreal .: (C,EX1) is set
K324(EX1) is Relation-like Function-like complex-yielding set
K295(C,K324(EX1)) is Relation-like Function-like set
|.(C - EX1).| is V11() real ext-real non negative Element of REAL
sqr (C - EX1) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(C - EX1) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((C - EX1),(C - EX1)) is Relation-like Function-like set
multreal .: ((C - EX1),(C - EX1)) is set
K383((sqr (C - EX1))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (C - EX1)),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (C - EX1))) is V11() real ext-real Element of REAL
p1 is Element of the carrier of (Euclid C)
dist (p,p1) is V11() real ext-real Element of REAL
the distance of (Euclid C) is non empty Relation-like [: the carrier of (Euclid C), the carrier of (Euclid C):] -defined REAL -valued Function-like total V30([: the carrier of (Euclid C), the carrier of (Euclid C):], REAL ) complex-yielding V174() V175() Element of bool [:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:]
[: the carrier of (Euclid C), the carrier of (Euclid C):] is non empty set
[:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:] is non empty non trivial V35() set
the distance of (Euclid C) . (p,p1) is V11() real ext-real Element of REAL
[p,p1] is non empty set
{p,p1} is non empty V35() set
{p} is non empty trivial V35() 1 -element set
{{p,p1},{p}} is non empty V35() V39() set
the distance of (Euclid C) . [p,p1] is V11() real ext-real set
C - r is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
- r is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
- r is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
r (#) compreal is Relation-like Function-like V35() complex-yielding V174() V175() set
K38(1) * r is Relation-like Function-like set
r (#) (K38(1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
K258((TOP-REAL C),C,(- r)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) . (C,(- r)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[C,(- r)] is non empty set
{C,(- r)} is non empty functional V35() V39() set
{{C,(- r)},{C}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [C,(- r)] is set
C + (- r) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (C,(- r)) is set
C - r is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
diffreal .: (C,r) is set
K324(r) is Relation-like Function-like complex-yielding set
K295(C,K324(r)) is Relation-like Function-like set
|.(C - r).| is V11() real ext-real non negative Element of REAL
sqr (C - r) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(C - r) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((C - r),(C - r)) is Relation-like Function-like set
multreal .: ((C - r),(C - r)) is set
K383((sqr (C - r))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (C - r)),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (C - r))) is V11() real ext-real Element of REAL
EX1 is Element of the carrier of (Euclid C)
dist (p,EX1) is V11() real ext-real Element of REAL
the distance of (Euclid C) is non empty Relation-like [: the carrier of (Euclid C), the carrier of (Euclid C):] -defined REAL -valued Function-like total V30([: the carrier of (Euclid C), the carrier of (Euclid C):], REAL ) complex-yielding V174() V175() Element of bool [:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:]
[: the carrier of (Euclid C), the carrier of (Euclid C):] is non empty set
[:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:] is non empty non trivial V35() set
the distance of (Euclid C) . (p,EX1) is V11() real ext-real Element of REAL
[p,EX1] is non empty set
{p,EX1} is non empty V35() set
{p} is non empty trivial V35() 1 -element set
{{p,EX1},{p}} is non empty V35() V39() set
the distance of (Euclid C) . [p,EX1] is V11() real ext-real set
EX1 is set
p1 is V11() real ext-real Element of REAL
1 - p1 is V11() real ext-real Element of REAL
(1 - p1) * r is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
(1 - p1) * r is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(1 - p1) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] ((1 - p1),(id REAL)) is set
r (#) ((1 - p1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
p1 * EX2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
p1 * EX2 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
p1 multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (p1,(id REAL)) is set
EX2 (#) (p1 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
((1 - p1) * r) + (p1 * EX2) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) . (((1 - p1) * r),(p1 * EX2)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[((1 - p1) * r),(p1 * EX2)] is non empty set
{((1 - p1) * r),(p1 * EX2)} is non empty functional V35() V39() set
{((1 - p1) * r)} is non empty trivial functional V35() V39() 1 -element set
{{((1 - p1) * r),(p1 * EX2)},{((1 - p1) * r)}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [((1 - p1) * r),(p1 * EX2)] is set
((1 - p1) * r) + (p1 * EX2) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (((1 - p1) * r),(p1 * EX2)) is set
(1 - p1) * (C - r) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
(1 - p1) * (C - r) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(C - r) (#) ((1 - p1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
|.((1 - p1) * (C - r)).| is V11() real ext-real non negative Element of REAL
sqr ((1 - p1) * (C - r)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
((1 - p1) * (C - r)) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (((1 - p1) * (C - r)),((1 - p1) * (C - r))) is Relation-like Function-like set
multreal .: (((1 - p1) * (C - r)),((1 - p1) * (C - r))) is set
K383((sqr ((1 - p1) * (C - r)))) is V11() real ext-real Element of REAL
K195(REAL,(sqr ((1 - p1) * (C - r))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr ((1 - p1) * (C - r)))) is V11() real ext-real Element of REAL
abs (1 - p1) is V11() real ext-real Element of REAL
(abs (1 - p1)) * |.(C - r).| is V11() real ext-real Element of REAL
(1 - p1) * C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
(1 - p1) * C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
C (#) ((1 - p1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
p1 * C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
p1 * C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
C (#) (p1 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
((1 - p1) * C) + (p1 * C) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) . (((1 - p1) * C),(p1 * C)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[((1 - p1) * C),(p1 * C)] is non empty set
{((1 - p1) * C),(p1 * C)} is non empty functional V35() V39() set
{((1 - p1) * C)} is non empty trivial functional V35() V39() 1 -element set
{{((1 - p1) * C),(p1 * C)},{((1 - p1) * C)}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [((1 - p1) * C),(p1 * C)] is set
((1 - p1) * C) + (p1 * C) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (((1 - p1) * C),(p1 * C)) is set
(1 - p1) + p1 is V11() real ext-real Element of REAL
((1 - p1) + p1) * C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
((1 - p1) + p1) * C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
((1 - p1) + p1) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (((1 - p1) + p1),(id REAL)) is set
C (#) (((1 - p1) + p1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
C - (((1 - p1) * r) + (p1 * EX2)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
- (((1 - p1) * r) + (p1 * EX2)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
- (((1 - p1) * r) + (p1 * EX2)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(((1 - p1) * r) + (p1 * EX2)) (#) compreal is Relation-like Function-like V35() complex-yielding V174() V175() set
K38(1) * (((1 - p1) * r) + (p1 * EX2)) is Relation-like Function-like set
(((1 - p1) * r) + (p1 * EX2)) (#) (K38(1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
K258((TOP-REAL C),C,(- (((1 - p1) * r) + (p1 * EX2)))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) . (C,(- (((1 - p1) * r) + (p1 * EX2)))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[C,(- (((1 - p1) * r) + (p1 * EX2)))] is non empty set
{C,(- (((1 - p1) * r) + (p1 * EX2)))} is non empty functional V35() V39() set
{{C,(- (((1 - p1) * r) + (p1 * EX2)))},{C}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [C,(- (((1 - p1) * r) + (p1 * EX2)))] is set
C + (- (((1 - p1) * r) + (p1 * EX2))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (C,(- (((1 - p1) * r) + (p1 * EX2)))) is set
C - (((1 - p1) * r) + (p1 * EX2)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
diffreal .: (C,(((1 - p1) * r) + (p1 * EX2))) is set
K324((((1 - p1) * r) + (p1 * EX2))) is Relation-like Function-like complex-yielding set
K295(C,K324((((1 - p1) * r) + (p1 * EX2)))) is Relation-like Function-like set
|.(C - (((1 - p1) * r) + (p1 * EX2))).| is V11() real ext-real non negative Element of REAL
sqr (C - (((1 - p1) * r) + (p1 * EX2))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(C - (((1 - p1) * r) + (p1 * EX2))) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((C - (((1 - p1) * r) + (p1 * EX2))),(C - (((1 - p1) * r) + (p1 * EX2)))) is Relation-like Function-like set
multreal .: ((C - (((1 - p1) * r) + (p1 * EX2))),(C - (((1 - p1) * r) + (p1 * EX2)))) is set
K383((sqr (C - (((1 - p1) * r) + (p1 * EX2))))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (C - (((1 - p1) * r) + (p1 * EX2)))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (C - (((1 - p1) * r) + (p1 * EX2))))) is V11() real ext-real Element of REAL
(((1 - p1) * C) + (p1 * C)) - ((1 - p1) * r) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
- ((1 - p1) * r) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
- ((1 - p1) * r) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
((1 - p1) * r) (#) compreal is Relation-like Function-like V35() complex-yielding V174() V175() set
K38(1) * ((1 - p1) * r) is Relation-like Function-like set
((1 - p1) * r) (#) (K38(1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
K258((TOP-REAL C),(((1 - p1) * C) + (p1 * C)),(- ((1 - p1) * r))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) . ((((1 - p1) * C) + (p1 * C)),(- ((1 - p1) * r))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[(((1 - p1) * C) + (p1 * C)),(- ((1 - p1) * r))] is non empty set
{(((1 - p1) * C) + (p1 * C)),(- ((1 - p1) * r))} is non empty functional V35() V39() set
{(((1 - p1) * C) + (p1 * C))} is non empty trivial functional V35() V39() 1 -element set
{{(((1 - p1) * C) + (p1 * C)),(- ((1 - p1) * r))},{(((1 - p1) * C) + (p1 * C))}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [(((1 - p1) * C) + (p1 * C)),(- ((1 - p1) * r))] is set
(((1 - p1) * C) + (p1 * C)) + (- ((1 - p1) * r)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: ((((1 - p1) * C) + (p1 * C)),(- ((1 - p1) * r))) is set
(((1 - p1) * C) + (p1 * C)) - ((1 - p1) * r) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
diffreal .: ((((1 - p1) * C) + (p1 * C)),((1 - p1) * r)) is set
K324(((1 - p1) * r)) is Relation-like Function-like complex-yielding set
K295((((1 - p1) * C) + (p1 * C)),K324(((1 - p1) * r))) is Relation-like Function-like set
((((1 - p1) * C) + (p1 * C)) - ((1 - p1) * r)) - (p1 * EX2) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
- (p1 * EX2) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
- (p1 * EX2) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(p1 * EX2) (#) compreal is Relation-like Function-like V35() complex-yielding V174() V175() set
K38(1) * (p1 * EX2) is Relation-like Function-like set
(p1 * EX2) (#) (K38(1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
K258((TOP-REAL C),((((1 - p1) * C) + (p1 * C)) - ((1 - p1) * r)),(- (p1 * EX2))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) . (((((1 - p1) * C) + (p1 * C)) - ((1 - p1) * r)),(- (p1 * EX2))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[((((1 - p1) * C) + (p1 * C)) - ((1 - p1) * r)),(- (p1 * EX2))] is non empty set
{((((1 - p1) * C) + (p1 * C)) - ((1 - p1) * r)),(- (p1 * EX2))} is non empty functional V35() V39() set
{((((1 - p1) * C) + (p1 * C)) - ((1 - p1) * r))} is non empty trivial functional V35() V39() 1 -element set
{{((((1 - p1) * C) + (p1 * C)) - ((1 - p1) * r)),(- (p1 * EX2))},{((((1 - p1) * C) + (p1 * C)) - ((1 - p1) * r))}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [((((1 - p1) * C) + (p1 * C)) - ((1 - p1) * r)),(- (p1 * EX2))] is set
((((1 - p1) * C) + (p1 * C)) - ((1 - p1) * r)) + (- (p1 * EX2)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (((((1 - p1) * C) + (p1 * C)) - ((1 - p1) * r)),(- (p1 * EX2))) is set
((((1 - p1) * C) + (p1 * C)) - ((1 - p1) * r)) - (p1 * EX2) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
diffreal .: (((((1 - p1) * C) + (p1 * C)) - ((1 - p1) * r)),(p1 * EX2)) is set
K324((p1 * EX2)) is Relation-like Function-like complex-yielding set
K295(((((1 - p1) * C) + (p1 * C)) - ((1 - p1) * r)),K324((p1 * EX2))) is Relation-like Function-like set
|.(((((1 - p1) * C) + (p1 * C)) - ((1 - p1) * r)) - (p1 * EX2)).| is V11() real ext-real non negative Element of REAL
sqr (((((1 - p1) * C) + (p1 * C)) - ((1 - p1) * r)) - (p1 * EX2)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(((((1 - p1) * C) + (p1 * C)) - ((1 - p1) * r)) - (p1 * EX2)) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((((((1 - p1) * C) + (p1 * C)) - ((1 - p1) * r)) - (p1 * EX2)),(((((1 - p1) * C) + (p1 * C)) - ((1 - p1) * r)) - (p1 * EX2))) is Relation-like Function-like set
multreal .: ((((((1 - p1) * C) + (p1 * C)) - ((1 - p1) * r)) - (p1 * EX2)),(((((1 - p1) * C) + (p1 * C)) - ((1 - p1) * r)) - (p1 * EX2))) is set
K383((sqr (((((1 - p1) * C) + (p1 * C)) - ((1 - p1) * r)) - (p1 * EX2)))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (((((1 - p1) * C) + (p1 * C)) - ((1 - p1) * r)) - (p1 * EX2))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (((((1 - p1) * C) + (p1 * C)) - ((1 - p1) * r)) - (p1 * EX2)))) is V11() real ext-real Element of REAL
((1 - p1) * C) + (- ((1 - p1) * r)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) . (((1 - p1) * C),(- ((1 - p1) * r))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[((1 - p1) * C),(- ((1 - p1) * r))] is non empty set
{((1 - p1) * C),(- ((1 - p1) * r))} is non empty functional V35() V39() set
{{((1 - p1) * C),(- ((1 - p1) * r))},{((1 - p1) * C)}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [((1 - p1) * C),(- ((1 - p1) * r))] is set
((1 - p1) * C) + (- ((1 - p1) * r)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (((1 - p1) * C),(- ((1 - p1) * r))) is set
(((1 - p1) * C) + (- ((1 - p1) * r))) + (p1 * C) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) . ((((1 - p1) * C) + (- ((1 - p1) * r))),(p1 * C)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[(((1 - p1) * C) + (- ((1 - p1) * r))),(p1 * C)] is non empty set
{(((1 - p1) * C) + (- ((1 - p1) * r))),(p1 * C)} is non empty functional V35() V39() set
{(((1 - p1) * C) + (- ((1 - p1) * r)))} is non empty trivial functional V35() V39() 1 -element set
{{(((1 - p1) * C) + (- ((1 - p1) * r))),(p1 * C)},{(((1 - p1) * C) + (- ((1 - p1) * r)))}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [(((1 - p1) * C) + (- ((1 - p1) * r))),(p1 * C)] is set
(((1 - p1) * C) + (- ((1 - p1) * r))) + (p1 * C) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: ((((1 - p1) * C) + (- ((1 - p1) * r))),(p1 * C)) is set
((((1 - p1) * C) + (- ((1 - p1) * r))) + (p1 * C)) + (- (p1 * EX2)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) . (((((1 - p1) * C) + (- ((1 - p1) * r))) + (p1 * C)),(- (p1 * EX2))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[((((1 - p1) * C) + (- ((1 - p1) * r))) + (p1 * C)),(- (p1 * EX2))] is non empty set
{((((1 - p1) * C) + (- ((1 - p1) * r))) + (p1 * C)),(- (p1 * EX2))} is non empty functional V35() V39() set
{((((1 - p1) * C) + (- ((1 - p1) * r))) + (p1 * C))} is non empty trivial functional V35() V39() 1 -element set
{{((((1 - p1) * C) + (- ((1 - p1) * r))) + (p1 * C)),(- (p1 * EX2))},{((((1 - p1) * C) + (- ((1 - p1) * r))) + (p1 * C))}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [((((1 - p1) * C) + (- ((1 - p1) * r))) + (p1 * C)),(- (p1 * EX2))] is set
((((1 - p1) * C) + (- ((1 - p1) * r))) + (p1 * C)) + (- (p1 * EX2)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (((((1 - p1) * C) + (- ((1 - p1) * r))) + (p1 * C)),(- (p1 * EX2))) is set
|.(((((1 - p1) * C) + (- ((1 - p1) * r))) + (p1 * C)) + (- (p1 * EX2))).| is V11() real ext-real non negative Element of REAL
sqr (((((1 - p1) * C) + (- ((1 - p1) * r))) + (p1 * C)) + (- (p1 * EX2))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(((((1 - p1) * C) + (- ((1 - p1) * r))) + (p1 * C)) + (- (p1 * EX2))) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((((((1 - p1) * C) + (- ((1 - p1) * r))) + (p1 * C)) + (- (p1 * EX2))),(((((1 - p1) * C) + (- ((1 - p1) * r))) + (p1 * C)) + (- (p1 * EX2)))) is Relation-like Function-like set
multreal .: ((((((1 - p1) * C) + (- ((1 - p1) * r))) + (p1 * C)) + (- (p1 * EX2))),(((((1 - p1) * C) + (- ((1 - p1) * r))) + (p1 * C)) + (- (p1 * EX2)))) is set
K383((sqr (((((1 - p1) * C) + (- ((1 - p1) * r))) + (p1 * C)) + (- (p1 * EX2))))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (((((1 - p1) * C) + (- ((1 - p1) * r))) + (p1 * C)) + (- (p1 * EX2)))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (((((1 - p1) * C) + (- ((1 - p1) * r))) + (p1 * C)) + (- (p1 * EX2))))) is V11() real ext-real Element of REAL
(p1 * C) + (- (p1 * EX2)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) . ((p1 * C),(- (p1 * EX2))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[(p1 * C),(- (p1 * EX2))] is non empty set
{(p1 * C),(- (p1 * EX2))} is non empty functional V35() V39() set
{(p1 * C)} is non empty trivial functional V35() V39() 1 -element set
{{(p1 * C),(- (p1 * EX2))},{(p1 * C)}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [(p1 * C),(- (p1 * EX2))] is set
(p1 * C) + (- (p1 * EX2)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: ((p1 * C),(- (p1 * EX2))) is set
(((1 - p1) * C) + (- ((1 - p1) * r))) + ((p1 * C) + (- (p1 * EX2))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) . ((((1 - p1) * C) + (- ((1 - p1) * r))),((p1 * C) + (- (p1 * EX2)))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[(((1 - p1) * C) + (- ((1 - p1) * r))),((p1 * C) + (- (p1 * EX2)))] is non empty set
{(((1 - p1) * C) + (- ((1 - p1) * r))),((p1 * C) + (- (p1 * EX2)))} is non empty functional V35() V39() set
{{(((1 - p1) * C) + (- ((1 - p1) * r))),((p1 * C) + (- (p1 * EX2)))},{(((1 - p1) * C) + (- ((1 - p1) * r)))}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [(((1 - p1) * C) + (- ((1 - p1) * r))),((p1 * C) + (- (p1 * EX2)))] is set
(((1 - p1) * C) + (- ((1 - p1) * r))) + ((p1 * C) + (- (p1 * EX2))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: ((((1 - p1) * C) + (- ((1 - p1) * r))),((p1 * C) + (- (p1 * EX2)))) is set
|.((((1 - p1) * C) + (- ((1 - p1) * r))) + ((p1 * C) + (- (p1 * EX2)))).| is V11() real ext-real non negative Element of REAL
sqr ((((1 - p1) * C) + (- ((1 - p1) * r))) + ((p1 * C) + (- (p1 * EX2)))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
((((1 - p1) * C) + (- ((1 - p1) * r))) + ((p1 * C) + (- (p1 * EX2)))) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (((((1 - p1) * C) + (- ((1 - p1) * r))) + ((p1 * C) + (- (p1 * EX2)))),((((1 - p1) * C) + (- ((1 - p1) * r))) + ((p1 * C) + (- (p1 * EX2))))) is Relation-like Function-like set
multreal .: (((((1 - p1) * C) + (- ((1 - p1) * r))) + ((p1 * C) + (- (p1 * EX2)))),((((1 - p1) * C) + (- ((1 - p1) * r))) + ((p1 * C) + (- (p1 * EX2))))) is set
K383((sqr ((((1 - p1) * C) + (- ((1 - p1) * r))) + ((p1 * C) + (- (p1 * EX2)))))) is V11() real ext-real Element of REAL
K195(REAL,(sqr ((((1 - p1) * C) + (- ((1 - p1) * r))) + ((p1 * C) + (- (p1 * EX2))))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr ((((1 - p1) * C) + (- ((1 - p1) * r))) + ((p1 * C) + (- (p1 * EX2)))))) is V11() real ext-real Element of REAL
(1 - p1) * (- r) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
(1 - p1) * (- r) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(- r) (#) ((1 - p1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
((1 - p1) * C) + ((1 - p1) * (- r)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) . (((1 - p1) * C),((1 - p1) * (- r))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[((1 - p1) * C),((1 - p1) * (- r))] is non empty set
{((1 - p1) * C),((1 - p1) * (- r))} is non empty functional V35() V39() set
{{((1 - p1) * C),((1 - p1) * (- r))},{((1 - p1) * C)}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [((1 - p1) * C),((1 - p1) * (- r))] is set
((1 - p1) * C) + ((1 - p1) * (- r)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (((1 - p1) * C),((1 - p1) * (- r))) is set
(((1 - p1) * C) + ((1 - p1) * (- r))) + ((p1 * C) + (- (p1 * EX2))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) . ((((1 - p1) * C) + ((1 - p1) * (- r))),((p1 * C) + (- (p1 * EX2)))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[(((1 - p1) * C) + ((1 - p1) * (- r))),((p1 * C) + (- (p1 * EX2)))] is non empty set
{(((1 - p1) * C) + ((1 - p1) * (- r))),((p1 * C) + (- (p1 * EX2)))} is non empty functional V35() V39() set
{(((1 - p1) * C) + ((1 - p1) * (- r)))} is non empty trivial functional V35() V39() 1 -element set
{{(((1 - p1) * C) + ((1 - p1) * (- r))),((p1 * C) + (- (p1 * EX2)))},{(((1 - p1) * C) + ((1 - p1) * (- r)))}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [(((1 - p1) * C) + ((1 - p1) * (- r))),((p1 * C) + (- (p1 * EX2)))] is set
(((1 - p1) * C) + ((1 - p1) * (- r))) + ((p1 * C) + (- (p1 * EX2))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: ((((1 - p1) * C) + ((1 - p1) * (- r))),((p1 * C) + (- (p1 * EX2)))) is set
|.((((1 - p1) * C) + ((1 - p1) * (- r))) + ((p1 * C) + (- (p1 * EX2)))).| is V11() real ext-real non negative Element of REAL
sqr ((((1 - p1) * C) + ((1 - p1) * (- r))) + ((p1 * C) + (- (p1 * EX2)))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
((((1 - p1) * C) + ((1 - p1) * (- r))) + ((p1 * C) + (- (p1 * EX2)))) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (((((1 - p1) * C) + ((1 - p1) * (- r))) + ((p1 * C) + (- (p1 * EX2)))),((((1 - p1) * C) + ((1 - p1) * (- r))) + ((p1 * C) + (- (p1 * EX2))))) is Relation-like Function-like set
multreal .: (((((1 - p1) * C) + ((1 - p1) * (- r))) + ((p1 * C) + (- (p1 * EX2)))),((((1 - p1) * C) + ((1 - p1) * (- r))) + ((p1 * C) + (- (p1 * EX2))))) is set
K383((sqr ((((1 - p1) * C) + ((1 - p1) * (- r))) + ((p1 * C) + (- (p1 * EX2)))))) is V11() real ext-real Element of REAL
K195(REAL,(sqr ((((1 - p1) * C) + ((1 - p1) * (- r))) + ((p1 * C) + (- (p1 * EX2))))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr ((((1 - p1) * C) + ((1 - p1) * (- r))) + ((p1 * C) + (- (p1 * EX2)))))) is V11() real ext-real Element of REAL
((1 - p1) * (C - r)) + ((p1 * C) + (- (p1 * EX2))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) . (((1 - p1) * (C - r)),((p1 * C) + (- (p1 * EX2)))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[((1 - p1) * (C - r)),((p1 * C) + (- (p1 * EX2)))] is non empty set
{((1 - p1) * (C - r)),((p1 * C) + (- (p1 * EX2)))} is non empty functional V35() V39() set
{((1 - p1) * (C - r))} is non empty trivial functional V35() V39() 1 -element set
{{((1 - p1) * (C - r)),((p1 * C) + (- (p1 * EX2)))},{((1 - p1) * (C - r))}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [((1 - p1) * (C - r)),((p1 * C) + (- (p1 * EX2)))] is set
((1 - p1) * (C - r)) + ((p1 * C) + (- (p1 * EX2))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (((1 - p1) * (C - r)),((p1 * C) + (- (p1 * EX2)))) is set
|.(((1 - p1) * (C - r)) + ((p1 * C) + (- (p1 * EX2)))).| is V11() real ext-real non negative Element of REAL
sqr (((1 - p1) * (C - r)) + ((p1 * C) + (- (p1 * EX2)))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(((1 - p1) * (C - r)) + ((p1 * C) + (- (p1 * EX2)))) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((((1 - p1) * (C - r)) + ((p1 * C) + (- (p1 * EX2)))),(((1 - p1) * (C - r)) + ((p1 * C) + (- (p1 * EX2))))) is Relation-like Function-like set
multreal .: ((((1 - p1) * (C - r)) + ((p1 * C) + (- (p1 * EX2)))),(((1 - p1) * (C - r)) + ((p1 * C) + (- (p1 * EX2))))) is set
K383((sqr (((1 - p1) * (C - r)) + ((p1 * C) + (- (p1 * EX2)))))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (((1 - p1) * (C - r)) + ((p1 * C) + (- (p1 * EX2))))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (((1 - p1) * (C - r)) + ((p1 * C) + (- (p1 * EX2)))))) is V11() real ext-real Element of REAL
p1 * (- EX2) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
p1 * (- EX2) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(- EX2) (#) (p1 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
(p1 * C) + (p1 * (- EX2)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) . ((p1 * C),(p1 * (- EX2))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[(p1 * C),(p1 * (- EX2))] is non empty set
{(p1 * C),(p1 * (- EX2))} is non empty functional V35() V39() set
{{(p1 * C),(p1 * (- EX2))},{(p1 * C)}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [(p1 * C),(p1 * (- EX2))] is set
(p1 * C) + (p1 * (- EX2)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: ((p1 * C),(p1 * (- EX2))) is set
((1 - p1) * (C - r)) + ((p1 * C) + (p1 * (- EX2))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) . (((1 - p1) * (C - r)),((p1 * C) + (p1 * (- EX2)))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[((1 - p1) * (C - r)),((p1 * C) + (p1 * (- EX2)))] is non empty set
{((1 - p1) * (C - r)),((p1 * C) + (p1 * (- EX2)))} is non empty functional V35() V39() set
{{((1 - p1) * (C - r)),((p1 * C) + (p1 * (- EX2)))},{((1 - p1) * (C - r))}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [((1 - p1) * (C - r)),((p1 * C) + (p1 * (- EX2)))] is set
((1 - p1) * (C - r)) + ((p1 * C) + (p1 * (- EX2))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (((1 - p1) * (C - r)),((p1 * C) + (p1 * (- EX2)))) is set
|.(((1 - p1) * (C - r)) + ((p1 * C) + (p1 * (- EX2)))).| is V11() real ext-real non negative Element of REAL
sqr (((1 - p1) * (C - r)) + ((p1 * C) + (p1 * (- EX2)))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(((1 - p1) * (C - r)) + ((p1 * C) + (p1 * (- EX2)))) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((((1 - p1) * (C - r)) + ((p1 * C) + (p1 * (- EX2)))),(((1 - p1) * (C - r)) + ((p1 * C) + (p1 * (- EX2))))) is Relation-like Function-like set
multreal .: ((((1 - p1) * (C - r)) + ((p1 * C) + (p1 * (- EX2)))),(((1 - p1) * (C - r)) + ((p1 * C) + (p1 * (- EX2))))) is set
K383((sqr (((1 - p1) * (C - r)) + ((p1 * C) + (p1 * (- EX2)))))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (((1 - p1) * (C - r)) + ((p1 * C) + (p1 * (- EX2))))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (((1 - p1) * (C - r)) + ((p1 * C) + (p1 * (- EX2)))))) is V11() real ext-real Element of REAL
p1 * (C - EX2) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
p1 * (C - EX2) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(C - EX2) (#) (p1 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
((1 - p1) * (C - r)) + (p1 * (C - EX2)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) . (((1 - p1) * (C - r)),(p1 * (C - EX2))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[((1 - p1) * (C - r)),(p1 * (C - EX2))] is non empty set
{((1 - p1) * (C - r)),(p1 * (C - EX2))} is non empty functional V35() V39() set
{{((1 - p1) * (C - r)),(p1 * (C - EX2))},{((1 - p1) * (C - r))}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [((1 - p1) * (C - r)),(p1 * (C - EX2))] is set
((1 - p1) * (C - r)) + (p1 * (C - EX2)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (((1 - p1) * (C - r)),(p1 * (C - EX2))) is set
|.(((1 - p1) * (C - r)) + (p1 * (C - EX2))).| is V11() real ext-real non negative Element of REAL
sqr (((1 - p1) * (C - r)) + (p1 * (C - EX2))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(((1 - p1) * (C - r)) + (p1 * (C - EX2))) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((((1 - p1) * (C - r)) + (p1 * (C - EX2))),(((1 - p1) * (C - r)) + (p1 * (C - EX2)))) is Relation-like Function-like set
multreal .: ((((1 - p1) * (C - r)) + (p1 * (C - EX2))),(((1 - p1) * (C - r)) + (p1 * (C - EX2)))) is set
K383((sqr (((1 - p1) * (C - r)) + (p1 * (C - EX2))))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (((1 - p1) * (C - r)) + (p1 * (C - EX2)))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (((1 - p1) * (C - r)) + (p1 * (C - EX2))))) is V11() real ext-real Element of REAL
|.(p1 * (C - EX2)).| is V11() real ext-real non negative Element of REAL
sqr (p1 * (C - EX2)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(p1 * (C - EX2)) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((p1 * (C - EX2)),(p1 * (C - EX2))) is Relation-like Function-like set
multreal .: ((p1 * (C - EX2)),(p1 * (C - EX2))) is set
K383((sqr (p1 * (C - EX2)))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (p1 * (C - EX2))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (p1 * (C - EX2)))) is V11() real ext-real Element of REAL
|.((1 - p1) * (C - r)).| + |.(p1 * (C - EX2)).| is V11() real ext-real non negative Element of REAL
abs p1 is V11() real ext-real Element of REAL
(abs p1) * |.(C - EX2).| is V11() real ext-real Element of REAL
(abs p1) * WH is V11() real ext-real Element of REAL
(abs (1 - p1)) * WH is V11() real ext-real Element of REAL
(1 - p1) * WH is V11() real ext-real Element of REAL
p1 * WH is V11() real ext-real Element of REAL
((1 - p1) * WH) + (p1 * WH) is V11() real ext-real Element of REAL
EX is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
C - EX is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
- EX is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
- EX is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
EX (#) compreal is Relation-like Function-like V35() complex-yielding V174() V175() set
K38(1) * EX is Relation-like Function-like set
EX (#) (K38(1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
K258((TOP-REAL C),C,(- EX)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) . (C,(- EX)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[C,(- EX)] is non empty set
{C,(- EX)} is non empty functional V35() V39() set
{{C,(- EX)},{C}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [C,(- EX)] is set
C + (- EX) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (C,(- EX)) is set
C - EX is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
diffreal .: (C,EX) is set
K324(EX) is Relation-like Function-like complex-yielding set
K295(C,K324(EX)) is Relation-like Function-like set
|.(C - EX).| is V11() real ext-real non negative Element of REAL
sqr (C - EX) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(C - EX) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((C - EX),(C - EX)) is Relation-like Function-like set
multreal .: ((C - EX),(C - EX)) is set
K383((sqr (C - EX))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (C - EX)),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (C - EX))) is V11() real ext-real Element of REAL
0 + p1 is V11() real ext-real Element of REAL
abs p1 is V11() real ext-real Element of REAL
(abs p1) * WH is V11() real ext-real Element of REAL
(abs p1) * |.(C - EX2).| is V11() real ext-real Element of REAL
(abs (1 - p1)) * WH is V11() real ext-real Element of REAL
(1 - p1) * WH is V11() real ext-real Element of REAL
p1 * WH is V11() real ext-real Element of REAL
((1 - p1) * WH) + (p1 * WH) is V11() real ext-real Element of REAL
EX is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
C - EX is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
- EX is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
- EX is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
EX (#) compreal is Relation-like Function-like V35() complex-yielding V174() V175() set
K38(1) * EX is Relation-like Function-like set
EX (#) (K38(1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
K258((TOP-REAL C),C,(- EX)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) . (C,(- EX)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[C,(- EX)] is non empty set
{C,(- EX)} is non empty functional V35() V39() set
{{C,(- EX)},{C}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [C,(- EX)] is set
C + (- EX) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (C,(- EX)) is set
C - EX is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
diffreal .: (C,EX) is set
K324(EX) is Relation-like Function-like complex-yielding set
K295(C,K324(EX)) is Relation-like Function-like set
|.(C - EX).| is V11() real ext-real non negative Element of REAL
sqr (C - EX) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(C - EX) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((C - EX),(C - EX)) is Relation-like Function-like set
multreal .: ((C - EX),(C - EX)) is set
K383((sqr (C - EX))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (C - EX)),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (C - EX))) is V11() real ext-real Element of REAL
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
Euclid C is non empty strict Reflexive discerning symmetric triangle Discerning MetrStruct
REAL C is non empty functional FinSequence-membered FinSequenceSet of REAL
C -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = C } is set
Pitag_dist C is non empty Relation-like [:(REAL C),(REAL C):] -defined REAL -valued Function-like total V30([:(REAL C),(REAL C):], REAL ) complex-yielding V174() V175() Element of bool [:[:(REAL C),(REAL C):],REAL:]
[:(REAL C),(REAL C):] is non empty set
[:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() set
MetrStruct(# (REAL C),(Pitag_dist C) #) is strict MetrStruct
the carrier of (Euclid C) is non empty set
[: the carrier of I[01], the carrier of (TOP-REAL C):] is non empty set
bool [: the carrier of I[01], the carrier of (TOP-REAL C):] is non empty set
p is V11() real ext-real Element of REAL
WH is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
p12 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
C is Element of the carrier of (Euclid C)
Ball (C,p) is bounded Element of bool the carrier of (Euclid C)
bool the carrier of (Euclid C) is non empty set
bool the carrier of (TOP-REAL C) is non empty set
r is Element of bool the carrier of (TOP-REAL C)
LSeg (WH,p12) is non empty closed connected compact bounded convex Element of bool the carrier of (TOP-REAL C)
{ (((1 - b1) * WH) + (b1 * p12)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
EX2 is Element of bool the carrier of (TOP-REAL C)
(TOP-REAL C) | EX2 is strict TopSpace-like SubSpace of TOP-REAL C
the carrier of ((TOP-REAL C) | EX2) is set
[: the carrier of I[01], the carrier of ((TOP-REAL C) | EX2):] is set
bool [: the carrier of I[01], the carrier of ((TOP-REAL C) | EX2):] is non empty set
EX1 is Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL C) | EX2) -valued Function-like V30( the carrier of I[01], the carrier of ((TOP-REAL C) | EX2)) Element of bool [: the carrier of I[01], the carrier of ((TOP-REAL C) | EX2):]
EX1 . 0 is set
EX1 . 1 is set
p1 is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL C) -valued Function-like total V30( the carrier of I[01], the carrier of (TOP-REAL C)) Element of bool [: the carrier of I[01], the carrier of (TOP-REAL C):]
p1 . 0 is set
p1 . 1 is set
rng p1 is Element of bool the carrier of (TOP-REAL C)
rng EX1 is Element of bool the carrier of ((TOP-REAL C) | EX2)
bool the carrier of ((TOP-REAL C) | EX2) is non empty set
[#] ((TOP-REAL C) | EX2) is non proper open closed dense Element of bool the carrier of ((TOP-REAL C) | EX2)
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
Euclid C is non empty strict Reflexive discerning symmetric triangle Discerning MetrStruct
REAL C is non empty functional FinSequence-membered FinSequenceSet of REAL
C -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = C } is set
Pitag_dist C is non empty Relation-like [:(REAL C),(REAL C):] -defined REAL -valued Function-like total V30([:(REAL C),(REAL C):], REAL ) complex-yielding V174() V175() Element of bool [:[:(REAL C),(REAL C):],REAL:]
[:(REAL C),(REAL C):] is non empty set
[:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() set
MetrStruct(# (REAL C),(Pitag_dist C) #) is strict MetrStruct
the carrier of (Euclid C) is non empty set
[: the carrier of I[01], the carrier of (TOP-REAL C):] is non empty set
bool [: the carrier of I[01], the carrier of (TOP-REAL C):] is non empty set
p is V11() real ext-real Element of REAL
WH is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
p12 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
r is Element of the carrier of (Euclid C)
Ball (r,p) is bounded Element of bool the carrier of (Euclid C)
bool the carrier of (Euclid C) is non empty set
EX2 is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL C) -valued Function-like total V30( the carrier of I[01], the carrier of (TOP-REAL C)) Element of bool [: the carrier of I[01], the carrier of (TOP-REAL C):]
EX2 . 0 is set
EX2 . 1 is set
rng EX2 is Element of bool the carrier of (TOP-REAL C)
bool the carrier of (TOP-REAL C) is non empty set
(rng EX2) \/ (Ball (r,p)) is set
LSeg (p12,C) is non empty closed connected compact bounded convex Element of bool the carrier of (TOP-REAL C)
{ (((1 - b1) * p12) + (b1 * C)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
(TOP-REAL C) | (LSeg (p12,C)) is non empty strict TopSpace-like SubSpace of TOP-REAL C
the carrier of ((TOP-REAL C) | (LSeg (p12,C))) is non empty set
[: the carrier of I[01], the carrier of ((TOP-REAL C) | (LSeg (p12,C))):] is non empty set
bool [: the carrier of I[01], the carrier of ((TOP-REAL C) | (LSeg (p12,C))):] is non empty set
EX1 is non empty Relation-like the carrier of I[01] -defined the carrier of ((TOP-REAL C) | (LSeg (p12,C))) -valued Function-like total V30( the carrier of I[01], the carrier of ((TOP-REAL C) | (LSeg (p12,C)))) Element of bool [: the carrier of I[01], the carrier of ((TOP-REAL C) | (LSeg (p12,C))):]
EX1 . 0 is set
EX1 . 1 is set
rng EX1 is Element of bool the carrier of ((TOP-REAL C) | (LSeg (p12,C)))
bool the carrier of ((TOP-REAL C) | (LSeg (p12,C))) is non empty set
[#] ((TOP-REAL C) | (LSeg (p12,C))) is non empty non proper open closed dense non boundary Element of bool the carrier of ((TOP-REAL C) | (LSeg (p12,C)))
p1 is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL C) -valued Function-like total V30( the carrier of I[01], the carrier of (TOP-REAL C)) Element of bool [: the carrier of I[01], the carrier of (TOP-REAL C):]
rng p1 is Element of bool the carrier of (TOP-REAL C)
(rng EX2) \/ (rng p1) is Element of bool the carrier of (TOP-REAL C)
EX is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL C) -valued Function-like total V30( the carrier of I[01], the carrier of (TOP-REAL C)) Element of bool [: the carrier of I[01], the carrier of (TOP-REAL C):]
EX . 0 is set
EX . 1 is set
rng EX is Element of bool the carrier of (TOP-REAL C)
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
Euclid C is non empty strict Reflexive discerning symmetric triangle Discerning MetrStruct
REAL C is non empty functional FinSequence-membered FinSequenceSet of REAL
C -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = C } is set
Pitag_dist C is non empty Relation-like [:(REAL C),(REAL C):] -defined REAL -valued Function-like total V30([:(REAL C),(REAL C):], REAL ) complex-yielding V174() V175() Element of bool [:[:(REAL C),(REAL C):],REAL:]
[:(REAL C),(REAL C):] is non empty set
[:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() set
MetrStruct(# (REAL C),(Pitag_dist C) #) is strict MetrStruct
the carrier of (Euclid C) is non empty set
bool the carrier of (TOP-REAL C) is non empty set
[: the carrier of I[01], the carrier of (TOP-REAL C):] is non empty set
bool [: the carrier of I[01], the carrier of (TOP-REAL C):] is non empty set
p is V11() real ext-real Element of REAL
WH is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
p12 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
r is Element of the carrier of (Euclid C)
Ball (r,p) is bounded Element of bool the carrier of (Euclid C)
bool the carrier of (Euclid C) is non empty set
EX2 is Element of bool the carrier of (TOP-REAL C)
EX1 is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL C) -valued Function-like total V30( the carrier of I[01], the carrier of (TOP-REAL C)) Element of bool [: the carrier of I[01], the carrier of (TOP-REAL C):]
rng EX1 is Element of bool the carrier of (TOP-REAL C)
EX1 . 0 is set
EX1 . 1 is set
(rng EX1) \/ (Ball (r,p)) is set
p1 is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL C) -valued Function-like total V30( the carrier of I[01], the carrier of (TOP-REAL C)) Element of bool [: the carrier of I[01], the carrier of (TOP-REAL C):]
p1 . 0 is set
p1 . 1 is set
rng p1 is Element of bool the carrier of (TOP-REAL C)
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
bool the carrier of (TOP-REAL C) is non empty set
[: the carrier of I[01], the carrier of (TOP-REAL C):] is non empty set
bool [: the carrier of I[01], the carrier of (TOP-REAL C):] is non empty set
p is Element of bool the carrier of (TOP-REAL C)
WH is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C) : ( not b1 = WH & b1 in p & ( for b2 being non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL C) -valued Function-like total V30( the carrier of I[01], the carrier of (TOP-REAL C)) Element of bool [: the carrier of I[01], the carrier of (TOP-REAL C):] holds
( not b2 is continuous or not rng b2 c= p or not b2 . 0 = WH or not b2 . 1 = b1 ) ) ) } is set
p12 is Element of bool the carrier of (TOP-REAL C)
the topology of (TOP-REAL C) is non empty Element of bool (bool the carrier of (TOP-REAL C))
bool (bool the carrier of (TOP-REAL C)) is non empty set
TopStruct(# the carrier of (TOP-REAL C), the topology of (TOP-REAL C) #) is non empty strict TopSpace-like TopStruct
Euclid C is non empty strict Reflexive discerning symmetric triangle Discerning MetrStruct
REAL C is non empty functional FinSequence-membered FinSequenceSet of REAL
C -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = C } is set
Pitag_dist C is non empty Relation-like [:(REAL C),(REAL C):] -defined REAL -valued Function-like total V30([:(REAL C),(REAL C):], REAL ) complex-yielding V174() V175() Element of bool [:[:(REAL C),(REAL C):],REAL:]
[:(REAL C),(REAL C):] is non empty set
[:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() set
MetrStruct(# (REAL C),(Pitag_dist C) #) is strict MetrStruct
TopSpaceMetr (Euclid C) is TopStruct
the carrier of (TopSpaceMetr (Euclid C)) is set
bool the carrier of (TopSpaceMetr (Euclid C)) is non empty set
r is set
EX2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the carrier of (Euclid C) is non empty set
EX2 is Element of the carrier of (Euclid C)
r is Element of bool the carrier of (TopSpaceMetr (Euclid C))
p1 is V11() real ext-real set
Ball (EX2,p1) is bounded Element of bool the carrier of (Euclid C)
bool the carrier of (Euclid C) is non empty set
EX is V11() real ext-real set
EX1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
t2 is V11() real ext-real Element of REAL
Ball (EX2,t2) is bounded Element of bool the carrier of (Euclid C)
Ball (EX2,EX) is bounded Element of bool the carrier of (Euclid C)
C is Element of bool the carrier of (TopSpaceMetr (Euclid C))
qt2 is set
r2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
q4 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
q4 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
r5 is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL C) -valued Function-like total V30( the carrier of I[01], the carrier of (TOP-REAL C)) Element of bool [: the carrier of I[01], the carrier of (TOP-REAL C):]
r5 . 0 is set
r5 . 1 is set
rng r5 is Element of bool the carrier of (TOP-REAL C)
r2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
q4 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
r5 is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL C) -valued Function-like total V30( the carrier of I[01], the carrier of (TOP-REAL C)) Element of bool [: the carrier of I[01], the carrier of (TOP-REAL C):]
rng r5 is Element of bool the carrier of (TOP-REAL C)
r5 . 0 is set
r5 . 1 is set
r2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
bool the carrier of (TOP-REAL C) is non empty set
[: the carrier of I[01], the carrier of (TOP-REAL C):] is non empty set
bool [: the carrier of I[01], the carrier of (TOP-REAL C):] is non empty set
p is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
WH is Element of bool the carrier of (TOP-REAL C)
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C) : ( b1 = p or ex b2 being non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL C) -valued Function-like total V30( the carrier of I[01], the carrier of (TOP-REAL C)) Element of bool [: the carrier of I[01], the carrier of (TOP-REAL C):] st
( b2 is continuous & rng b2 c= WH & b2 . 0 = p & b2 . 1 = b1 ) ) } is set
p12 is Element of bool the carrier of (TOP-REAL C)
the topology of (TOP-REAL C) is non empty Element of bool (bool the carrier of (TOP-REAL C))
bool (bool the carrier of (TOP-REAL C)) is non empty set
TopStruct(# the carrier of (TOP-REAL C), the topology of (TOP-REAL C) #) is non empty strict TopSpace-like TopStruct
Euclid C is non empty strict Reflexive discerning symmetric triangle Discerning MetrStruct
REAL C is non empty functional FinSequence-membered FinSequenceSet of REAL
C -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = C } is set
Pitag_dist C is non empty Relation-like [:(REAL C),(REAL C):] -defined REAL -valued Function-like total V30([:(REAL C),(REAL C):], REAL ) complex-yielding V174() V175() Element of bool [:[:(REAL C),(REAL C):],REAL:]
[:(REAL C),(REAL C):] is non empty set
[:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() set
MetrStruct(# (REAL C),(Pitag_dist C) #) is strict MetrStruct
TopSpaceMetr (Euclid C) is TopStruct
the carrier of (TopSpaceMetr (Euclid C)) is set
bool the carrier of (TopSpaceMetr (Euclid C)) is non empty set
the carrier of (Euclid C) is non empty set
EX2 is Element of the carrier of (Euclid C)
C is Element of bool the carrier of (TopSpaceMetr (Euclid C))
p1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
EX1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
EX is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL C) -valued Function-like total V30( the carrier of I[01], the carrier of (TOP-REAL C)) Element of bool [: the carrier of I[01], the carrier of (TOP-REAL C):]
rng EX is Element of bool the carrier of (TOP-REAL C)
EX . 0 is set
EX . 1 is set
EX is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL C) -valued Function-like total V30( the carrier of I[01], the carrier of (TOP-REAL C)) Element of bool [: the carrier of I[01], the carrier of (TOP-REAL C):]
rng EX is Element of bool the carrier of (TOP-REAL C)
EX . 0 is set
EX . 1 is set
dom EX is V183() V184() V185() Element of bool the carrier of I[01]
bool the carrier of I[01] is non empty set
EX1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
EX is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL C) -valued Function-like total V30( the carrier of I[01], the carrier of (TOP-REAL C)) Element of bool [: the carrier of I[01], the carrier of (TOP-REAL C):]
rng EX is Element of bool the carrier of (TOP-REAL C)
EX . 0 is set
EX . 1 is set
EX1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
EX1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
r is Element of bool the carrier of (TopSpaceMetr (Euclid C))
EX is V11() real ext-real set
Ball (EX2,EX) is bounded Element of bool the carrier of (Euclid C)
bool the carrier of (Euclid C) is non empty set
t2 is V11() real ext-real set
qt2 is V11() real ext-real Element of REAL
Ball (EX2,qt2) is bounded Element of bool the carrier of (Euclid C)
Ball (EX2,t2) is bounded Element of bool the carrier of (Euclid C)
r2 is set
q4 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
q4 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
r5 is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL C) -valued Function-like total V30( the carrier of I[01], the carrier of (TOP-REAL C)) Element of bool [: the carrier of I[01], the carrier of (TOP-REAL C):]
r5 . 0 is set
r5 . 1 is set
rng r5 is Element of bool the carrier of (TOP-REAL C)
r5 is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL C) -valued Function-like total V30( the carrier of I[01], the carrier of (TOP-REAL C)) Element of bool [: the carrier of I[01], the carrier of (TOP-REAL C):]
rng r5 is Element of bool the carrier of (TOP-REAL C)
r5 . 0 is set
r5 . 1 is set
r5 is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL C) -valued Function-like total V30( the carrier of I[01], the carrier of (TOP-REAL C)) Element of bool [: the carrier of I[01], the carrier of (TOP-REAL C):]
rng r5 is Element of bool the carrier of (TOP-REAL C)
r5 . 0 is set
r5 . 1 is set
q4 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
bool the carrier of (TOP-REAL C) is non empty set
[: the carrier of I[01], the carrier of (TOP-REAL C):] is non empty set
bool [: the carrier of I[01], the carrier of (TOP-REAL C):] is non empty set
p is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
WH is Element of bool the carrier of (TOP-REAL C)
p12 is Element of bool the carrier of (TOP-REAL C)
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C) : ( b1 = p or ex b2 being non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL C) -valued Function-like total V30( the carrier of I[01], the carrier of (TOP-REAL C)) Element of bool [: the carrier of I[01], the carrier of (TOP-REAL C):] st
( b2 is continuous & rng b2 c= p12 & b2 . 0 = p & b2 . 1 = b1 ) ) } is set
C is set
r is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
EX2 is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL C) -valued Function-like total V30( the carrier of I[01], the carrier of (TOP-REAL C)) Element of bool [: the carrier of I[01], the carrier of (TOP-REAL C):]
rng EX2 is Element of bool the carrier of (TOP-REAL C)
EX2 . 0 is set
EX2 . 1 is set
EX2 is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL C) -valued Function-like total V30( the carrier of I[01], the carrier of (TOP-REAL C)) Element of bool [: the carrier of I[01], the carrier of (TOP-REAL C):]
rng EX2 is Element of bool the carrier of (TOP-REAL C)
EX2 . 0 is set
EX2 . 1 is set
dom EX2 is V183() V184() V185() Element of bool the carrier of I[01]
bool the carrier of I[01] is non empty set
EX1 is Element of bool the carrier of (TOP-REAL C)
EX2 is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL C) -valued Function-like total V30( the carrier of I[01], the carrier of (TOP-REAL C)) Element of bool [: the carrier of I[01], the carrier of (TOP-REAL C):]
rng EX2 is Element of bool the carrier of (TOP-REAL C)
EX2 . 0 is set
EX2 . 1 is set
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
bool the carrier of (TOP-REAL C) is non empty set
[: the carrier of I[01], the carrier of (TOP-REAL C):] is non empty set
bool [: the carrier of I[01], the carrier of (TOP-REAL C):] is non empty set
p is Element of bool the carrier of (TOP-REAL C)
WH is Element of bool the carrier of (TOP-REAL C)
p12 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C) : ( b1 = p12 or ex b2 being non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL C) -valued Function-like total V30( the carrier of I[01], the carrier of (TOP-REAL C)) Element of bool [: the carrier of I[01], the carrier of (TOP-REAL C):] st
( b2 is continuous & rng b2 c= WH & b2 . 0 = p12 & b2 . 1 = b1 ) ) } is set
WH \ p is Element of bool the carrier of (TOP-REAL C)
(TOP-REAL C) | WH is strict TopSpace-like SubSpace of TOP-REAL C
[#] ((TOP-REAL C) | WH) is non proper open closed dense Element of bool the carrier of ((TOP-REAL C) | WH)
the carrier of ((TOP-REAL C) | WH) is set
bool the carrier of ((TOP-REAL C) | WH) is non empty set
EX2 is Element of bool the carrier of (TOP-REAL C)
EX1 is Element of bool the carrier of ((TOP-REAL C) | WH)
p1 is Element of bool the carrier of ((TOP-REAL C) | WH)
p \/ (WH \ p) is Element of bool the carrier of (TOP-REAL C)
p \/ WH is Element of bool the carrier of (TOP-REAL C)
EX is Element of bool the carrier of ((TOP-REAL C) | WH)
t2 is Element of bool the carrier of ((TOP-REAL C) | WH)
EX \/ t2 is Element of bool the carrier of ((TOP-REAL C) | WH)
qt2 is set
r2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
q4 is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL C) -valued Function-like total V30( the carrier of I[01], the carrier of (TOP-REAL C)) Element of bool [: the carrier of I[01], the carrier of (TOP-REAL C):]
rng q4 is Element of bool the carrier of (TOP-REAL C)
q4 . 0 is set
q4 . 1 is set
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C) : ( not b1 = p12 & b1 in WH & ( for b2 being non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL C) -valued Function-like total V30( the carrier of I[01], the carrier of (TOP-REAL C)) Element of bool [: the carrier of I[01], the carrier of (TOP-REAL C):] holds
( not b2 is continuous or not rng b2 c= WH or not b2 . 0 = p12 or not b2 . 1 = b1 ) ) ) } is set
r2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
q4 is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL C) -valued Function-like total V30( the carrier of I[01], the carrier of (TOP-REAL C)) Element of bool [: the carrier of I[01], the carrier of (TOP-REAL C):]
rng q4 is Element of bool the carrier of (TOP-REAL C)
q4 . 0 is set
q4 . 1 is set
r5 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
r2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the topology of (TOP-REAL C) is non empty Element of bool (bool the carrier of (TOP-REAL C))
bool (bool the carrier of (TOP-REAL C)) is non empty set
qt2 is Element of bool the carrier of (TOP-REAL C)
p /\ ([#] ((TOP-REAL C) | WH)) is Element of bool the carrier of ((TOP-REAL C) | WH)
the topology of ((TOP-REAL C) | WH) is non empty Element of bool (bool the carrier of ((TOP-REAL C) | WH))
bool (bool the carrier of ((TOP-REAL C) | WH)) is non empty set
EX2 /\ ([#] ((TOP-REAL C) | WH)) is Element of bool the carrier of ((TOP-REAL C) | WH)
C is non empty Element of bool the carrier of (TOP-REAL C)
(TOP-REAL C) | C is non empty strict TopSpace-like SubSpace of TOP-REAL C
{} ((TOP-REAL C) | WH) is empty trivial ordinal natural V11() real ext-real non positive non negative Function-like functional V35() V39() cardinal {} -element FinSequence-membered open closed boundary nowhere_dense V183() V184() V185() V186() V187() V188() V189() Element of bool the carrier of ((TOP-REAL C) | WH)
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
bool the carrier of (TOP-REAL C) is non empty set
[: the carrier of I[01], the carrier of (TOP-REAL C):] is non empty set
bool [: the carrier of I[01], the carrier of (TOP-REAL C):] is non empty set
p is Element of bool the carrier of (TOP-REAL C)
WH is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
p12 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C) : ( b1 = WH or ex b2 being non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL C) -valued Function-like total V30( the carrier of I[01], the carrier of (TOP-REAL C)) Element of bool [: the carrier of I[01], the carrier of (TOP-REAL C):] st
( b2 is continuous & rng b2 c= p & b2 . 0 = WH & b2 . 1 = b1 ) ) } is set
r is set
EX2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
EX1 is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL C) -valued Function-like total V30( the carrier of I[01], the carrier of (TOP-REAL C)) Element of bool [: the carrier of I[01], the carrier of (TOP-REAL C):]
rng EX1 is Element of bool the carrier of (TOP-REAL C)
EX1 . 0 is set
EX1 . 1 is set
r is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
EX2 is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL C) -valued Function-like total V30( the carrier of I[01], the carrier of (TOP-REAL C)) Element of bool [: the carrier of I[01], the carrier of (TOP-REAL C):]
rng EX2 is Element of bool the carrier of (TOP-REAL C)
EX2 . 0 is set
EX2 . 1 is set
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
bool the carrier of (TOP-REAL C) is non empty set
p is Element of bool the carrier of (TOP-REAL C)
p ` is Element of bool the carrier of (TOP-REAL C)
the carrier of (TOP-REAL C) \ p is set
WH is V11() real ext-real set
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C) : |.b1.| = WH } is set
the topology of (TOP-REAL C) is non empty Element of bool (bool the carrier of (TOP-REAL C))
bool (bool the carrier of (TOP-REAL C)) is non empty set
TopStruct(# the carrier of (TOP-REAL C), the topology of (TOP-REAL C) #) is non empty strict TopSpace-like TopStruct
Euclid C is non empty strict Reflexive discerning symmetric triangle Discerning MetrStruct
REAL C is non empty functional FinSequence-membered FinSequenceSet of REAL
C -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = C } is set
Pitag_dist C is non empty Relation-like [:(REAL C),(REAL C):] -defined REAL -valued Function-like total V30([:(REAL C),(REAL C):], REAL ) complex-yielding V174() V175() Element of bool [:[:(REAL C),(REAL C):],REAL:]
[:(REAL C),(REAL C):] is non empty set
[:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() set
MetrStruct(# (REAL C),(Pitag_dist C) #) is strict MetrStruct
TopSpaceMetr (Euclid C) is TopStruct
the carrier of (TopSpaceMetr (Euclid C)) is set
bool the carrier of (TopSpaceMetr (Euclid C)) is non empty set
the carrier of (Euclid C) is non empty set
C is Element of bool the carrier of (TopSpaceMetr (Euclid C))
r is Element of the carrier of (Euclid C)
EX2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.EX2.| is V11() real ext-real non negative Element of REAL
sqr EX2 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
sqrreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
EX2 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (EX2,EX2) is Relation-like Function-like set
multreal .: (EX2,EX2) is set
K383((sqr EX2)) is V11() real ext-real Element of REAL
addreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K195(REAL,(sqr EX2),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr EX2)) is V11() real ext-real Element of REAL
p12 is V11() real ext-real Element of REAL
p12 - |.EX2.| is V11() real ext-real Element of REAL
(p12 - |.EX2.|) / 2 is V11() real ext-real Element of REAL
Ball (r,((p12 - |.EX2.|) / 2)) is bounded Element of bool the carrier of (Euclid C)
bool the carrier of (Euclid C) is non empty set
p1 is set
EX is Element of the carrier of (Euclid C)
dist (r,EX) is V11() real ext-real Element of REAL
the distance of (Euclid C) is non empty Relation-like [: the carrier of (Euclid C), the carrier of (Euclid C):] -defined REAL -valued Function-like total V30([: the carrier of (Euclid C), the carrier of (Euclid C):], REAL ) complex-yielding V174() V175() Element of bool [:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:]
[: the carrier of (Euclid C), the carrier of (Euclid C):] is non empty set
[:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:] is non empty non trivial V35() set
the distance of (Euclid C) . (r,EX) is V11() real ext-real Element of REAL
[r,EX] is non empty set
{r,EX} is non empty V35() set
{r} is non empty trivial V35() 1 -element set
{{r,EX},{r}} is non empty V35() V39() set
the distance of (Euclid C) . [r,EX] is V11() real ext-real set
t2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
t2 - EX2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
- EX2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
- EX2 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
compreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
EX2 (#) compreal is Relation-like Function-like V35() complex-yielding V174() V175() set
K38(1) is V11() real ext-real non positive set
K38(1) * EX2 is Relation-like Function-like set
K38(1) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
id REAL is non empty Relation-like REAL -defined REAL -valued Function-like one-to-one total V30( REAL , REAL ) complex-yielding V174() V175() increasing V179() Element of bool [:REAL,REAL:]
multreal [;] (K38(1),(id REAL)) is set
EX2 (#) (K38(1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
K258((TOP-REAL C),t2,(- EX2)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) is non empty Relation-like [: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):] -defined the carrier of (TOP-REAL C) -valued Function-like total V30([: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C)) Element of bool [:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):]
[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):] is non empty set
[:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):] is non empty set
bool [:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):] is non empty set
the U7 of (TOP-REAL C) . (t2,(- EX2)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[t2,(- EX2)] is non empty set
{t2,(- EX2)} is non empty functional V35() V39() set
{t2} is non empty trivial functional V35() V39() 1 -element set
{{t2,(- EX2)},{t2}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [t2,(- EX2)] is set
t2 + (- EX2) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (t2,(- EX2)) is set
t2 - EX2 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
diffreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K174(REAL,addreal,(id REAL),compreal) is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
diffreal .: (t2,EX2) is set
K324(EX2) is Relation-like Function-like complex-yielding set
K295(t2,K324(EX2)) is Relation-like Function-like set
|.(t2 - EX2).| is V11() real ext-real non negative Element of REAL
sqr (t2 - EX2) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(t2 - EX2) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((t2 - EX2),(t2 - EX2)) is Relation-like Function-like set
multreal .: ((t2 - EX2),(t2 - EX2)) is set
K383((sqr (t2 - EX2))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (t2 - EX2)),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (t2 - EX2))) is V11() real ext-real Element of REAL
|.t2.| is V11() real ext-real non negative Element of REAL
sqr t2 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
t2 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (t2,t2) is Relation-like Function-like set
multreal .: (t2,t2) is set
K383((sqr t2)) is V11() real ext-real Element of REAL
K195(REAL,(sqr t2),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr t2)) is V11() real ext-real Element of REAL
|.t2.| - |.EX2.| is V11() real ext-real Element of REAL
((p12 - |.EX2.|) / 2) + ((p12 - |.EX2.|) / 2) is V11() real ext-real Element of REAL
qt2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.qt2.| is V11() real ext-real non negative Element of REAL
sqr qt2 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
qt2 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (qt2,qt2) is Relation-like Function-like set
multreal .: (qt2,qt2) is set
K383((sqr qt2)) is V11() real ext-real Element of REAL
K195(REAL,(sqr qt2),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr qt2)) is V11() real ext-real Element of REAL
((p12 - |.EX2.|) / 2) - ((p12 - |.EX2.|) / 2) is V11() real ext-real Element of REAL
|.EX2.| - p12 is V11() real ext-real Element of REAL
(|.EX2.| - p12) / 2 is V11() real ext-real Element of REAL
Ball (r,((|.EX2.| - p12) / 2)) is bounded Element of bool the carrier of (Euclid C)
bool the carrier of (Euclid C) is non empty set
p1 is set
EX is Element of the carrier of (Euclid C)
dist (r,EX) is V11() real ext-real Element of REAL
the distance of (Euclid C) is non empty Relation-like [: the carrier of (Euclid C), the carrier of (Euclid C):] -defined REAL -valued Function-like total V30([: the carrier of (Euclid C), the carrier of (Euclid C):], REAL ) complex-yielding V174() V175() Element of bool [:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:]
[: the carrier of (Euclid C), the carrier of (Euclid C):] is non empty set
[:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:] is non empty non trivial V35() set
the distance of (Euclid C) . (r,EX) is V11() real ext-real Element of REAL
[r,EX] is non empty set
{r,EX} is non empty V35() set
{r} is non empty trivial V35() 1 -element set
{{r,EX},{r}} is non empty V35() V39() set
the distance of (Euclid C) . [r,EX] is V11() real ext-real set
t2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
EX2 - t2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
- t2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
- t2 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
compreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
t2 (#) compreal is Relation-like Function-like V35() complex-yielding V174() V175() set
K38(1) is V11() real ext-real non positive set
K38(1) * t2 is Relation-like Function-like set
K38(1) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
id REAL is non empty Relation-like REAL -defined REAL -valued Function-like one-to-one total V30( REAL , REAL ) complex-yielding V174() V175() increasing V179() Element of bool [:REAL,REAL:]
multreal [;] (K38(1),(id REAL)) is set
t2 (#) (K38(1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
K258((TOP-REAL C),EX2,(- t2)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) is non empty Relation-like [: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):] -defined the carrier of (TOP-REAL C) -valued Function-like total V30([: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C)) Element of bool [:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):]
[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):] is non empty set
[:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):] is non empty set
bool [:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):] is non empty set
the U7 of (TOP-REAL C) . (EX2,(- t2)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[EX2,(- t2)] is non empty set
{EX2,(- t2)} is non empty functional V35() V39() set
{EX2} is non empty trivial functional V35() V39() 1 -element set
{{EX2,(- t2)},{EX2}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [EX2,(- t2)] is set
EX2 + (- t2) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (EX2,(- t2)) is set
EX2 - t2 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
diffreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K174(REAL,addreal,(id REAL),compreal) is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
diffreal .: (EX2,t2) is set
K324(t2) is Relation-like Function-like complex-yielding set
K295(EX2,K324(t2)) is Relation-like Function-like set
|.(EX2 - t2).| is V11() real ext-real non negative Element of REAL
sqr (EX2 - t2) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(EX2 - t2) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((EX2 - t2),(EX2 - t2)) is Relation-like Function-like set
multreal .: ((EX2 - t2),(EX2 - t2)) is set
K383((sqr (EX2 - t2))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (EX2 - t2)),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (EX2 - t2))) is V11() real ext-real Element of REAL
|.t2.| is V11() real ext-real non negative Element of REAL
sqr t2 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
t2 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (t2,t2) is Relation-like Function-like set
multreal .: (t2,t2) is set
K383((sqr t2)) is V11() real ext-real Element of REAL
K195(REAL,(sqr t2),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr t2)) is V11() real ext-real Element of REAL
|.EX2.| - |.t2.| is V11() real ext-real Element of REAL
((|.EX2.| - p12) / 2) + ((|.EX2.| - p12) / 2) is V11() real ext-real Element of REAL
qt2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.qt2.| is V11() real ext-real non negative Element of REAL
sqr qt2 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
qt2 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (qt2,qt2) is Relation-like Function-like set
multreal .: (qt2,qt2) is set
K383((sqr qt2)) is V11() real ext-real Element of REAL
K195(REAL,(sqr qt2),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr qt2)) is V11() real ext-real Element of REAL
((|.EX2.| - p12) / 2) - ((|.EX2.| - p12) / 2) is V11() real ext-real Element of REAL
EX1 is V11() real ext-real set
Ball (r,EX1) is bounded Element of bool the carrier of (Euclid C)
bool the carrier of (Euclid C) is non empty set
p1 is V11() real ext-real set
Ball (r,p1) is bounded Element of bool the carrier of (Euclid C)
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
bool the carrier of (TOP-REAL C) is non empty set
p is non empty Element of bool the carrier of (TOP-REAL C)
(TOP-REAL C) | p is non empty strict TopSpace-like SubSpace of TOP-REAL C
the topology of (TOP-REAL C) is non empty Element of bool (bool the carrier of (TOP-REAL C))
bool (bool the carrier of (TOP-REAL C)) is non empty set
TopStruct(# the carrier of (TOP-REAL C), the topology of (TOP-REAL C) #) is non empty strict TopSpace-like TopStruct
Euclid C is non empty strict Reflexive discerning symmetric triangle Discerning MetrStruct
REAL C is non empty functional FinSequence-membered FinSequenceSet of REAL
C -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = C } is set
Pitag_dist C is non empty Relation-like [:(REAL C),(REAL C):] -defined REAL -valued Function-like total V30([:(REAL C),(REAL C):], REAL ) complex-yielding V174() V175() Element of bool [:[:(REAL C),(REAL C):],REAL:]
[:(REAL C),(REAL C):] is non empty set
[:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() set
MetrStruct(# (REAL C),(Pitag_dist C) #) is strict MetrStruct
TopSpaceMetr (Euclid C) is TopStruct
the carrier of ((TOP-REAL C) | p) is non empty set
bool the carrier of ((TOP-REAL C) | p) is non empty set
WH is non empty Element of bool the carrier of ((TOP-REAL C) | p)
p12 is Element of bool the carrier of ((TOP-REAL C) | p)
((TOP-REAL C) | p) | WH is non empty strict TopSpace-like SubSpace of (TOP-REAL C) | p
the carrier of (((TOP-REAL C) | p) | WH) is non empty set
bool the carrier of (((TOP-REAL C) | p) | WH) is non empty set
C is Element of bool the carrier of (((TOP-REAL C) | p) | WH)
[#] (((TOP-REAL C) | p) | WH) is non empty non proper open closed dense non boundary Element of bool the carrier of (((TOP-REAL C) | p) | WH)
the carrier of (TopSpaceMetr (Euclid C)) is set
bool the carrier of (TopSpaceMetr (Euclid C)) is non empty set
r is Element of bool the carrier of (TOP-REAL C)
the carrier of (Euclid C) is non empty set
[#] ((TOP-REAL C) | p) is non empty non proper open closed dense non boundary Element of bool the carrier of ((TOP-REAL C) | p)
EX1 is Element of bool the carrier of (TOP-REAL C)
EX1 /\ ([#] ((TOP-REAL C) | p)) is Element of bool the carrier of ((TOP-REAL C) | p)
EX1 /\ p is Element of bool the carrier of (TOP-REAL C)
EX is Element of the carrier of (Euclid C)
p1 is Element of bool the carrier of (TopSpaceMetr (Euclid C))
t2 is V11() real ext-real set
Ball (EX,t2) is bounded Element of bool the carrier of (Euclid C)
bool the carrier of (Euclid C) is non empty set
qt2 is V11() real ext-real Element of REAL
Ball (EX,qt2) is bounded Element of bool the carrier of (Euclid C)
q4 is Element of bool the carrier of (((TOP-REAL C) | p) | WH)
r2 is Element of bool the carrier of ((TOP-REAL C) | p)
Q is Element of bool the carrier of (TOP-REAL C)
r5 is Element of bool the carrier of (((TOP-REAL C) | p) | WH)
r5 /\ p12 is Element of bool the carrier of ((TOP-REAL C) | p)
{} (((TOP-REAL C) | p) | WH) is empty trivial proper ordinal natural V11() real ext-real non positive non negative Function-like functional V35() V39() cardinal {} -element FinSequence-membered open closed boundary nowhere_dense V183() V184() V185() V186() V187() V188() V189() Element of bool the carrier of (((TOP-REAL C) | p) | WH)
P3 is Element of bool the carrier of (TOP-REAL C)
r0 is Element of bool the carrier of ((TOP-REAL C) | p)
EX2 is Element of bool the carrier of (TopSpaceMetr (Euclid C))
[#] ((TOP-REAL C) | p) is non empty non proper open closed dense non boundary Element of bool the carrier of ((TOP-REAL C) | p)
r /\ p is Element of bool the carrier of (TOP-REAL C)
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
bool the carrier of (TOP-REAL C) is non empty set
p is non empty Element of bool the carrier of (TOP-REAL C)
(TOP-REAL C) | p is non empty strict TopSpace-like SubSpace of TOP-REAL C
WH is Element of bool the carrier of (TOP-REAL C)
WH ` is Element of bool the carrier of (TOP-REAL C)
the carrier of (TOP-REAL C) \ WH is set
p12 is V11() real ext-real set
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C) : |.b1.| = p12 } is set
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
[: the carrier of (TOP-REAL C), the carrier of R^1:] is non empty complex-yielding V174() V175() set
bool [: the carrier of (TOP-REAL C), the carrier of R^1:] is non empty set
p is non empty Relation-like the carrier of (TOP-REAL C) -defined the carrier of R^1 -valued Function-like total V30( the carrier of (TOP-REAL C), the carrier of R^1) complex-yielding V174() V175() Element of bool [: the carrier of (TOP-REAL C), the carrier of R^1:]
the topology of (TOP-REAL C) is non empty Element of bool (bool the carrier of (TOP-REAL C))
bool the carrier of (TOP-REAL C) is non empty set
bool (bool the carrier of (TOP-REAL C)) is non empty set
TopStruct(# the carrier of (TOP-REAL C), the topology of (TOP-REAL C) #) is non empty strict TopSpace-like TopStruct
Euclid C is non empty strict Reflexive discerning symmetric triangle Discerning MetrStruct
REAL C is non empty functional FinSequence-membered FinSequenceSet of REAL
C -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = C } is set
Pitag_dist C is non empty Relation-like [:(REAL C),(REAL C):] -defined REAL -valued Function-like total V30([:(REAL C),(REAL C):], REAL ) complex-yielding V174() V175() Element of bool [:[:(REAL C),(REAL C):],REAL:]
[:(REAL C),(REAL C):] is non empty set
[:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() set
MetrStruct(# (REAL C),(Pitag_dist C) #) is strict MetrStruct
TopSpaceMetr (Euclid C) is TopStruct
the carrier of (TopSpaceMetr (Euclid C)) is set
the carrier of (TopSpaceMetr RealSpace) is set
[: the carrier of (TopSpaceMetr (Euclid C)), the carrier of (TopSpaceMetr RealSpace):] is set
bool [: the carrier of (TopSpaceMetr (Euclid C)), the carrier of (TopSpaceMetr RealSpace):] is non empty set
the carrier of (Euclid C) is non empty set
the carrier of RealSpace is non empty V183() V184() V185() set
p12 is V11() real ext-real set
r is V11() real ext-real Element of the carrier of RealSpace
WH is Relation-like the carrier of (TopSpaceMetr (Euclid C)) -defined the carrier of (TopSpaceMetr RealSpace) -valued Function-like V30( the carrier of (TopSpaceMetr (Euclid C)), the carrier of (TopSpaceMetr RealSpace)) Element of bool [: the carrier of (TopSpaceMetr (Euclid C)), the carrier of (TopSpaceMetr RealSpace):]
C is Element of the carrier of (Euclid C)
WH . C is set
EX1 is Element of the carrier of (Euclid C)
WH . EX1 is set
dist (C,EX1) is V11() real ext-real Element of REAL
the distance of (Euclid C) is non empty Relation-like [: the carrier of (Euclid C), the carrier of (Euclid C):] -defined REAL -valued Function-like total V30([: the carrier of (Euclid C), the carrier of (Euclid C):], REAL ) complex-yielding V174() V175() Element of bool [:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:]
[: the carrier of (Euclid C), the carrier of (Euclid C):] is non empty set
[:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:] is non empty non trivial V35() set
the distance of (Euclid C) . (C,EX1) is V11() real ext-real Element of REAL
[C,EX1] is non empty set
{C,EX1} is non empty V35() set
{C} is non empty trivial V35() 1 -element set
{{C,EX1},{C}} is non empty V35() V39() set
the distance of (Euclid C) . [C,EX1] is V11() real ext-real set
p1 is V11() real ext-real Element of the carrier of RealSpace
dist (r,p1) is V11() real ext-real Element of REAL
the distance of RealSpace is non empty Relation-like [: the carrier of RealSpace, the carrier of RealSpace:] -defined REAL -valued Function-like total V30([: the carrier of RealSpace, the carrier of RealSpace:], REAL ) complex-yielding V174() V175() Element of bool [:[: the carrier of RealSpace, the carrier of RealSpace:],REAL:]
[: the carrier of RealSpace, the carrier of RealSpace:] is non empty complex-yielding V174() V175() set
[:[: the carrier of RealSpace, the carrier of RealSpace:],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[: the carrier of RealSpace, the carrier of RealSpace:],REAL:] is non empty non trivial V35() set
the distance of RealSpace . (r,p1) is V11() real ext-real Element of REAL
[r,p1] is non empty set
{r,p1} is non empty V35() V183() V184() V185() set
{r} is non empty trivial V35() 1 -element V183() V184() V185() set
{{r,p1},{r}} is non empty V35() V39() set
the distance of RealSpace . [r,p1] is V11() real ext-real set
EX is V11() real ext-real Element of REAL
t2 is V11() real ext-real Element of REAL
EX - t2 is V11() real ext-real Element of REAL
abs (EX - t2) is V11() real ext-real Element of REAL
r2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.r2.| is V11() real ext-real non negative Element of REAL
sqr r2 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
sqrreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
r2 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (r2,r2) is Relation-like Function-like set
multreal .: (r2,r2) is set
K383((sqr r2)) is V11() real ext-real Element of REAL
addreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K195(REAL,(sqr r2),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr r2)) is V11() real ext-real Element of REAL
qt2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.qt2.| is V11() real ext-real non negative Element of REAL
sqr qt2 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
qt2 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (qt2,qt2) is Relation-like Function-like set
multreal .: (qt2,qt2) is set
K383((sqr qt2)) is V11() real ext-real Element of REAL
K195(REAL,(sqr qt2),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr qt2)) is V11() real ext-real Element of REAL
r2 - qt2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
- qt2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
- qt2 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
compreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
qt2 (#) compreal is Relation-like Function-like V35() complex-yielding V174() V175() set
K38(1) is V11() real ext-real non positive set
K38(1) * qt2 is Relation-like Function-like set
K38(1) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
id REAL is non empty Relation-like REAL -defined REAL -valued Function-like one-to-one total V30( REAL , REAL ) complex-yielding V174() V175() increasing V179() Element of bool [:REAL,REAL:]
multreal [;] (K38(1),(id REAL)) is set
qt2 (#) (K38(1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
K258((TOP-REAL C),r2,(- qt2)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) is non empty Relation-like [: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):] -defined the carrier of (TOP-REAL C) -valued Function-like total V30([: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C)) Element of bool [:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):]
[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):] is non empty set
[:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):] is non empty set
bool [:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):] is non empty set
the U7 of (TOP-REAL C) . (r2,(- qt2)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[r2,(- qt2)] is non empty set
{r2,(- qt2)} is non empty functional V35() V39() set
{r2} is non empty trivial functional V35() V39() 1 -element set
{{r2,(- qt2)},{r2}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [r2,(- qt2)] is set
r2 + (- qt2) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (r2,(- qt2)) is set
r2 - qt2 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
diffreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K174(REAL,addreal,(id REAL),compreal) is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
diffreal .: (r2,qt2) is set
K324(qt2) is Relation-like Function-like complex-yielding set
K295(r2,K324(qt2)) is Relation-like Function-like set
|.(r2 - qt2).| is V11() real ext-real non negative Element of REAL
sqr (r2 - qt2) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(r2 - qt2) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((r2 - qt2),(r2 - qt2)) is Relation-like Function-like set
multreal .: ((r2 - qt2),(r2 - qt2)) is set
K383((sqr (r2 - qt2))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (r2 - qt2)),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (r2 - qt2))) is V11() real ext-real Element of REAL
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
[: the carrier of (TOP-REAL C), the carrier of R^1:] is non empty complex-yielding V174() V175() set
bool [: the carrier of (TOP-REAL C), the carrier of R^1:] is non empty set
p is set
WH is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.WH.| is V11() real ext-real non negative Element of REAL
sqr WH is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
sqrreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
WH (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (WH,WH) is Relation-like Function-like set
multreal .: (WH,WH) is set
K383((sqr WH)) is V11() real ext-real Element of REAL
addreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K195(REAL,(sqr WH),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr WH)) is V11() real ext-real Element of REAL
p is Relation-like Function-like set
dom p is set
rng p is set
WH is set
p12 is set
p . p12 is set
C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.C.| is V11() real ext-real non negative Element of REAL
sqr C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
sqrreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
C (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (C,C) is Relation-like Function-like set
multreal .: (C,C) is set
K383((sqr C)) is V11() real ext-real Element of REAL
addreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K195(REAL,(sqr C),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr C)) is V11() real ext-real Element of REAL
p12 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
p . p12 is set
|.p12.| is V11() real ext-real non negative Element of REAL
sqr p12 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
sqrreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
p12 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (p12,p12) is Relation-like Function-like set
multreal .: (p12,p12) is set
K383((sqr p12)) is V11() real ext-real Element of REAL
addreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K195(REAL,(sqr p12),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr p12)) is V11() real ext-real Element of REAL
C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.C.| is V11() real ext-real non negative Element of REAL
sqr C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
C (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (C,C) is Relation-like Function-like set
multreal .: (C,C) is set
K383((sqr C)) is V11() real ext-real Element of REAL
K195(REAL,(sqr C),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr C)) is V11() real ext-real Element of REAL
WH is non empty Relation-like the carrier of (TOP-REAL C) -defined the carrier of R^1 -valued Function-like total V30( the carrier of (TOP-REAL C), the carrier of R^1) complex-yielding V174() V175() Element of bool [: the carrier of (TOP-REAL C), the carrier of R^1:]
[: the carrier of I[01], the carrier of R^1:] is non empty complex-yielding V174() V175() set
bool [: the carrier of I[01], the carrier of R^1:] is non empty set
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
[: the carrier of I[01], the carrier of (TOP-REAL C):] is non empty set
bool [: the carrier of I[01], the carrier of (TOP-REAL C):] is non empty set
p is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL C) -valued Function-like total V30( the carrier of I[01], the carrier of (TOP-REAL C)) Element of bool [: the carrier of I[01], the carrier of (TOP-REAL C):]
[: the carrier of (TOP-REAL C), the carrier of R^1:] is non empty complex-yielding V174() V175() set
bool [: the carrier of (TOP-REAL C), the carrier of R^1:] is non empty set
WH is non empty Relation-like the carrier of (TOP-REAL C) -defined the carrier of R^1 -valued Function-like total V30( the carrier of (TOP-REAL C), the carrier of R^1) complex-yielding V174() V175() Element of bool [: the carrier of (TOP-REAL C), the carrier of R^1:]
WH * p is non empty Relation-like the carrier of I[01] -defined the carrier of R^1 -valued Function-like total V30( the carrier of I[01], the carrier of R^1) complex-yielding V174() V175() Element of bool [: the carrier of I[01], the carrier of R^1:]
C is V11() real ext-real Element of the carrier of I[01]
(WH * p) . C is V11() real ext-real Element of REAL
p . C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.(p . C).| is V11() real ext-real non negative Element of REAL
sqr (p . C) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
sqrreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
(p . C) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((p . C),(p . C)) is Relation-like Function-like set
multreal .: ((p . C),(p . C)) is set
K383((sqr (p . C))) is V11() real ext-real Element of REAL
addreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K195(REAL,(sqr (p . C)),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (p . C))) is V11() real ext-real Element of REAL
dom p is V183() V184() V185() Element of bool the carrier of I[01]
bool the carrier of I[01] is non empty set
WH . (p . C) is V11() real ext-real Element of REAL
r is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.r.| is V11() real ext-real non negative Element of REAL
sqr r is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
r (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (r,r) is Relation-like Function-like set
multreal .: (r,r) is set
K383((sqr r)) is V11() real ext-real Element of REAL
K195(REAL,(sqr r),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr r)) is V11() real ext-real Element of REAL
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
[: the carrier of I[01], the carrier of (TOP-REAL C):] is non empty set
bool [: the carrier of I[01], the carrier of (TOP-REAL C):] is non empty set
p12 is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL C) -valued Function-like total V30( the carrier of I[01], the carrier of (TOP-REAL C)) Element of bool [: the carrier of I[01], the carrier of (TOP-REAL C):]
p12 /. 0 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.(p12 /. 0).| is V11() real ext-real non negative Element of REAL
sqr (p12 /. 0) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
sqrreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
(p12 /. 0) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((p12 /. 0),(p12 /. 0)) is Relation-like Function-like set
multreal .: ((p12 /. 0),(p12 /. 0)) is set
K383((sqr (p12 /. 0))) is V11() real ext-real Element of REAL
addreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K195(REAL,(sqr (p12 /. 0)),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (p12 /. 0))) is V11() real ext-real Element of REAL
p12 /. 1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.(p12 /. 1).| is V11() real ext-real non negative Element of REAL
sqr (p12 /. 1) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(p12 /. 1) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((p12 /. 1),(p12 /. 1)) is Relation-like Function-like set
multreal .: ((p12 /. 1),(p12 /. 1)) is set
K383((sqr (p12 /. 1))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (p12 /. 1)),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (p12 /. 1))) is V11() real ext-real Element of REAL
C is V11() real ext-real Element of REAL
r is non empty Relation-like the carrier of I[01] -defined the carrier of R^1 -valued Function-like total V30( the carrier of I[01], the carrier of R^1) complex-yielding V174() V175() Element of bool [: the carrier of I[01], the carrier of R^1:]
r . 0 is V11() real ext-real Element of REAL
WH is V11() real ext-real Element of the carrier of I[01]
p12 . WH is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.(p12 . WH).| is V11() real ext-real non negative Element of REAL
sqr (p12 . WH) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(p12 . WH) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((p12 . WH),(p12 . WH)) is Relation-like Function-like set
multreal .: ((p12 . WH),(p12 . WH)) is set
K383((sqr (p12 . WH))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (p12 . WH)),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (p12 . WH))) is V11() real ext-real Element of REAL
r . 1 is V11() real ext-real Element of REAL
p is V11() real ext-real Element of the carrier of I[01]
p12 . p is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.(p12 . p).| is V11() real ext-real non negative Element of REAL
sqr (p12 . p) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(p12 . p) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((p12 . p),(p12 . p)) is Relation-like Function-like set
multreal .: ((p12 . p),(p12 . p)) is set
K383((sqr (p12 . p))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (p12 . p)),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (p12 . p))) is V11() real ext-real Element of REAL
p1 is V11() real ext-real Element of REAL
r . p1 is V11() real ext-real Element of REAL
p12 /. p1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.(p12 /. p1).| is V11() real ext-real non negative Element of REAL
sqr (p12 /. p1) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(p12 /. p1) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((p12 /. p1),(p12 /. p1)) is Relation-like Function-like set
multreal .: ((p12 /. p1),(p12 /. p1)) is set
K383((sqr (p12 /. p1))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (p12 /. p1)),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (p12 /. p1))) is V11() real ext-real Element of REAL
EX is V11() real ext-real Element of the carrier of I[01]
p12 . EX is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.(p12 . EX).| is V11() real ext-real non negative Element of REAL
sqr (p12 . EX) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(p12 . EX) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((p12 . EX),(p12 . EX)) is Relation-like Function-like set
multreal .: ((p12 . EX),(p12 . EX)) is set
K383((sqr (p12 . EX))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (p12 . EX)),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (p12 . EX))) is V11() real ext-real Element of REAL
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
p is V11() real ext-real Element of REAL
<*p*> is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() FinSequence of REAL
abs p is V11() real ext-real Element of REAL
WH is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.WH.| is V11() real ext-real non negative Element of REAL
sqr WH is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
sqrreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
WH (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (WH,WH) is Relation-like Function-like set
multreal .: (WH,WH) is set
K383((sqr WH)) is V11() real ext-real Element of REAL
addreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K195(REAL,(sqr WH),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr WH)) is V11() real ext-real Element of REAL
p12 is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of REAL 1
len p12 is non empty ordinal natural V11() real ext-real positive non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
WH /. 1 is V11() real ext-real Element of REAL
p12 . 1 is V11() real ext-real Element of REAL
sqr p12 is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of 1 -tuples_on REAL
p12 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (p12,p12) is Relation-like Function-like set
multreal .: (p12,p12) is set
len (sqr p12) is non empty ordinal natural V11() real ext-real positive non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
(sqr p12) . 1 is V11() real ext-real Element of REAL
(WH /. 1) ^2 is V11() real ext-real Element of REAL
K37((WH /. 1),(WH /. 1)) is V11() real ext-real set
<*((WH /. 1) ^2)*> is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() FinSequence of REAL
sqrt ((WH /. 1) ^2) is V11() real ext-real Element of REAL
abs (WH /. 1) is V11() real ext-real Element of REAL
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
bool the carrier of (TOP-REAL C) is non empty set
p is Element of bool the carrier of (TOP-REAL C)
(C,p) is Element of bool the carrier of (TOP-REAL C)
{ b1 where b1 is Element of bool the carrier of (TOP-REAL C) : (C,p,b1) } is set
union { b1 where b1 is Element of bool the carrier of (TOP-REAL C) : (C,p,b1) } is set
WH is V11() real ext-real Element of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C) : |.b1.| = WH } is set
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C) : not WH <= |.b1.| } is set
p12 is set
C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.C.| is V11() real ext-real non negative Element of REAL
sqr C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
sqrreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
C (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (C,C) is Relation-like Function-like set
multreal .: (C,C) is set
K383((sqr C)) is V11() real ext-real Element of REAL
addreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K195(REAL,(sqr C),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr C)) is V11() real ext-real Element of REAL
Euclid C is non empty strict Reflexive discerning symmetric triangle Discerning MetrStruct
REAL C is non empty functional FinSequence-membered FinSequenceSet of REAL
C -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = C } is set
Pitag_dist C is non empty Relation-like [:(REAL C),(REAL C):] -defined REAL -valued Function-like total V30([:(REAL C),(REAL C):], REAL ) complex-yielding V174() V175() Element of bool [:[:(REAL C),(REAL C):],REAL:]
[:(REAL C),(REAL C):] is non empty set
[:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() set
MetrStruct(# (REAL C),(Pitag_dist C) #) is strict MetrStruct
the carrier of (Euclid C) is non empty set
bool the carrier of (Euclid C) is non empty set
p12 is Element of bool the carrier of (Euclid C)
C is Element of bool the carrier of (TOP-REAL C)
p ` is Element of bool the carrier of (TOP-REAL C)
the carrier of (TOP-REAL C) \ p is set
(TOP-REAL C) | (p `) is strict TopSpace-like SubSpace of TOP-REAL C
the carrier of ((TOP-REAL C) | (p `)) is set
r is Element of bool the carrier of (TOP-REAL C)
Down (r,(p `)) is Element of bool the carrier of ((TOP-REAL C) | (p `))
bool the carrier of ((TOP-REAL C) | (p `)) is non empty set
r /\ (p `) is Element of bool the carrier of (TOP-REAL C)
Component_of (Down (r,(p `))) is Element of bool the carrier of ((TOP-REAL C) | (p `))
EX1 is set
p1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
EX is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.EX.| is V11() real ext-real non negative Element of REAL
sqr EX is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
sqrreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
EX (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (EX,EX) is Relation-like Function-like set
multreal .: (EX,EX) is set
K383((sqr EX)) is V11() real ext-real Element of REAL
addreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K195(REAL,(sqr EX),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr EX)) is V11() real ext-real Element of REAL
t2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.t2.| is V11() real ext-real non negative Element of REAL
sqr t2 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
t2 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (t2,t2) is Relation-like Function-like set
multreal .: (t2,t2) is set
K383((sqr t2)) is V11() real ext-real Element of REAL
K195(REAL,(sqr t2),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr t2)) is V11() real ext-real Element of REAL
(TOP-REAL C) | r is strict TopSpace-like SubSpace of TOP-REAL C
((TOP-REAL C) | (p `)) | (Down (r,(p `))) is strict TopSpace-like SubSpace of (TOP-REAL C) | (p `)
0. (TOP-REAL C) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like V62( TOP-REAL C) complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the ZeroF of (TOP-REAL C) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.(0. (TOP-REAL C)).| is V11() real ext-real non negative Element of REAL
sqr (0. (TOP-REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
sqrreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
(0. (TOP-REAL C)) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((0. (TOP-REAL C)),(0. (TOP-REAL C))) is Relation-like Function-like set
multreal .: ((0. (TOP-REAL C)),(0. (TOP-REAL C))) is set
K383((sqr (0. (TOP-REAL C)))) is V11() real ext-real Element of REAL
addreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K195(REAL,(sqr (0. (TOP-REAL C))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (0. (TOP-REAL C)))) is V11() real ext-real Element of REAL
EX1 is non empty Element of bool the carrier of (TOP-REAL C)
(TOP-REAL C) | EX1 is non empty strict TopSpace-like SubSpace of TOP-REAL C
p1 is Element of bool the carrier of (TOP-REAL C)
EX is Element of bool the carrier of (Euclid C)
qt2 is non empty Element of bool the carrier of (TOP-REAL C)
(TOP-REAL C) | qt2 is non empty strict TopSpace-like SubSpace of TOP-REAL C
r5 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.r5.| is V11() real ext-real non negative Element of REAL
sqr r5 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
r5 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (r5,r5) is Relation-like Function-like set
multreal .: (r5,r5) is set
K383((sqr r5)) is V11() real ext-real Element of REAL
K195(REAL,(sqr r5),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr r5)) is V11() real ext-real Element of REAL
t2 is Element of bool the carrier of (Euclid C)
Down (p1,(p `)) is Element of bool the carrier of ((TOP-REAL C) | (p `))
p1 /\ (p `) is Element of bool the carrier of (TOP-REAL C)
q4 is non empty TopSpace-like TopStruct
[#] ((TOP-REAL C) | (p `)) is non proper open closed dense Element of bool the carrier of ((TOP-REAL C) | (p `))
r0 is Element of bool the carrier of (TOP-REAL C)
r0 /\ ([#] ((TOP-REAL C) | (p `))) is Element of bool the carrier of ((TOP-REAL C) | (p `))
r0 /\ (p `) is Element of bool the carrier of (TOP-REAL C)
[: the carrier of I[01], the carrier of (TOP-REAL C):] is non empty set
bool [: the carrier of I[01], the carrier of (TOP-REAL C):] is non empty set
Q is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL C) -valued Function-like total V30( the carrier of I[01], the carrier of (TOP-REAL C)) Element of bool [: the carrier of I[01], the carrier of (TOP-REAL C):]
rng Q is Element of bool the carrier of (TOP-REAL C)
Q . 0 is set
Q . 1 is set
Q /. 1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.(Q /. 1).| is V11() real ext-real non negative Element of REAL
sqr (Q /. 1) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(Q /. 1) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((Q /. 1),(Q /. 1)) is Relation-like Function-like set
multreal .: ((Q /. 1),(Q /. 1)) is set
K383((sqr (Q /. 1))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (Q /. 1)),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (Q /. 1))) is V11() real ext-real Element of REAL
Q /. 0 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.(Q /. 0).| is V11() real ext-real non negative Element of REAL
sqr (Q /. 0) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(Q /. 0) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((Q /. 0),(Q /. 0)) is Relation-like Function-like set
multreal .: ((Q /. 0),(Q /. 0)) is set
K383((sqr (Q /. 0))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (Q /. 0)),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (Q /. 0))) is V11() real ext-real Element of REAL
P3 is V11() real ext-real Element of the carrier of I[01]
Q /. P3 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
Q . P3 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.(Q /. P3).| is V11() real ext-real non negative Element of REAL
sqr (Q /. P3) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(Q /. P3) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((Q /. P3),(Q /. P3)) is Relation-like Function-like set
multreal .: ((Q /. P3),(Q /. P3)) is set
K383((sqr (Q /. P3))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (Q /. P3)),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (Q /. P3))) is V11() real ext-real Element of REAL
[#] I[01] is non empty non proper open closed dense non boundary V183() V184() V185() Element of bool the carrier of I[01]
bool the carrier of I[01] is non empty set
dom Q is V183() V184() V185() Element of bool the carrier of I[01]
W3 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
p /\ (p `) is Element of bool the carrier of (TOP-REAL C)
{} the carrier of (TOP-REAL C) is empty trivial proper ordinal natural V11() real ext-real non positive non negative Function-like functional V35() V39() cardinal {} -element FinSequence-membered open closed boundary nowhere_dense V183() V184() V185() V186() V187() V188() V189() symmetric circled bounded Element of bool the carrier of (TOP-REAL C)
EX2 is Element of bool the carrier of (TOP-REAL C)
p1 is set
EX is set
t2 is set
qt2 is Element of bool the carrier of (TOP-REAL C)
q4 is Element of bool the carrier of ((TOP-REAL C) | (p `))
r2 is Element of the carrier of ((TOP-REAL C) | (p `))
p1 is non empty Element of bool the carrier of (TOP-REAL C)
(TOP-REAL C) | p1 is non empty strict TopSpace-like SubSpace of TOP-REAL C
the carrier of ((TOP-REAL C) | p1) is non empty set
q4 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.q4.| is V11() real ext-real non negative Element of REAL
sqr q4 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
q4 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (q4,q4) is Relation-like Function-like set
multreal .: (q4,q4) is set
K383((sqr q4)) is V11() real ext-real Element of REAL
K195(REAL,(sqr q4),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr q4)) is V11() real ext-real Element of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C) : not |.b1.| <= WH } is set
r5 is set
r0 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.r0.| is V11() real ext-real non negative Element of REAL
sqr r0 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
r0 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (r0,r0) is Relation-like Function-like set
multreal .: (r0,r0) is set
K383((sqr r0)) is V11() real ext-real Element of REAL
K195(REAL,(sqr r0),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr r0)) is V11() real ext-real Element of REAL
Q is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.Q.| is V11() real ext-real non negative Element of REAL
sqr Q is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
Q (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (Q,Q) is Relation-like Function-like set
multreal .: (Q,Q) is set
K383((sqr Q)) is V11() real ext-real Element of REAL
K195(REAL,(sqr Q),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr Q)) is V11() real ext-real Element of REAL
r5 is Element of bool the carrier of ((TOP-REAL C) | (p `))
Q is set
P3 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.P3.| is V11() real ext-real non negative Element of REAL
sqr P3 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
P3 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (P3,P3) is Relation-like Function-like set
multreal .: (P3,P3) is set
K383((sqr P3)) is V11() real ext-real Element of REAL
K195(REAL,(sqr P3),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr P3)) is V11() real ext-real Element of REAL
Q is Element of bool the carrier of (TOP-REAL C)
(TOP-REAL C) | Q is strict TopSpace-like SubSpace of TOP-REAL C
P3 is Element of bool the carrier of (Euclid C)
W3 is set
Q is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.Q.| is V11() real ext-real non negative Element of REAL
sqr Q is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
Q (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (Q,Q) is Relation-like Function-like set
multreal .: (Q,Q) is set
K383((sqr Q)) is V11() real ext-real Element of REAL
K195(REAL,(sqr Q),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr Q)) is V11() real ext-real Element of REAL
P2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.P2.| is V11() real ext-real non negative Element of REAL
sqr P2 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
P2 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (P2,P2) is Relation-like Function-like set
multreal .: (P2,P2) is set
K383((sqr P2)) is V11() real ext-real Element of REAL
K195(REAL,(sqr P2),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr P2)) is V11() real ext-real Element of REAL
(p `) ` is Element of bool the carrier of (TOP-REAL C)
the carrier of (TOP-REAL C) \ (p `) is set
P3 /\ ((p `) `) is Element of bool the carrier of (TOP-REAL C)
Q \ (p `) is Element of bool the carrier of (TOP-REAL C)
r0 is Element of bool the carrier of ((TOP-REAL C) | (p `))
Down (Q,(p `)) is Element of bool the carrier of ((TOP-REAL C) | (p `))
Q /\ (p `) is Element of bool the carrier of (TOP-REAL C)
Component_of r0 is Element of bool the carrier of ((TOP-REAL C) | (p `))
Up (Component_of r0) is Element of bool the carrier of (TOP-REAL C)
(C,p) is Element of bool the carrier of (TOP-REAL C)
{ b1 where b1 is Element of bool the carrier of (TOP-REAL C) : (C,p,b1) } is set
union { b1 where b1 is Element of bool the carrier of (TOP-REAL C) : (C,p,b1) } is set
((TOP-REAL C) | (p `)) | r0 is strict TopSpace-like SubSpace of (TOP-REAL C) | (p `)
(C,p) /\ (C,p) is Element of bool the carrier of (TOP-REAL C)
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C) : not |.b1.| <= WH } is set
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C) : not |.b1.| <= WH } is set
1 + 1 is non empty ordinal natural V11() real ext-real positive non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
EX is set
t2 is set
qt2 is Element of bool the carrier of (TOP-REAL C)
q4 is Element of bool the carrier of ((TOP-REAL C) | (p `))
r2 is Element of the carrier of ((TOP-REAL C) | (p `))
p1 is non empty Element of bool the carrier of (TOP-REAL C)
(TOP-REAL C) | p1 is non empty strict TopSpace-like SubSpace of TOP-REAL C
the carrier of ((TOP-REAL C) | p1) is non empty set
q4 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.q4.| is V11() real ext-real non negative Element of REAL
sqr q4 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
q4 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (q4,q4) is Relation-like Function-like set
multreal .: (q4,q4) is set
K383((sqr q4)) is V11() real ext-real Element of REAL
K195(REAL,(sqr q4),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr q4)) is V11() real ext-real Element of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C) : not |.b1.| <= WH } is set
r5 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.r5.| is V11() real ext-real non negative Element of REAL
sqr r5 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
r5 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (r5,r5) is Relation-like Function-like set
multreal .: (r5,r5) is set
K383((sqr r5)) is V11() real ext-real Element of REAL
K195(REAL,(sqr r5),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr r5)) is V11() real ext-real Element of REAL
r0 is V11() real ext-real Element of REAL
<*r0*> is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() FinSequence of REAL
abs r0 is V11() real ext-real Element of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C) : ex b2 being V11() real ext-real Element of REAL st
( b1 = <*b2*> & not b2 <= WH ) } is set
- WH is V11() real ext-real Element of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C) : ex b2 being V11() real ext-real Element of REAL st
( b1 = <*b2*> & not - WH <= b2 ) } is set
- r0 is V11() real ext-real Element of REAL
- WH is V11() real ext-real Element of REAL
- (- r0) is V11() real ext-real Element of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C) : ex b2 being V11() real ext-real Element of REAL st
( b1 = <*b2*> & not b2 <= WH ) } is set
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C) : ex b2 being V11() real ext-real Element of REAL st
( b1 = <*b2*> & not - WH <= b2 ) } is set
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C) : ex b2 being V11() real ext-real Element of REAL st
( b1 = <*b2*> & not b2 <= WH ) } is set
- WH is V11() real ext-real Element of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C) : ex b2 being V11() real ext-real Element of REAL st
( b1 = <*b2*> & not - WH <= b2 ) } is set
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C) : ex b2 being V11() real ext-real Element of REAL st
( b1 = <*b2*> & not b2 <= WH ) } is set
- WH is V11() real ext-real Element of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C) : ex b2 being V11() real ext-real Element of REAL st
( b1 = <*b2*> & not - WH <= b2 ) } is set
Q is set
P3 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
W3 is V11() real ext-real Element of REAL
<*W3*> is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() FinSequence of REAL
W3 is V11() real ext-real Element of REAL
<*W3*> is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() FinSequence of REAL
Q is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
len Q is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
P3 /. 1 is V11() real ext-real Element of REAL
Q . 1 is V11() real ext-real Element of REAL
sqr Q is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of C -tuples_on REAL
Q (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (Q,Q) is Relation-like Function-like set
multreal .: (Q,Q) is set
(sqr Q) . 1 is V11() real ext-real Element of REAL
(P3 /. 1) ^2 is V11() real ext-real Element of REAL
K37((P3 /. 1),(P3 /. 1)) is V11() real ext-real set
sqrt ((P3 /. 1) ^2) is V11() real ext-real Element of REAL
abs (P3 /. 1) is V11() real ext-real Element of REAL
abs W3 is V11() real ext-real Element of REAL
len (sqr Q) is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
<*((P3 /. 1) ^2)*> is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() FinSequence of REAL
|.P3.| is V11() real ext-real non negative Element of REAL
sqr P3 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
P3 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (P3,P3) is Relation-like Function-like set
multreal .: (P3,P3) is set
K383((sqr P3)) is V11() real ext-real Element of REAL
K195(REAL,(sqr P3),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr P3)) is V11() real ext-real Element of REAL
P2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.P2.| is V11() real ext-real non negative Element of REAL
sqr P2 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
P2 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (P2,P2) is Relation-like Function-like set
multreal .: (P2,P2) is set
K383((sqr P2)) is V11() real ext-real Element of REAL
K195(REAL,(sqr P2),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr P2)) is V11() real ext-real Element of REAL
P3 is set
W3 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
Q is V11() real ext-real Element of REAL
<*Q*> is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() FinSequence of REAL
P3 is Element of bool the carrier of (TOP-REAL C)
Q is Element of bool the carrier of ((TOP-REAL C) | (p `))
P2 is set
W2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.W2.| is V11() real ext-real non negative Element of REAL
sqr W2 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
W2 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (W2,W2) is Relation-like Function-like set
multreal .: (W2,W2) is set
K383((sqr W2)) is V11() real ext-real Element of REAL
K195(REAL,(sqr W2),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr W2)) is V11() real ext-real Element of REAL
P2 is Element of bool the carrier of (TOP-REAL C)
W3 is Element of bool the carrier of (Euclid C)
W2 is Element of bool the carrier of (Euclid C)
z is set
q is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
r is V11() real ext-real Element of REAL
<*r*> is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() FinSequence of REAL
r is V11() real ext-real Element of REAL
<*r*> is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() FinSequence of REAL
abs r is V11() real ext-real Element of REAL
xr is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
len xr is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
q /. 1 is V11() real ext-real Element of REAL
xr . 1 is V11() real ext-real Element of REAL
sqr xr is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of C -tuples_on REAL
xr (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (xr,xr) is Relation-like Function-like set
multreal .: (xr,xr) is set
(sqr xr) . 1 is V11() real ext-real Element of REAL
(q /. 1) ^2 is V11() real ext-real Element of REAL
K37((q /. 1),(q /. 1)) is V11() real ext-real set
len (sqr xr) is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
<*((q /. 1) ^2)*> is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() FinSequence of REAL
sqrt ((q /. 1) ^2) is V11() real ext-real Element of REAL
abs (q /. 1) is V11() real ext-real Element of REAL
|.q.| is V11() real ext-real non negative Element of REAL
sqr q is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
q (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (q,q) is Relation-like Function-like set
multreal .: (q,q) is set
K383((sqr q)) is V11() real ext-real Element of REAL
K195(REAL,(sqr q),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr q)) is V11() real ext-real Element of REAL
W2 /\ p is Element of bool the carrier of (TOP-REAL C)
the Element of W2 /\ p is Element of W2 /\ p
q is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.q.| is V11() real ext-real non negative Element of REAL
sqr q is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
q (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (q,q) is Relation-like Function-like set
multreal .: (q,q) is set
K383((sqr q)) is V11() real ext-real Element of REAL
K195(REAL,(sqr q),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr q)) is V11() real ext-real Element of REAL
r is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.r.| is V11() real ext-real non negative Element of REAL
sqr r is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
r (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (r,r) is Relation-like Function-like set
multreal .: (r,r) is set
K383((sqr r)) is V11() real ext-real Element of REAL
K195(REAL,(sqr r),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr r)) is V11() real ext-real Element of REAL
W3 /\ p is Element of bool the carrier of (TOP-REAL C)
(p `) ` is Element of bool the carrier of (TOP-REAL C)
the carrier of (TOP-REAL C) \ (p `) is set
W3 /\ ((p `) `) is Element of bool the carrier of (TOP-REAL C)
W3 \ (p `) is Element of bool the carrier of (Euclid C)
(TOP-REAL C) | P3 is strict TopSpace-like SubSpace of TOP-REAL C
Q is Element of bool the carrier of ((TOP-REAL C) | (p `))
((TOP-REAL C) | (p `)) | Q is strict TopSpace-like SubSpace of (TOP-REAL C) | (p `)
Component_of Q is Element of bool the carrier of ((TOP-REAL C) | (p `))
Down (P3,(p `)) is Element of bool the carrier of ((TOP-REAL C) | (p `))
P3 /\ (p `) is Element of bool the carrier of (TOP-REAL C)
Up (Component_of Q) is Element of bool the carrier of (TOP-REAL C)
(C,p) is Element of bool the carrier of (TOP-REAL C)
{ b1 where b1 is Element of bool the carrier of (TOP-REAL C) : (C,p,b1) } is set
union { b1 where b1 is Element of bool the carrier of (TOP-REAL C) : (C,p,b1) } is set
(C,p) /\ (C,p) is Element of bool the carrier of (TOP-REAL C)
Q is set
P3 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
W3 is V11() real ext-real Element of REAL
<*W3*> is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() FinSequence of REAL
W3 is V11() real ext-real Element of REAL
<*W3*> is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() FinSequence of REAL
- 0 is empty trivial ordinal natural V11() real ext-real non positive non negative Function-like functional V35() V39() cardinal {} -element FinSequence-membered V183() V184() V185() V186() V187() V188() V189() Element of REAL
Q is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
len Q is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
P3 /. 1 is V11() real ext-real Element of REAL
Q . 1 is V11() real ext-real Element of REAL
sqr Q is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of C -tuples_on REAL
Q (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (Q,Q) is Relation-like Function-like set
multreal .: (Q,Q) is set
(sqr Q) . 1 is V11() real ext-real Element of REAL
(P3 /. 1) ^2 is V11() real ext-real Element of REAL
K37((P3 /. 1),(P3 /. 1)) is V11() real ext-real set
len (sqr Q) is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
<*((P3 /. 1) ^2)*> is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() FinSequence of REAL
sqrt ((P3 /. 1) ^2) is V11() real ext-real Element of REAL
abs (P3 /. 1) is V11() real ext-real Element of REAL
abs W3 is V11() real ext-real Element of REAL
|.P3.| is V11() real ext-real non negative Element of REAL
sqr P3 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
P3 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (P3,P3) is Relation-like Function-like set
multreal .: (P3,P3) is set
K383((sqr P3)) is V11() real ext-real Element of REAL
K195(REAL,(sqr P3),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr P3)) is V11() real ext-real Element of REAL
- W3 is V11() real ext-real Element of REAL
P2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.P2.| is V11() real ext-real non negative Element of REAL
sqr P2 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
P2 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (P2,P2) is Relation-like Function-like set
multreal .: (P2,P2) is set
K383((sqr P2)) is V11() real ext-real Element of REAL
K195(REAL,(sqr P2),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr P2)) is V11() real ext-real Element of REAL
P3 is set
W3 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
Q is V11() real ext-real Element of REAL
<*Q*> is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() FinSequence of REAL
P3 is Element of bool the carrier of (TOP-REAL C)
Q is Element of bool the carrier of ((TOP-REAL C) | (p `))
P2 is set
W2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.W2.| is V11() real ext-real non negative Element of REAL
sqr W2 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
W2 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (W2,W2) is Relation-like Function-like set
multreal .: (W2,W2) is set
K383((sqr W2)) is V11() real ext-real Element of REAL
K195(REAL,(sqr W2),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr W2)) is V11() real ext-real Element of REAL
P2 is Element of bool the carrier of (TOP-REAL C)
W3 is Element of bool the carrier of (Euclid C)
W2 is Element of bool the carrier of (Euclid C)
z is set
q is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
r is V11() real ext-real Element of REAL
<*r*> is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() FinSequence of REAL
r is V11() real ext-real Element of REAL
<*r*> is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() FinSequence of REAL
- 0 is empty trivial ordinal natural V11() real ext-real non positive non negative Function-like functional V35() V39() cardinal {} -element FinSequence-membered V183() V184() V185() V186() V187() V188() V189() Element of REAL
- r is V11() real ext-real Element of REAL
- (- WH) is V11() real ext-real Element of REAL
xr is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
len xr is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
q /. 1 is V11() real ext-real Element of REAL
xr . 1 is V11() real ext-real Element of REAL
sqr xr is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of C -tuples_on REAL
xr (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (xr,xr) is Relation-like Function-like set
multreal .: (xr,xr) is set
(sqr xr) . 1 is V11() real ext-real Element of REAL
(q /. 1) ^2 is V11() real ext-real Element of REAL
K37((q /. 1),(q /. 1)) is V11() real ext-real set
len (sqr xr) is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
<*((q /. 1) ^2)*> is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() FinSequence of REAL
sqrt ((q /. 1) ^2) is V11() real ext-real Element of REAL
abs (q /. 1) is V11() real ext-real Element of REAL
abs r is V11() real ext-real Element of REAL
|.q.| is V11() real ext-real non negative Element of REAL
sqr q is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
q (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (q,q) is Relation-like Function-like set
multreal .: (q,q) is set
K383((sqr q)) is V11() real ext-real Element of REAL
K195(REAL,(sqr q),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr q)) is V11() real ext-real Element of REAL
W2 /\ p is Element of bool the carrier of (TOP-REAL C)
the Element of W2 /\ p is Element of W2 /\ p
q is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.q.| is V11() real ext-real non negative Element of REAL
sqr q is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
q (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (q,q) is Relation-like Function-like set
multreal .: (q,q) is set
K383((sqr q)) is V11() real ext-real Element of REAL
K195(REAL,(sqr q),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr q)) is V11() real ext-real Element of REAL
r is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.r.| is V11() real ext-real non negative Element of REAL
sqr r is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
r (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (r,r) is Relation-like Function-like set
multreal .: (r,r) is set
K383((sqr r)) is V11() real ext-real Element of REAL
K195(REAL,(sqr r),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr r)) is V11() real ext-real Element of REAL
W3 /\ p is Element of bool the carrier of (TOP-REAL C)
(p `) ` is Element of bool the carrier of (TOP-REAL C)
the carrier of (TOP-REAL C) \ (p `) is set
W3 /\ ((p `) `) is Element of bool the carrier of (TOP-REAL C)
W3 \ (p `) is Element of bool the carrier of (Euclid C)
(TOP-REAL C) | P3 is strict TopSpace-like SubSpace of TOP-REAL C
Q is Element of bool the carrier of ((TOP-REAL C) | (p `))
((TOP-REAL C) | (p `)) | Q is strict TopSpace-like SubSpace of (TOP-REAL C) | (p `)
Component_of Q is Element of bool the carrier of ((TOP-REAL C) | (p `))
Down (P3,(p `)) is Element of bool the carrier of ((TOP-REAL C) | (p `))
P3 /\ (p `) is Element of bool the carrier of (TOP-REAL C)
Up (Component_of Q) is Element of bool the carrier of (TOP-REAL C)
(C,p) is Element of bool the carrier of (TOP-REAL C)
{ b1 where b1 is Element of bool the carrier of (TOP-REAL C) : (C,p,b1) } is set
union { b1 where b1 is Element of bool the carrier of (TOP-REAL C) : (C,p,b1) } is set
(C,p) /\ (C,p) is Element of bool the carrier of (TOP-REAL C)
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C) : not |.b1.| <= WH } is set
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C) : not |.b1.| <= WH } is set
p1 is Element of bool the carrier of (TOP-REAL C)
EX is Element of bool the carrier of (TOP-REAL C)
C is non empty compact bounded non horizontal non vertical Element of bool the carrier of (TOP-REAL 2)
SpStSeq C is non empty non trivial Relation-like NAT -defined the carrier of (TOP-REAL 2) -valued Function-like non constant V35() FinSequence-like FinSubsequence-like V262( the carrier of (TOP-REAL 2)) special unfolded s.c.c. standard rectangular clockwise_oriented FinSequence of the carrier of (TOP-REAL 2)
GoB (SpStSeq C) is Relation-like non empty-yielding NAT -defined the carrier of (TOP-REAL 2) * -valued Function-like V35() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of the carrier of (TOP-REAL 2) *
len (GoB (SpStSeq C)) is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
width (GoB (SpStSeq C)) is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
(SpStSeq C) /. 1 is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
(GoB (SpStSeq C)) * (1,2) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
(SpStSeq C) /. 2 is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
(GoB (SpStSeq C)) * (2,2) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
(SpStSeq C) /. 3 is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
(GoB (SpStSeq C)) * (2,1) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
(SpStSeq C) /. 4 is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
(GoB (SpStSeq C)) * (1,1) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
(SpStSeq C) /. 5 is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
L~ (SpStSeq C) is non empty closed compact bounded non horizontal non vertical Jordan Element of bool the carrier of (TOP-REAL 2)
N-bound (L~ (SpStSeq C)) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (SpStSeq C)) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj2 is non empty Relation-like the carrier of (TOP-REAL 2) -defined REAL -valued Function-like total V30( the carrier of (TOP-REAL 2), REAL ) complex-yielding V174() V175() Element of bool [: the carrier of (TOP-REAL 2),REAL:]
proj2 | (L~ (SpStSeq C)) is non empty Relation-like the carrier of ((TOP-REAL 2) | (L~ (SpStSeq C))) -defined REAL -valued Function-like total V30( the carrier of ((TOP-REAL 2) | (L~ (SpStSeq C))), REAL ) complex-yielding V174() V175() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ (SpStSeq C))),REAL:]
the carrier of ((TOP-REAL 2) | (L~ (SpStSeq C))) is non empty set
[: the carrier of ((TOP-REAL 2) | (L~ (SpStSeq C))),REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [: the carrier of ((TOP-REAL 2) | (L~ (SpStSeq C))),REAL:] is non empty non trivial V35() set
upper_bound (proj2 | (L~ (SpStSeq C))) is V11() real ext-real Element of REAL
(proj2 | (L~ (SpStSeq C))) .: the carrier of ((TOP-REAL 2) | (L~ (SpStSeq C))) is V183() V184() V185() Element of bool REAL
upper_bound ((proj2 | (L~ (SpStSeq C))) .: the carrier of ((TOP-REAL 2) | (L~ (SpStSeq C)))) is V11() real ext-real Element of REAL
S-bound (L~ (SpStSeq C)) is V11() real ext-real Element of REAL
lower_bound (proj2 | (L~ (SpStSeq C))) is V11() real ext-real Element of REAL
lower_bound ((proj2 | (L~ (SpStSeq C))) .: the carrier of ((TOP-REAL 2) | (L~ (SpStSeq C)))) is V11() real ext-real Element of REAL
len (SpStSeq C) is non empty ordinal natural V11() real ext-real positive non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
Seg (len (SpStSeq C)) is non empty V35() len (SpStSeq C) -element V183() V184() V185() V186() V187() V188() Element of bool NAT
dom (SpStSeq C) is non empty non trivial V35() V183() V184() V185() V186() V187() V188() Element of bool NAT
X_axis (SpStSeq C) is non empty Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
dom (X_axis (SpStSeq C)) is V35() V183() V184() V185() V186() V187() V188() Element of bool NAT
W-min (L~ (SpStSeq C)) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
W-bound (L~ (SpStSeq C)) is V11() real ext-real Element of REAL
proj1 is non empty Relation-like the carrier of (TOP-REAL 2) -defined REAL -valued Function-like total V30( the carrier of (TOP-REAL 2), REAL ) complex-yielding V174() V175() Element of bool [: the carrier of (TOP-REAL 2),REAL:]
proj1 | (L~ (SpStSeq C)) is non empty Relation-like the carrier of ((TOP-REAL 2) | (L~ (SpStSeq C))) -defined REAL -valued Function-like total V30( the carrier of ((TOP-REAL 2) | (L~ (SpStSeq C))), REAL ) complex-yielding V174() V175() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ (SpStSeq C))),REAL:]
lower_bound (proj1 | (L~ (SpStSeq C))) is V11() real ext-real Element of REAL
(proj1 | (L~ (SpStSeq C))) .: the carrier of ((TOP-REAL 2) | (L~ (SpStSeq C))) is V183() V184() V185() Element of bool REAL
lower_bound ((proj1 | (L~ (SpStSeq C))) .: the carrier of ((TOP-REAL 2) | (L~ (SpStSeq C)))) is V11() real ext-real Element of REAL
W-most (L~ (SpStSeq C)) is Element of bool the carrier of (TOP-REAL 2)
SW-corner (L~ (SpStSeq C)) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
|[(W-bound (L~ (SpStSeq C))),(S-bound (L~ (SpStSeq C)))]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
NW-corner (L~ (SpStSeq C)) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
|[(W-bound (L~ (SpStSeq C))),(N-bound (L~ (SpStSeq C)))]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner (L~ (SpStSeq C))),(NW-corner (L~ (SpStSeq C)))) is non empty closed connected compact bounded convex Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * (SW-corner (L~ (SpStSeq C)))) + (b1 * (NW-corner (L~ (SpStSeq C))))) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
(LSeg ((SW-corner (L~ (SpStSeq C))),(NW-corner (L~ (SpStSeq C))))) /\ (L~ (SpStSeq C)) is closed Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ (SpStSeq C))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (SpStSeq C))) is Relation-like the carrier of ((TOP-REAL 2) | (W-most (L~ (SpStSeq C)))) -defined REAL -valued Function-like total V30( the carrier of ((TOP-REAL 2) | (W-most (L~ (SpStSeq C)))), REAL ) complex-yielding V174() V175() Element of bool [: the carrier of ((TOP-REAL 2) | (W-most (L~ (SpStSeq C)))),REAL:]
the carrier of ((TOP-REAL 2) | (W-most (L~ (SpStSeq C)))) is set
[: the carrier of ((TOP-REAL 2) | (W-most (L~ (SpStSeq C)))),REAL:] is complex-yielding V174() V175() set
bool [: the carrier of ((TOP-REAL 2) | (W-most (L~ (SpStSeq C)))),REAL:] is non empty set
lower_bound (proj2 | (W-most (L~ (SpStSeq C)))) is V11() real ext-real Element of REAL
(proj2 | (W-most (L~ (SpStSeq C)))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ (SpStSeq C)))) is V183() V184() V185() Element of bool REAL
lower_bound ((proj2 | (W-most (L~ (SpStSeq C)))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ (SpStSeq C))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (SpStSeq C))),(lower_bound (proj2 | (W-most (L~ (SpStSeq C)))))]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
(X_axis (SpStSeq C)) . 4 is V11() real ext-real Element of REAL
((SpStSeq C) /. 4) `1 is V11() real ext-real Element of REAL
((SpStSeq C) /. 4) . 1 is V11() real ext-real Element of REAL
S-max (L~ (SpStSeq C)) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
S-most (L~ (SpStSeq C)) is Element of bool the carrier of (TOP-REAL 2)
SE-corner (L~ (SpStSeq C)) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
E-bound (L~ (SpStSeq C)) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ (SpStSeq C))) is V11() real ext-real Element of REAL
upper_bound ((proj1 | (L~ (SpStSeq C))) .: the carrier of ((TOP-REAL 2) | (L~ (SpStSeq C)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (SpStSeq C))),(S-bound (L~ (SpStSeq C)))]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner (L~ (SpStSeq C))),(SE-corner (L~ (SpStSeq C)))) is non empty closed connected compact bounded convex Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * (SW-corner (L~ (SpStSeq C)))) + (b1 * (SE-corner (L~ (SpStSeq C))))) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
(LSeg ((SW-corner (L~ (SpStSeq C))),(SE-corner (L~ (SpStSeq C))))) /\ (L~ (SpStSeq C)) is closed Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (S-most (L~ (SpStSeq C))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (S-most (L~ (SpStSeq C))) is Relation-like the carrier of ((TOP-REAL 2) | (S-most (L~ (SpStSeq C)))) -defined REAL -valued Function-like total V30( the carrier of ((TOP-REAL 2) | (S-most (L~ (SpStSeq C)))), REAL ) complex-yielding V174() V175() Element of bool [: the carrier of ((TOP-REAL 2) | (S-most (L~ (SpStSeq C)))),REAL:]
the carrier of ((TOP-REAL 2) | (S-most (L~ (SpStSeq C)))) is set
[: the carrier of ((TOP-REAL 2) | (S-most (L~ (SpStSeq C)))),REAL:] is complex-yielding V174() V175() set
bool [: the carrier of ((TOP-REAL 2) | (S-most (L~ (SpStSeq C)))),REAL:] is non empty set
upper_bound (proj1 | (S-most (L~ (SpStSeq C)))) is V11() real ext-real Element of REAL
(proj1 | (S-most (L~ (SpStSeq C)))) .: the carrier of ((TOP-REAL 2) | (S-most (L~ (SpStSeq C)))) is V183() V184() V185() Element of bool REAL
upper_bound ((proj1 | (S-most (L~ (SpStSeq C)))) .: the carrier of ((TOP-REAL 2) | (S-most (L~ (SpStSeq C))))) is V11() real ext-real Element of REAL
|[(upper_bound (proj1 | (S-most (L~ (SpStSeq C))))),(S-bound (L~ (SpStSeq C)))]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
E-min (L~ (SpStSeq C)) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
E-most (L~ (SpStSeq C)) is Element of bool the carrier of (TOP-REAL 2)
NE-corner (L~ (SpStSeq C)) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
|[(E-bound (L~ (SpStSeq C))),(N-bound (L~ (SpStSeq C)))]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner (L~ (SpStSeq C))),(NE-corner (L~ (SpStSeq C)))) is non empty closed connected compact bounded convex Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * (SE-corner (L~ (SpStSeq C)))) + (b1 * (NE-corner (L~ (SpStSeq C))))) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
(LSeg ((SE-corner (L~ (SpStSeq C))),(NE-corner (L~ (SpStSeq C))))) /\ (L~ (SpStSeq C)) is closed Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ (SpStSeq C))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (SpStSeq C))) is Relation-like the carrier of ((TOP-REAL 2) | (E-most (L~ (SpStSeq C)))) -defined REAL -valued Function-like total V30( the carrier of ((TOP-REAL 2) | (E-most (L~ (SpStSeq C)))), REAL ) complex-yielding V174() V175() Element of bool [: the carrier of ((TOP-REAL 2) | (E-most (L~ (SpStSeq C)))),REAL:]
the carrier of ((TOP-REAL 2) | (E-most (L~ (SpStSeq C)))) is set
[: the carrier of ((TOP-REAL 2) | (E-most (L~ (SpStSeq C)))),REAL:] is complex-yielding V174() V175() set
bool [: the carrier of ((TOP-REAL 2) | (E-most (L~ (SpStSeq C)))),REAL:] is non empty set
lower_bound (proj2 | (E-most (L~ (SpStSeq C)))) is V11() real ext-real Element of REAL
(proj2 | (E-most (L~ (SpStSeq C)))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ (SpStSeq C)))) is V183() V184() V185() Element of bool REAL
lower_bound ((proj2 | (E-most (L~ (SpStSeq C)))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ (SpStSeq C))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (SpStSeq C))),(lower_bound (proj2 | (E-most (L~ (SpStSeq C)))))]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
(X_axis (SpStSeq C)) . 3 is V11() real ext-real Element of REAL
((SpStSeq C) /. 3) `1 is V11() real ext-real Element of REAL
((SpStSeq C) /. 3) . 1 is V11() real ext-real Element of REAL
1 + 1 is non empty ordinal natural V11() real ext-real positive non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
(SpStSeq C) /. (1 + 1) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
N-max (L~ (SpStSeq C)) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
N-most (L~ (SpStSeq C)) is Element of bool the carrier of (TOP-REAL 2)
LSeg ((NW-corner (L~ (SpStSeq C))),(NE-corner (L~ (SpStSeq C)))) is non empty closed closed connected compact compact bounded horizontal convex Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * (NW-corner (L~ (SpStSeq C)))) + (b1 * (NE-corner (L~ (SpStSeq C))))) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
(LSeg ((NW-corner (L~ (SpStSeq C))),(NE-corner (L~ (SpStSeq C))))) /\ (L~ (SpStSeq C)) is closed Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (N-most (L~ (SpStSeq C))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most (L~ (SpStSeq C))) is Relation-like the carrier of ((TOP-REAL 2) | (N-most (L~ (SpStSeq C)))) -defined REAL -valued Function-like total V30( the carrier of ((TOP-REAL 2) | (N-most (L~ (SpStSeq C)))), REAL ) complex-yielding V174() V175() Element of bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ (SpStSeq C)))),REAL:]
the carrier of ((TOP-REAL 2) | (N-most (L~ (SpStSeq C)))) is set
[: the carrier of ((TOP-REAL 2) | (N-most (L~ (SpStSeq C)))),REAL:] is complex-yielding V174() V175() set
bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ (SpStSeq C)))),REAL:] is non empty set
upper_bound (proj1 | (N-most (L~ (SpStSeq C)))) is V11() real ext-real Element of REAL
(proj1 | (N-most (L~ (SpStSeq C)))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ (SpStSeq C)))) is V183() V184() V185() Element of bool REAL
upper_bound ((proj1 | (N-most (L~ (SpStSeq C)))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ (SpStSeq C))))) is V11() real ext-real Element of REAL
|[(upper_bound (proj1 | (N-most (L~ (SpStSeq C))))),(N-bound (L~ (SpStSeq C)))]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
Y_axis (SpStSeq C) is non empty Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
dom (Y_axis (SpStSeq C)) is V35() V183() V184() V185() V186() V187() V188() Element of bool NAT
(Y_axis (SpStSeq C)) . 3 is V11() real ext-real Element of REAL
((SpStSeq C) /. 3) `2 is V11() real ext-real Element of REAL
((SpStSeq C) /. 3) . 2 is V11() real ext-real Element of REAL
N-min (L~ (SpStSeq C)) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
lower_bound (proj1 | (N-most (L~ (SpStSeq C)))) is V11() real ext-real Element of REAL
lower_bound ((proj1 | (N-most (L~ (SpStSeq C)))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ (SpStSeq C))))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (N-most (L~ (SpStSeq C))))),(N-bound (L~ (SpStSeq C)))]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
(Y_axis (SpStSeq C)) . 1 is V11() real ext-real Element of REAL
((SpStSeq C) /. 1) `2 is V11() real ext-real Element of REAL
((SpStSeq C) /. 1) . 2 is V11() real ext-real Element of REAL
S-min (L~ (SpStSeq C)) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
lower_bound (proj1 | (S-most (L~ (SpStSeq C)))) is V11() real ext-real Element of REAL
lower_bound ((proj1 | (S-most (L~ (SpStSeq C)))) .: the carrier of ((TOP-REAL 2) | (S-most (L~ (SpStSeq C))))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (S-most (L~ (SpStSeq C))))),(S-bound (L~ (SpStSeq C)))]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
E-max (L~ (SpStSeq C)) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
upper_bound (proj2 | (E-most (L~ (SpStSeq C)))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (E-most (L~ (SpStSeq C)))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ (SpStSeq C))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (SpStSeq C))),(upper_bound (proj2 | (E-most (L~ (SpStSeq C)))))]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
(X_axis (SpStSeq C)) . 2 is V11() real ext-real Element of REAL
((SpStSeq C) /. 2) `1 is V11() real ext-real Element of REAL
((SpStSeq C) /. 2) . 1 is V11() real ext-real Element of REAL
(Y_axis (SpStSeq C)) . 4 is V11() real ext-real Element of REAL
((SpStSeq C) /. 4) `2 is V11() real ext-real Element of REAL
((SpStSeq C) /. 4) . 2 is V11() real ext-real Element of REAL
(Y_axis (SpStSeq C)) . 2 is V11() real ext-real Element of REAL
((SpStSeq C) /. 2) `2 is V11() real ext-real Element of REAL
((SpStSeq C) /. 2) . 2 is V11() real ext-real Element of REAL
{(S-bound (L~ (SpStSeq C))),(N-bound (L~ (SpStSeq C)))} is non empty V35() V183() V184() V185() Element of bool REAL
rng (Y_axis (SpStSeq C)) is V35() V183() V184() V185() Element of bool REAL
WH is set
W-max (L~ (SpStSeq C)) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
upper_bound (proj2 | (W-most (L~ (SpStSeq C)))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (W-most (L~ (SpStSeq C)))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ (SpStSeq C))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (SpStSeq C))),(upper_bound (proj2 | (W-most (L~ (SpStSeq C)))))]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
(X_axis (SpStSeq C)) . 1 is V11() real ext-real Element of REAL
((SpStSeq C) /. 1) `1 is V11() real ext-real Element of REAL
((SpStSeq C) /. 1) . 1 is V11() real ext-real Element of REAL
{(W-bound (L~ (SpStSeq C))),(E-bound (L~ (SpStSeq C)))} is non empty V35() V183() V184() V185() Element of bool REAL
rng (X_axis (SpStSeq C)) is V35() V183() V184() V185() Element of bool REAL
WH is set
Incr (X_axis (SpStSeq C)) is non empty Relation-like NAT -defined REAL -valued Function-like one-to-one V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V179() FinSequence of REAL
Incr (Y_axis (SpStSeq C)) is non empty Relation-like NAT -defined REAL -valued Function-like one-to-one V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V179() FinSequence of REAL
GoB ((Incr (X_axis (SpStSeq C))),(Incr (Y_axis (SpStSeq C)))) is Relation-like non empty-yielding NAT -defined the carrier of (TOP-REAL 2) * -valued Function-like V35() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of the carrier of (TOP-REAL 2) *
(X_axis (SpStSeq C)) . 5 is V11() real ext-real Element of REAL
((SpStSeq C) /. 5) `1 is V11() real ext-real Element of REAL
((SpStSeq C) /. 5) . 1 is V11() real ext-real Element of REAL
WH is set
p12 is set
(X_axis (SpStSeq C)) . p12 is V11() real ext-real Element of REAL
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
1 + 2 is non empty ordinal natural V11() real ext-real positive non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
1 + 3 is non empty ordinal natural V11() real ext-real positive non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
1 + 4 is non empty ordinal natural V11() real ext-real positive non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
rng (Incr (X_axis (SpStSeq C))) is V35() V183() V184() V185() Element of bool REAL
(Y_axis (SpStSeq C)) . 5 is V11() real ext-real Element of REAL
((SpStSeq C) /. 5) `2 is V11() real ext-real Element of REAL
((SpStSeq C) /. 5) . 2 is V11() real ext-real Element of REAL
WH is set
p12 is set
(Y_axis (SpStSeq C)) . p12 is V11() real ext-real Element of REAL
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
1 + 2 is non empty ordinal natural V11() real ext-real positive non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
1 + 3 is non empty ordinal natural V11() real ext-real positive non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
1 + 4 is non empty ordinal natural V11() real ext-real positive non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
card (rng (Y_axis (SpStSeq C))) is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of omega
len (Incr (Y_axis (SpStSeq C))) is non empty ordinal natural V11() real ext-real positive non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
card (rng (X_axis (SpStSeq C))) is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of omega
len (Incr (X_axis (SpStSeq C))) is non empty ordinal natural V11() real ext-real positive non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
Seg (len (GoB (SpStSeq C))) is V35() len (GoB (SpStSeq C)) -element V183() V184() V185() V186() V187() V188() Element of bool NAT
rng (GoB (SpStSeq C)) is functional V35() FinSequence-membered Element of bool ( the carrier of (TOP-REAL 2) *)
bool ( the carrier of (TOP-REAL 2) *) is non empty set
len (GoB ((Incr (X_axis (SpStSeq C))),(Incr (Y_axis (SpStSeq C))))) is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
rng (GoB ((Incr (X_axis (SpStSeq C))),(Incr (Y_axis (SpStSeq C))))) is functional V35() FinSequence-membered Element of bool ( the carrier of (TOP-REAL 2) *)
width (GoB ((Incr (X_axis (SpStSeq C))),(Incr (Y_axis (SpStSeq C))))) is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
WH is Relation-like NAT -defined Function-like V35() FinSequence-like FinSubsequence-like set
len WH is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
p12 is Relation-like NAT -defined the carrier of (TOP-REAL 2) -valued Function-like V35() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len p12 is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
C is ordinal natural V11() real ext-real non negative V35() cardinal set
r is Relation-like NAT -defined Function-like V35() FinSequence-like FinSubsequence-like set
len r is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
EX2 is Relation-like NAT -defined Function-like V35() FinSequence-like FinSubsequence-like set
len EX2 is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
Seg (width (GoB (SpStSeq C))) is V35() width (GoB (SpStSeq C)) -element V183() V184() V185() V186() V187() V188() Element of bool NAT
[1,1] is non empty Element of [:NAT,NAT:]
{1,1} is non empty V35() V39() V183() V184() V185() V186() V187() V188() set
{1} is non empty trivial V35() V39() 1 -element V183() V184() V185() V186() V187() V188() set
{{1,1},{1}} is non empty V35() V39() set
[:(Seg (len (GoB (SpStSeq C)))),(Seg (width (GoB (SpStSeq C)))):] is INT -valued RAT -valued V35() complex-yielding V174() V175() V176() set
Indices (GoB (SpStSeq C)) is set
[1,(width (GoB (SpStSeq C)))] is non empty Element of [:NAT,NAT:]
{1,(width (GoB (SpStSeq C)))} is non empty V35() V39() V183() V184() V185() V186() V187() V188() set
{{1,(width (GoB (SpStSeq C)))},{1}} is non empty V35() V39() set
[(len (GoB (SpStSeq C))),1] is non empty Element of [:NAT,NAT:]
{(len (GoB (SpStSeq C))),1} is non empty V35() V39() V183() V184() V185() V186() V187() V188() set
{(len (GoB (SpStSeq C)))} is non empty trivial V35() V39() 1 -element V183() V184() V185() V186() V187() V188() set
{{(len (GoB (SpStSeq C))),1},{(len (GoB (SpStSeq C)))}} is non empty V35() V39() set
(S-max (L~ (SpStSeq C))) `1 is V11() real ext-real Element of REAL
(S-max (L~ (SpStSeq C))) . 1 is V11() real ext-real Element of REAL
SE-corner C is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
E-bound C is V11() real ext-real Element of REAL
(TOP-REAL 2) | C is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | C is non empty Relation-like the carrier of ((TOP-REAL 2) | C) -defined REAL -valued Function-like total V30( the carrier of ((TOP-REAL 2) | C), REAL ) complex-yielding V174() V175() 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 non empty non trivial V35() complex-yielding V174() V175() set
bool [: the carrier of ((TOP-REAL 2) | C),REAL:] is non empty non trivial V35() set
upper_bound (proj1 | C) is V11() real ext-real Element of REAL
(proj1 | C) .: the carrier of ((TOP-REAL 2) | C) is V183() V184() V185() Element of bool REAL
upper_bound ((proj1 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
S-bound C is V11() real ext-real Element of REAL
proj2 | C is non empty Relation-like the carrier of ((TOP-REAL 2) | C) -defined REAL -valued Function-like total V30( the carrier of ((TOP-REAL 2) | C), REAL ) complex-yielding V174() V175() Element of bool [: the carrier of ((TOP-REAL 2) | C),REAL:]
lower_bound (proj2 | C) is V11() real ext-real Element of REAL
(proj2 | C) .: the carrier of ((TOP-REAL 2) | C) is V183() V184() V185() Element of bool REAL
lower_bound ((proj2 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
|[(E-bound C),(S-bound C)]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
(SE-corner C) `1 is V11() real ext-real Element of REAL
(SE-corner C) . 1 is V11() real ext-real Element of REAL
(Incr (X_axis (SpStSeq C))) . 2 is V11() real ext-real Element of REAL
(Incr (Y_axis (SpStSeq C))) . 1 is V11() real ext-real Element of REAL
|[((Incr (X_axis (SpStSeq C))) . 2),((Incr (Y_axis (SpStSeq C))) . 1)]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
|[((Incr (X_axis (SpStSeq C))) . 2),((Incr (Y_axis (SpStSeq C))) . 1)]| `1 is V11() real ext-real Element of REAL
|[((Incr (X_axis (SpStSeq C))) . 2),((Incr (Y_axis (SpStSeq C))) . 1)]| . 1 is V11() real ext-real Element of REAL
(GoB (SpStSeq C)) * ((len (GoB (SpStSeq C))),1) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
((GoB (SpStSeq C)) * ((len (GoB (SpStSeq C))),1)) `1 is V11() real ext-real Element of REAL
((GoB (SpStSeq C)) * ((len (GoB (SpStSeq C))),1)) . 1 is V11() real ext-real Element of REAL
(S-min (L~ (SpStSeq C))) `1 is V11() real ext-real Element of REAL
(S-min (L~ (SpStSeq C))) . 1 is V11() real ext-real Element of REAL
SW-corner C is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
W-bound C is V11() real ext-real Element of REAL
lower_bound (proj1 | C) is V11() real ext-real Element of REAL
lower_bound ((proj1 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
|[(W-bound C),(S-bound C)]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
(SW-corner C) `1 is V11() real ext-real Element of REAL
(SW-corner C) . 1 is V11() real ext-real Element of REAL
(Incr (X_axis (SpStSeq C))) . 1 is V11() real ext-real Element of REAL
|[((Incr (X_axis (SpStSeq C))) . 1),((Incr (Y_axis (SpStSeq C))) . 1)]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
|[((Incr (X_axis (SpStSeq C))) . 1),((Incr (Y_axis (SpStSeq C))) . 1)]| `1 is V11() real ext-real Element of REAL
|[((Incr (X_axis (SpStSeq C))) . 1),((Incr (Y_axis (SpStSeq C))) . 1)]| . 1 is V11() real ext-real Element of REAL
((GoB (SpStSeq C)) * (1,1)) `1 is V11() real ext-real Element of REAL
((GoB (SpStSeq C)) * (1,1)) . 1 is V11() real ext-real Element of REAL
[(len (GoB (SpStSeq C))),(width (GoB (SpStSeq C)))] is non empty Element of [:NAT,NAT:]
{(len (GoB (SpStSeq C))),(width (GoB (SpStSeq C)))} is non empty V35() V39() V183() V184() V185() V186() V187() V188() set
{{(len (GoB (SpStSeq C))),(width (GoB (SpStSeq C)))},{(len (GoB (SpStSeq C)))}} is non empty V35() V39() set
(W-max (L~ (SpStSeq C))) `1 is V11() real ext-real Element of REAL
(W-max (L~ (SpStSeq C))) . 1 is V11() real ext-real Element of REAL
(Incr (Y_axis (SpStSeq C))) . (1 + 1) is V11() real ext-real Element of REAL
|[((Incr (X_axis (SpStSeq C))) . 1),((Incr (Y_axis (SpStSeq C))) . (1 + 1))]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
|[((Incr (X_axis (SpStSeq C))) . 1),((Incr (Y_axis (SpStSeq C))) . (1 + 1))]| `1 is V11() real ext-real Element of REAL
|[((Incr (X_axis (SpStSeq C))) . 1),((Incr (Y_axis (SpStSeq C))) . (1 + 1))]| . 1 is V11() real ext-real Element of REAL
(GoB (SpStSeq C)) * (1,(width (GoB (SpStSeq C)))) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
((GoB (SpStSeq C)) * (1,(width (GoB (SpStSeq C))))) `1 is V11() real ext-real Element of REAL
((GoB (SpStSeq C)) * (1,(width (GoB (SpStSeq C))))) . 1 is V11() real ext-real Element of REAL
|[(((SpStSeq C) /. 3) `1),(((SpStSeq C) /. 3) `2)]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
|[(((SpStSeq C) /. 4) `1),(((SpStSeq C) /. 4) `2)]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
|[(((SpStSeq C) /. 1) `1),(((SpStSeq C) /. 1) `2)]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
((SpStSeq C) /. (1 + 1)) `1 is V11() real ext-real Element of REAL
((SpStSeq C) /. (1 + 1)) . 1 is V11() real ext-real Element of REAL
((SpStSeq C) /. (1 + 1)) `2 is V11() real ext-real Element of REAL
((SpStSeq C) /. (1 + 1)) . 2 is V11() real ext-real Element of REAL
|[(((SpStSeq C) /. (1 + 1)) `1),(((SpStSeq C) /. (1 + 1)) `2)]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
rng (Incr (Y_axis (SpStSeq C))) is V35() V183() V184() V185() Element of bool REAL
(Incr (Y_axis (SpStSeq C))) . 2 is V11() real ext-real Element of REAL
(N-min (L~ (SpStSeq C))) `2 is V11() real ext-real Element of REAL
(N-min (L~ (SpStSeq C))) . 2 is V11() real ext-real Element of REAL
|[((Incr (X_axis (SpStSeq C))) . 1),((Incr (Y_axis (SpStSeq C))) . 2)]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
|[((Incr (X_axis (SpStSeq C))) . 1),((Incr (Y_axis (SpStSeq C))) . 2)]| `2 is V11() real ext-real Element of REAL
|[((Incr (X_axis (SpStSeq C))) . 1),((Incr (Y_axis (SpStSeq C))) . 2)]| . 2 is V11() real ext-real Element of REAL
((GoB (SpStSeq C)) * (1,(width (GoB (SpStSeq C))))) `2 is V11() real ext-real Element of REAL
((GoB (SpStSeq C)) * (1,(width (GoB (SpStSeq C))))) . 2 is V11() real ext-real Element of REAL
(S-min (L~ (SpStSeq C))) `2 is V11() real ext-real Element of REAL
(S-min (L~ (SpStSeq C))) . 2 is V11() real ext-real Element of REAL
|[((Incr (X_axis (SpStSeq C))) . 1),((Incr (Y_axis (SpStSeq C))) . 1)]| `2 is V11() real ext-real Element of REAL
|[((Incr (X_axis (SpStSeq C))) . 1),((Incr (Y_axis (SpStSeq C))) . 1)]| . 2 is V11() real ext-real Element of REAL
((GoB (SpStSeq C)) * (1,1)) `2 is V11() real ext-real Element of REAL
((GoB (SpStSeq C)) * (1,1)) . 2 is V11() real ext-real Element of REAL
(N-max (L~ (SpStSeq C))) `2 is V11() real ext-real Element of REAL
(N-max (L~ (SpStSeq C))) . 2 is V11() real ext-real Element of REAL
|[((Incr (X_axis (SpStSeq C))) . 2),((Incr (Y_axis (SpStSeq C))) . 2)]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
|[((Incr (X_axis (SpStSeq C))) . 2),((Incr (Y_axis (SpStSeq C))) . 2)]| `2 is V11() real ext-real Element of REAL
|[((Incr (X_axis (SpStSeq C))) . 2),((Incr (Y_axis (SpStSeq C))) . 2)]| . 2 is V11() real ext-real Element of REAL
(GoB (SpStSeq C)) * ((len (GoB (SpStSeq C))),(width (GoB (SpStSeq C)))) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
((GoB (SpStSeq C)) * ((len (GoB (SpStSeq C))),(width (GoB (SpStSeq C))))) `2 is V11() real ext-real Element of REAL
((GoB (SpStSeq C)) * ((len (GoB (SpStSeq C))),(width (GoB (SpStSeq C))))) . 2 is V11() real ext-real Element of REAL
(S-max (L~ (SpStSeq C))) `2 is V11() real ext-real Element of REAL
(S-max (L~ (SpStSeq C))) . 2 is V11() real ext-real Element of REAL
|[((Incr (X_axis (SpStSeq C))) . 2),((Incr (Y_axis (SpStSeq C))) . 1)]| `2 is V11() real ext-real Element of REAL
|[((Incr (X_axis (SpStSeq C))) . 2),((Incr (Y_axis (SpStSeq C))) . 1)]| . 2 is V11() real ext-real Element of REAL
((GoB (SpStSeq C)) * ((len (GoB (SpStSeq C))),1)) `2 is V11() real ext-real Element of REAL
((GoB (SpStSeq C)) * ((len (GoB (SpStSeq C))),1)) . 2 is V11() real ext-real Element of REAL
(N-max (L~ (SpStSeq C))) `1 is V11() real ext-real Element of REAL
(N-max (L~ (SpStSeq C))) . 1 is V11() real ext-real Element of REAL
NE-corner C is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
N-bound C is V11() real ext-real Element of REAL
upper_bound (proj2 | C) is V11() real ext-real Element of REAL
upper_bound ((proj2 | C) .: the carrier of ((TOP-REAL 2) | C)) is V11() real ext-real Element of REAL
|[(E-bound C),(N-bound C)]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
(NE-corner C) `1 is V11() real ext-real Element of REAL
(NE-corner C) . 1 is V11() real ext-real Element of REAL
(Incr (X_axis (SpStSeq C))) . (1 + 1) is V11() real ext-real Element of REAL
|[((Incr (X_axis (SpStSeq C))) . (1 + 1)),((Incr (Y_axis (SpStSeq C))) . (1 + 1))]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
|[((Incr (X_axis (SpStSeq C))) . (1 + 1)),((Incr (Y_axis (SpStSeq C))) . (1 + 1))]| `1 is V11() real ext-real Element of REAL
|[((Incr (X_axis (SpStSeq C))) . (1 + 1)),((Incr (Y_axis (SpStSeq C))) . (1 + 1))]| . 1 is V11() real ext-real Element of REAL
((GoB (SpStSeq C)) * ((len (GoB (SpStSeq C))),(width (GoB (SpStSeq C))))) `1 is V11() real ext-real Element of REAL
((GoB (SpStSeq C)) * ((len (GoB (SpStSeq C))),(width (GoB (SpStSeq C))))) . 1 is V11() real ext-real Element of REAL
C is non empty compact bounded non horizontal non vertical Element of bool the carrier of (TOP-REAL 2)
SpStSeq C is non empty non trivial Relation-like NAT -defined the carrier of (TOP-REAL 2) -valued Function-like non constant V35() FinSequence-like FinSubsequence-like V262( the carrier of (TOP-REAL 2)) special unfolded s.c.c. standard rectangular clockwise_oriented FinSequence of the carrier of (TOP-REAL 2)
LeftComp (SpStSeq C) is non empty Element of bool the carrier of (TOP-REAL 2)
the Element of LeftComp (SpStSeq C) is Element of LeftComp (SpStSeq C)
(SpStSeq C) /. 1 is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
(SpStSeq C) /. 2 is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
((SpStSeq C) /. 1) + ((SpStSeq C) /. 2) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) is non empty Relation-like [: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):] -defined the carrier of (TOP-REAL 2) -valued Function-like total V30([: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2)) 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):] is non empty set
[:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):] is 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
the U7 of (TOP-REAL 2) . (((SpStSeq C) /. 1),((SpStSeq C) /. 2)) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
[((SpStSeq C) /. 1),((SpStSeq C) /. 2)] is non empty set
{((SpStSeq C) /. 1),((SpStSeq C) /. 2)} is non empty functional V35() V39() set
{((SpStSeq C) /. 1)} is non empty trivial functional V35() V39() 1 -element set
{{((SpStSeq C) /. 1),((SpStSeq C) /. 2)},{((SpStSeq C) /. 1)}} is non empty V35() V39() set
the U7 of (TOP-REAL 2) . [((SpStSeq C) /. 1),((SpStSeq C) /. 2)] is set
((SpStSeq C) /. 1) + ((SpStSeq C) /. 2) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
addreal .: (((SpStSeq C) /. 1),((SpStSeq C) /. 2)) is set
1 / 2 is V11() real ext-real non negative Element of REAL
(1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2)) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
(1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(1 / 2) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
id REAL is non empty Relation-like REAL -defined REAL -valued Function-like one-to-one total V30( REAL , REAL ) complex-yielding V174() V175() increasing V179() Element of bool [:REAL,REAL:]
multreal [;] ((1 / 2),(id REAL)) is set
(((SpStSeq C) /. 1) + ((SpStSeq C) /. 2)) (#) ((1 / 2) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
|.((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2))).| is V11() real ext-real non negative Element of REAL
sqr ((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
sqrreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2))) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2))),((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2)))) is Relation-like Function-like set
multreal .: (((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2))),((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2)))) is set
K383((sqr ((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2))))) is V11() real ext-real Element of REAL
K195(REAL,(sqr ((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2)))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr ((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2))))) is V11() real ext-real Element of REAL
r is non empty non trivial Relation-like NAT -defined the carrier of (TOP-REAL 2) -valued Function-like non constant V35() FinSequence-like FinSubsequence-like V262( the carrier of (TOP-REAL 2)) special unfolded s.c.c. standard FinSequence of the carrier of (TOP-REAL 2)
L~ r is non empty closed compact bounded non horizontal non vertical Element of bool the carrier of (TOP-REAL 2)
E-bound (L~ r) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ r) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is non empty Relation-like the carrier of (TOP-REAL 2) -defined REAL -valued Function-like total V30( the carrier of (TOP-REAL 2), REAL ) complex-yielding V174() V175() Element of bool [: the carrier of (TOP-REAL 2),REAL:]
proj1 | (L~ r) is non empty Relation-like the carrier of ((TOP-REAL 2) | (L~ r)) -defined REAL -valued Function-like total V30( the carrier of ((TOP-REAL 2) | (L~ r)), REAL ) complex-yielding V174() V175() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ r)),REAL:]
the carrier of ((TOP-REAL 2) | (L~ r)) is non empty set
[: the carrier of ((TOP-REAL 2) | (L~ r)),REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [: the carrier of ((TOP-REAL 2) | (L~ r)),REAL:] is non empty non trivial V35() set
upper_bound (proj1 | (L~ r)) is V11() real ext-real Element of REAL
(proj1 | (L~ r)) .: the carrier of ((TOP-REAL 2) | (L~ r)) is V183() V184() V185() Element of bool REAL
upper_bound ((proj1 | (L~ r)) .: the carrier of ((TOP-REAL 2) | (L~ r))) is V11() real ext-real Element of REAL
W-bound (L~ r) is V11() real ext-real Element of REAL
lower_bound (proj1 | (L~ r)) is V11() real ext-real Element of REAL
lower_bound ((proj1 | (L~ r)) .: the carrier of ((TOP-REAL 2) | (L~ r))) is V11() real ext-real Element of REAL
N-min (L~ r) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
N-most (L~ r) is Element of bool the carrier of (TOP-REAL 2)
NW-corner (L~ r) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
N-bound (L~ r) is V11() real ext-real Element of REAL
proj2 is non empty Relation-like the carrier of (TOP-REAL 2) -defined REAL -valued Function-like total V30( the carrier of (TOP-REAL 2), REAL ) complex-yielding V174() V175() Element of bool [: the carrier of (TOP-REAL 2),REAL:]
proj2 | (L~ r) is non empty Relation-like the carrier of ((TOP-REAL 2) | (L~ r)) -defined REAL -valued Function-like total V30( the carrier of ((TOP-REAL 2) | (L~ r)), REAL ) complex-yielding V174() V175() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ r)),REAL:]
upper_bound (proj2 | (L~ r)) is V11() real ext-real Element of REAL
(proj2 | (L~ r)) .: the carrier of ((TOP-REAL 2) | (L~ r)) is V183() V184() V185() Element of bool REAL
upper_bound ((proj2 | (L~ r)) .: the carrier of ((TOP-REAL 2) | (L~ r))) is V11() real ext-real Element of REAL
|[(W-bound (L~ r)),(N-bound (L~ r))]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
NE-corner (L~ r) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
|[(E-bound (L~ r)),(N-bound (L~ r))]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
LSeg ((NW-corner (L~ r)),(NE-corner (L~ r))) is non empty closed closed connected compact compact bounded horizontal convex Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * (NW-corner (L~ r))) + (b1 * (NE-corner (L~ r)))) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
(LSeg ((NW-corner (L~ r)),(NE-corner (L~ r)))) /\ (L~ r) is closed Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (N-most (L~ r)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most (L~ r)) is Relation-like the carrier of ((TOP-REAL 2) | (N-most (L~ r))) -defined REAL -valued Function-like total V30( the carrier of ((TOP-REAL 2) | (N-most (L~ r))), REAL ) complex-yielding V174() V175() Element of bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ r))),REAL:]
the carrier of ((TOP-REAL 2) | (N-most (L~ r))) is set
[: the carrier of ((TOP-REAL 2) | (N-most (L~ r))),REAL:] is complex-yielding V174() V175() set
bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ r))),REAL:] is non empty set
lower_bound (proj1 | (N-most (L~ r))) is V11() real ext-real Element of REAL
(proj1 | (N-most (L~ r))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ r))) is V183() V184() V185() Element of bool REAL
lower_bound ((proj1 | (N-most (L~ r))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ r)))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (N-most (L~ r)))),(N-bound (L~ r))]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
(N-min (L~ r)) `2 is V11() real ext-real Element of REAL
(N-min (L~ r)) . 2 is V11() real ext-real Element of REAL
N-max (L~ r) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
upper_bound (proj1 | (N-most (L~ r))) is V11() real ext-real Element of REAL
upper_bound ((proj1 | (N-most (L~ r))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ r)))) is V11() real ext-real Element of REAL
|[(upper_bound (proj1 | (N-most (L~ r)))),(N-bound (L~ r))]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
(N-max (L~ r)) `2 is V11() real ext-real Element of REAL
(N-max (L~ r)) . 2 is V11() real ext-real Element of REAL
((N-min (L~ r)) `2) + ((N-max (L~ r)) `2) is V11() real ext-real Element of REAL
(N-bound (L~ r)) + (N-bound (L~ r)) is V11() real ext-real Element of REAL
L~ (SpStSeq C) is non empty closed compact bounded non horizontal non vertical Jordan Element of bool the carrier of (TOP-REAL 2)
N-bound (L~ (SpStSeq C)) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (SpStSeq C)) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (L~ (SpStSeq C)) is non empty Relation-like the carrier of ((TOP-REAL 2) | (L~ (SpStSeq C))) -defined REAL -valued Function-like total V30( the carrier of ((TOP-REAL 2) | (L~ (SpStSeq C))), REAL ) complex-yielding V174() V175() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ (SpStSeq C))),REAL:]
the carrier of ((TOP-REAL 2) | (L~ (SpStSeq C))) is non empty set
[: the carrier of ((TOP-REAL 2) | (L~ (SpStSeq C))),REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [: the carrier of ((TOP-REAL 2) | (L~ (SpStSeq C))),REAL:] is non empty non trivial V35() set
upper_bound (proj2 | (L~ (SpStSeq C))) is V11() real ext-real Element of REAL
(proj2 | (L~ (SpStSeq C))) .: the carrier of ((TOP-REAL 2) | (L~ (SpStSeq C))) is V183() V184() V185() Element of bool REAL
upper_bound ((proj2 | (L~ (SpStSeq C))) .: the carrier of ((TOP-REAL 2) | (L~ (SpStSeq C)))) is V11() real ext-real Element of REAL
2 * (N-bound (L~ (SpStSeq C))) is V11() real ext-real Element of REAL
N-min (L~ (SpStSeq C)) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
N-most (L~ (SpStSeq C)) is Element of bool the carrier of (TOP-REAL 2)
NW-corner (L~ (SpStSeq C)) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
W-bound (L~ (SpStSeq C)) is V11() real ext-real Element of REAL
proj1 | (L~ (SpStSeq C)) is non empty Relation-like the carrier of ((TOP-REAL 2) | (L~ (SpStSeq C))) -defined REAL -valued Function-like total V30( the carrier of ((TOP-REAL 2) | (L~ (SpStSeq C))), REAL ) complex-yielding V174() V175() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ (SpStSeq C))),REAL:]
lower_bound (proj1 | (L~ (SpStSeq C))) is V11() real ext-real Element of REAL
(proj1 | (L~ (SpStSeq C))) .: the carrier of ((TOP-REAL 2) | (L~ (SpStSeq C))) is V183() V184() V185() Element of bool REAL
lower_bound ((proj1 | (L~ (SpStSeq C))) .: the carrier of ((TOP-REAL 2) | (L~ (SpStSeq C)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (SpStSeq C))),(N-bound (L~ (SpStSeq C)))]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
NE-corner (L~ (SpStSeq C)) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
E-bound (L~ (SpStSeq C)) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ (SpStSeq C))) is V11() real ext-real Element of REAL
upper_bound ((proj1 | (L~ (SpStSeq C))) .: the carrier of ((TOP-REAL 2) | (L~ (SpStSeq C)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (SpStSeq C))),(N-bound (L~ (SpStSeq C)))]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
LSeg ((NW-corner (L~ (SpStSeq C))),(NE-corner (L~ (SpStSeq C)))) is non empty closed closed connected compact compact bounded horizontal convex Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * (NW-corner (L~ (SpStSeq C)))) + (b1 * (NE-corner (L~ (SpStSeq C))))) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
(LSeg ((NW-corner (L~ (SpStSeq C))),(NE-corner (L~ (SpStSeq C))))) /\ (L~ (SpStSeq C)) is closed Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (N-most (L~ (SpStSeq C))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most (L~ (SpStSeq C))) is Relation-like the carrier of ((TOP-REAL 2) | (N-most (L~ (SpStSeq C)))) -defined REAL -valued Function-like total V30( the carrier of ((TOP-REAL 2) | (N-most (L~ (SpStSeq C)))), REAL ) complex-yielding V174() V175() Element of bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ (SpStSeq C)))),REAL:]
the carrier of ((TOP-REAL 2) | (N-most (L~ (SpStSeq C)))) is set
[: the carrier of ((TOP-REAL 2) | (N-most (L~ (SpStSeq C)))),REAL:] is complex-yielding V174() V175() set
bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ (SpStSeq C)))),REAL:] is non empty set
lower_bound (proj1 | (N-most (L~ (SpStSeq C)))) is V11() real ext-real Element of REAL
(proj1 | (N-most (L~ (SpStSeq C)))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ (SpStSeq C)))) is V183() V184() V185() Element of bool REAL
lower_bound ((proj1 | (N-most (L~ (SpStSeq C)))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ (SpStSeq C))))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (N-most (L~ (SpStSeq C))))),(N-bound (L~ (SpStSeq C)))]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
(N-min (L~ (SpStSeq C))) `2 is V11() real ext-real Element of REAL
(N-min (L~ (SpStSeq C))) . 2 is V11() real ext-real Element of REAL
N-max (L~ (SpStSeq C)) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
upper_bound (proj1 | (N-most (L~ (SpStSeq C)))) is V11() real ext-real Element of REAL
upper_bound ((proj1 | (N-most (L~ (SpStSeq C)))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ (SpStSeq C))))) is V11() real ext-real Element of REAL
|[(upper_bound (proj1 | (N-most (L~ (SpStSeq C))))),(N-bound (L~ (SpStSeq C)))]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
(N-max (L~ (SpStSeq C))) `2 is V11() real ext-real Element of REAL
(N-max (L~ (SpStSeq C))) . 2 is V11() real ext-real Element of REAL
((N-min (L~ (SpStSeq C))) `2) + ((N-max (L~ (SpStSeq C))) `2) is V11() real ext-real Element of REAL
(1 / 2) * (((N-min (L~ (SpStSeq C))) `2) + ((N-max (L~ (SpStSeq C))) `2)) is V11() real ext-real Element of REAL
len r is non empty ordinal natural V11() real ext-real positive non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
Seg (len r) is non empty V35() len r -element V183() V184() V185() V186() V187() V188() Element of bool NAT
dom r is non empty non trivial V35() V183() V184() V185() V186() V187() V188() Element of bool NAT
Y_axis r is non empty Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
dom (Y_axis r) is V35() V183() V184() V185() V186() V187() V188() Element of bool NAT
(Y_axis r) . 5 is V11() real ext-real Element of REAL
r /. 5 is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
(r /. 5) `2 is V11() real ext-real Element of REAL
(r /. 5) . 2 is V11() real ext-real Element of REAL
r /. 4 is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
S-min (L~ r) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
S-most (L~ r) is Element of bool the carrier of (TOP-REAL 2)
SW-corner (L~ r) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
S-bound (L~ r) is V11() real ext-real Element of REAL
lower_bound (proj2 | (L~ r)) is V11() real ext-real Element of REAL
lower_bound ((proj2 | (L~ r)) .: the carrier of ((TOP-REAL 2) | (L~ r))) is V11() real ext-real Element of REAL
|[(W-bound (L~ r)),(S-bound (L~ r))]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
SE-corner (L~ r) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
|[(E-bound (L~ r)),(S-bound (L~ r))]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner (L~ r)),(SE-corner (L~ r))) is non empty closed connected compact bounded convex Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * (SW-corner (L~ r))) + (b1 * (SE-corner (L~ r)))) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
(LSeg ((SW-corner (L~ r)),(SE-corner (L~ r)))) /\ (L~ r) is closed Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (S-most (L~ r)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (S-most (L~ r)) is Relation-like the carrier of ((TOP-REAL 2) | (S-most (L~ r))) -defined REAL -valued Function-like total V30( the carrier of ((TOP-REAL 2) | (S-most (L~ r))), REAL ) complex-yielding V174() V175() Element of bool [: the carrier of ((TOP-REAL 2) | (S-most (L~ r))),REAL:]
the carrier of ((TOP-REAL 2) | (S-most (L~ r))) is set
[: the carrier of ((TOP-REAL 2) | (S-most (L~ r))),REAL:] is complex-yielding V174() V175() set
bool [: the carrier of ((TOP-REAL 2) | (S-most (L~ r))),REAL:] is non empty set
lower_bound (proj1 | (S-most (L~ r))) is V11() real ext-real Element of REAL
(proj1 | (S-most (L~ r))) .: the carrier of ((TOP-REAL 2) | (S-most (L~ r))) is V183() V184() V185() Element of bool REAL
lower_bound ((proj1 | (S-most (L~ r))) .: the carrier of ((TOP-REAL 2) | (S-most (L~ r)))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (S-most (L~ r)))),(S-bound (L~ r))]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
(Y_axis r) . 4 is V11() real ext-real Element of REAL
(r /. 4) `2 is V11() real ext-real Element of REAL
(r /. 4) . 2 is V11() real ext-real Element of REAL
r /. 3 is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
S-max (L~ r) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
upper_bound (proj1 | (S-most (L~ r))) is V11() real ext-real Element of REAL
upper_bound ((proj1 | (S-most (L~ r))) .: the carrier of ((TOP-REAL 2) | (S-most (L~ r)))) is V11() real ext-real Element of REAL
|[(upper_bound (proj1 | (S-most (L~ r)))),(S-bound (L~ r))]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
(Y_axis r) . 3 is V11() real ext-real Element of REAL
(r /. 3) `2 is V11() real ext-real Element of REAL
(r /. 3) . 2 is V11() real ext-real Element of REAL
X_axis r is non empty Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
dom (X_axis r) is V35() V183() V184() V185() V186() V187() V188() Element of bool NAT
E-min (L~ r) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
E-most (L~ r) is Element of bool the carrier of (TOP-REAL 2)
LSeg ((SE-corner (L~ r)),(NE-corner (L~ r))) is non empty closed connected compact bounded convex Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * (SE-corner (L~ r))) + (b1 * (NE-corner (L~ r)))) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
(LSeg ((SE-corner (L~ r)),(NE-corner (L~ r)))) /\ (L~ r) is closed Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ r)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ r)) is Relation-like the carrier of ((TOP-REAL 2) | (E-most (L~ r))) -defined REAL -valued Function-like total V30( the carrier of ((TOP-REAL 2) | (E-most (L~ r))), REAL ) complex-yielding V174() V175() Element of bool [: the carrier of ((TOP-REAL 2) | (E-most (L~ r))),REAL:]
the carrier of ((TOP-REAL 2) | (E-most (L~ r))) is set
[: the carrier of ((TOP-REAL 2) | (E-most (L~ r))),REAL:] is complex-yielding V174() V175() set
bool [: the carrier of ((TOP-REAL 2) | (E-most (L~ r))),REAL:] is non empty set
lower_bound (proj2 | (E-most (L~ r))) is V11() real ext-real Element of REAL
(proj2 | (E-most (L~ r))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ r))) is V183() V184() V185() Element of bool REAL
lower_bound ((proj2 | (E-most (L~ r))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ r)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ r)),(lower_bound (proj2 | (E-most (L~ r))))]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
(X_axis r) . 3 is V11() real ext-real Element of REAL
(r /. 3) `1 is V11() real ext-real Element of REAL
(r /. 3) . 1 is V11() real ext-real Element of REAL
(X_axis r) . 5 is V11() real ext-real Element of REAL
(r /. 5) `1 is V11() real ext-real Element of REAL
(r /. 5) . 1 is V11() real ext-real Element of REAL
EX2 is V11() real ext-real Element of REAL
|.((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2))).| + EX2 is V11() real ext-real Element of REAL
(|.((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2))).| + EX2) + 1 is V11() real ext-real Element of REAL
|[0,((|.((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2))).| + EX2) + 1)]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
|[0,((|.((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2))).| + EX2) + 1)]| + ((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2))) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) . (|[0,((|.((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2))).| + EX2) + 1)]|,((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2)))) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
[|[0,((|.((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2))).| + EX2) + 1)]|,((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2)))] is non empty set
{|[0,((|.((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2))).| + EX2) + 1)]|,((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2)))} is non empty functional V35() V39() set
{|[0,((|.((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2))).| + EX2) + 1)]|} is non empty trivial functional V35() V39() 1 -element set
{{|[0,((|.((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2))).| + EX2) + 1)]|,((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2)))},{|[0,((|.((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2))).| + EX2) + 1)]|}} is non empty V35() V39() set
the U7 of (TOP-REAL 2) . [|[0,((|.((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2))).| + EX2) + 1)]|,((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2)))] is set
|[0,((|.((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2))).| + EX2) + 1)]| + ((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (|[0,((|.((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2))).| + EX2) + 1)]|,((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2)))) is set
r /. 1 is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
W-min (L~ r) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
W-most (L~ r) is Element of bool the carrier of (TOP-REAL 2)
LSeg ((SW-corner (L~ r)),(NW-corner (L~ r))) is non empty closed connected compact bounded convex Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * (SW-corner (L~ r))) + (b1 * (NW-corner (L~ r)))) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
(LSeg ((SW-corner (L~ r)),(NW-corner (L~ r)))) /\ (L~ r) is closed Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ r)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ r)) is Relation-like the carrier of ((TOP-REAL 2) | (W-most (L~ r))) -defined REAL -valued Function-like total V30( the carrier of ((TOP-REAL 2) | (W-most (L~ r))), REAL ) complex-yielding V174() V175() Element of bool [: the carrier of ((TOP-REAL 2) | (W-most (L~ r))),REAL:]
the carrier of ((TOP-REAL 2) | (W-most (L~ r))) is set
[: the carrier of ((TOP-REAL 2) | (W-most (L~ r))),REAL:] is complex-yielding V174() V175() set
bool [: the carrier of ((TOP-REAL 2) | (W-most (L~ r))),REAL:] is non empty set
lower_bound (proj2 | (W-most (L~ r))) is V11() real ext-real Element of REAL
(proj2 | (W-most (L~ r))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ r))) is V183() V184() V185() Element of bool REAL
lower_bound ((proj2 | (W-most (L~ r))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ r)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ r)),(lower_bound (proj2 | (W-most (L~ r))))]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
(X_axis r) . 4 is V11() real ext-real Element of REAL
(r /. 4) `1 is V11() real ext-real Element of REAL
(r /. 4) . 1 is V11() real ext-real Element of REAL
GoB r is Relation-like non empty-yielding NAT -defined the carrier of (TOP-REAL 2) * -valued Function-like V35() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of the carrier of (TOP-REAL 2) *
Incr (X_axis r) is non empty Relation-like NAT -defined REAL -valued Function-like one-to-one V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V179() FinSequence of REAL
Incr (Y_axis r) is non empty Relation-like NAT -defined REAL -valued Function-like one-to-one V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V179() FinSequence of REAL
GoB ((Incr (X_axis r)),(Incr (Y_axis r))) is Relation-like non empty-yielding NAT -defined the carrier of (TOP-REAL 2) * -valued Function-like V35() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of the carrier of (TOP-REAL 2) *
r /. 2 is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
E-max (L~ r) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
upper_bound (proj2 | (E-most (L~ r))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (E-most (L~ r))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ r)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ r)),(upper_bound (proj2 | (E-most (L~ r))))]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
(X_axis r) . 2 is V11() real ext-real Element of REAL
(r /. 2) `1 is V11() real ext-real Element of REAL
(r /. 2) . 1 is V11() real ext-real Element of REAL
(Y_axis r) . 1 is V11() real ext-real Element of REAL
(r /. 1) `2 is V11() real ext-real Element of REAL
(r /. 1) . 2 is V11() real ext-real Element of REAL
rng (X_axis r) is V35() V183() V184() V185() Element of bool REAL
len (X_axis r) is non empty ordinal natural V11() real ext-real positive non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
(X_axis r) . 1 is V11() real ext-real Element of REAL
(r /. 1) `1 is V11() real ext-real Element of REAL
(r /. 1) . 1 is V11() real ext-real Element of REAL
{((r /. 1) `1),((r /. 2) `1)} is non empty V35() V183() V184() V185() Element of bool REAL
p1 is set
{((r /. 1) `1)} is non empty trivial V35() 1 -element V183() V184() V185() Element of bool REAL
{((r /. 2) `1)} is non empty trivial V35() 1 -element V183() V184() V185() Element of bool REAL
{((r /. 1) `1)} \/ {((r /. 2) `1)} is non empty V35() V183() V184() V185() Element of bool REAL
card ({((r /. 1) `1)} \/ {((r /. 2) `1)}) is non empty ordinal natural V11() real ext-real positive non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of omega
card (rng (X_axis r)) is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of omega
1 + 1 is non empty ordinal natural V11() real ext-real positive non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
r /. (1 + 1) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
card {((r /. 1) `1)} is non empty ordinal natural V11() real ext-real positive non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of omega
(card {((r /. 1) `1)}) + 1 is non empty ordinal natural V11() real ext-real positive non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
len (GoB r) is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
(len (GoB r)) + 1 is non empty ordinal natural V11() real ext-real positive non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
(Y_axis r) . 2 is V11() real ext-real Element of REAL
(r /. 2) `2 is V11() real ext-real Element of REAL
(r /. 2) . 2 is V11() real ext-real Element of REAL
rng (Y_axis r) is V35() V183() V184() V185() Element of bool REAL
{(S-bound (L~ r)),(N-bound (L~ r))} is non empty V35() V183() V184() V185() Element of bool REAL
p1 is set
EX is set
(Y_axis r) . EX is V11() real ext-real Element of REAL
t2 is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
1 + 2 is non empty ordinal natural V11() real ext-real positive non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
1 + 3 is non empty ordinal natural V11() real ext-real positive non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
1 + 4 is non empty ordinal natural V11() real ext-real positive non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
p1 is set
width (GoB r) is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
card (rng (Y_axis r)) is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of omega
Seg (width (GoB r)) is V35() width (GoB r) -element V183() V184() V185() V186() V187() V188() Element of bool NAT
E-max (L~ (SpStSeq C)) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
E-most (L~ (SpStSeq C)) is Element of bool the carrier of (TOP-REAL 2)
SE-corner (L~ (SpStSeq C)) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
S-bound (L~ (SpStSeq C)) is V11() real ext-real Element of REAL
lower_bound (proj2 | (L~ (SpStSeq C))) is V11() real ext-real Element of REAL
lower_bound ((proj2 | (L~ (SpStSeq C))) .: the carrier of ((TOP-REAL 2) | (L~ (SpStSeq C)))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (SpStSeq C))),(S-bound (L~ (SpStSeq C)))]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
LSeg ((SE-corner (L~ (SpStSeq C))),(NE-corner (L~ (SpStSeq C)))) is non empty closed connected compact bounded convex Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * (SE-corner (L~ (SpStSeq C)))) + (b1 * (NE-corner (L~ (SpStSeq C))))) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
(LSeg ((SE-corner (L~ (SpStSeq C))),(NE-corner (L~ (SpStSeq C))))) /\ (L~ (SpStSeq C)) is closed Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (E-most (L~ (SpStSeq C))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (E-most (L~ (SpStSeq C))) is Relation-like the carrier of ((TOP-REAL 2) | (E-most (L~ (SpStSeq C)))) -defined REAL -valued Function-like total V30( the carrier of ((TOP-REAL 2) | (E-most (L~ (SpStSeq C)))), REAL ) complex-yielding V174() V175() Element of bool [: the carrier of ((TOP-REAL 2) | (E-most (L~ (SpStSeq C)))),REAL:]
the carrier of ((TOP-REAL 2) | (E-most (L~ (SpStSeq C)))) is set
[: the carrier of ((TOP-REAL 2) | (E-most (L~ (SpStSeq C)))),REAL:] is complex-yielding V174() V175() set
bool [: the carrier of ((TOP-REAL 2) | (E-most (L~ (SpStSeq C)))),REAL:] is non empty set
upper_bound (proj2 | (E-most (L~ (SpStSeq C)))) is V11() real ext-real Element of REAL
(proj2 | (E-most (L~ (SpStSeq C)))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ (SpStSeq C)))) is V183() V184() V185() Element of bool REAL
upper_bound ((proj2 | (E-most (L~ (SpStSeq C)))) .: the carrier of ((TOP-REAL 2) | (E-most (L~ (SpStSeq C))))) is V11() real ext-real Element of REAL
|[(E-bound (L~ (SpStSeq C))),(upper_bound (proj2 | (E-most (L~ (SpStSeq C)))))]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
(E-max (L~ (SpStSeq C))) `1 is V11() real ext-real Element of REAL
(E-max (L~ (SpStSeq C))) . 1 is V11() real ext-real Element of REAL
|[((E-max (L~ (SpStSeq C))) `1),((N-max (L~ (SpStSeq C))) `2)]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
W-max (L~ r) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
upper_bound (proj2 | (W-most (L~ r))) is V11() real ext-real Element of REAL
upper_bound ((proj2 | (W-most (L~ r))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ r)))) is V11() real ext-real Element of REAL
|[(W-bound (L~ r)),(upper_bound (proj2 | (W-most (L~ r))))]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
W-max (L~ (SpStSeq C)) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
W-most (L~ (SpStSeq C)) is Element of bool the carrier of (TOP-REAL 2)
SW-corner (L~ (SpStSeq C)) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
|[(W-bound (L~ (SpStSeq C))),(S-bound (L~ (SpStSeq C)))]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
LSeg ((SW-corner (L~ (SpStSeq C))),(NW-corner (L~ (SpStSeq C)))) is non empty closed connected compact bounded convex Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * (SW-corner (L~ (SpStSeq C)))) + (b1 * (NW-corner (L~ (SpStSeq C))))) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
(LSeg ((SW-corner (L~ (SpStSeq C))),(NW-corner (L~ (SpStSeq C))))) /\ (L~ (SpStSeq C)) is closed Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (W-most (L~ (SpStSeq C))) is strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (W-most (L~ (SpStSeq C))) is Relation-like the carrier of ((TOP-REAL 2) | (W-most (L~ (SpStSeq C)))) -defined REAL -valued Function-like total V30( the carrier of ((TOP-REAL 2) | (W-most (L~ (SpStSeq C)))), REAL ) complex-yielding V174() V175() Element of bool [: the carrier of ((TOP-REAL 2) | (W-most (L~ (SpStSeq C)))),REAL:]
the carrier of ((TOP-REAL 2) | (W-most (L~ (SpStSeq C)))) is set
[: the carrier of ((TOP-REAL 2) | (W-most (L~ (SpStSeq C)))),REAL:] is complex-yielding V174() V175() set
bool [: the carrier of ((TOP-REAL 2) | (W-most (L~ (SpStSeq C)))),REAL:] is non empty set
upper_bound (proj2 | (W-most (L~ (SpStSeq C)))) is V11() real ext-real Element of REAL
(proj2 | (W-most (L~ (SpStSeq C)))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ (SpStSeq C)))) is V183() V184() V185() Element of bool REAL
upper_bound ((proj2 | (W-most (L~ (SpStSeq C)))) .: the carrier of ((TOP-REAL 2) | (W-most (L~ (SpStSeq C))))) is V11() real ext-real Element of REAL
|[(W-bound (L~ (SpStSeq C))),(upper_bound (proj2 | (W-most (L~ (SpStSeq C)))))]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
(W-max (L~ (SpStSeq C))) `1 is V11() real ext-real Element of REAL
(W-max (L~ (SpStSeq C))) . 1 is V11() real ext-real Element of REAL
|[((W-max (L~ (SpStSeq C))) `1),((N-min (L~ (SpStSeq C))) `2)]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
((W-max (L~ (SpStSeq C))) `1) + ((E-max (L~ (SpStSeq C))) `1) is V11() real ext-real Element of REAL
|[(((W-max (L~ (SpStSeq C))) `1) + ((E-max (L~ (SpStSeq C))) `1)),(((N-min (L~ (SpStSeq C))) `2) + ((N-max (L~ (SpStSeq C))) `2))]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
(1 / 2) * (((W-max (L~ (SpStSeq C))) `1) + ((E-max (L~ (SpStSeq C))) `1)) is V11() real ext-real Element of REAL
|[((1 / 2) * (((W-max (L~ (SpStSeq C))) `1) + ((E-max (L~ (SpStSeq C))) `1))),(N-bound (L~ (SpStSeq C)))]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
0 + ((1 / 2) * (((W-max (L~ (SpStSeq C))) `1) + ((E-max (L~ (SpStSeq C))) `1))) is V11() real ext-real Element of REAL
((|.((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2))).| + EX2) + 1) + (N-bound (L~ (SpStSeq C))) is V11() real ext-real Element of REAL
|[(0 + ((1 / 2) * (((W-max (L~ (SpStSeq C))) `1) + ((E-max (L~ (SpStSeq C))) `1)))),(((|.((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2))).| + EX2) + 1) + (N-bound (L~ (SpStSeq C))))]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
|[((1 / 2) * (((W-max (L~ (SpStSeq C))) `1) + ((E-max (L~ (SpStSeq C))) `1))),(((|.((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2))).| + EX2) + 1) + (N-bound (L~ (SpStSeq C))))]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
(GoB r) * (1,1) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
((GoB r) * (1,1)) `1 is V11() real ext-real Element of REAL
((GoB r) * (1,1)) . 1 is V11() real ext-real Element of REAL
(((GoB r) * (1,1)) `1) + (((GoB r) * (1,1)) `1) is V11() real ext-real Element of REAL
2 * (((GoB r) * (1,1)) `1) is V11() real ext-real Element of REAL
(1 / 2) * (2 * (((GoB r) * (1,1)) `1)) is V11() real ext-real Element of REAL
{(W-bound (L~ r)),(E-bound (L~ r))} is non empty V35() V183() V184() V185() Element of bool REAL
p1 is set
EX is set
(X_axis r) . EX is V11() real ext-real Element of REAL
t2 is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
1 + 2 is non empty ordinal natural V11() real ext-real positive non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
1 + 3 is non empty ordinal natural V11() real ext-real positive non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
1 + 4 is non empty ordinal natural V11() real ext-real positive non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
p1 is set
(GoB r) * ((1 + 1),1) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
((GoB r) * ((1 + 1),1)) `1 is V11() real ext-real Element of REAL
((GoB r) * ((1 + 1),1)) . 1 is V11() real ext-real Element of REAL
(((GoB r) * ((1 + 1),1)) `1) + (((GoB r) * ((1 + 1),1)) `1) is V11() real ext-real Element of REAL
2 * (((GoB r) * ((1 + 1),1)) `1) is V11() real ext-real Element of REAL
(1 / 2) * (2 * (((GoB r) * ((1 + 1),1)) `1)) is V11() real ext-real Element of REAL
rng (GoB r) is functional V35() FinSequence-membered Element of bool ( the carrier of (TOP-REAL 2) *)
bool ( the carrier of (TOP-REAL 2) *) is non empty set
len (GoB ((Incr (X_axis r)),(Incr (Y_axis r)))) is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
len (Incr (X_axis r)) is non empty ordinal natural V11() real ext-real positive non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
rng (GoB ((Incr (X_axis r)),(Incr (Y_axis r)))) is functional V35() FinSequence-membered Element of bool ( the carrier of (TOP-REAL 2) *)
width (GoB ((Incr (X_axis r)),(Incr (Y_axis r)))) is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
p1 is Relation-like NAT -defined Function-like V35() FinSequence-like FinSubsequence-like set
len p1 is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
EX is Relation-like NAT -defined the carrier of (TOP-REAL 2) -valued Function-like V35() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len EX is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
t2 is ordinal natural V11() real ext-real non negative V35() cardinal set
qt2 is Relation-like NAT -defined Function-like V35() FinSequence-like FinSubsequence-like set
len qt2 is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
r2 is Relation-like NAT -defined Function-like V35() FinSequence-like FinSubsequence-like set
len r2 is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
Seg (len (GoB r)) is V35() len (GoB r) -element V183() V184() V185() V186() V187() V188() Element of bool NAT
[(len (GoB r)),(width (GoB r))] is non empty Element of [:NAT,NAT:]
{(len (GoB r)),(width (GoB r))} is non empty V35() V39() V183() V184() V185() V186() V187() V188() set
{(len (GoB r))} is non empty trivial V35() V39() 1 -element V183() V184() V185() V186() V187() V188() set
{{(len (GoB r)),(width (GoB r))},{(len (GoB r))}} is non empty V35() V39() set
[:(Seg (len (GoB r))),(Seg (width (GoB r))):] is INT -valued RAT -valued V35() complex-yielding V174() V175() V176() set
Indices (GoB r) is set
[1,(width (GoB r))] is non empty Element of [:NAT,NAT:]
{1,(width (GoB r))} is non empty V35() V39() V183() V184() V185() V186() V187() V188() set
{1} is non empty trivial V35() V39() 1 -element V183() V184() V185() V186() V187() V188() set
{{1,(width (GoB r))},{1}} is non empty V35() V39() set
(GoB r) * (1,(width (GoB r))) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
|[0,((|.((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2))).| + EX2) + 1)]| `1 is V11() real ext-real Element of REAL
|[0,((|.((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2))).| + EX2) + 1)]| . 1 is V11() real ext-real Element of REAL
|[0,((|.((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2))).| + EX2) + 1)]| `2 is V11() real ext-real Element of REAL
|[0,((|.((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2))).| + EX2) + 1)]| . 2 is V11() real ext-real Element of REAL
|.|[0,((|.((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2))).| + EX2) + 1)]|.| is V11() real ext-real non negative Element of REAL
sqr |[0,((|.((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2))).| + EX2) + 1)]| is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
|[0,((|.((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2))).| + EX2) + 1)]| (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (|[0,((|.((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2))).| + EX2) + 1)]|,|[0,((|.((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2))).| + EX2) + 1)]|) is Relation-like Function-like set
multreal .: (|[0,((|.((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2))).| + EX2) + 1)]|,|[0,((|.((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2))).| + EX2) + 1)]|) is set
K383((sqr |[0,((|.((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2))).| + EX2) + 1)]|)) is V11() real ext-real Element of REAL
K195(REAL,(sqr |[0,((|.((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2))).| + EX2) + 1)]|),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr |[0,((|.((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2))).| + EX2) + 1)]|)) is V11() real ext-real Element of REAL
|.|[0,((|.((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2))).| + EX2) + 1)]|.| - |.((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2))).| is V11() real ext-real Element of REAL
|.(|[0,((|.((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2))).| + EX2) + 1)]| + ((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2)))).| is V11() real ext-real non negative Element of REAL
sqr (|[0,((|.((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2))).| + EX2) + 1)]| + ((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2)))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(|[0,((|.((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2))).| + EX2) + 1)]| + ((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2)))) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((|[0,((|.((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2))).| + EX2) + 1)]| + ((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2)))),(|[0,((|.((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2))).| + EX2) + 1)]| + ((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2))))) is Relation-like Function-like set
multreal .: ((|[0,((|.((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2))).| + EX2) + 1)]| + ((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2)))),(|[0,((|.((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2))).| + EX2) + 1)]| + ((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2))))) is set
K383((sqr (|[0,((|.((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2))).| + EX2) + 1)]| + ((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2)))))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (|[0,((|.((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2))).| + EX2) + 1)]| + ((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2))))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (|[0,((|.((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2))).| + EX2) + 1)]| + ((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2)))))) is V11() real ext-real Element of REAL
EX2 + 1 is V11() real ext-real Element of REAL
left_cell (r,1) is Element of bool the carrier of (TOP-REAL 2)
Int (left_cell (r,1)) is open Element of bool the carrier of (TOP-REAL 2)
(width (GoB r)) + 1 is non empty ordinal natural V11() real ext-real positive non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
(GoB r) * ((len (GoB r)),(width (GoB r))) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
cell ((GoB r),1,(width (GoB r))) is Element of bool the carrier of (TOP-REAL 2)
((GoB r) * (1,(width (GoB r)))) `2 is V11() real ext-real Element of REAL
((GoB r) * (1,(width (GoB r)))) . 2 is V11() real ext-real Element of REAL
{ |[b1,b2]| where b1, b2 is V11() real ext-real Element of REAL : ( not b1 <= ((GoB r) * (1,1)) `1 & not ((GoB r) * ((1 + 1),1)) `1 <= b1 & not b2 <= ((GoB r) * (1,(width (GoB r)))) `2 ) } is set
p12 is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
|.p12.| is V11() real ext-real non negative Element of REAL
sqr p12 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
p12 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (p12,p12) is Relation-like Function-like set
multreal .: (p12,p12) is set
K383((sqr p12)) is V11() real ext-real Element of REAL
K195(REAL,(sqr p12),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr p12)) is V11() real ext-real Element of REAL
(|[0,((|.((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2))).| + EX2) + 1)]| `1) ^2 is V11() real ext-real Element of REAL
K37((|[0,((|.((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2))).| + EX2) + 1)]| `1),(|[0,((|.((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2))).| + EX2) + 1)]| `1)) is V11() real ext-real set
(|[0,((|.((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2))).| + EX2) + 1)]| `2) ^2 is V11() real ext-real Element of REAL
K37((|[0,((|.((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2))).| + EX2) + 1)]| `2),(|[0,((|.((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2))).| + EX2) + 1)]| `2)) is V11() real ext-real set
((|[0,((|.((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2))).| + EX2) + 1)]| `1) ^2) + ((|[0,((|.((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2))).| + EX2) + 1)]| `2) ^2) is V11() real ext-real Element of REAL
sqrt (((|[0,((|.((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2))).| + EX2) + 1)]| `1) ^2) + ((|[0,((|.((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2))).| + EX2) + 1)]| `2) ^2)) is V11() real ext-real Element of REAL
(N-bound (L~ (SpStSeq C))) + ((|.((1 / 2) * (((SpStSeq C) /. 1) + ((SpStSeq C) /. 2))).| + EX2) + 1) is V11() real ext-real Element of REAL
C is non empty compact bounded non horizontal non vertical Element of bool the carrier of (TOP-REAL 2)
SpStSeq C is non empty non trivial Relation-like NAT -defined the carrier of (TOP-REAL 2) -valued Function-like non constant V35() FinSequence-like FinSubsequence-like V262( the carrier of (TOP-REAL 2)) special unfolded s.c.c. standard rectangular clockwise_oriented FinSequence of the carrier of (TOP-REAL 2)
LeftComp (SpStSeq C) is non empty Element of bool the carrier of (TOP-REAL 2)
L~ (SpStSeq C) is non empty closed compact bounded non horizontal non vertical Jordan Element of bool the carrier of (TOP-REAL 2)
(2,(L~ (SpStSeq C))) is Element of bool the carrier of (TOP-REAL 2)
{ b1 where b1 is Element of bool the carrier of (TOP-REAL 2) : (2, L~ (SpStSeq C),b1) } is set
union { b1 where b1 is Element of bool the carrier of (TOP-REAL 2) : (2, L~ (SpStSeq C),b1) } is set
(L~ (SpStSeq C)) ` is open Element of bool the carrier of (TOP-REAL 2)
the carrier of (TOP-REAL 2) \ (L~ (SpStSeq C)) is set
p12 is set
C is TopSpace-like TopStruct
the carrier of C is set
bool the carrier of C is non empty set
p is Element of bool the carrier of C
WH is Element of bool the carrier of C
p12 is Element of bool the carrier of C
p12 /\ p is Element of bool the carrier of C
{} C is empty trivial ordinal natural V11() real ext-real non positive non negative Function-like functional V35() V39() cardinal {} -element FinSequence-membered open closed boundary nowhere_dense V183() V184() V185() V186() V187() V188() V189() Element of bool the carrier of C
p /\ WH is Element of bool the carrier of C
C is non empty compact bounded non horizontal non vertical Element of bool the carrier of (TOP-REAL 2)
SpStSeq C is non empty non trivial Relation-like NAT -defined the carrier of (TOP-REAL 2) -valued Function-like non constant V35() FinSequence-like FinSubsequence-like V262( the carrier of (TOP-REAL 2)) special unfolded s.c.c. standard rectangular clockwise_oriented FinSequence of the carrier of (TOP-REAL 2)
L~ (SpStSeq C) is non empty closed compact bounded non horizontal non vertical Jordan Element of bool the carrier of (TOP-REAL 2)
(L~ (SpStSeq C)) ` is open Element of bool the carrier of (TOP-REAL 2)
the carrier of (TOP-REAL 2) \ (L~ (SpStSeq C)) is set
LeftComp (SpStSeq C) is non empty Element of bool the carrier of (TOP-REAL 2)
p is Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | ((L~ (SpStSeq C)) `) is strict TopSpace-like SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | ((L~ (SpStSeq C)) `)) is set
bool the carrier of ((TOP-REAL 2) | ((L~ (SpStSeq C)) `)) is non empty set
p12 is V11() real ext-real Element of REAL
C is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
|.C.| is V11() real ext-real non negative Element of REAL
sqr C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
sqrreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
C (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (C,C) is Relation-like Function-like set
multreal .: (C,C) is set
K383((sqr C)) is V11() real ext-real Element of REAL
addreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K195(REAL,(sqr C),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr C)) is V11() real ext-real Element of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2) : not p12 <= |.b1.| } is set
r is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
|.r.| is V11() real ext-real non negative Element of REAL
sqr r is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
r (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (r,r) is Relation-like Function-like set
multreal .: (r,r) is set
K383((sqr r)) is V11() real ext-real Element of REAL
K195(REAL,(sqr r),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr r)) is V11() real ext-real Element of REAL
(REAL 2) \ { b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2) : not p12 <= |.b1.| } is functional FinSequence-membered Element of bool (REAL 2)
bool (REAL 2) is non empty set
r is Element of bool the carrier of (TOP-REAL 2)
the carrier of (TOP-REAL 2) \ (L~ (SpStSeq C)) is Element of bool the carrier of (TOP-REAL 2)
EX2 is set
EX1 is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
|.EX1.| is V11() real ext-real non negative Element of REAL
sqr EX1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
EX1 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (EX1,EX1) is Relation-like Function-like set
multreal .: (EX1,EX1) is set
K383((sqr EX1)) is V11() real ext-real Element of REAL
K195(REAL,(sqr EX1),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr EX1)) is V11() real ext-real Element of REAL
r /\ ( the carrier of (TOP-REAL 2) \ (L~ (SpStSeq C))) is Element of bool the carrier of (TOP-REAL 2)
Down (r,((L~ (SpStSeq C)) `)) is Element of bool the carrier of ((TOP-REAL 2) | ((L~ (SpStSeq C)) `))
r /\ ((L~ (SpStSeq C)) `) is Element of bool the carrier of (TOP-REAL 2)
EX2 is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
|.EX2.| is V11() real ext-real non negative Element of REAL
sqr EX2 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
EX2 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (EX2,EX2) is Relation-like Function-like set
multreal .: (EX2,EX2) is set
K383((sqr EX2)) is V11() real ext-real Element of REAL
K195(REAL,(sqr EX2),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr EX2)) is V11() real ext-real Element of REAL
EX1 is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
|.EX1.| is V11() real ext-real non negative Element of REAL
sqr EX1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
EX1 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (EX1,EX1) is Relation-like Function-like set
multreal .: (EX1,EX1) is set
K383((sqr EX1)) is V11() real ext-real Element of REAL
K195(REAL,(sqr EX1),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr EX1)) is V11() real ext-real Element of REAL
EX1 is Element of bool the carrier of ((TOP-REAL 2) | ((L~ (SpStSeq C)) `))
p1 is Element of bool the carrier of ((TOP-REAL 2) | ((L~ (SpStSeq C)) `))
C is non empty compact bounded non horizontal non vertical Element of bool the carrier of (TOP-REAL 2)
SpStSeq C is non empty non trivial Relation-like NAT -defined the carrier of (TOP-REAL 2) -valued Function-like non constant V35() FinSequence-like FinSubsequence-like V262( the carrier of (TOP-REAL 2)) special unfolded s.c.c. standard rectangular clockwise_oriented FinSequence of the carrier of (TOP-REAL 2)
RightComp (SpStSeq C) is non empty Element of bool the carrier of (TOP-REAL 2)
L~ (SpStSeq C) is non empty closed compact bounded non horizontal non vertical Jordan Element of bool the carrier of (TOP-REAL 2)
(2,(L~ (SpStSeq C))) is Element of bool the carrier of (TOP-REAL 2)
{ b1 where b1 is Element of bool the carrier of (TOP-REAL 2) : (2, L~ (SpStSeq C),b1) } is set
union { b1 where b1 is Element of bool the carrier of (TOP-REAL 2) : (2, L~ (SpStSeq C),b1) } is set
(L~ (SpStSeq C)) ` is open Element of bool the carrier of (TOP-REAL 2)
the carrier of (TOP-REAL 2) \ (L~ (SpStSeq C)) is set
LeftComp (SpStSeq C) is non empty Element of bool the carrier of (TOP-REAL 2)
p12 is set
C is non empty compact bounded non horizontal non vertical Element of bool the carrier of (TOP-REAL 2)
SpStSeq C is non empty non trivial Relation-like NAT -defined the carrier of (TOP-REAL 2) -valued Function-like non constant V35() FinSequence-like FinSubsequence-like V262( the carrier of (TOP-REAL 2)) special unfolded s.c.c. standard rectangular clockwise_oriented FinSequence of the carrier of (TOP-REAL 2)
LeftComp (SpStSeq C) is non empty Element of bool the carrier of (TOP-REAL 2)
L~ (SpStSeq C) is non empty closed compact bounded non horizontal non vertical Jordan Element of bool the carrier of (TOP-REAL 2)
(2,(L~ (SpStSeq C))) is Element of bool the carrier of (TOP-REAL 2)
{ b1 where b1 is Element of bool the carrier of (TOP-REAL 2) : (2, L~ (SpStSeq C),b1) } is set
union { b1 where b1 is Element of bool the carrier of (TOP-REAL 2) : (2, L~ (SpStSeq C),b1) } is set
RightComp (SpStSeq C) is non empty Element of bool the carrier of (TOP-REAL 2)
(2,(L~ (SpStSeq C))) is Element of bool the carrier of (TOP-REAL 2)
{ b1 where b1 is Element of bool the carrier of (TOP-REAL 2) : (2, L~ (SpStSeq C),b1) } is set
union { b1 where b1 is Element of bool the carrier of (TOP-REAL 2) : (2, L~ (SpStSeq C),b1) } is set
(L~ (SpStSeq C)) ` is open Element of bool the carrier of (TOP-REAL 2)
the carrier of (TOP-REAL 2) \ (L~ (SpStSeq C)) is set
(LeftComp (SpStSeq C)) \/ (RightComp (SpStSeq C)) is non empty Element of bool the carrier of (TOP-REAL 2)
WH is set
WH is set
C is non empty compact bounded non horizontal non vertical Element of bool the carrier of (TOP-REAL 2)
SpStSeq C is non empty non trivial Relation-like NAT -defined the carrier of (TOP-REAL 2) -valued Function-like non constant V35() FinSequence-like FinSubsequence-like V262( the carrier of (TOP-REAL 2)) special unfolded s.c.c. standard rectangular clockwise_oriented FinSequence of the carrier of (TOP-REAL 2)
L~ (SpStSeq C) is non empty closed compact bounded non horizontal non vertical Jordan Element of bool the carrier of (TOP-REAL 2)
(2,(L~ (SpStSeq C))) is Element of bool the carrier of (TOP-REAL 2)
{ b1 where b1 is Element of bool the carrier of (TOP-REAL 2) : (2, L~ (SpStSeq C),b1) } is set
union { b1 where b1 is Element of bool the carrier of (TOP-REAL 2) : (2, L~ (SpStSeq C),b1) } is set
(2,(L~ (SpStSeq C))) is Element of bool the carrier of (TOP-REAL 2)
{ b1 where b1 is Element of bool the carrier of (TOP-REAL 2) : (2, L~ (SpStSeq C),b1) } is set
union { b1 where b1 is Element of bool the carrier of (TOP-REAL 2) : (2, L~ (SpStSeq C),b1) } is set
LeftComp (SpStSeq C) is non empty Element of bool the carrier of (TOP-REAL 2)
(L~ (SpStSeq C)) ` is open Element of bool the carrier of (TOP-REAL 2)
the carrier of (TOP-REAL 2) \ (L~ (SpStSeq C)) is set
RightComp (SpStSeq C) is non empty Element of bool the carrier of (TOP-REAL 2)
C is non empty TopSpace-like TopStruct
the carrier of C is non empty set
bool the carrier of C is non empty set
p is Element of bool the carrier of C
p ` is Element of bool the carrier of C
the carrier of C \ p is set
Cl (p `) is closed Element of bool the carrier of C
[#] C is non empty non proper open closed dense non boundary Element of bool the carrier of C
C is set
r is Element of bool the carrier of C
p12 is Element of bool the carrier of C
EX2 is set
C | (p `) is strict TopSpace-like SubSpace of C
the carrier of (C | (p `)) is set
EX1 is Element of the carrier of (C | (p `))
Component_of EX1 is Element of bool the carrier of (C | (p `))
bool the carrier of (C | (p `)) is non empty set
WH is non empty Element of bool the carrier of C
C | WH is non empty strict TopSpace-like SubSpace of C
p1 is Element of bool the carrier of C
r /\ p1 is Element of bool the carrier of C
WH is set
p12 is Element of bool the carrier of C
C is Element of bool the carrier of C
p12 /\ C is Element of bool the carrier of C
r is Element of bool the carrier of (C | (p `))
(p `) /\ p12 is Element of bool the carrier of C
{} C is empty trivial proper ordinal natural V11() real ext-real non positive non negative Function-like functional V35() V39() cardinal {} -element FinSequence-membered open closed boundary nowhere_dense V183() V184() V185() V186() V187() V188() V189() Element of bool the carrier of C
the carrier of C \ p is Element of bool the carrier of C
C is Element of bool the carrier of (TOP-REAL 2)
C ` is Element of bool the carrier of (TOP-REAL 2)
the carrier of (TOP-REAL 2) \ C is set
(TOP-REAL 2) | (C `) is strict TopSpace-like SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | (C `)) is set
bool the carrier of ((TOP-REAL 2) | (C `)) is non empty set
p is Element of bool the carrier of (TOP-REAL 2)
WH is Element of bool the carrier of (TOP-REAL 2)
p \/ WH is Element of bool the carrier of (TOP-REAL 2)
Cl p is closed Element of bool the carrier of (TOP-REAL 2)
(Cl p) \ p is Element of bool the carrier of (TOP-REAL 2)
Cl WH is closed Element of bool the carrier of (TOP-REAL 2)
(Cl WH) \ WH is Element of bool the carrier of (TOP-REAL 2)
(p \/ WH) ` is Element of bool the carrier of (TOP-REAL 2)
the carrier of (TOP-REAL 2) \ (p \/ WH) is set
p ` is Element of bool the carrier of (TOP-REAL 2)
the carrier of (TOP-REAL 2) \ p is set
WH ` is Element of bool the carrier of (TOP-REAL 2)
the carrier of (TOP-REAL 2) \ WH is set
(p `) /\ (WH `) is Element of bool the carrier of (TOP-REAL 2)
p12 is Element of bool the carrier of ((TOP-REAL 2) | (C `))
C is Element of bool the carrier of ((TOP-REAL 2) | (C `))
r is set
EX2 is Element of bool the carrier of (TOP-REAL 2)
EX1 is Element of bool the carrier of (TOP-REAL 2)
p1 is Element of bool the carrier of ((TOP-REAL 2) | (C `))
Cl p1 is closed Element of bool the carrier of ((TOP-REAL 2) | (C `))
Cl C is closed Element of bool the carrier of ((TOP-REAL 2) | (C `))
p1 /\ C is Element of bool the carrier of ((TOP-REAL 2) | (C `))
p1 /\ (C `) is Element of bool the carrier of (TOP-REAL 2)
p1 /\ p is Element of bool the carrier of (TOP-REAL 2)
p1 /\ WH is Element of bool the carrier of (TOP-REAL 2)
(p1 /\ p) \/ (p1 /\ WH) is Element of bool the carrier of (TOP-REAL 2)
EX2 /\ EX1 is Element of bool the carrier of (TOP-REAL 2)
(p \/ WH) /\ EX2 is Element of bool the carrier of (TOP-REAL 2)
Cl (p \/ WH) is closed Element of bool the carrier of (TOP-REAL 2)
(Cl p) \/ (Cl WH) is closed Element of bool the carrier of (TOP-REAL 2)
p is Element of bool the carrier of (TOP-REAL 2)
WH is Element of bool the carrier of (TOP-REAL 2)
p \/ WH is Element of bool the carrier of (TOP-REAL 2)
Cl p is closed Element of bool the carrier of (TOP-REAL 2)
(Cl p) \ p is Element of bool the carrier of (TOP-REAL 2)
Cl WH is closed Element of bool the carrier of (TOP-REAL 2)
(Cl WH) \ WH is Element of bool the carrier of (TOP-REAL 2)
p is Element of bool the carrier of (TOP-REAL 2)
WH is Element of bool the carrier of (TOP-REAL 2)
p \/ WH is Element of bool the carrier of (TOP-REAL 2)
Cl p is closed Element of bool the carrier of (TOP-REAL 2)
(Cl p) \ p is Element of bool the carrier of (TOP-REAL 2)
Cl WH is closed Element of bool the carrier of (TOP-REAL 2)
(Cl WH) \ WH is Element of bool the carrier of (TOP-REAL 2)
r is set
EX2 is Element of bool the carrier of (TOP-REAL 2)
p12 is Element of bool the carrier of ((TOP-REAL 2) | (C `))
C is Element of bool the carrier of ((TOP-REAL 2) | (C `))
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
bool the carrier of (TOP-REAL C) is non empty set
p is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
{p} is non empty trivial functional V35() V39() 1 -element compact bounded Element of bool the carrier of (TOP-REAL C)
WH is Element of bool the carrier of (TOP-REAL C)
WH ` is Element of bool the carrier of (TOP-REAL C)
the carrier of (TOP-REAL C) \ WH is set
Cl (WH `) is closed Element of bool the carrier of (TOP-REAL C)
p12 is set
Euclid C is non empty strict Reflexive discerning symmetric triangle Discerning MetrStruct
REAL C is non empty functional FinSequence-membered FinSequenceSet of REAL
C -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = C } is set
Pitag_dist C is non empty Relation-like [:(REAL C),(REAL C):] -defined REAL -valued Function-like total V30([:(REAL C),(REAL C):], REAL ) complex-yielding V174() V175() Element of bool [:[:(REAL C),(REAL C):],REAL:]
[:(REAL C),(REAL C):] is non empty set
[:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() set
MetrStruct(# (REAL C),(Pitag_dist C) #) is strict MetrStruct
the carrier of (Euclid C) is non empty set
r is Element of bool the carrier of (TOP-REAL C)
the topology of (TOP-REAL C) is non empty Element of bool (bool the carrier of (TOP-REAL C))
bool (bool the carrier of (TOP-REAL C)) is non empty set
TopStruct(# the carrier of (TOP-REAL C), the topology of (TOP-REAL C) #) is non empty strict TopSpace-like TopStruct
TopSpaceMetr (Euclid C) is TopStruct
the carrier of (TopSpaceMetr (Euclid C)) is set
bool the carrier of (TopSpaceMetr (Euclid C)) is non empty set
EX2 is Element of bool the carrier of (TopSpaceMetr (Euclid C))
C is Element of the carrier of (Euclid C)
EX1 is V11() real ext-real set
Ball (C,EX1) is bounded Element of bool the carrier of (Euclid C)
bool the carrier of (Euclid C) is non empty set
1.REAL C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
1* C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
C |-> 1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of C -tuples_on REAL
Seg C is V35() C -element V183() V184() V185() V186() V187() V188() Element of bool NAT
(Seg C) --> 1 is Relation-like Seg C -defined INT -valued RAT -valued {1} -valued Function-like total V30( Seg C,{1}) V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() V176() Element of bool [:(Seg C),{1}:]
{1} is non empty trivial V35() V39() 1 -element V183() V184() V185() V186() V187() V188() set
[:(Seg C),{1}:] is INT -valued RAT -valued V35() complex-yielding V174() V175() V176() set
bool [:(Seg C),{1}:] is non empty V35() V39() set
p1 is V11() real ext-real Element of REAL
p1 / 2 is V11() real ext-real Element of REAL
sqrt C is V11() real ext-real Element of REAL
(p1 / 2) / (sqrt C) is V11() real ext-real Element of REAL
((p1 / 2) / (sqrt C)) * (1.REAL C) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
((p1 / 2) / (sqrt C)) * (1.REAL C) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
((p1 / 2) / (sqrt C)) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
id REAL is non empty Relation-like REAL -defined REAL -valued Function-like one-to-one total V30( REAL , REAL ) complex-yielding V174() V175() increasing V179() Element of bool [:REAL,REAL:]
multreal [;] (((p1 / 2) / (sqrt C)),(id REAL)) is set
(1.REAL C) (#) (((p1 / 2) / (sqrt C)) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
p - (((p1 / 2) / (sqrt C)) * (1.REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
- (((p1 / 2) / (sqrt C)) * (1.REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
- (((p1 / 2) / (sqrt C)) * (1.REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
compreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
(((p1 / 2) / (sqrt C)) * (1.REAL C)) (#) compreal is Relation-like Function-like V35() complex-yielding V174() V175() set
K38(1) is V11() real ext-real non positive set
K38(1) * (((p1 / 2) / (sqrt C)) * (1.REAL C)) is Relation-like Function-like set
K38(1) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (K38(1),(id REAL)) is set
(((p1 / 2) / (sqrt C)) * (1.REAL C)) (#) (K38(1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
K258((TOP-REAL C),p,(- (((p1 / 2) / (sqrt C)) * (1.REAL C)))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) is non empty Relation-like [: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):] -defined the carrier of (TOP-REAL C) -valued Function-like total V30([: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C)) Element of bool [:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):]
[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):] is non empty set
[:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):] is non empty set
bool [:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):] is non empty set
the U7 of (TOP-REAL C) . (p,(- (((p1 / 2) / (sqrt C)) * (1.REAL C)))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[p,(- (((p1 / 2) / (sqrt C)) * (1.REAL C)))] is non empty set
{p,(- (((p1 / 2) / (sqrt C)) * (1.REAL C)))} is non empty functional V35() V39() set
{p} is non empty trivial functional V35() V39() 1 -element set
{{p,(- (((p1 / 2) / (sqrt C)) * (1.REAL C)))},{p}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [p,(- (((p1 / 2) / (sqrt C)) * (1.REAL C)))] is set
p + (- (((p1 / 2) / (sqrt C)) * (1.REAL C))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
addreal .: (p,(- (((p1 / 2) / (sqrt C)) * (1.REAL C)))) is set
p - (((p1 / 2) / (sqrt C)) * (1.REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
diffreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K174(REAL,addreal,(id REAL),compreal) is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
diffreal .: (p,(((p1 / 2) / (sqrt C)) * (1.REAL C))) is set
K324((((p1 / 2) / (sqrt C)) * (1.REAL C))) is Relation-like Function-like complex-yielding set
K295(p,K324((((p1 / 2) / (sqrt C)) * (1.REAL C)))) is Relation-like Function-like set
p - (p - (((p1 / 2) / (sqrt C)) * (1.REAL C))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
- (p - (((p1 / 2) / (sqrt C)) * (1.REAL C))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
- (p - (((p1 / 2) / (sqrt C)) * (1.REAL C))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(p - (((p1 / 2) / (sqrt C)) * (1.REAL C))) (#) compreal is Relation-like Function-like V35() complex-yielding V174() V175() set
K38(1) * (p - (((p1 / 2) / (sqrt C)) * (1.REAL C))) is Relation-like Function-like set
(p - (((p1 / 2) / (sqrt C)) * (1.REAL C))) (#) (K38(1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
K258((TOP-REAL C),p,(- (p - (((p1 / 2) / (sqrt C)) * (1.REAL C))))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) . (p,(- (p - (((p1 / 2) / (sqrt C)) * (1.REAL C))))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[p,(- (p - (((p1 / 2) / (sqrt C)) * (1.REAL C))))] is non empty set
{p,(- (p - (((p1 / 2) / (sqrt C)) * (1.REAL C))))} is non empty functional V35() V39() set
{{p,(- (p - (((p1 / 2) / (sqrt C)) * (1.REAL C))))},{p}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [p,(- (p - (((p1 / 2) / (sqrt C)) * (1.REAL C))))] is set
p + (- (p - (((p1 / 2) / (sqrt C)) * (1.REAL C)))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (p,(- (p - (((p1 / 2) / (sqrt C)) * (1.REAL C))))) is set
p - (p - (((p1 / 2) / (sqrt C)) * (1.REAL C))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
diffreal .: (p,(p - (((p1 / 2) / (sqrt C)) * (1.REAL C)))) is set
K324((p - (((p1 / 2) / (sqrt C)) * (1.REAL C)))) is Relation-like Function-like complex-yielding set
K295(p,K324((p - (((p1 / 2) / (sqrt C)) * (1.REAL C))))) is Relation-like Function-like set
|.(p - (p - (((p1 / 2) / (sqrt C)) * (1.REAL C)))).| is V11() real ext-real non negative Element of REAL
sqr (p - (p - (((p1 / 2) / (sqrt C)) * (1.REAL C)))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
sqrreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
(p - (p - (((p1 / 2) / (sqrt C)) * (1.REAL C)))) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((p - (p - (((p1 / 2) / (sqrt C)) * (1.REAL C)))),(p - (p - (((p1 / 2) / (sqrt C)) * (1.REAL C))))) is Relation-like Function-like set
multreal .: ((p - (p - (((p1 / 2) / (sqrt C)) * (1.REAL C)))),(p - (p - (((p1 / 2) / (sqrt C)) * (1.REAL C))))) is set
K383((sqr (p - (p - (((p1 / 2) / (sqrt C)) * (1.REAL C)))))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (p - (p - (((p1 / 2) / (sqrt C)) * (1.REAL C))))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (p - (p - (((p1 / 2) / (sqrt C)) * (1.REAL C)))))) is V11() real ext-real Element of REAL
p - p is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
- p is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
- p is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
p (#) compreal is Relation-like Function-like V35() complex-yielding V174() V175() set
K38(1) * p is Relation-like Function-like set
p (#) (K38(1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
K258((TOP-REAL C),p,(- p)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) . (p,(- p)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[p,(- p)] is non empty set
{p,(- p)} is non empty functional V35() V39() set
{{p,(- p)},{p}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [p,(- p)] is set
p + (- p) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (p,(- p)) is set
p - p is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
diffreal .: (p,p) is set
K324(p) is Relation-like Function-like complex-yielding set
K295(p,K324(p)) is Relation-like Function-like set
(p - p) + (((p1 / 2) / (sqrt C)) * (1.REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) . ((p - p),(((p1 / 2) / (sqrt C)) * (1.REAL C))) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[(p - p),(((p1 / 2) / (sqrt C)) * (1.REAL C))] is non empty set
{(p - p),(((p1 / 2) / (sqrt C)) * (1.REAL C))} is non empty functional V35() V39() set
{(p - p)} is non empty trivial functional V35() V39() 1 -element set
{{(p - p),(((p1 / 2) / (sqrt C)) * (1.REAL C))},{(p - p)}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [(p - p),(((p1 / 2) / (sqrt C)) * (1.REAL C))] is set
(p - p) + (((p1 / 2) / (sqrt C)) * (1.REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: ((p - p),(((p1 / 2) / (sqrt C)) * (1.REAL C))) is set
|.((p - p) + (((p1 / 2) / (sqrt C)) * (1.REAL C))).| is V11() real ext-real non negative Element of REAL
sqr ((p - p) + (((p1 / 2) / (sqrt C)) * (1.REAL C))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
((p - p) + (((p1 / 2) / (sqrt C)) * (1.REAL C))) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (((p - p) + (((p1 / 2) / (sqrt C)) * (1.REAL C))),((p - p) + (((p1 / 2) / (sqrt C)) * (1.REAL C)))) is Relation-like Function-like set
multreal .: (((p - p) + (((p1 / 2) / (sqrt C)) * (1.REAL C))),((p - p) + (((p1 / 2) / (sqrt C)) * (1.REAL C)))) is set
K383((sqr ((p - p) + (((p1 / 2) / (sqrt C)) * (1.REAL C))))) is V11() real ext-real Element of REAL
K195(REAL,(sqr ((p - p) + (((p1 / 2) / (sqrt C)) * (1.REAL C)))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr ((p - p) + (((p1 / 2) / (sqrt C)) * (1.REAL C))))) is V11() real ext-real Element of REAL
(((p1 / 2) / (sqrt C)) * (1.REAL C)) + p is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) . ((((p1 / 2) / (sqrt C)) * (1.REAL C)),p) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[(((p1 / 2) / (sqrt C)) * (1.REAL C)),p] is non empty set
{(((p1 / 2) / (sqrt C)) * (1.REAL C)),p} is non empty functional V35() V39() set
{(((p1 / 2) / (sqrt C)) * (1.REAL C))} is non empty trivial functional V35() V39() 1 -element set
{{(((p1 / 2) / (sqrt C)) * (1.REAL C)),p},{(((p1 / 2) / (sqrt C)) * (1.REAL C))}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [(((p1 / 2) / (sqrt C)) * (1.REAL C)),p] is set
(((p1 / 2) / (sqrt C)) * (1.REAL C)) + p is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: ((((p1 / 2) / (sqrt C)) * (1.REAL C)),p) is set
((((p1 / 2) / (sqrt C)) * (1.REAL C)) + p) - p is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
K258((TOP-REAL C),((((p1 / 2) / (sqrt C)) * (1.REAL C)) + p),(- p)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) . (((((p1 / 2) / (sqrt C)) * (1.REAL C)) + p),(- p)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[((((p1 / 2) / (sqrt C)) * (1.REAL C)) + p),(- p)] is non empty set
{((((p1 / 2) / (sqrt C)) * (1.REAL C)) + p),(- p)} is non empty functional V35() V39() set
{((((p1 / 2) / (sqrt C)) * (1.REAL C)) + p)} is non empty trivial functional V35() V39() 1 -element set
{{((((p1 / 2) / (sqrt C)) * (1.REAL C)) + p),(- p)},{((((p1 / 2) / (sqrt C)) * (1.REAL C)) + p)}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [((((p1 / 2) / (sqrt C)) * (1.REAL C)) + p),(- p)] is set
((((p1 / 2) / (sqrt C)) * (1.REAL C)) + p) + (- p) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (((((p1 / 2) / (sqrt C)) * (1.REAL C)) + p),(- p)) is set
((((p1 / 2) / (sqrt C)) * (1.REAL C)) + p) - p is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
diffreal .: (((((p1 / 2) / (sqrt C)) * (1.REAL C)) + p),p) is set
K295(((((p1 / 2) / (sqrt C)) * (1.REAL C)) + p),K324(p)) is Relation-like Function-like set
|.(((((p1 / 2) / (sqrt C)) * (1.REAL C)) + p) - p).| is V11() real ext-real non negative Element of REAL
sqr (((((p1 / 2) / (sqrt C)) * (1.REAL C)) + p) - p) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(((((p1 / 2) / (sqrt C)) * (1.REAL C)) + p) - p) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((((((p1 / 2) / (sqrt C)) * (1.REAL C)) + p) - p),(((((p1 / 2) / (sqrt C)) * (1.REAL C)) + p) - p)) is Relation-like Function-like set
multreal .: ((((((p1 / 2) / (sqrt C)) * (1.REAL C)) + p) - p),(((((p1 / 2) / (sqrt C)) * (1.REAL C)) + p) - p)) is set
K383((sqr (((((p1 / 2) / (sqrt C)) * (1.REAL C)) + p) - p))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (((((p1 / 2) / (sqrt C)) * (1.REAL C)) + p) - p)),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (((((p1 / 2) / (sqrt C)) * (1.REAL C)) + p) - p))) is V11() real ext-real Element of REAL
|.(((p1 / 2) / (sqrt C)) * (1.REAL C)).| is V11() real ext-real non negative Element of REAL
sqr (((p1 / 2) / (sqrt C)) * (1.REAL C)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(((p1 / 2) / (sqrt C)) * (1.REAL C)) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((((p1 / 2) / (sqrt C)) * (1.REAL C)),(((p1 / 2) / (sqrt C)) * (1.REAL C))) is Relation-like Function-like set
multreal .: ((((p1 / 2) / (sqrt C)) * (1.REAL C)),(((p1 / 2) / (sqrt C)) * (1.REAL C))) is set
K383((sqr (((p1 / 2) / (sqrt C)) * (1.REAL C)))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (((p1 / 2) / (sqrt C)) * (1.REAL C))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (((p1 / 2) / (sqrt C)) * (1.REAL C)))) is V11() real ext-real Element of REAL
abs ((p1 / 2) / (sqrt C)) is V11() real ext-real Element of REAL
|.(1.REAL C).| is V11() real ext-real non negative Element of REAL
sqr (1.REAL C) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(1.REAL C) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((1.REAL C),(1.REAL C)) is Relation-like Function-like set
multreal .: ((1.REAL C),(1.REAL C)) is set
K383((sqr (1.REAL C))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (1.REAL C)),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (1.REAL C))) is V11() real ext-real Element of REAL
(abs ((p1 / 2) / (sqrt C))) * |.(1.REAL C).| is V11() real ext-real Element of REAL
(abs ((p1 / 2) / (sqrt C))) * (sqrt C) is V11() real ext-real Element of REAL
abs (p1 / 2) is V11() real ext-real Element of REAL
abs (sqrt C) is V11() real ext-real Element of REAL
(abs (p1 / 2)) / (abs (sqrt C)) is V11() real ext-real Element of REAL
((abs (p1 / 2)) / (abs (sqrt C))) * (sqrt C) is V11() real ext-real Element of REAL
(abs (p1 / 2)) / (sqrt C) is V11() real ext-real Element of REAL
((abs (p1 / 2)) / (sqrt C)) * (sqrt C) is V11() real ext-real Element of REAL
t2 is Element of the carrier of (Euclid C)
dist (C,t2) is V11() real ext-real Element of REAL
the distance of (Euclid C) is non empty Relation-like [: the carrier of (Euclid C), the carrier of (Euclid C):] -defined REAL -valued Function-like total V30([: the carrier of (Euclid C), the carrier of (Euclid C):], REAL ) complex-yielding V174() V175() Element of bool [:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:]
[: the carrier of (Euclid C), the carrier of (Euclid C):] is non empty set
[:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:] is non empty non trivial V35() set
the distance of (Euclid C) . (C,t2) is V11() real ext-real Element of REAL
[C,t2] is non empty set
{C,t2} is non empty V35() set
{C} is non empty trivial V35() 1 -element set
{{C,t2},{C}} is non empty V35() V39() set
the distance of (Euclid C) . [C,t2] is V11() real ext-real set
Ball (C,p1) is bounded Element of bool the carrier of (Euclid C)
[#] (TOP-REAL C) is 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 C)
C is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
C `1 is V11() real ext-real Element of REAL
C . 1 is V11() real ext-real Element of REAL
p is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
p `2 is V11() real ext-real Element of REAL
p . 2 is V11() real ext-real Element of REAL
C `2 is V11() real ext-real Element of REAL
C . 2 is V11() real ext-real Element of REAL
- (C `2) is V11() real ext-real Element of REAL
p `1 is V11() real ext-real Element of REAL
p . 1 is V11() real ext-real Element of REAL
WH is V11() real ext-real Element of REAL
WH * p is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
WH * p is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
WH multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
id REAL is non empty Relation-like REAL -defined REAL -valued Function-like one-to-one total V30( REAL , REAL ) complex-yielding V174() V175() increasing V179() Element of bool [:REAL,REAL:]
multreal [;] (WH,(id REAL)) is set
p (#) (WH multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
WH * WH is V11() real ext-real Element of REAL
1 + (WH * WH) is V11() real ext-real Element of REAL
0 + 0 is empty trivial ordinal natural V11() real ext-real non positive non negative Function-like functional V35() V39() cardinal {} -element FinSequence-membered V116() V117() V183() V184() V185() V186() V187() V188() V189() Element of NAT
WH * (- (C `2)) is V11() real ext-real Element of REAL
WH * (C `1) is V11() real ext-real Element of REAL
|[(WH * (- (C `2))),(WH * (C `1))]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
WH * (WH * (C `1)) is V11() real ext-real Element of REAL
- (WH * (WH * (C `1))) is V11() real ext-real Element of REAL
(WH * WH) * (C `1) is V11() real ext-real Element of REAL
- ((WH * WH) * (C `1)) is V11() real ext-real Element of REAL
(1 + (WH * WH)) * (C `1) is V11() real ext-real Element of REAL
(WH * WH) * (C `2) is V11() real ext-real Element of REAL
- ((WH * WH) * (C `2)) is V11() real ext-real Element of REAL
(1 + (WH * WH)) * (C `2) is V11() real ext-real Element of REAL
C is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
p is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
LSeg (C,p) is non empty closed connected compact bounded convex Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * C) + (b1 * p)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
{C} is non empty trivial functional V35() V39() 1 -element compact bounded Element of bool the carrier of (TOP-REAL 2)
(LSeg (C,p)) ` is open Element of bool the carrier of (TOP-REAL 2)
the carrier of (TOP-REAL 2) \ (LSeg (C,p)) is set
Cl ((LSeg (C,p)) `) is closed Element of bool the carrier of (TOP-REAL 2)
p12 is set
C - p is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
- p is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
- p is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
compreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
p (#) compreal is Relation-like Function-like V35() complex-yielding V174() V175() set
K38(1) is V11() real ext-real non positive set
K38(1) * p is Relation-like Function-like set
K38(1) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
id REAL is non empty Relation-like REAL -defined REAL -valued Function-like one-to-one total V30( REAL , REAL ) complex-yielding V174() V175() increasing V179() Element of bool [:REAL,REAL:]
multreal [;] (K38(1),(id REAL)) is set
p (#) (K38(1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
K258((TOP-REAL 2),C,(- p)) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) is non empty Relation-like [: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):] -defined the carrier of (TOP-REAL 2) -valued Function-like total V30([: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2)) 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):] is non empty set
[:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):] is 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
the U7 of (TOP-REAL 2) . (C,(- p)) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
[C,(- p)] is non empty set
{C,(- p)} is non empty functional V35() V39() set
{C} is non empty trivial functional V35() V39() 1 -element set
{{C,(- p)},{C}} is non empty V35() V39() set
the U7 of (TOP-REAL 2) . [C,(- p)] is set
C + (- p) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
addreal .: (C,(- p)) is set
C - p is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
diffreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K174(REAL,addreal,(id REAL),compreal) is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
diffreal .: (C,p) is set
K324(p) is Relation-like Function-like complex-yielding set
K295(C,K324(p)) is Relation-like Function-like set
EX2 is V11() real ext-real Element of REAL
1 - EX2 is V11() real ext-real Element of REAL
(1 - EX2) * C is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
(1 - EX2) * C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(1 - EX2) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] ((1 - EX2),(id REAL)) is set
C (#) ((1 - EX2) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
EX2 * p is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
EX2 * p is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
EX2 multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (EX2,(id REAL)) is set
p (#) (EX2 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
((1 - EX2) * C) + (EX2 * p) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) . (((1 - EX2) * C),(EX2 * p)) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
[((1 - EX2) * C),(EX2 * p)] is non empty set
{((1 - EX2) * C),(EX2 * p)} is non empty functional V35() V39() set
{((1 - EX2) * C)} is non empty trivial functional V35() V39() 1 -element set
{{((1 - EX2) * C),(EX2 * p)},{((1 - EX2) * C)}} is non empty V35() V39() set
the U7 of (TOP-REAL 2) . [((1 - EX2) * C),(EX2 * p)] is set
((1 - EX2) * C) + (EX2 * p) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (((1 - EX2) * C),(EX2 * p)) is set
|.(C - p).| is V11() real ext-real non negative Element of REAL
sqr (C - p) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
sqrreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
(C - p) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((C - p),(C - p)) is Relation-like Function-like set
multreal .: ((C - p),(C - p)) is set
K383((sqr (C - p))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (C - p)),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (C - p))) is V11() real ext-real Element of REAL
p1 is Element of bool the carrier of (TOP-REAL 2)
the topology of (TOP-REAL 2) is non empty Element of bool (bool the carrier of (TOP-REAL 2))
bool (bool the carrier of (TOP-REAL 2)) is non empty set
TopStruct(# the carrier of (TOP-REAL 2), the topology of (TOP-REAL 2) #) is non empty strict TopSpace-like TopStruct
TopSpaceMetr (Euclid 2) is TopStruct
the carrier of (TopSpaceMetr (Euclid 2)) is set
bool the carrier of (TopSpaceMetr (Euclid 2)) is non empty set
EX is Element of bool the carrier of (TopSpaceMetr (Euclid 2))
C is Element of the carrier of (Euclid 2)
t2 is V11() real ext-real set
Ball (C,t2) is bounded Element of bool the carrier of (Euclid 2)
bool the carrier of (Euclid 2) is non empty set
qt2 is V11() real ext-real Element of REAL
qt2 / 2 is V11() real ext-real Element of REAL
(C - p) `2 is V11() real ext-real Element of REAL
(C - p) . 2 is V11() real ext-real Element of REAL
- ((C - p) `2) is V11() real ext-real Element of REAL
(C - p) `1 is V11() real ext-real Element of REAL
(C - p) . 1 is V11() real ext-real Element of REAL
|[(- ((C - p) `2)),((C - p) `1)]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
(qt2 / 2) / |.(C - p).| is V11() real ext-real Element of REAL
((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]| is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]| is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
((qt2 / 2) / |.(C - p).|) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (((qt2 / 2) / |.(C - p).|),(id REAL)) is set
|[(- ((C - p) `2)),((C - p) `1)]| (#) (((qt2 / 2) / |.(C - p).|) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
(((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|) + (((1 - EX2) * C) + (EX2 * p)) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) . ((((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|),(((1 - EX2) * C) + (EX2 * p))) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
[(((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|),(((1 - EX2) * C) + (EX2 * p))] is non empty set
{(((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|),(((1 - EX2) * C) + (EX2 * p))} is non empty functional V35() V39() set
{(((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|)} is non empty trivial functional V35() V39() 1 -element set
{{(((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|),(((1 - EX2) * C) + (EX2 * p))},{(((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|)}} is non empty V35() V39() set
the U7 of (TOP-REAL 2) . [(((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|),(((1 - EX2) * C) + (EX2 * p))] is set
(((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|) + (((1 - EX2) * C) + (EX2 * p)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: ((((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|),(((1 - EX2) * C) + (EX2 * p))) is set
q4 is V11() real ext-real Element of REAL
1 - q4 is V11() real ext-real Element of REAL
(1 - q4) * C is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
(1 - q4) * C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(1 - q4) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] ((1 - q4),(id REAL)) is set
C (#) ((1 - q4) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
q4 * p is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
q4 * p is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
q4 multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (q4,(id REAL)) is set
p (#) (q4 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
((1 - q4) * C) + (q4 * p) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) . (((1 - q4) * C),(q4 * p)) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
[((1 - q4) * C),(q4 * p)] is non empty set
{((1 - q4) * C),(q4 * p)} is non empty functional V35() V39() set
{((1 - q4) * C)} is non empty trivial functional V35() V39() 1 -element set
{{((1 - q4) * C),(q4 * p)},{((1 - q4) * C)}} is non empty V35() V39() set
the U7 of (TOP-REAL 2) . [((1 - q4) * C),(q4 * p)] is set
((1 - q4) * C) + (q4 * p) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (((1 - q4) * C),(q4 * p)) is set
EX2 - q4 is V11() real ext-real Element of REAL
(((1 - EX2) * C) + (EX2 * p)) - (((1 - EX2) * C) + (EX2 * p)) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
- (((1 - EX2) * C) + (EX2 * p)) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
- (((1 - EX2) * C) + (EX2 * p)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(((1 - EX2) * C) + (EX2 * p)) (#) compreal is Relation-like Function-like V35() complex-yielding V174() V175() set
K38(1) * (((1 - EX2) * C) + (EX2 * p)) is Relation-like Function-like set
(((1 - EX2) * C) + (EX2 * p)) (#) (K38(1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
K258((TOP-REAL 2),(((1 - EX2) * C) + (EX2 * p)),(- (((1 - EX2) * C) + (EX2 * p)))) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) . ((((1 - EX2) * C) + (EX2 * p)),(- (((1 - EX2) * C) + (EX2 * p)))) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
[(((1 - EX2) * C) + (EX2 * p)),(- (((1 - EX2) * C) + (EX2 * p)))] is non empty set
{(((1 - EX2) * C) + (EX2 * p)),(- (((1 - EX2) * C) + (EX2 * p)))} is non empty functional V35() V39() set
{(((1 - EX2) * C) + (EX2 * p))} is non empty trivial functional V35() V39() 1 -element set
{{(((1 - EX2) * C) + (EX2 * p)),(- (((1 - EX2) * C) + (EX2 * p)))},{(((1 - EX2) * C) + (EX2 * p))}} is non empty V35() V39() set
the U7 of (TOP-REAL 2) . [(((1 - EX2) * C) + (EX2 * p)),(- (((1 - EX2) * C) + (EX2 * p)))] is set
(((1 - EX2) * C) + (EX2 * p)) + (- (((1 - EX2) * C) + (EX2 * p))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: ((((1 - EX2) * C) + (EX2 * p)),(- (((1 - EX2) * C) + (EX2 * p)))) is set
(((1 - EX2) * C) + (EX2 * p)) - (((1 - EX2) * C) + (EX2 * p)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
diffreal .: ((((1 - EX2) * C) + (EX2 * p)),(((1 - EX2) * C) + (EX2 * p))) is set
K324((((1 - EX2) * C) + (EX2 * p))) is Relation-like Function-like complex-yielding set
K295((((1 - EX2) * C) + (EX2 * p)),K324((((1 - EX2) * C) + (EX2 * p)))) is Relation-like Function-like set
2 " is non empty V11() real ext-real positive non negative Element of REAL
qt2 * (2 ") is V11() real ext-real Element of REAL
|.(C - p).| " is V11() real ext-real non negative Element of REAL
(qt2 * (2 ")) * (|.(C - p).| ") is V11() real ext-real Element of REAL
(2 ") * (|.(C - p).| ") is V11() real ext-real non negative Element of REAL
qt2 * ((2 ") * (|.(C - p).| ")) is V11() real ext-real Element of REAL
(0. (TOP-REAL 2)) `1 is V11() real ext-real Element of REAL
(0. (TOP-REAL 2)) . 1 is V11() real ext-real Element of REAL
(0. (TOP-REAL 2)) `2 is V11() real ext-real Element of REAL
(0. (TOP-REAL 2)) . 2 is V11() real ext-real Element of REAL
((((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|) + (((1 - EX2) * C) + (EX2 * p))) - (((1 - EX2) * C) + (EX2 * p)) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
K258((TOP-REAL 2),((((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|) + (((1 - EX2) * C) + (EX2 * p))),(- (((1 - EX2) * C) + (EX2 * p)))) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) . (((((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|) + (((1 - EX2) * C) + (EX2 * p))),(- (((1 - EX2) * C) + (EX2 * p)))) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
[((((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|) + (((1 - EX2) * C) + (EX2 * p))),(- (((1 - EX2) * C) + (EX2 * p)))] is non empty set
{((((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|) + (((1 - EX2) * C) + (EX2 * p))),(- (((1 - EX2) * C) + (EX2 * p)))} is non empty functional V35() V39() set
{((((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|) + (((1 - EX2) * C) + (EX2 * p)))} is non empty trivial functional V35() V39() 1 -element set
{{((((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|) + (((1 - EX2) * C) + (EX2 * p))),(- (((1 - EX2) * C) + (EX2 * p)))},{((((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|) + (((1 - EX2) * C) + (EX2 * p)))}} is non empty V35() V39() set
the U7 of (TOP-REAL 2) . [((((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|) + (((1 - EX2) * C) + (EX2 * p))),(- (((1 - EX2) * C) + (EX2 * p)))] is set
((((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|) + (((1 - EX2) * C) + (EX2 * p))) + (- (((1 - EX2) * C) + (EX2 * p))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (((((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|) + (((1 - EX2) * C) + (EX2 * p))),(- (((1 - EX2) * C) + (EX2 * p)))) is set
((((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|) + (((1 - EX2) * C) + (EX2 * p))) - (((1 - EX2) * C) + (EX2 * p)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
diffreal .: (((((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|) + (((1 - EX2) * C) + (EX2 * p))),(((1 - EX2) * C) + (EX2 * p))) is set
K295(((((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|) + (((1 - EX2) * C) + (EX2 * p))),K324((((1 - EX2) * C) + (EX2 * p)))) is Relation-like Function-like set
(((1 - q4) * C) + (q4 * p)) - ((1 - EX2) * C) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
- ((1 - EX2) * C) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
- ((1 - EX2) * C) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
((1 - EX2) * C) (#) compreal is Relation-like Function-like V35() complex-yielding V174() V175() set
K38(1) * ((1 - EX2) * C) is Relation-like Function-like set
((1 - EX2) * C) (#) (K38(1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
K258((TOP-REAL 2),(((1 - q4) * C) + (q4 * p)),(- ((1 - EX2) * C))) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) . ((((1 - q4) * C) + (q4 * p)),(- ((1 - EX2) * C))) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
[(((1 - q4) * C) + (q4 * p)),(- ((1 - EX2) * C))] is non empty set
{(((1 - q4) * C) + (q4 * p)),(- ((1 - EX2) * C))} is non empty functional V35() V39() set
{(((1 - q4) * C) + (q4 * p))} is non empty trivial functional V35() V39() 1 -element set
{{(((1 - q4) * C) + (q4 * p)),(- ((1 - EX2) * C))},{(((1 - q4) * C) + (q4 * p))}} is non empty V35() V39() set
the U7 of (TOP-REAL 2) . [(((1 - q4) * C) + (q4 * p)),(- ((1 - EX2) * C))] is set
(((1 - q4) * C) + (q4 * p)) + (- ((1 - EX2) * C)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: ((((1 - q4) * C) + (q4 * p)),(- ((1 - EX2) * C))) is set
(((1 - q4) * C) + (q4 * p)) - ((1 - EX2) * C) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
diffreal .: ((((1 - q4) * C) + (q4 * p)),((1 - EX2) * C)) is set
K324(((1 - EX2) * C)) is Relation-like Function-like complex-yielding set
K295((((1 - q4) * C) + (q4 * p)),K324(((1 - EX2) * C))) is Relation-like Function-like set
((((1 - q4) * C) + (q4 * p)) - ((1 - EX2) * C)) - (EX2 * p) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
- (EX2 * p) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
- (EX2 * p) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(EX2 * p) (#) compreal is Relation-like Function-like V35() complex-yielding V174() V175() set
K38(1) * (EX2 * p) is Relation-like Function-like set
(EX2 * p) (#) (K38(1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
K258((TOP-REAL 2),((((1 - q4) * C) + (q4 * p)) - ((1 - EX2) * C)),(- (EX2 * p))) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) . (((((1 - q4) * C) + (q4 * p)) - ((1 - EX2) * C)),(- (EX2 * p))) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
[((((1 - q4) * C) + (q4 * p)) - ((1 - EX2) * C)),(- (EX2 * p))] is non empty set
{((((1 - q4) * C) + (q4 * p)) - ((1 - EX2) * C)),(- (EX2 * p))} is non empty functional V35() V39() set
{((((1 - q4) * C) + (q4 * p)) - ((1 - EX2) * C))} is non empty trivial functional V35() V39() 1 -element set
{{((((1 - q4) * C) + (q4 * p)) - ((1 - EX2) * C)),(- (EX2 * p))},{((((1 - q4) * C) + (q4 * p)) - ((1 - EX2) * C))}} is non empty V35() V39() set
the U7 of (TOP-REAL 2) . [((((1 - q4) * C) + (q4 * p)) - ((1 - EX2) * C)),(- (EX2 * p))] is set
((((1 - q4) * C) + (q4 * p)) - ((1 - EX2) * C)) + (- (EX2 * p)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (((((1 - q4) * C) + (q4 * p)) - ((1 - EX2) * C)),(- (EX2 * p))) is set
((((1 - q4) * C) + (q4 * p)) - ((1 - EX2) * C)) - (EX2 * p) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
diffreal .: (((((1 - q4) * C) + (q4 * p)) - ((1 - EX2) * C)),(EX2 * p)) is set
K324((EX2 * p)) is Relation-like Function-like complex-yielding set
K295(((((1 - q4) * C) + (q4 * p)) - ((1 - EX2) * C)),K324((EX2 * p))) is Relation-like Function-like set
((1 - q4) * C) - ((1 - EX2) * C) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
K258((TOP-REAL 2),((1 - q4) * C),(- ((1 - EX2) * C))) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) . (((1 - q4) * C),(- ((1 - EX2) * C))) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
[((1 - q4) * C),(- ((1 - EX2) * C))] is non empty set
{((1 - q4) * C),(- ((1 - EX2) * C))} is non empty functional V35() V39() set
{{((1 - q4) * C),(- ((1 - EX2) * C))},{((1 - q4) * C)}} is non empty V35() V39() set
the U7 of (TOP-REAL 2) . [((1 - q4) * C),(- ((1 - EX2) * C))] is set
((1 - q4) * C) + (- ((1 - EX2) * C)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (((1 - q4) * C),(- ((1 - EX2) * C))) is set
((1 - q4) * C) - ((1 - EX2) * C) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
diffreal .: (((1 - q4) * C),((1 - EX2) * C)) is set
K295(((1 - q4) * C),K324(((1 - EX2) * C))) is Relation-like Function-like set
(((1 - q4) * C) - ((1 - EX2) * C)) + (q4 * p) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) . ((((1 - q4) * C) - ((1 - EX2) * C)),(q4 * p)) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
[(((1 - q4) * C) - ((1 - EX2) * C)),(q4 * p)] is non empty set
{(((1 - q4) * C) - ((1 - EX2) * C)),(q4 * p)} is non empty functional V35() V39() set
{(((1 - q4) * C) - ((1 - EX2) * C))} is non empty trivial functional V35() V39() 1 -element set
{{(((1 - q4) * C) - ((1 - EX2) * C)),(q4 * p)},{(((1 - q4) * C) - ((1 - EX2) * C))}} is non empty V35() V39() set
the U7 of (TOP-REAL 2) . [(((1 - q4) * C) - ((1 - EX2) * C)),(q4 * p)] is set
(((1 - q4) * C) - ((1 - EX2) * C)) + (q4 * p) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: ((((1 - q4) * C) - ((1 - EX2) * C)),(q4 * p)) is set
((((1 - q4) * C) - ((1 - EX2) * C)) + (q4 * p)) - (EX2 * p) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
K258((TOP-REAL 2),((((1 - q4) * C) - ((1 - EX2) * C)) + (q4 * p)),(- (EX2 * p))) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) . (((((1 - q4) * C) - ((1 - EX2) * C)) + (q4 * p)),(- (EX2 * p))) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
[((((1 - q4) * C) - ((1 - EX2) * C)) + (q4 * p)),(- (EX2 * p))] is non empty set
{((((1 - q4) * C) - ((1 - EX2) * C)) + (q4 * p)),(- (EX2 * p))} is non empty functional V35() V39() set
{((((1 - q4) * C) - ((1 - EX2) * C)) + (q4 * p))} is non empty trivial functional V35() V39() 1 -element set
{{((((1 - q4) * C) - ((1 - EX2) * C)) + (q4 * p)),(- (EX2 * p))},{((((1 - q4) * C) - ((1 - EX2) * C)) + (q4 * p))}} is non empty V35() V39() set
the U7 of (TOP-REAL 2) . [((((1 - q4) * C) - ((1 - EX2) * C)) + (q4 * p)),(- (EX2 * p))] is set
((((1 - q4) * C) - ((1 - EX2) * C)) + (q4 * p)) + (- (EX2 * p)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (((((1 - q4) * C) - ((1 - EX2) * C)) + (q4 * p)),(- (EX2 * p))) is set
((((1 - q4) * C) - ((1 - EX2) * C)) + (q4 * p)) - (EX2 * p) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
diffreal .: (((((1 - q4) * C) - ((1 - EX2) * C)) + (q4 * p)),(EX2 * p)) is set
K295(((((1 - q4) * C) - ((1 - EX2) * C)) + (q4 * p)),K324((EX2 * p))) is Relation-like Function-like set
(1 - q4) - (1 - EX2) is V11() real ext-real Element of REAL
((1 - q4) - (1 - EX2)) * C is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
((1 - q4) - (1 - EX2)) * C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
((1 - q4) - (1 - EX2)) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (((1 - q4) - (1 - EX2)),(id REAL)) is set
C (#) (((1 - q4) - (1 - EX2)) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
(((1 - q4) - (1 - EX2)) * C) + (q4 * p) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) . ((((1 - q4) - (1 - EX2)) * C),(q4 * p)) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
[(((1 - q4) - (1 - EX2)) * C),(q4 * p)] is non empty set
{(((1 - q4) - (1 - EX2)) * C),(q4 * p)} is non empty functional V35() V39() set
{(((1 - q4) - (1 - EX2)) * C)} is non empty trivial functional V35() V39() 1 -element set
{{(((1 - q4) - (1 - EX2)) * C),(q4 * p)},{(((1 - q4) - (1 - EX2)) * C)}} is non empty V35() V39() set
the U7 of (TOP-REAL 2) . [(((1 - q4) - (1 - EX2)) * C),(q4 * p)] is set
(((1 - q4) - (1 - EX2)) * C) + (q4 * p) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: ((((1 - q4) - (1 - EX2)) * C),(q4 * p)) is set
((((1 - q4) - (1 - EX2)) * C) + (q4 * p)) - (EX2 * p) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
K258((TOP-REAL 2),((((1 - q4) - (1 - EX2)) * C) + (q4 * p)),(- (EX2 * p))) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) . (((((1 - q4) - (1 - EX2)) * C) + (q4 * p)),(- (EX2 * p))) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
[((((1 - q4) - (1 - EX2)) * C) + (q4 * p)),(- (EX2 * p))] is non empty set
{((((1 - q4) - (1 - EX2)) * C) + (q4 * p)),(- (EX2 * p))} is non empty functional V35() V39() set
{((((1 - q4) - (1 - EX2)) * C) + (q4 * p))} is non empty trivial functional V35() V39() 1 -element set
{{((((1 - q4) - (1 - EX2)) * C) + (q4 * p)),(- (EX2 * p))},{((((1 - q4) - (1 - EX2)) * C) + (q4 * p))}} is non empty V35() V39() set
the U7 of (TOP-REAL 2) . [((((1 - q4) - (1 - EX2)) * C) + (q4 * p)),(- (EX2 * p))] is set
((((1 - q4) - (1 - EX2)) * C) + (q4 * p)) + (- (EX2 * p)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (((((1 - q4) - (1 - EX2)) * C) + (q4 * p)),(- (EX2 * p))) is set
((((1 - q4) - (1 - EX2)) * C) + (q4 * p)) - (EX2 * p) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
diffreal .: (((((1 - q4) - (1 - EX2)) * C) + (q4 * p)),(EX2 * p)) is set
K295(((((1 - q4) - (1 - EX2)) * C) + (q4 * p)),K324((EX2 * p))) is Relation-like Function-like set
(EX2 - q4) * C is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
(EX2 - q4) * C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(EX2 - q4) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] ((EX2 - q4),(id REAL)) is set
C (#) ((EX2 - q4) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
(q4 * p) - (EX2 * p) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
K258((TOP-REAL 2),(q4 * p),(- (EX2 * p))) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) . ((q4 * p),(- (EX2 * p))) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
[(q4 * p),(- (EX2 * p))] is non empty set
{(q4 * p),(- (EX2 * p))} is non empty functional V35() V39() set
{(q4 * p)} is non empty trivial functional V35() V39() 1 -element set
{{(q4 * p),(- (EX2 * p))},{(q4 * p)}} is non empty V35() V39() set
the U7 of (TOP-REAL 2) . [(q4 * p),(- (EX2 * p))] is set
(q4 * p) + (- (EX2 * p)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: ((q4 * p),(- (EX2 * p))) is set
(q4 * p) - (EX2 * p) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
diffreal .: ((q4 * p),(EX2 * p)) is set
K295((q4 * p),K324((EX2 * p))) is Relation-like Function-like set
((EX2 - q4) * C) + ((q4 * p) - (EX2 * p)) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) . (((EX2 - q4) * C),((q4 * p) - (EX2 * p))) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
[((EX2 - q4) * C),((q4 * p) - (EX2 * p))] is non empty set
{((EX2 - q4) * C),((q4 * p) - (EX2 * p))} is non empty functional V35() V39() set
{((EX2 - q4) * C)} is non empty trivial functional V35() V39() 1 -element set
{{((EX2 - q4) * C),((q4 * p) - (EX2 * p))},{((EX2 - q4) * C)}} is non empty V35() V39() set
the U7 of (TOP-REAL 2) . [((EX2 - q4) * C),((q4 * p) - (EX2 * p))] is set
((EX2 - q4) * C) + ((q4 * p) - (EX2 * p)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (((EX2 - q4) * C),((q4 * p) - (EX2 * p))) is set
q4 - EX2 is V11() real ext-real Element of REAL
(q4 - EX2) * p is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
(q4 - EX2) * p is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(q4 - EX2) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] ((q4 - EX2),(id REAL)) is set
p (#) ((q4 - EX2) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
((EX2 - q4) * C) + ((q4 - EX2) * p) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) . (((EX2 - q4) * C),((q4 - EX2) * p)) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
[((EX2 - q4) * C),((q4 - EX2) * p)] is non empty set
{((EX2 - q4) * C),((q4 - EX2) * p)} is non empty functional V35() V39() set
{{((EX2 - q4) * C),((q4 - EX2) * p)},{((EX2 - q4) * C)}} is non empty V35() V39() set
the U7 of (TOP-REAL 2) . [((EX2 - q4) * C),((q4 - EX2) * p)] is set
((EX2 - q4) * C) + ((q4 - EX2) * p) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (((EX2 - q4) * C),((q4 - EX2) * p)) is set
- (EX2 - q4) is V11() real ext-real Element of REAL
(- (EX2 - q4)) * p is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
(- (EX2 - q4)) * p is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(- (EX2 - q4)) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] ((- (EX2 - q4)),(id REAL)) is set
p (#) ((- (EX2 - q4)) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
((EX2 - q4) * C) + ((- (EX2 - q4)) * p) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) . (((EX2 - q4) * C),((- (EX2 - q4)) * p)) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
[((EX2 - q4) * C),((- (EX2 - q4)) * p)] is non empty set
{((EX2 - q4) * C),((- (EX2 - q4)) * p)} is non empty functional V35() V39() set
{{((EX2 - q4) * C),((- (EX2 - q4)) * p)},{((EX2 - q4) * C)}} is non empty V35() V39() set
the U7 of (TOP-REAL 2) . [((EX2 - q4) * C),((- (EX2 - q4)) * p)] is set
((EX2 - q4) * C) + ((- (EX2 - q4)) * p) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (((EX2 - q4) * C),((- (EX2 - q4)) * p)) is set
(EX2 - q4) * p is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
(EX2 - q4) * p is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
p (#) ((EX2 - q4) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
((EX2 - q4) * C) - ((EX2 - q4) * p) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
- ((EX2 - q4) * p) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
- ((EX2 - q4) * p) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
((EX2 - q4) * p) (#) compreal is Relation-like Function-like V35() complex-yielding V174() V175() set
K38(1) * ((EX2 - q4) * p) is Relation-like Function-like set
((EX2 - q4) * p) (#) (K38(1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
K258((TOP-REAL 2),((EX2 - q4) * C),(- ((EX2 - q4) * p))) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) . (((EX2 - q4) * C),(- ((EX2 - q4) * p))) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
[((EX2 - q4) * C),(- ((EX2 - q4) * p))] is non empty set
{((EX2 - q4) * C),(- ((EX2 - q4) * p))} is non empty functional V35() V39() set
{{((EX2 - q4) * C),(- ((EX2 - q4) * p))},{((EX2 - q4) * C)}} is non empty V35() V39() set
the U7 of (TOP-REAL 2) . [((EX2 - q4) * C),(- ((EX2 - q4) * p))] is set
((EX2 - q4) * C) + (- ((EX2 - q4) * p)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (((EX2 - q4) * C),(- ((EX2 - q4) * p))) is set
((EX2 - q4) * C) - ((EX2 - q4) * p) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
diffreal .: (((EX2 - q4) * C),((EX2 - q4) * p)) is set
K324(((EX2 - q4) * p)) is Relation-like Function-like complex-yielding set
K295(((EX2 - q4) * C),K324(((EX2 - q4) * p))) is Relation-like Function-like set
(EX2 - q4) * (C - p) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
(EX2 - q4) * (C - p) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(C - p) (#) ((EX2 - q4) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
1 / (EX2 - q4) is V11() real ext-real Element of REAL
(1 / (EX2 - q4)) * (EX2 - q4) is V11() real ext-real Element of REAL
((1 / (EX2 - q4)) * (EX2 - q4)) * (C - p) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
((1 / (EX2 - q4)) * (EX2 - q4)) * (C - p) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
((1 / (EX2 - q4)) * (EX2 - q4)) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (((1 / (EX2 - q4)) * (EX2 - q4)),(id REAL)) is set
(C - p) (#) (((1 / (EX2 - q4)) * (EX2 - q4)) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
(1 / (EX2 - q4)) * (((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
(1 / (EX2 - q4)) * (((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(1 / (EX2 - q4)) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] ((1 / (EX2 - q4)),(id REAL)) is set
(((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|) (#) ((1 / (EX2 - q4)) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
1 * (C - p) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
1 * (C - p) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
1 multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (1,(id REAL)) is set
(C - p) (#) (1 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
(1 / (EX2 - q4)) * ((qt2 / 2) / |.(C - p).|) is V11() real ext-real Element of REAL
((1 / (EX2 - q4)) * ((qt2 / 2) / |.(C - p).|)) * |[(- ((C - p) `2)),((C - p) `1)]| is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
((1 / (EX2 - q4)) * ((qt2 / 2) / |.(C - p).|)) * |[(- ((C - p) `2)),((C - p) `1)]| is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
((1 / (EX2 - q4)) * ((qt2 / 2) / |.(C - p).|)) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (((1 / (EX2 - q4)) * ((qt2 / 2) / |.(C - p).|)),(id REAL)) is set
|[(- ((C - p) `2)),((C - p) `1)]| (#) (((1 / (EX2 - q4)) * ((qt2 / 2) / |.(C - p).|)) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
|[(- ((C - p) `2)),((C - p) `1)]| `2 is V11() real ext-real Element of REAL
|[(- ((C - p) `2)),((C - p) `1)]| . 2 is V11() real ext-real Element of REAL
|[(- ((C - p) `2)),((C - p) `1)]| `1 is V11() real ext-real Element of REAL
|[(- ((C - p) `2)),((C - p) `1)]| . 1 is V11() real ext-real Element of REAL
the carrier of (TOP-REAL 2) \ (LSeg (C,p)) is Element of bool the carrier of (TOP-REAL 2)
- (((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
- (((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|) (#) compreal is Relation-like Function-like V35() complex-yielding V174() V175() set
K38(1) * (((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|) is Relation-like Function-like set
(((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|) (#) (K38(1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
(((1 - EX2) * C) + (EX2 * p)) + (- (((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|)) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) . ((((1 - EX2) * C) + (EX2 * p)),(- (((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|))) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
[(((1 - EX2) * C) + (EX2 * p)),(- (((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|))] is non empty set
{(((1 - EX2) * C) + (EX2 * p)),(- (((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|))} is non empty functional V35() V39() set
{{(((1 - EX2) * C) + (EX2 * p)),(- (((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|))},{(((1 - EX2) * C) + (EX2 * p))}} is non empty V35() V39() set
the U7 of (TOP-REAL 2) . [(((1 - EX2) * C) + (EX2 * p)),(- (((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|))] is set
(((1 - EX2) * C) + (EX2 * p)) + (- (((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: ((((1 - EX2) * C) + (EX2 * p)),(- (((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|))) is set
((((1 - EX2) * C) + (EX2 * p)) + (- (((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|))) - (((1 - EX2) * C) + (EX2 * p)) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
K258((TOP-REAL 2),((((1 - EX2) * C) + (EX2 * p)) + (- (((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|))),(- (((1 - EX2) * C) + (EX2 * p)))) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) . (((((1 - EX2) * C) + (EX2 * p)) + (- (((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|))),(- (((1 - EX2) * C) + (EX2 * p)))) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
[((((1 - EX2) * C) + (EX2 * p)) + (- (((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|))),(- (((1 - EX2) * C) + (EX2 * p)))] is non empty set
{((((1 - EX2) * C) + (EX2 * p)) + (- (((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|))),(- (((1 - EX2) * C) + (EX2 * p)))} is non empty functional V35() V39() set
{((((1 - EX2) * C) + (EX2 * p)) + (- (((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|)))} is non empty trivial functional V35() V39() 1 -element set
{{((((1 - EX2) * C) + (EX2 * p)) + (- (((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|))),(- (((1 - EX2) * C) + (EX2 * p)))},{((((1 - EX2) * C) + (EX2 * p)) + (- (((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|)))}} is non empty V35() V39() set
the U7 of (TOP-REAL 2) . [((((1 - EX2) * C) + (EX2 * p)) + (- (((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|))),(- (((1 - EX2) * C) + (EX2 * p)))] is set
((((1 - EX2) * C) + (EX2 * p)) + (- (((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|))) + (- (((1 - EX2) * C) + (EX2 * p))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (((((1 - EX2) * C) + (EX2 * p)) + (- (((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|))),(- (((1 - EX2) * C) + (EX2 * p)))) is set
((((1 - EX2) * C) + (EX2 * p)) + (- (((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|))) - (((1 - EX2) * C) + (EX2 * p)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
diffreal .: (((((1 - EX2) * C) + (EX2 * p)) + (- (((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|))),(((1 - EX2) * C) + (EX2 * p))) is set
K295(((((1 - EX2) * C) + (EX2 * p)) + (- (((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|))),K324((((1 - EX2) * C) + (EX2 * p)))) is Relation-like Function-like set
(((1 - EX2) * C) + (EX2 * p)) - ((((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|) + (((1 - EX2) * C) + (EX2 * p))) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
- ((((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|) + (((1 - EX2) * C) + (EX2 * p))) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
- ((((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|) + (((1 - EX2) * C) + (EX2 * p))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
((((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|) + (((1 - EX2) * C) + (EX2 * p))) (#) compreal is Relation-like Function-like V35() complex-yielding V174() V175() set
K38(1) * ((((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|) + (((1 - EX2) * C) + (EX2 * p))) is Relation-like Function-like set
((((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|) + (((1 - EX2) * C) + (EX2 * p))) (#) (K38(1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
K258((TOP-REAL 2),(((1 - EX2) * C) + (EX2 * p)),(- ((((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|) + (((1 - EX2) * C) + (EX2 * p))))) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) . ((((1 - EX2) * C) + (EX2 * p)),(- ((((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|) + (((1 - EX2) * C) + (EX2 * p))))) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
[(((1 - EX2) * C) + (EX2 * p)),(- ((((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|) + (((1 - EX2) * C) + (EX2 * p))))] is non empty set
{(((1 - EX2) * C) + (EX2 * p)),(- ((((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|) + (((1 - EX2) * C) + (EX2 * p))))} is non empty functional V35() V39() set
{{(((1 - EX2) * C) + (EX2 * p)),(- ((((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|) + (((1 - EX2) * C) + (EX2 * p))))},{(((1 - EX2) * C) + (EX2 * p))}} is non empty V35() V39() set
the U7 of (TOP-REAL 2) . [(((1 - EX2) * C) + (EX2 * p)),(- ((((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|) + (((1 - EX2) * C) + (EX2 * p))))] is set
(((1 - EX2) * C) + (EX2 * p)) + (- ((((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|) + (((1 - EX2) * C) + (EX2 * p)))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: ((((1 - EX2) * C) + (EX2 * p)),(- ((((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|) + (((1 - EX2) * C) + (EX2 * p))))) is set
(((1 - EX2) * C) + (EX2 * p)) - ((((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|) + (((1 - EX2) * C) + (EX2 * p))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
diffreal .: ((((1 - EX2) * C) + (EX2 * p)),((((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|) + (((1 - EX2) * C) + (EX2 * p)))) is set
K324(((((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|) + (((1 - EX2) * C) + (EX2 * p)))) is Relation-like Function-like complex-yielding set
K295((((1 - EX2) * C) + (EX2 * p)),K324(((((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|) + (((1 - EX2) * C) + (EX2 * p))))) is Relation-like Function-like set
|.((((1 - EX2) * C) + (EX2 * p)) - ((((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|) + (((1 - EX2) * C) + (EX2 * p)))).| is V11() real ext-real non negative Element of REAL
sqr ((((1 - EX2) * C) + (EX2 * p)) - ((((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|) + (((1 - EX2) * C) + (EX2 * p)))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
((((1 - EX2) * C) + (EX2 * p)) - ((((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|) + (((1 - EX2) * C) + (EX2 * p)))) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (((((1 - EX2) * C) + (EX2 * p)) - ((((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|) + (((1 - EX2) * C) + (EX2 * p)))),((((1 - EX2) * C) + (EX2 * p)) - ((((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|) + (((1 - EX2) * C) + (EX2 * p))))) is Relation-like Function-like set
multreal .: (((((1 - EX2) * C) + (EX2 * p)) - ((((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|) + (((1 - EX2) * C) + (EX2 * p)))),((((1 - EX2) * C) + (EX2 * p)) - ((((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|) + (((1 - EX2) * C) + (EX2 * p))))) is set
K383((sqr ((((1 - EX2) * C) + (EX2 * p)) - ((((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|) + (((1 - EX2) * C) + (EX2 * p)))))) is V11() real ext-real Element of REAL
K195(REAL,(sqr ((((1 - EX2) * C) + (EX2 * p)) - ((((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|) + (((1 - EX2) * C) + (EX2 * p))))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr ((((1 - EX2) * C) + (EX2 * p)) - ((((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|) + (((1 - EX2) * C) + (EX2 * p)))))) is V11() real ext-real Element of REAL
(((1 - EX2) * C) + (EX2 * p)) - (((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
K258((TOP-REAL 2),(((1 - EX2) * C) + (EX2 * p)),(- (((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|))) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
(((1 - EX2) * C) + (EX2 * p)) - (((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
diffreal .: ((((1 - EX2) * C) + (EX2 * p)),(((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|)) is set
K324((((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|)) is Relation-like Function-like complex-yielding set
K295((((1 - EX2) * C) + (EX2 * p)),K324((((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|))) is Relation-like Function-like set
((((1 - EX2) * C) + (EX2 * p)) - (((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|)) - (((1 - EX2) * C) + (EX2 * p)) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
K258((TOP-REAL 2),((((1 - EX2) * C) + (EX2 * p)) - (((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|)),(- (((1 - EX2) * C) + (EX2 * p)))) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) . (((((1 - EX2) * C) + (EX2 * p)) - (((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|)),(- (((1 - EX2) * C) + (EX2 * p)))) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
[((((1 - EX2) * C) + (EX2 * p)) - (((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|)),(- (((1 - EX2) * C) + (EX2 * p)))] is non empty set
{((((1 - EX2) * C) + (EX2 * p)) - (((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|)),(- (((1 - EX2) * C) + (EX2 * p)))} is non empty functional V35() V39() set
{((((1 - EX2) * C) + (EX2 * p)) - (((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|))} is non empty trivial functional V35() V39() 1 -element set
{{((((1 - EX2) * C) + (EX2 * p)) - (((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|)),(- (((1 - EX2) * C) + (EX2 * p)))},{((((1 - EX2) * C) + (EX2 * p)) - (((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|))}} is non empty V35() V39() set
the U7 of (TOP-REAL 2) . [((((1 - EX2) * C) + (EX2 * p)) - (((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|)),(- (((1 - EX2) * C) + (EX2 * p)))] is set
((((1 - EX2) * C) + (EX2 * p)) - (((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|)) + (- (((1 - EX2) * C) + (EX2 * p))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (((((1 - EX2) * C) + (EX2 * p)) - (((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|)),(- (((1 - EX2) * C) + (EX2 * p)))) is set
((((1 - EX2) * C) + (EX2 * p)) - (((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|)) - (((1 - EX2) * C) + (EX2 * p)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
diffreal .: (((((1 - EX2) * C) + (EX2 * p)) - (((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|)),(((1 - EX2) * C) + (EX2 * p))) is set
K295(((((1 - EX2) * C) + (EX2 * p)) - (((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|)),K324((((1 - EX2) * C) + (EX2 * p)))) is Relation-like Function-like set
|.(((((1 - EX2) * C) + (EX2 * p)) - (((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|)) - (((1 - EX2) * C) + (EX2 * p))).| is V11() real ext-real non negative Element of REAL
sqr (((((1 - EX2) * C) + (EX2 * p)) - (((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|)) - (((1 - EX2) * C) + (EX2 * p))) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(((((1 - EX2) * C) + (EX2 * p)) - (((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|)) - (((1 - EX2) * C) + (EX2 * p))) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((((((1 - EX2) * C) + (EX2 * p)) - (((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|)) - (((1 - EX2) * C) + (EX2 * p))),(((((1 - EX2) * C) + (EX2 * p)) - (((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|)) - (((1 - EX2) * C) + (EX2 * p)))) is Relation-like Function-like set
multreal .: ((((((1 - EX2) * C) + (EX2 * p)) - (((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|)) - (((1 - EX2) * C) + (EX2 * p))),(((((1 - EX2) * C) + (EX2 * p)) - (((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|)) - (((1 - EX2) * C) + (EX2 * p)))) is set
K383((sqr (((((1 - EX2) * C) + (EX2 * p)) - (((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|)) - (((1 - EX2) * C) + (EX2 * p))))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (((((1 - EX2) * C) + (EX2 * p)) - (((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|)) - (((1 - EX2) * C) + (EX2 * p)))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (((((1 - EX2) * C) + (EX2 * p)) - (((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|)) - (((1 - EX2) * C) + (EX2 * p))))) is V11() real ext-real Element of REAL
|.(- (((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|)).| is V11() real ext-real non negative Element of REAL
sqr (- (((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|)) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(- (((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|)) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((- (((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|)),(- (((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|))) is Relation-like Function-like set
multreal .: ((- (((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|)),(- (((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|))) is set
K383((sqr (- (((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|)))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (- (((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|))),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (- (((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|)))) is V11() real ext-real Element of REAL
|.(((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|).| is V11() real ext-real non negative Element of REAL
sqr (((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|),(((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|)) is Relation-like Function-like set
multreal .: ((((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|),(((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|)) is set
K383((sqr (((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|)),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (((qt2 / 2) / |.(C - p).|) * |[(- ((C - p) `2)),((C - p) `1)]|))) is V11() real ext-real Element of REAL
abs ((qt2 / 2) / |.(C - p).|) is V11() real ext-real Element of REAL
|.|[(- ((C - p) `2)),((C - p) `1)]|.| is V11() real ext-real non negative Element of REAL
sqr |[(- ((C - p) `2)),((C - p) `1)]| is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
|[(- ((C - p) `2)),((C - p) `1)]| (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (|[(- ((C - p) `2)),((C - p) `1)]|,|[(- ((C - p) `2)),((C - p) `1)]|) is Relation-like Function-like set
multreal .: (|[(- ((C - p) `2)),((C - p) `1)]|,|[(- ((C - p) `2)),((C - p) `1)]|) is set
K383((sqr |[(- ((C - p) `2)),((C - p) `1)]|)) is V11() real ext-real Element of REAL
K195(REAL,(sqr |[(- ((C - p) `2)),((C - p) `1)]|),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr |[(- ((C - p) `2)),((C - p) `1)]|)) is V11() real ext-real Element of REAL
(abs ((qt2 / 2) / |.(C - p).|)) * |.|[(- ((C - p) `2)),((C - p) `1)]|.| is V11() real ext-real Element of REAL
(- ((C - p) `2)) ^2 is V11() real ext-real Element of REAL
K37((- ((C - p) `2)),(- ((C - p) `2))) is V11() real ext-real set
((C - p) `1) ^2 is V11() real ext-real Element of REAL
K37(((C - p) `1),((C - p) `1)) is V11() real ext-real set
((- ((C - p) `2)) ^2) + (((C - p) `1) ^2) is V11() real ext-real Element of REAL
sqrt (((- ((C - p) `2)) ^2) + (((C - p) `1) ^2)) is V11() real ext-real Element of REAL
(abs ((qt2 / 2) / |.(C - p).|)) * (sqrt (((- ((C - p) `2)) ^2) + (((C - p) `1) ^2))) is V11() real ext-real Element of REAL
((C - p) `2) ^2 is V11() real ext-real Element of REAL
K37(((C - p) `2),((C - p) `2)) is V11() real ext-real set
(((C - p) `1) ^2) + (((C - p) `2) ^2) is V11() real ext-real Element of REAL
sqrt ((((C - p) `1) ^2) + (((C - p) `2) ^2)) is V11() real ext-real Element of REAL
(abs ((qt2 / 2) / |.(C - p).|)) * (sqrt ((((C - p) `1) ^2) + (((C - p) `2) ^2))) is V11() real ext-real Element of REAL
(abs ((qt2 / 2) / |.(C - p).|)) * |.(C - p).| is V11() real ext-real Element of REAL
abs (qt2 / 2) is V11() real ext-real Element of REAL
abs |.(C - p).| is V11() real ext-real Element of REAL
(abs (qt2 / 2)) / (abs |.(C - p).|) is V11() real ext-real Element of REAL
((abs (qt2 / 2)) / (abs |.(C - p).|)) * |.(C - p).| is V11() real ext-real Element of REAL
(abs (qt2 / 2)) / |.(C - p).| is V11() real ext-real Element of REAL
((abs (qt2 / 2)) / |.(C - p).|) * |.(C - p).| is V11() real ext-real Element of REAL
q4 is Element of the carrier of (Euclid 2)
dist (C,q4) is V11() real ext-real Element of REAL
the distance of (Euclid 2) is non empty Relation-like [: the carrier of (Euclid 2), the carrier of (Euclid 2):] -defined REAL -valued Function-like total V30([: the carrier of (Euclid 2), the carrier of (Euclid 2):], REAL ) complex-yielding V174() V175() Element of bool [:[: the carrier of (Euclid 2), the carrier of (Euclid 2):],REAL:]
[: the carrier of (Euclid 2), the carrier of (Euclid 2):] is non empty set
[:[: the carrier of (Euclid 2), the carrier of (Euclid 2):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[: the carrier of (Euclid 2), the carrier of (Euclid 2):],REAL:] is non empty non trivial V35() set
the distance of (Euclid 2) . (C,q4) is V11() real ext-real Element of REAL
[C,q4] is non empty set
{C,q4} is non empty V35() set
{C} is non empty trivial V35() 1 -element set
{{C,q4},{C}} is non empty V35() V39() set
the distance of (Euclid 2) . [C,q4] is V11() real ext-real set
Ball (C,qt2) is bounded Element of bool the carrier of (Euclid 2)
the carrier of (TOP-REAL 2) \ (LSeg (C,p)) is Element of bool the carrier of (TOP-REAL 2)
[#] (TOP-REAL 2) is 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 2)
C is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
p is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
LSeg (C,p) is non empty closed connected compact bounded convex Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * C) + (b1 * p)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
C is Relation-like NAT -defined the carrier of (TOP-REAL 2) -valued Function-like V35() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ C is closed compact bounded Element of bool the carrier of (TOP-REAL 2)
len C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
{ (LSeg (C,b1)) where b1 is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT : ( 1 <= b1 & b1 + 1 <= len C ) } is set
union { (LSeg (C,b1)) where b1 is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT : ( 1 <= b1 & b1 + 1 <= len C ) } is set
{ (LSeg (C,b1)) where b1 is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT : ( 1 <= b1 & b1 + 1 <= a1 ) } is set
union { (LSeg (C,b1)) where b1 is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT : ( 1 <= b1 & b1 + 1 <= a1 ) } is set
p is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
{ (LSeg (C,b1)) where b1 is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT : ( 1 <= b1 & b1 + 1 <= p ) } is set
union { (LSeg (C,b1)) where b1 is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT : ( 1 <= b1 & b1 + 1 <= p ) } is set
p + 1 is non empty ordinal natural V11() real ext-real positive non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
{ (LSeg (C,b1)) where b1 is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT : ( 1 <= b1 & b1 + 1 <= p + 1 ) } is set
union { (LSeg (C,b1)) where b1 is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT : ( 1 <= b1 & b1 + 1 <= p + 1 ) } is set
LSeg (C,p) is closed Element of bool the carrier of (TOP-REAL 2)
C /. p is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
C /. (p + 1) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
LSeg ((C /. p),(C /. (p + 1))) is non empty closed closed boundary nowhere_dense connected connected compact compact bounded bounded convex Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * (C /. p)) + (b1 * (C /. (p + 1)))) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
LSeg (C,p) is closed Element of bool the carrier of (TOP-REAL 2)
LSeg (C,p) is closed Element of bool the carrier of (TOP-REAL 2)
LSeg (C,p) is closed Element of bool the carrier of (TOP-REAL 2)
WH is set
p12 is set
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
LSeg (C,C) is closed Element of bool the carrier of (TOP-REAL 2)
C + 1 is non empty ordinal natural V11() real ext-real positive non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
WH is Element of bool the carrier of (TOP-REAL 2)
p12 is Element of bool the carrier of (TOP-REAL 2)
WH \/ (LSeg (C,p)) is Element of bool the carrier of (TOP-REAL 2)
C is set
r is set
EX2 is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
LSeg (C,EX2) is closed Element of bool the carrier of (TOP-REAL 2)
EX2 + 1 is non empty ordinal natural V11() real ext-real positive non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
C is set
r is set
EX2 is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
LSeg (C,EX2) is closed Element of bool the carrier of (TOP-REAL 2)
EX2 + 1 is non empty ordinal natural V11() real ext-real positive non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
{ (LSeg (C,b1)) where b1 is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT : ( 1 <= b1 & b1 + 1 <= 0 ) } is set
union { (LSeg (C,b1)) where b1 is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT : ( 1 <= b1 & b1 + 1 <= 0 ) } is set
p is set
WH is set
p12 is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
LSeg (C,p12) is closed Element of bool the carrier of (TOP-REAL 2)
p12 + 1 is non empty ordinal natural V11() real ext-real positive non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
p is Element of bool the carrier of (TOP-REAL 2)
C is Relation-like NAT -defined the carrier of (TOP-REAL 2) -valued Function-like V35() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ C is closed compact bounded Element of bool the carrier of (TOP-REAL 2)
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
Euclid C is non empty strict Reflexive discerning symmetric triangle Discerning MetrStruct
REAL C is non empty functional FinSequence-membered FinSequenceSet of REAL
C -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = C } is set
Pitag_dist C is non empty Relation-like [:(REAL C),(REAL C):] -defined REAL -valued Function-like total V30([:(REAL C),(REAL C):], REAL ) complex-yielding V174() V175() Element of bool [:[:(REAL C),(REAL C):],REAL:]
[:(REAL C),(REAL C):] is non empty set
[:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() set
MetrStruct(# (REAL C),(Pitag_dist C) #) is strict MetrStruct
the carrier of (Euclid C) is non empty set
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
p is V11() real ext-real Element of REAL
WH is Element of the carrier of (Euclid C)
Ball (WH,p) is bounded Element of bool the carrier of (Euclid C)
bool the carrier of (Euclid C) is non empty set
p12 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
p12 - C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
- C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
- C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
compreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
C (#) compreal is Relation-like Function-like V35() complex-yielding V174() V175() set
K38(1) is V11() real ext-real non positive set
K38(1) * C is Relation-like Function-like set
K38(1) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
id REAL is non empty Relation-like REAL -defined REAL -valued Function-like one-to-one total V30( REAL , REAL ) complex-yielding V174() V175() increasing V179() Element of bool [:REAL,REAL:]
multreal [;] (K38(1),(id REAL)) is set
C (#) (K38(1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
K258((TOP-REAL C),p12,(- C)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) is non empty Relation-like [: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):] -defined the carrier of (TOP-REAL C) -valued Function-like total V30([: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C)) Element of bool [:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):]
[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):] is non empty set
[:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):] is non empty set
bool [:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):] is non empty set
the U7 of (TOP-REAL C) . (p12,(- C)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[p12,(- C)] is non empty set
{p12,(- C)} is non empty functional V35() V39() set
{p12} is non empty trivial functional V35() V39() 1 -element set
{{p12,(- C)},{p12}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [p12,(- C)] is set
p12 + (- C) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
addreal .: (p12,(- C)) is set
p12 - C is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
diffreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K174(REAL,addreal,(id REAL),compreal) is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
diffreal .: (p12,C) is set
K324(C) is Relation-like Function-like complex-yielding set
K295(p12,K324(C)) is Relation-like Function-like set
|.(p12 - C).| is V11() real ext-real non negative Element of REAL
sqr (p12 - C) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
sqrreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
(p12 - C) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((p12 - C),(p12 - C)) is Relation-like Function-like set
multreal .: ((p12 - C),(p12 - C)) is set
K383((sqr (p12 - C))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (p12 - C)),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (p12 - C))) is V11() real ext-real Element of REAL
C - p12 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
- p12 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
- p12 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
p12 (#) compreal is Relation-like Function-like V35() complex-yielding V174() V175() set
K38(1) * p12 is Relation-like Function-like set
p12 (#) (K38(1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
K258((TOP-REAL C),C,(- p12)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) . (C,(- p12)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[C,(- p12)] is non empty set
{C,(- p12)} is non empty functional V35() V39() set
{C} is non empty trivial functional V35() V39() 1 -element set
{{C,(- p12)},{C}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [C,(- p12)] is set
C + (- p12) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (C,(- p12)) is set
C - p12 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
diffreal .: (C,p12) is set
K324(p12) is Relation-like Function-like complex-yielding set
K295(C,K324(p12)) is Relation-like Function-like set
|.(C - p12).| is V11() real ext-real non negative Element of REAL
sqr (C - p12) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(C - p12) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((C - p12),(C - p12)) is Relation-like Function-like set
multreal .: ((C - p12),(C - p12)) is set
K383((sqr (C - p12))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (C - p12)),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (C - p12))) is V11() real ext-real Element of REAL
r is Element of the carrier of (Euclid C)
dist (WH,r) is V11() real ext-real Element of REAL
the distance of (Euclid C) is non empty Relation-like [: the carrier of (Euclid C), the carrier of (Euclid C):] -defined REAL -valued Function-like total V30([: the carrier of (Euclid C), the carrier of (Euclid C):], REAL ) complex-yielding V174() V175() Element of bool [:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:]
[: the carrier of (Euclid C), the carrier of (Euclid C):] is non empty set
[:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:] is non empty non trivial V35() set
the distance of (Euclid C) . (WH,r) is V11() real ext-real Element of REAL
[WH,r] is non empty set
{WH,r} is non empty V35() set
{WH} is non empty trivial V35() 1 -element set
{{WH,r},{WH}} is non empty V35() V39() set
the distance of (Euclid C) . [WH,r] is V11() real ext-real set
C is non empty compact bounded non horizontal non vertical Element of bool the carrier of (TOP-REAL 2)
SpStSeq C is non empty non trivial Relation-like NAT -defined the carrier of (TOP-REAL 2) -valued Function-like non constant V35() FinSequence-like FinSubsequence-like V262( the carrier of (TOP-REAL 2)) special unfolded s.c.c. standard rectangular clockwise_oriented FinSequence of the carrier of (TOP-REAL 2)
L~ (SpStSeq C) is non empty closed boundary nowhere_dense compact bounded bounded non horizontal non vertical Jordan Element of bool the carrier of (TOP-REAL 2)
(2,(L~ (SpStSeq C))) is Element of bool the carrier of (TOP-REAL 2)
{ b1 where b1 is Element of bool the carrier of (TOP-REAL 2) : (2, L~ (SpStSeq C),b1) } is set
union { b1 where b1 is Element of bool the carrier of (TOP-REAL 2) : (2, L~ (SpStSeq C),b1) } is set
p is V11() real ext-real Element of REAL
WH is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
the Element of (2,(L~ (SpStSeq C))) is Element of (2,(L~ (SpStSeq C)))
(L~ (SpStSeq C)) ` is open dense Element of bool the carrier of (TOP-REAL 2)
the carrier of (TOP-REAL 2) \ (L~ (SpStSeq C)) is set
(TOP-REAL 2) | ((L~ (SpStSeq C)) `) is strict TopSpace-like SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | ((L~ (SpStSeq C)) `)) is set
bool the carrier of ((TOP-REAL 2) | ((L~ (SpStSeq C)) `)) is non empty set
r is Element of bool the carrier of (TOP-REAL 2)
EX2 is Element of bool the carrier of (TOP-REAL 2)
r \/ EX2 is Element of bool the carrier of (TOP-REAL 2)
Cl r is closed Element of bool the carrier of (TOP-REAL 2)
(Cl r) \ r is Element of bool the carrier of (TOP-REAL 2)
Cl EX2 is closed Element of bool the carrier of (TOP-REAL 2)
(Cl EX2) \ EX2 is Element of bool the carrier of (TOP-REAL 2)
Down (EX2,((L~ (SpStSeq C)) `)) is Element of bool the carrier of ((TOP-REAL 2) | ((L~ (SpStSeq C)) `))
EX2 /\ ((L~ (SpStSeq C)) `) is Element of bool the carrier of (TOP-REAL 2)
EX1 is Element of bool the carrier of ((TOP-REAL 2) | ((L~ (SpStSeq C)) `))
[#] ((TOP-REAL 2) | ((L~ (SpStSeq C)) `)) is non proper open closed dense Element of bool the carrier of ((TOP-REAL 2) | ((L~ (SpStSeq C)) `))
Down (r,((L~ (SpStSeq C)) `)) is Element of bool the carrier of ((TOP-REAL 2) | ((L~ (SpStSeq C)) `))
r /\ ((L~ (SpStSeq C)) `) is Element of bool the carrier of (TOP-REAL 2)
EX1 /\ (Down (r,((L~ (SpStSeq C)) `))) is Element of bool the carrier of ((TOP-REAL 2) | ((L~ (SpStSeq C)) `))
{} ((TOP-REAL 2) | ((L~ (SpStSeq C)) `)) is empty trivial ordinal natural V11() real ext-real non positive non negative Function-like functional V35() V39() cardinal {} -element FinSequence-membered open closed boundary nowhere_dense V183() V184() V185() V186() V187() V188() V189() Element of bool the carrier of ((TOP-REAL 2) | ((L~ (SpStSeq C)) `))
Cl (2,(L~ (SpStSeq C))) is closed Element of bool the carrier of (TOP-REAL 2)
p1 is Element of the carrier of (Euclid 2)
Ball (p1,p) is bounded Element of bool the carrier of (Euclid 2)
bool the carrier of (Euclid 2) is non empty set
the distance of (Euclid 2) is non empty Relation-like [: the carrier of (Euclid 2), the carrier of (Euclid 2):] -defined REAL -valued Function-like total V30([: the carrier of (Euclid 2), the carrier of (Euclid 2):], REAL ) complex-yielding V174() V175() Element of bool [:[: the carrier of (Euclid 2), the carrier of (Euclid 2):],REAL:]
[: the carrier of (Euclid 2), the carrier of (Euclid 2):] is non empty set
[:[: the carrier of (Euclid 2), the carrier of (Euclid 2):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[: the carrier of (Euclid 2), the carrier of (Euclid 2):],REAL:] is non empty non trivial V35() set
dist (p1,p1) is V11() real ext-real Element of REAL
the distance of (Euclid 2) . (p1,p1) is V11() real ext-real Element of REAL
[p1,p1] is non empty set
{p1,p1} is non empty V35() set
{p1} is non empty trivial V35() 1 -element set
{{p1,p1},{p1}} is non empty V35() V39() set
the distance of (Euclid 2) . [p1,p1] is V11() real ext-real set
EX is Element of bool the carrier of (TOP-REAL 2)
t2 is set
qt2 is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
WH - qt2 is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
- qt2 is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
- qt2 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
compreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
qt2 (#) compreal is Relation-like Function-like V35() complex-yielding V174() V175() set
K38(1) is V11() real ext-real non positive set
K38(1) * qt2 is Relation-like Function-like set
K38(1) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
id REAL is non empty Relation-like REAL -defined REAL -valued Function-like one-to-one total V30( REAL , REAL ) complex-yielding V174() V175() increasing V179() Element of bool [:REAL,REAL:]
multreal [;] (K38(1),(id REAL)) is set
qt2 (#) (K38(1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
K258((TOP-REAL 2),WH,(- qt2)) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) is non empty Relation-like [: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):] -defined the carrier of (TOP-REAL 2) -valued Function-like total V30([: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2)) 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):] is non empty set
[:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):] is 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
the U7 of (TOP-REAL 2) . (WH,(- qt2)) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
[WH,(- qt2)] is non empty set
{WH,(- qt2)} is non empty functional V35() V39() set
{WH} is non empty trivial functional V35() V39() 1 -element set
{{WH,(- qt2)},{WH}} is non empty V35() V39() set
the U7 of (TOP-REAL 2) . [WH,(- qt2)] is set
WH + (- qt2) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
addreal .: (WH,(- qt2)) is set
WH - qt2 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
diffreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K174(REAL,addreal,(id REAL),compreal) is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
diffreal .: (WH,qt2) is set
K324(qt2) is Relation-like Function-like complex-yielding set
K295(WH,K324(qt2)) is Relation-like Function-like set
|.(WH - qt2).| is V11() real ext-real non negative Element of REAL
sqr (WH - qt2) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
sqrreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
(WH - qt2) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((WH - qt2),(WH - qt2)) is Relation-like Function-like set
multreal .: ((WH - qt2),(WH - qt2)) is set
K383((sqr (WH - qt2))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (WH - qt2)),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (WH - qt2))) is V11() real ext-real Element of REAL
EX1 /\ (Down (EX2,((L~ (SpStSeq C)) `))) is Element of bool the carrier of ((TOP-REAL 2) | ((L~ (SpStSeq C)) `))
{} ((TOP-REAL 2) | ((L~ (SpStSeq C)) `)) is empty trivial ordinal natural V11() real ext-real non positive non negative Function-like functional V35() V39() cardinal {} -element FinSequence-membered open closed boundary nowhere_dense V183() V184() V185() V186() V187() V188() V189() Element of bool the carrier of ((TOP-REAL 2) | ((L~ (SpStSeq C)) `))
Cl (2,(L~ (SpStSeq C))) is closed Element of bool the carrier of (TOP-REAL 2)
p1 is Element of the carrier of (Euclid 2)
Ball (p1,p) is bounded Element of bool the carrier of (Euclid 2)
bool the carrier of (Euclid 2) is non empty set
the distance of (Euclid 2) is non empty Relation-like [: the carrier of (Euclid 2), the carrier of (Euclid 2):] -defined REAL -valued Function-like total V30([: the carrier of (Euclid 2), the carrier of (Euclid 2):], REAL ) complex-yielding V174() V175() Element of bool [:[: the carrier of (Euclid 2), the carrier of (Euclid 2):],REAL:]
[: the carrier of (Euclid 2), the carrier of (Euclid 2):] is non empty set
[:[: the carrier of (Euclid 2), the carrier of (Euclid 2):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[: the carrier of (Euclid 2), the carrier of (Euclid 2):],REAL:] is non empty non trivial V35() set
dist (p1,p1) is V11() real ext-real Element of REAL
the distance of (Euclid 2) . (p1,p1) is V11() real ext-real Element of REAL
[p1,p1] is non empty set
{p1,p1} is non empty V35() set
{p1} is non empty trivial V35() 1 -element set
{{p1,p1},{p1}} is non empty V35() V39() set
the distance of (Euclid 2) . [p1,p1] is V11() real ext-real set
EX is Element of bool the carrier of (TOP-REAL 2)
t2 is set
qt2 is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
WH - qt2 is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
- qt2 is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
- qt2 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
compreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
qt2 (#) compreal is Relation-like Function-like V35() complex-yielding V174() V175() set
K38(1) is V11() real ext-real non positive set
K38(1) * qt2 is Relation-like Function-like set
K38(1) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
id REAL is non empty Relation-like REAL -defined REAL -valued Function-like one-to-one total V30( REAL , REAL ) complex-yielding V174() V175() increasing V179() Element of bool [:REAL,REAL:]
multreal [;] (K38(1),(id REAL)) is set
qt2 (#) (K38(1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
K258((TOP-REAL 2),WH,(- qt2)) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) is non empty Relation-like [: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):] -defined the carrier of (TOP-REAL 2) -valued Function-like total V30([: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2)) 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):] is non empty set
[:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):] is 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
the U7 of (TOP-REAL 2) . (WH,(- qt2)) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
[WH,(- qt2)] is non empty set
{WH,(- qt2)} is non empty functional V35() V39() set
{WH} is non empty trivial functional V35() V39() 1 -element set
{{WH,(- qt2)},{WH}} is non empty V35() V39() set
the U7 of (TOP-REAL 2) . [WH,(- qt2)] is set
WH + (- qt2) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
addreal .: (WH,(- qt2)) is set
WH - qt2 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
diffreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K174(REAL,addreal,(id REAL),compreal) is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
diffreal .: (WH,qt2) is set
K324(qt2) is Relation-like Function-like complex-yielding set
K295(WH,K324(qt2)) is Relation-like Function-like set
|.(WH - qt2).| is V11() real ext-real non negative Element of REAL
sqr (WH - qt2) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
sqrreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
(WH - qt2) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((WH - qt2),(WH - qt2)) is Relation-like Function-like set
multreal .: ((WH - qt2),(WH - qt2)) is set
K383((sqr (WH - qt2))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (WH - qt2)),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (WH - qt2))) is V11() real ext-real Element of REAL
{(0. (TOP-REAL 0))} is non empty trivial functional V35() V39() 1 -element V183() V184() V185() V186() V187() V188() Element of bool REAL
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
bool the carrier of (TOP-REAL C) is non empty set
p is Element of bool the carrier of (TOP-REAL C)
(C,p) is Element of bool the carrier of (TOP-REAL C)
{ b1 where b1 is Element of bool the carrier of (TOP-REAL C) : (C,p,b1) } is set
union { b1 where b1 is Element of bool the carrier of (TOP-REAL C) : (C,p,b1) } is set
WH is V11() real ext-real Element of REAL
REAL C is non empty functional FinSequence-membered FinSequenceSet of REAL
C -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = C } is set
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C) : not WH <= |.b1.| } is set
(REAL C) \ { b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C) : not WH <= |.b1.| } is functional FinSequence-membered Element of bool (REAL C)
bool (REAL C) is non empty set
C is Element of bool the carrier of (TOP-REAL C)
p ` is Element of bool the carrier of (TOP-REAL C)
the carrier of (TOP-REAL C) \ p is set
r is set
EX2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.EX2.| is V11() real ext-real non negative Element of REAL
sqr EX2 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
sqrreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
EX2 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (EX2,EX2) is Relation-like Function-like set
multreal .: (EX2,EX2) is set
K383((sqr EX2)) is V11() real ext-real Element of REAL
addreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K195(REAL,(sqr EX2),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr EX2)) is V11() real ext-real Element of REAL
Down (C,(p `)) is Element of bool the carrier of ((TOP-REAL C) | (p `))
(TOP-REAL C) | (p `) is strict TopSpace-like SubSpace of TOP-REAL C
the carrier of ((TOP-REAL C) | (p `)) is set
bool the carrier of ((TOP-REAL C) | (p `)) is non empty set
C /\ (p `) is Element of bool the carrier of (TOP-REAL C)
r is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.r.| is V11() real ext-real non negative Element of REAL
sqr r is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
sqrreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
r (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (r,r) is Relation-like Function-like set
multreal .: (r,r) is set
K383((sqr r)) is V11() real ext-real Element of REAL
addreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K195(REAL,(sqr r),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr r)) is V11() real ext-real Element of REAL
EX2 is set
EX1 is Element of bool the carrier of (TOP-REAL C)
p1 is Element of bool the carrier of ((TOP-REAL C) | (p `))
EX is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.EX.| is V11() real ext-real non negative Element of REAL
sqr EX is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
EX (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (EX,EX) is Relation-like Function-like set
multreal .: (EX,EX) is set
K383((sqr EX)) is V11() real ext-real Element of REAL
K195(REAL,(sqr EX),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr EX)) is V11() real ext-real Element of REAL
C /\ p1 is Element of bool the carrier of ((TOP-REAL C) | (p `))
{} ((TOP-REAL C) | (p `)) is empty trivial ordinal natural V11() real ext-real non positive non negative Function-like functional V35() V39() cardinal {} -element FinSequence-membered open closed boundary nowhere_dense V183() V184() V185() V186() V187() V188() V189() Element of bool the carrier of ((TOP-REAL C) | (p `))
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C) : for b2 being V11() real ext-real Element of REAL holds
( not b1 = |[b2]| or WH <= b2 ) } is set
r is set
EX2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
- WH is V11() real ext-real Element of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C) : for b2 being V11() real ext-real Element of REAL holds
( not b1 = |[b2]| or b2 <= - WH ) } is set
EX2 is set
EX1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
1 + 1 is non empty ordinal natural V11() real ext-real positive non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
EX2 is Element of bool the carrier of (TOP-REAL C)
r is Element of bool the carrier of (TOP-REAL C)
EX2 \/ r is Element of bool the carrier of (TOP-REAL C)
EX1 is set
p1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
EX is V11() real ext-real Element of REAL
<*EX*> is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() FinSequence of REAL
|.p1.| is V11() real ext-real non negative Element of REAL
sqr p1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
sqrreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
p1 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (p1,p1) is Relation-like Function-like set
multreal .: (p1,p1) is set
K383((sqr p1)) is V11() real ext-real Element of REAL
addreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K195(REAL,(sqr p1),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr p1)) is V11() real ext-real Element of REAL
abs EX is V11() real ext-real Element of REAL
t2 is V11() real ext-real Element of REAL
|[t2]| is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
t2 is V11() real ext-real Element of REAL
|[t2]| is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
EX1 is set
p1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.p1.| is V11() real ext-real non negative Element of REAL
sqr p1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
sqrreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
p1 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (p1,p1) is Relation-like Function-like set
multreal .: (p1,p1) is set
K383((sqr p1)) is V11() real ext-real Element of REAL
addreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K195(REAL,(sqr p1),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr p1)) is V11() real ext-real Element of REAL
EX is V11() real ext-real Element of REAL
<*EX*> is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() FinSequence of REAL
t2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
abs EX is V11() real ext-real Element of REAL
- 0 is empty trivial ordinal natural V11() real ext-real non positive non negative Function-like functional V35() V39() cardinal {} -element FinSequence-membered V183() V184() V185() V186() V187() V188() V189() Element of REAL
abs EX is V11() real ext-real Element of REAL
- EX is V11() real ext-real Element of REAL
t2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
abs EX is V11() real ext-real Element of REAL
abs EX is V11() real ext-real Element of REAL
p1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.p1.| is V11() real ext-real non negative Element of REAL
sqr p1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
sqrreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
p1 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (p1,p1) is Relation-like Function-like set
multreal .: (p1,p1) is set
K383((sqr p1)) is V11() real ext-real Element of REAL
addreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K195(REAL,(sqr p1),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr p1)) is V11() real ext-real Element of REAL
EX is V11() real ext-real Element of REAL
<*EX*> is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() FinSequence of REAL
t2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
abs EX is V11() real ext-real Element of REAL
abs EX is V11() real ext-real Element of REAL
abs EX is V11() real ext-real Element of REAL
abs EX is V11() real ext-real Element of REAL
Down (r,(p `)) is Element of bool the carrier of ((TOP-REAL C) | (p `))
r /\ (p `) is Element of bool the carrier of (TOP-REAL C)
EX1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
p1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
LSeg (EX1,p1) is non empty closed connected compact bounded convex Element of bool the carrier of (TOP-REAL C)
{ (((1 - b1) * EX1) + (b1 * p1)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
EX is V11() real ext-real Element of REAL
<*EX*> is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() FinSequence of REAL
t2 is V11() real ext-real Element of REAL
<*t2*> is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() FinSequence of REAL
qt2 is set
r2 is V11() real ext-real Element of REAL
1 - r2 is V11() real ext-real Element of REAL
(1 - r2) * EX1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
(1 - r2) * EX1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(1 - r2) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
id REAL is non empty Relation-like REAL -defined REAL -valued Function-like one-to-one total V30( REAL , REAL ) complex-yielding V174() V175() increasing V179() Element of bool [:REAL,REAL:]
multreal [;] ((1 - r2),(id REAL)) is set
EX1 (#) ((1 - r2) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
r2 * p1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
r2 * p1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
r2 multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (r2,(id REAL)) is set
p1 (#) (r2 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
((1 - r2) * EX1) + (r2 * p1) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) is non empty Relation-like [: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):] -defined the carrier of (TOP-REAL C) -valued Function-like total V30([: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C)) Element of bool [:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):]
[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):] is non empty set
[:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):] is non empty set
bool [:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):] is non empty set
the U7 of (TOP-REAL C) . (((1 - r2) * EX1),(r2 * p1)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[((1 - r2) * EX1),(r2 * p1)] is non empty set
{((1 - r2) * EX1),(r2 * p1)} is non empty functional V35() V39() set
{((1 - r2) * EX1)} is non empty trivial functional V35() V39() 1 -element set
{{((1 - r2) * EX1),(r2 * p1)},{((1 - r2) * EX1)}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [((1 - r2) * EX1),(r2 * p1)] is set
((1 - r2) * EX1) + (r2 * p1) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
addreal .: (((1 - r2) * EX1),(r2 * p1)) is set
(1 - r2) * EX is V11() real ext-real Element of REAL
|[((1 - r2) * EX)]| is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
r2 * t2 is V11() real ext-real Element of REAL
|[(r2 * t2)]| is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
((1 - r2) * EX) + (r2 * t2) is V11() real ext-real Element of REAL
|[(((1 - r2) * EX) + (r2 * t2))]| is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
q4 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
r5 is V11() real ext-real Element of REAL
|[r5]| is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
(1 - r2) * WH is V11() real ext-real Element of REAL
r0 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
r2 * WH is V11() real ext-real Element of REAL
((1 - r2) * WH) + (r2 * WH) is V11() real ext-real Element of REAL
r0 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
Down (EX2,(p `)) is Element of bool the carrier of ((TOP-REAL C) | (p `))
EX2 /\ (p `) is Element of bool the carrier of (TOP-REAL C)
EX1 is V11() real ext-real Element of REAL
abs EX1 is V11() real ext-real Element of REAL
abs WH is V11() real ext-real Element of REAL
(abs EX1) + (abs WH) is V11() real ext-real Element of REAL
abs ((abs EX1) + (abs WH)) is V11() real ext-real Element of REAL
|[((abs EX1) + (abs WH))]| is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
EX is V11() real ext-real Element of REAL
|[EX]| is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
(abs WH) + (abs EX1) is V11() real ext-real Element of REAL
|.|[((abs EX1) + (abs WH))]|.| is V11() real ext-real non negative Element of REAL
sqr |[((abs EX1) + (abs WH))]| is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
sqrreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
|[((abs EX1) + (abs WH))]| (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (|[((abs EX1) + (abs WH))]|,|[((abs EX1) + (abs WH))]|) is Relation-like Function-like set
multreal .: (|[((abs EX1) + (abs WH))]|,|[((abs EX1) + (abs WH))]|) is set
K383((sqr |[((abs EX1) + (abs WH))]|)) is V11() real ext-real Element of REAL
addreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K195(REAL,(sqr |[((abs EX1) + (abs WH))]|),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr |[((abs EX1) + (abs WH))]|)) is V11() real ext-real Element of REAL
EX1 is V11() real ext-real Element of REAL
abs EX1 is V11() real ext-real Element of REAL
(abs EX1) + (abs WH) is V11() real ext-real Element of REAL
abs ((abs EX1) + (abs WH)) is V11() real ext-real Element of REAL
- ((abs EX1) + (abs WH)) is V11() real ext-real Element of REAL
|[(- ((abs EX1) + (abs WH)))]| is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
EX is V11() real ext-real Element of REAL
|[EX]| is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
- (abs WH) is V11() real ext-real Element of REAL
(abs WH) + (abs EX1) is V11() real ext-real Element of REAL
- ((abs WH) + (abs EX1)) is V11() real ext-real Element of REAL
|.|[(- ((abs EX1) + (abs WH)))]|.| is V11() real ext-real non negative Element of REAL
sqr |[(- ((abs EX1) + (abs WH)))]| is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
|[(- ((abs EX1) + (abs WH)))]| (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (|[(- ((abs EX1) + (abs WH)))]|,|[(- ((abs EX1) + (abs WH)))]|) is Relation-like Function-like set
multreal .: (|[(- ((abs EX1) + (abs WH)))]|,|[(- ((abs EX1) + (abs WH)))]|) is set
K383((sqr |[(- ((abs EX1) + (abs WH)))]|)) is V11() real ext-real Element of REAL
K195(REAL,(sqr |[(- ((abs EX1) + (abs WH)))]|),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr |[(- ((abs EX1) + (abs WH)))]|)) is V11() real ext-real Element of REAL
abs (- ((abs EX1) + (abs WH))) is V11() real ext-real Element of REAL
EX1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
p1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
LSeg (EX1,p1) is non empty closed connected compact bounded convex Element of bool the carrier of (TOP-REAL C)
{ (((1 - b1) * EX1) + (b1 * p1)) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
EX is V11() real ext-real Element of REAL
<*EX*> is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() FinSequence of REAL
t2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
t2 is V11() real ext-real Element of REAL
<*t2*> is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() FinSequence of REAL
qt2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
qt2 is set
r2 is V11() real ext-real Element of REAL
1 - r2 is V11() real ext-real Element of REAL
(1 - r2) * EX1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
(1 - r2) * EX1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
(1 - r2) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
id REAL is non empty Relation-like REAL -defined REAL -valued Function-like one-to-one total V30( REAL , REAL ) complex-yielding V174() V175() increasing V179() Element of bool [:REAL,REAL:]
multreal [;] ((1 - r2),(id REAL)) is set
EX1 (#) ((1 - r2) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
r2 * p1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
r2 * p1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
r2 multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
multreal [;] (r2,(id REAL)) is set
p1 (#) (r2 multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
((1 - r2) * EX1) + (r2 * p1) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the U7 of (TOP-REAL C) is non empty Relation-like [: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):] -defined the carrier of (TOP-REAL C) -valued Function-like total V30([: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C)) Element of bool [:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):]
[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):] is non empty set
[:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):] is non empty set
bool [:[: the carrier of (TOP-REAL C), the carrier of (TOP-REAL C):], the carrier of (TOP-REAL C):] is non empty set
the U7 of (TOP-REAL C) . (((1 - r2) * EX1),(r2 * p1)) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[((1 - r2) * EX1),(r2 * p1)] is non empty set
{((1 - r2) * EX1),(r2 * p1)} is non empty functional V35() V39() set
{((1 - r2) * EX1)} is non empty trivial functional V35() V39() 1 -element set
{{((1 - r2) * EX1),(r2 * p1)},{((1 - r2) * EX1)}} is non empty V35() V39() set
the U7 of (TOP-REAL C) . [((1 - r2) * EX1),(r2 * p1)] is set
((1 - r2) * EX1) + (r2 * p1) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal .: (((1 - r2) * EX1),(r2 * p1)) is set
r2 * EX is V11() real ext-real Element of REAL
|[(r2 * EX)]| is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
|[t2]| is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
(1 - r2) * |[t2]| is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
(1 - r2) * |[t2]| is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
|[t2]| (#) ((1 - r2) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
(1 - r2) * t2 is V11() real ext-real Element of REAL
|[((1 - r2) * t2)]| is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
((1 - r2) * t2) + (r2 * EX) is V11() real ext-real Element of REAL
|[(((1 - r2) * t2) + (r2 * EX))]| is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
q4 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
r5 is V11() real ext-real Element of REAL
|[r5]| is non empty trivial Relation-like NAT -defined REAL -valued Function-like one-to-one constant V35() 1 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() increasing V178() V179() V180() Element of the carrier of (TOP-REAL 1)
(1 - r2) * (- WH) is V11() real ext-real Element of REAL
r2 * (- WH) is V11() real ext-real Element of REAL
((1 - r2) * (- WH)) + (r2 * (- WH)) is V11() real ext-real Element of REAL
EX1 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.EX1.| is V11() real ext-real non negative Element of REAL
sqr EX1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
EX1 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (EX1,EX1) is Relation-like Function-like set
multreal .: (EX1,EX1) is set
K383((sqr EX1)) is V11() real ext-real Element of REAL
K195(REAL,(sqr EX1),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr EX1)) is V11() real ext-real Element of REAL
p1 is set
EX is Element of bool the carrier of (TOP-REAL C)
t2 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.t2.| is V11() real ext-real non negative Element of REAL
sqr t2 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
t2 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (t2,t2) is Relation-like Function-like set
multreal .: (t2,t2) is set
K383((sqr t2)) is V11() real ext-real Element of REAL
K195(REAL,(sqr t2),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr t2)) is V11() real ext-real Element of REAL
t2 is Element of bool the carrier of ((TOP-REAL C) | (p `))
EX2 /\ t2 is Element of bool the carrier of ((TOP-REAL C) | (p `))
{} ((TOP-REAL C) | (p `)) is empty trivial ordinal natural V11() real ext-real non positive non negative Function-like functional V35() V39() cardinal {} -element FinSequence-membered open closed boundary nowhere_dense V183() V184() V185() V186() V187() V188() V189() Element of bool the carrier of ((TOP-REAL C) | (p `))
r /\ t2 is Element of bool the carrier of ((TOP-REAL C) | (p `))
{} ((TOP-REAL C) | (p `)) is empty trivial ordinal natural V11() real ext-real non positive non negative Function-like functional V35() V39() cardinal {} -element FinSequence-membered open closed boundary nowhere_dense V183() V184() V185() V186() V187() V188() V189() Element of bool the carrier of ((TOP-REAL C) | (p `))
0 + 1 is non empty ordinal natural V11() real ext-real positive non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
p12 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.p12.| is V11() real ext-real non negative Element of REAL
sqr p12 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
sqrreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
p12 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (p12,p12) is Relation-like Function-like set
multreal .: (p12,p12) is set
K383((sqr p12)) is V11() real ext-real Element of REAL
addreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K195(REAL,(sqr p12),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr p12)) is V11() real ext-real Element of REAL
0. (TOP-REAL C) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like V62( TOP-REAL C) complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
the ZeroF of (TOP-REAL C) is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
[#] (TOP-REAL C) is 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 C)
p12 is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
|.p12.| is V11() real ext-real non negative Element of REAL
sqr p12 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
sqrreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
p12 (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt (p12,p12) is Relation-like Function-like set
multreal .: (p12,p12) is set
K383((sqr p12)) is V11() real ext-real Element of REAL
addreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K195(REAL,(sqr p12),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr p12)) is V11() real ext-real Element of REAL
C is non empty TopSpace-like TopStruct
the carrier of C is non empty set
bool the carrier of C is non empty set
WH is Element of bool the carrier of C
p12 is Element of bool the carrier of C
p is Element of bool the carrier of C
p \/ WH is Element of bool the carrier of C
p12 /\ the carrier of C is Element of bool the carrier of C
p12 /\ p is Element of bool the carrier of C
p12 /\ WH is Element of bool the carrier of C
(p12 /\ p) \/ (p12 /\ WH) is Element of bool the carrier of C
{} C is empty trivial proper ordinal natural V11() real ext-real non positive non negative Function-like functional V35() V39() cardinal {} -element FinSequence-membered open closed boundary nowhere_dense V183() V184() V185() V186() V187() V188() V189() Element of bool the carrier of C
C is Element of bool the carrier of (TOP-REAL 2)
(2,C) is Element of bool the carrier of (TOP-REAL 2)
{ b1 where b1 is Element of bool the carrier of (TOP-REAL 2) : (2,C,b1) } is set
union { b1 where b1 is Element of bool the carrier of (TOP-REAL 2) : (2,C,b1) } is set
C ` is Element of bool the carrier of (TOP-REAL 2)
the carrier of (TOP-REAL 2) \ C is set
(TOP-REAL 2) | (C `) is strict TopSpace-like SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | (C `)) is set
bool the carrier of ((TOP-REAL 2) | (C `)) is non empty set
WH is Element of bool the carrier of (TOP-REAL 2)
p12 is Element of bool the carrier of (TOP-REAL 2)
WH \/ p12 is Element of bool the carrier of (TOP-REAL 2)
Cl WH is closed Element of bool the carrier of (TOP-REAL 2)
(Cl WH) \ WH is Element of bool the carrier of (TOP-REAL 2)
Cl p12 is closed Element of bool the carrier of (TOP-REAL 2)
(Cl p12) \ p12 is Element of bool the carrier of (TOP-REAL 2)
(2,C) is Element of bool the carrier of (TOP-REAL 2)
{ b1 where b1 is Element of bool the carrier of (TOP-REAL 2) : (2,C,b1) } is set
union { b1 where b1 is Element of bool the carrier of (TOP-REAL 2) : (2,C,b1) } is set
C is Element of bool the carrier of ((TOP-REAL 2) | (C `))
Down (WH,(C `)) is Element of bool the carrier of ((TOP-REAL 2) | (C `))
WH /\ (C `) is Element of bool the carrier of (TOP-REAL 2)
Down (p12,(C `)) is Element of bool the carrier of ((TOP-REAL 2) | (C `))
p12 /\ (C `) is Element of bool the carrier of (TOP-REAL 2)
p is non empty Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | p is non empty strict TopSpace-like SubSpace of TOP-REAL 2
{} ((TOP-REAL 2) | (C `)) is empty trivial ordinal natural V11() real ext-real non positive non negative Function-like functional V35() V39() cardinal {} -element FinSequence-membered open closed boundary nowhere_dense V183() V184() V185() V186() V187() V188() V189() Element of bool the carrier of ((TOP-REAL 2) | (C `))
r is set
EX2 is set
EX1 is Element of bool the carrier of (TOP-REAL 2)
p1 is Element of bool the carrier of ((TOP-REAL 2) | (C `))
p1 /\ (Down (p12,(C `))) is Element of bool the carrier of ((TOP-REAL 2) | (C `))
EX1 /\ (WH \/ p12) is Element of bool the carrier of (TOP-REAL 2)
EX1 /\ WH is Element of bool the carrier of (TOP-REAL 2)
EX1 /\ p12 is Element of bool the carrier of (TOP-REAL 2)
(EX1 /\ WH) \/ (EX1 /\ p12) is Element of bool the carrier of (TOP-REAL 2)
p12 /\ (2,C) is Element of bool the carrier of (TOP-REAL 2)
(Down (WH,(C `))) \/ (Down (p12,(C `))) is Element of bool the carrier of ((TOP-REAL 2) | (C `))
[#] ((TOP-REAL 2) | (C `)) is non proper open closed dense Element of bool the carrier of ((TOP-REAL 2) | (C `))
(2,C) \/ (2,C) is Element of bool the carrier of (TOP-REAL 2)
EX1 is set
EX1 is set
C is non empty compact bounded non horizontal non vertical Element of bool the carrier of (TOP-REAL 2)
SpStSeq C is non empty non trivial Relation-like NAT -defined the carrier of (TOP-REAL 2) -valued Function-like non constant V35() FinSequence-like FinSubsequence-like V262( the carrier of (TOP-REAL 2)) special unfolded s.c.c. standard rectangular clockwise_oriented FinSequence of the carrier of (TOP-REAL 2)
L~ (SpStSeq C) is non empty closed boundary nowhere_dense compact bounded bounded non horizontal non vertical Jordan Element of bool the carrier of (TOP-REAL 2)
(2,(L~ (SpStSeq C))) is Element of bool the carrier of (TOP-REAL 2)
{ b1 where b1 is Element of bool the carrier of (TOP-REAL 2) : (2, L~ (SpStSeq C),b1) } is set
union { b1 where b1 is Element of bool the carrier of (TOP-REAL 2) : (2, L~ (SpStSeq C),b1) } is set
p is V11() real ext-real Element of REAL
WH is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
the Element of (2,(L~ (SpStSeq C))) is Element of (2,(L~ (SpStSeq C)))
(L~ (SpStSeq C)) ` is open dense Element of bool the carrier of (TOP-REAL 2)
the carrier of (TOP-REAL 2) \ (L~ (SpStSeq C)) is set
(TOP-REAL 2) | ((L~ (SpStSeq C)) `) is strict TopSpace-like SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | ((L~ (SpStSeq C)) `)) is set
bool the carrier of ((TOP-REAL 2) | ((L~ (SpStSeq C)) `)) is non empty set
r is Element of bool the carrier of (TOP-REAL 2)
EX2 is Element of bool the carrier of (TOP-REAL 2)
r \/ EX2 is Element of bool the carrier of (TOP-REAL 2)
Cl r is closed Element of bool the carrier of (TOP-REAL 2)
(Cl r) \ r is Element of bool the carrier of (TOP-REAL 2)
Cl EX2 is closed Element of bool the carrier of (TOP-REAL 2)
(Cl EX2) \ EX2 is Element of bool the carrier of (TOP-REAL 2)
Down (EX2,((L~ (SpStSeq C)) `)) is Element of bool the carrier of ((TOP-REAL 2) | ((L~ (SpStSeq C)) `))
EX2 /\ ((L~ (SpStSeq C)) `) is Element of bool the carrier of (TOP-REAL 2)
EX1 is Element of bool the carrier of ((TOP-REAL 2) | ((L~ (SpStSeq C)) `))
Down (r,((L~ (SpStSeq C)) `)) is Element of bool the carrier of ((TOP-REAL 2) | ((L~ (SpStSeq C)) `))
r /\ ((L~ (SpStSeq C)) `) is Element of bool the carrier of (TOP-REAL 2)
EX1 /\ (Down (r,((L~ (SpStSeq C)) `))) is Element of bool the carrier of ((TOP-REAL 2) | ((L~ (SpStSeq C)) `))
{} ((TOP-REAL 2) | ((L~ (SpStSeq C)) `)) is empty trivial ordinal natural V11() real ext-real non positive non negative Function-like functional V35() V39() cardinal {} -element FinSequence-membered open closed boundary nowhere_dense V183() V184() V185() V186() V187() V188() V189() Element of bool the carrier of ((TOP-REAL 2) | ((L~ (SpStSeq C)) `))
Cl (2,(L~ (SpStSeq C))) is closed Element of bool the carrier of (TOP-REAL 2)
p1 is Element of the carrier of (Euclid 2)
Ball (p1,p) is bounded Element of bool the carrier of (Euclid 2)
bool the carrier of (Euclid 2) is non empty set
the distance of (Euclid 2) is non empty Relation-like [: the carrier of (Euclid 2), the carrier of (Euclid 2):] -defined REAL -valued Function-like total V30([: the carrier of (Euclid 2), the carrier of (Euclid 2):], REAL ) complex-yielding V174() V175() Element of bool [:[: the carrier of (Euclid 2), the carrier of (Euclid 2):],REAL:]
[: the carrier of (Euclid 2), the carrier of (Euclid 2):] is non empty set
[:[: the carrier of (Euclid 2), the carrier of (Euclid 2):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[: the carrier of (Euclid 2), the carrier of (Euclid 2):],REAL:] is non empty non trivial V35() set
dist (p1,p1) is V11() real ext-real Element of REAL
the distance of (Euclid 2) . (p1,p1) is V11() real ext-real Element of REAL
[p1,p1] is non empty set
{p1,p1} is non empty V35() set
{p1} is non empty trivial V35() 1 -element set
{{p1,p1},{p1}} is non empty V35() V39() set
the distance of (Euclid 2) . [p1,p1] is V11() real ext-real set
EX is Element of bool the carrier of (TOP-REAL 2)
t2 is set
qt2 is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
WH - qt2 is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
- qt2 is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
- qt2 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
compreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
qt2 (#) compreal is Relation-like Function-like V35() complex-yielding V174() V175() set
K38(1) is V11() real ext-real non positive set
K38(1) * qt2 is Relation-like Function-like set
K38(1) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
id REAL is non empty Relation-like REAL -defined REAL -valued Function-like one-to-one total V30( REAL , REAL ) complex-yielding V174() V175() increasing V179() Element of bool [:REAL,REAL:]
multreal [;] (K38(1),(id REAL)) is set
qt2 (#) (K38(1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
K258((TOP-REAL 2),WH,(- qt2)) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) is non empty Relation-like [: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):] -defined the carrier of (TOP-REAL 2) -valued Function-like total V30([: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2)) 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):] is non empty set
[:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):] is 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
the U7 of (TOP-REAL 2) . (WH,(- qt2)) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
[WH,(- qt2)] is non empty set
{WH,(- qt2)} is non empty functional V35() V39() set
{WH} is non empty trivial functional V35() V39() 1 -element set
{{WH,(- qt2)},{WH}} is non empty V35() V39() set
the U7 of (TOP-REAL 2) . [WH,(- qt2)] is set
WH + (- qt2) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
addreal .: (WH,(- qt2)) is set
WH - qt2 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
diffreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K174(REAL,addreal,(id REAL),compreal) is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
diffreal .: (WH,qt2) is set
K324(qt2) is Relation-like Function-like complex-yielding set
K295(WH,K324(qt2)) is Relation-like Function-like set
|.(WH - qt2).| is V11() real ext-real non negative Element of REAL
sqr (WH - qt2) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
sqrreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
(WH - qt2) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((WH - qt2),(WH - qt2)) is Relation-like Function-like set
multreal .: ((WH - qt2),(WH - qt2)) is set
K383((sqr (WH - qt2))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (WH - qt2)),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (WH - qt2))) is V11() real ext-real Element of REAL
EX1 /\ (Down (EX2,((L~ (SpStSeq C)) `))) is Element of bool the carrier of ((TOP-REAL 2) | ((L~ (SpStSeq C)) `))
{} ((TOP-REAL 2) | ((L~ (SpStSeq C)) `)) is empty trivial ordinal natural V11() real ext-real non positive non negative Function-like functional V35() V39() cardinal {} -element FinSequence-membered open closed boundary nowhere_dense V183() V184() V185() V186() V187() V188() V189() Element of bool the carrier of ((TOP-REAL 2) | ((L~ (SpStSeq C)) `))
Cl (2,(L~ (SpStSeq C))) is closed Element of bool the carrier of (TOP-REAL 2)
p1 is Element of the carrier of (Euclid 2)
Ball (p1,p) is bounded Element of bool the carrier of (Euclid 2)
bool the carrier of (Euclid 2) is non empty set
the distance of (Euclid 2) is non empty Relation-like [: the carrier of (Euclid 2), the carrier of (Euclid 2):] -defined REAL -valued Function-like total V30([: the carrier of (Euclid 2), the carrier of (Euclid 2):], REAL ) complex-yielding V174() V175() Element of bool [:[: the carrier of (Euclid 2), the carrier of (Euclid 2):],REAL:]
[: the carrier of (Euclid 2), the carrier of (Euclid 2):] is non empty set
[:[: the carrier of (Euclid 2), the carrier of (Euclid 2):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[: the carrier of (Euclid 2), the carrier of (Euclid 2):],REAL:] is non empty non trivial V35() set
dist (p1,p1) is V11() real ext-real Element of REAL
the distance of (Euclid 2) . (p1,p1) is V11() real ext-real Element of REAL
[p1,p1] is non empty set
{p1,p1} is non empty V35() set
{p1} is non empty trivial V35() 1 -element set
{{p1,p1},{p1}} is non empty V35() V39() set
the distance of (Euclid 2) . [p1,p1] is V11() real ext-real set
EX is Element of bool the carrier of (TOP-REAL 2)
t2 is set
qt2 is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
WH - qt2 is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
- qt2 is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
- qt2 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
compreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
qt2 (#) compreal is Relation-like Function-like V35() complex-yielding V174() V175() set
K38(1) is V11() real ext-real non positive set
K38(1) * qt2 is Relation-like Function-like set
K38(1) multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
id REAL is non empty Relation-like REAL -defined REAL -valued Function-like one-to-one total V30( REAL , REAL ) complex-yielding V174() V175() increasing V179() Element of bool [:REAL,REAL:]
multreal [;] (K38(1),(id REAL)) is set
qt2 (#) (K38(1) multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
K258((TOP-REAL 2),WH,(- qt2)) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) is non empty Relation-like [: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):] -defined the carrier of (TOP-REAL 2) -valued Function-like total V30([: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2)) 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):] is non empty set
[:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):] is 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
the U7 of (TOP-REAL 2) . (WH,(- qt2)) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
[WH,(- qt2)] is non empty set
{WH,(- qt2)} is non empty functional V35() V39() set
{WH} is non empty trivial functional V35() V39() 1 -element set
{{WH,(- qt2)},{WH}} is non empty V35() V39() set
the U7 of (TOP-REAL 2) . [WH,(- qt2)] is set
WH + (- qt2) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
addreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
addreal .: (WH,(- qt2)) is set
WH - qt2 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
diffreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
K174(REAL,addreal,(id REAL),compreal) is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like total V30([:REAL,REAL:], REAL ) complex-yielding V174() V175() Element of bool [:[:REAL,REAL:],REAL:]
diffreal .: (WH,qt2) is set
K324(qt2) is Relation-like Function-like complex-yielding set
K295(WH,K324(qt2)) is Relation-like Function-like set
|.(WH - qt2).| is V11() real ext-real non negative Element of REAL
sqr (WH - qt2) is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
sqrreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
(WH - qt2) (#) sqrreal is Relation-like Function-like V35() complex-yielding V174() V175() set
mlt ((WH - qt2),(WH - qt2)) is Relation-like Function-like set
multreal .: ((WH - qt2),(WH - qt2)) is set
K383((sqr (WH - qt2))) is V11() real ext-real Element of REAL
K195(REAL,(sqr (WH - qt2)),addreal) is V11() real ext-real Element of REAL
sqrt K383((sqr (WH - qt2))) is V11() real ext-real Element of REAL
C is non empty non trivial Relation-like NAT -defined the carrier of (TOP-REAL 2) -valued Function-like non constant V35() FinSequence-like FinSubsequence-like V262( the carrier of (TOP-REAL 2)) special unfolded s.c.c. standard clockwise_oriented FinSequence of the carrier of (TOP-REAL 2)
C /. 1 is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
L~ C is non empty closed boundary nowhere_dense compact bounded bounded non horizontal non vertical Element of bool the carrier of (TOP-REAL 2)
N-min (L~ C) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
N-most (L~ C) is Element of bool the carrier of (TOP-REAL 2)
NW-corner (L~ C) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
W-bound (L~ C) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ C) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is non empty Relation-like the carrier of (TOP-REAL 2) -defined REAL -valued Function-like total V30( the carrier of (TOP-REAL 2), REAL ) complex-yielding V174() V175() Element of bool [: the carrier of (TOP-REAL 2),REAL:]
proj1 | (L~ C) is non empty Relation-like the carrier of ((TOP-REAL 2) | (L~ C)) -defined REAL -valued Function-like total V30( the carrier of ((TOP-REAL 2) | (L~ C)), REAL ) complex-yielding V174() V175() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ C)),REAL:]
the carrier of ((TOP-REAL 2) | (L~ C)) is non empty set
[: the carrier of ((TOP-REAL 2) | (L~ C)),REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [: the carrier of ((TOP-REAL 2) | (L~ C)),REAL:] is non empty non trivial V35() set
lower_bound (proj1 | (L~ C)) is V11() real ext-real Element of REAL
(proj1 | (L~ C)) .: the carrier of ((TOP-REAL 2) | (L~ C)) is V183() V184() V185() Element of bool REAL
lower_bound ((proj1 | (L~ C)) .: the carrier of ((TOP-REAL 2) | (L~ C))) is V11() real ext-real Element of REAL
N-bound (L~ C) is V11() real ext-real Element of REAL
proj2 is non empty Relation-like the carrier of (TOP-REAL 2) -defined REAL -valued Function-like total V30( the carrier of (TOP-REAL 2), REAL ) complex-yielding V174() V175() Element of bool [: the carrier of (TOP-REAL 2),REAL:]
proj2 | (L~ C) is non empty Relation-like the carrier of ((TOP-REAL 2) | (L~ C)) -defined REAL -valued Function-like total V30( the carrier of ((TOP-REAL 2) | (L~ C)), REAL ) complex-yielding V174() V175() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ C)),REAL:]
upper_bound (proj2 | (L~ C)) is V11() real ext-real Element of REAL
(proj2 | (L~ C)) .: the carrier of ((TOP-REAL 2) | (L~ C)) is V183() V184() V185() Element of bool REAL
upper_bound ((proj2 | (L~ C)) .: the carrier of ((TOP-REAL 2) | (L~ C))) is V11() real ext-real Element of REAL
|[(W-bound (L~ C)),(N-bound (L~ C))]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
NE-corner (L~ C) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
E-bound (L~ C) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ C)) is V11() real ext-real Element of REAL
upper_bound ((proj1 | (L~ C)) .: the carrier of ((TOP-REAL 2) | (L~ C))) is V11() real ext-real Element of REAL
|[(E-bound (L~ C)),(N-bound (L~ C))]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
LSeg ((NW-corner (L~ C)),(NE-corner (L~ C))) is non empty closed closed boundary nowhere_dense connected compact compact bounded bounded horizontal convex Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * (NW-corner (L~ C))) + (b1 * (NE-corner (L~ C)))) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
(LSeg ((NW-corner (L~ C)),(NE-corner (L~ C)))) /\ (L~ C) is closed Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (N-most (L~ C)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most (L~ C)) is Relation-like the carrier of ((TOP-REAL 2) | (N-most (L~ C))) -defined REAL -valued Function-like total V30( the carrier of ((TOP-REAL 2) | (N-most (L~ C))), REAL ) complex-yielding V174() V175() Element of bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ C))),REAL:]
the carrier of ((TOP-REAL 2) | (N-most (L~ C))) is set
[: the carrier of ((TOP-REAL 2) | (N-most (L~ C))),REAL:] is complex-yielding V174() V175() set
bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ C))),REAL:] is non empty set
lower_bound (proj1 | (N-most (L~ C))) is V11() real ext-real Element of REAL
(proj1 | (N-most (L~ C))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ C))) is V183() V184() V185() Element of bool REAL
lower_bound ((proj1 | (N-most (L~ C))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ C)))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (N-most (L~ C)))),(N-bound (L~ C))]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
LeftComp C is non empty Element of bool the carrier of (TOP-REAL 2)
p is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
p `1 is V11() real ext-real Element of REAL
p . 1 is V11() real ext-real Element of REAL
SpStSeq (L~ C) is non empty non trivial Relation-like NAT -defined the carrier of (TOP-REAL 2) -valued Function-like non constant V35() FinSequence-like FinSubsequence-like V262( the carrier of (TOP-REAL 2)) special unfolded s.c.c. standard rectangular clockwise_oriented FinSequence of the carrier of (TOP-REAL 2)
LeftComp (SpStSeq (L~ C)) is non empty Element of bool the carrier of (TOP-REAL 2)
L~ (SpStSeq (L~ C)) is non empty closed boundary nowhere_dense compact bounded bounded non horizontal non vertical Jordan Element of bool the carrier of (TOP-REAL 2)
W-bound (L~ (SpStSeq (L~ C))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (SpStSeq (L~ C))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ (SpStSeq (L~ C))) is non empty Relation-like the carrier of ((TOP-REAL 2) | (L~ (SpStSeq (L~ C)))) -defined REAL -valued Function-like total V30( the carrier of ((TOP-REAL 2) | (L~ (SpStSeq (L~ C)))), REAL ) complex-yielding V174() V175() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ (SpStSeq (L~ C)))),REAL:]
the carrier of ((TOP-REAL 2) | (L~ (SpStSeq (L~ C)))) is non empty set
[: the carrier of ((TOP-REAL 2) | (L~ (SpStSeq (L~ C)))),REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [: the carrier of ((TOP-REAL 2) | (L~ (SpStSeq (L~ C)))),REAL:] is non empty non trivial V35() set
lower_bound (proj1 | (L~ (SpStSeq (L~ C)))) is V11() real ext-real Element of REAL
(proj1 | (L~ (SpStSeq (L~ C)))) .: the carrier of ((TOP-REAL 2) | (L~ (SpStSeq (L~ C)))) is V183() V184() V185() Element of bool REAL
lower_bound ((proj1 | (L~ (SpStSeq (L~ C)))) .: the carrier of ((TOP-REAL 2) | (L~ (SpStSeq (L~ C))))) is V11() real ext-real Element of REAL
C is non empty non trivial Relation-like NAT -defined the carrier of (TOP-REAL 2) -valued Function-like non constant V35() FinSequence-like FinSubsequence-like V262( the carrier of (TOP-REAL 2)) special unfolded s.c.c. standard clockwise_oriented FinSequence of the carrier of (TOP-REAL 2)
C /. 1 is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
L~ C is non empty closed boundary nowhere_dense compact bounded bounded non horizontal non vertical Element of bool the carrier of (TOP-REAL 2)
N-min (L~ C) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
N-most (L~ C) is Element of bool the carrier of (TOP-REAL 2)
NW-corner (L~ C) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
W-bound (L~ C) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ C) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is non empty Relation-like the carrier of (TOP-REAL 2) -defined REAL -valued Function-like total V30( the carrier of (TOP-REAL 2), REAL ) complex-yielding V174() V175() Element of bool [: the carrier of (TOP-REAL 2),REAL:]
proj1 | (L~ C) is non empty Relation-like the carrier of ((TOP-REAL 2) | (L~ C)) -defined REAL -valued Function-like total V30( the carrier of ((TOP-REAL 2) | (L~ C)), REAL ) complex-yielding V174() V175() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ C)),REAL:]
the carrier of ((TOP-REAL 2) | (L~ C)) is non empty set
[: the carrier of ((TOP-REAL 2) | (L~ C)),REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [: the carrier of ((TOP-REAL 2) | (L~ C)),REAL:] is non empty non trivial V35() set
lower_bound (proj1 | (L~ C)) is V11() real ext-real Element of REAL
(proj1 | (L~ C)) .: the carrier of ((TOP-REAL 2) | (L~ C)) is V183() V184() V185() Element of bool REAL
lower_bound ((proj1 | (L~ C)) .: the carrier of ((TOP-REAL 2) | (L~ C))) is V11() real ext-real Element of REAL
N-bound (L~ C) is V11() real ext-real Element of REAL
proj2 is non empty Relation-like the carrier of (TOP-REAL 2) -defined REAL -valued Function-like total V30( the carrier of (TOP-REAL 2), REAL ) complex-yielding V174() V175() Element of bool [: the carrier of (TOP-REAL 2),REAL:]
proj2 | (L~ C) is non empty Relation-like the carrier of ((TOP-REAL 2) | (L~ C)) -defined REAL -valued Function-like total V30( the carrier of ((TOP-REAL 2) | (L~ C)), REAL ) complex-yielding V174() V175() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ C)),REAL:]
upper_bound (proj2 | (L~ C)) is V11() real ext-real Element of REAL
(proj2 | (L~ C)) .: the carrier of ((TOP-REAL 2) | (L~ C)) is V183() V184() V185() Element of bool REAL
upper_bound ((proj2 | (L~ C)) .: the carrier of ((TOP-REAL 2) | (L~ C))) is V11() real ext-real Element of REAL
|[(W-bound (L~ C)),(N-bound (L~ C))]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
NE-corner (L~ C) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
E-bound (L~ C) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ C)) is V11() real ext-real Element of REAL
upper_bound ((proj1 | (L~ C)) .: the carrier of ((TOP-REAL 2) | (L~ C))) is V11() real ext-real Element of REAL
|[(E-bound (L~ C)),(N-bound (L~ C))]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
LSeg ((NW-corner (L~ C)),(NE-corner (L~ C))) is non empty closed closed boundary nowhere_dense connected compact compact bounded bounded horizontal convex Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * (NW-corner (L~ C))) + (b1 * (NE-corner (L~ C)))) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
(LSeg ((NW-corner (L~ C)),(NE-corner (L~ C)))) /\ (L~ C) is closed Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (N-most (L~ C)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most (L~ C)) is Relation-like the carrier of ((TOP-REAL 2) | (N-most (L~ C))) -defined REAL -valued Function-like total V30( the carrier of ((TOP-REAL 2) | (N-most (L~ C))), REAL ) complex-yielding V174() V175() Element of bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ C))),REAL:]
the carrier of ((TOP-REAL 2) | (N-most (L~ C))) is set
[: the carrier of ((TOP-REAL 2) | (N-most (L~ C))),REAL:] is complex-yielding V174() V175() set
bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ C))),REAL:] is non empty set
lower_bound (proj1 | (N-most (L~ C))) is V11() real ext-real Element of REAL
(proj1 | (N-most (L~ C))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ C))) is V183() V184() V185() Element of bool REAL
lower_bound ((proj1 | (N-most (L~ C))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ C)))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (N-most (L~ C)))),(N-bound (L~ C))]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
LeftComp C is non empty Element of bool the carrier of (TOP-REAL 2)
p is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
p `1 is V11() real ext-real Element of REAL
p . 1 is V11() real ext-real Element of REAL
SpStSeq (L~ C) is non empty non trivial Relation-like NAT -defined the carrier of (TOP-REAL 2) -valued Function-like non constant V35() FinSequence-like FinSubsequence-like V262( the carrier of (TOP-REAL 2)) special unfolded s.c.c. standard rectangular clockwise_oriented FinSequence of the carrier of (TOP-REAL 2)
LeftComp (SpStSeq (L~ C)) is non empty Element of bool the carrier of (TOP-REAL 2)
L~ (SpStSeq (L~ C)) is non empty closed boundary nowhere_dense compact bounded bounded non horizontal non vertical Jordan Element of bool the carrier of (TOP-REAL 2)
E-bound (L~ (SpStSeq (L~ C))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (SpStSeq (L~ C))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (L~ (SpStSeq (L~ C))) is non empty Relation-like the carrier of ((TOP-REAL 2) | (L~ (SpStSeq (L~ C)))) -defined REAL -valued Function-like total V30( the carrier of ((TOP-REAL 2) | (L~ (SpStSeq (L~ C)))), REAL ) complex-yielding V174() V175() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ (SpStSeq (L~ C)))),REAL:]
the carrier of ((TOP-REAL 2) | (L~ (SpStSeq (L~ C)))) is non empty set
[: the carrier of ((TOP-REAL 2) | (L~ (SpStSeq (L~ C)))),REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [: the carrier of ((TOP-REAL 2) | (L~ (SpStSeq (L~ C)))),REAL:] is non empty non trivial V35() set
upper_bound (proj1 | (L~ (SpStSeq (L~ C)))) is V11() real ext-real Element of REAL
(proj1 | (L~ (SpStSeq (L~ C)))) .: the carrier of ((TOP-REAL 2) | (L~ (SpStSeq (L~ C)))) is V183() V184() V185() Element of bool REAL
upper_bound ((proj1 | (L~ (SpStSeq (L~ C)))) .: the carrier of ((TOP-REAL 2) | (L~ (SpStSeq (L~ C))))) is V11() real ext-real Element of REAL
C is non empty non trivial Relation-like NAT -defined the carrier of (TOP-REAL 2) -valued Function-like non constant V35() FinSequence-like FinSubsequence-like V262( the carrier of (TOP-REAL 2)) special unfolded s.c.c. standard clockwise_oriented FinSequence of the carrier of (TOP-REAL 2)
C /. 1 is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
L~ C is non empty closed boundary nowhere_dense compact bounded bounded non horizontal non vertical Element of bool the carrier of (TOP-REAL 2)
N-min (L~ C) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
N-most (L~ C) is Element of bool the carrier of (TOP-REAL 2)
NW-corner (L~ C) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
W-bound (L~ C) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ C) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is non empty Relation-like the carrier of (TOP-REAL 2) -defined REAL -valued Function-like total V30( the carrier of (TOP-REAL 2), REAL ) complex-yielding V174() V175() Element of bool [: the carrier of (TOP-REAL 2),REAL:]
proj1 | (L~ C) is non empty Relation-like the carrier of ((TOP-REAL 2) | (L~ C)) -defined REAL -valued Function-like total V30( the carrier of ((TOP-REAL 2) | (L~ C)), REAL ) complex-yielding V174() V175() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ C)),REAL:]
the carrier of ((TOP-REAL 2) | (L~ C)) is non empty set
[: the carrier of ((TOP-REAL 2) | (L~ C)),REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [: the carrier of ((TOP-REAL 2) | (L~ C)),REAL:] is non empty non trivial V35() set
lower_bound (proj1 | (L~ C)) is V11() real ext-real Element of REAL
(proj1 | (L~ C)) .: the carrier of ((TOP-REAL 2) | (L~ C)) is V183() V184() V185() Element of bool REAL
lower_bound ((proj1 | (L~ C)) .: the carrier of ((TOP-REAL 2) | (L~ C))) is V11() real ext-real Element of REAL
N-bound (L~ C) is V11() real ext-real Element of REAL
proj2 is non empty Relation-like the carrier of (TOP-REAL 2) -defined REAL -valued Function-like total V30( the carrier of (TOP-REAL 2), REAL ) complex-yielding V174() V175() Element of bool [: the carrier of (TOP-REAL 2),REAL:]
proj2 | (L~ C) is non empty Relation-like the carrier of ((TOP-REAL 2) | (L~ C)) -defined REAL -valued Function-like total V30( the carrier of ((TOP-REAL 2) | (L~ C)), REAL ) complex-yielding V174() V175() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ C)),REAL:]
upper_bound (proj2 | (L~ C)) is V11() real ext-real Element of REAL
(proj2 | (L~ C)) .: the carrier of ((TOP-REAL 2) | (L~ C)) is V183() V184() V185() Element of bool REAL
upper_bound ((proj2 | (L~ C)) .: the carrier of ((TOP-REAL 2) | (L~ C))) is V11() real ext-real Element of REAL
|[(W-bound (L~ C)),(N-bound (L~ C))]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
NE-corner (L~ C) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
E-bound (L~ C) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ C)) is V11() real ext-real Element of REAL
upper_bound ((proj1 | (L~ C)) .: the carrier of ((TOP-REAL 2) | (L~ C))) is V11() real ext-real Element of REAL
|[(E-bound (L~ C)),(N-bound (L~ C))]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
LSeg ((NW-corner (L~ C)),(NE-corner (L~ C))) is non empty closed closed boundary nowhere_dense connected compact compact bounded bounded horizontal convex Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * (NW-corner (L~ C))) + (b1 * (NE-corner (L~ C)))) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
(LSeg ((NW-corner (L~ C)),(NE-corner (L~ C)))) /\ (L~ C) is closed Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (N-most (L~ C)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most (L~ C)) is Relation-like the carrier of ((TOP-REAL 2) | (N-most (L~ C))) -defined REAL -valued Function-like total V30( the carrier of ((TOP-REAL 2) | (N-most (L~ C))), REAL ) complex-yielding V174() V175() Element of bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ C))),REAL:]
the carrier of ((TOP-REAL 2) | (N-most (L~ C))) is set
[: the carrier of ((TOP-REAL 2) | (N-most (L~ C))),REAL:] is complex-yielding V174() V175() set
bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ C))),REAL:] is non empty set
lower_bound (proj1 | (N-most (L~ C))) is V11() real ext-real Element of REAL
(proj1 | (N-most (L~ C))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ C))) is V183() V184() V185() Element of bool REAL
lower_bound ((proj1 | (N-most (L~ C))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ C)))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (N-most (L~ C)))),(N-bound (L~ C))]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
S-bound (L~ C) is V11() real ext-real Element of REAL
lower_bound (proj2 | (L~ C)) is V11() real ext-real Element of REAL
lower_bound ((proj2 | (L~ C)) .: the carrier of ((TOP-REAL 2) | (L~ C))) is V11() real ext-real Element of REAL
LeftComp C is non empty Element of bool the carrier of (TOP-REAL 2)
p is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
p `2 is V11() real ext-real Element of REAL
p . 2 is V11() real ext-real Element of REAL
SpStSeq (L~ C) is non empty non trivial Relation-like NAT -defined the carrier of (TOP-REAL 2) -valued Function-like non constant V35() FinSequence-like FinSubsequence-like V262( the carrier of (TOP-REAL 2)) special unfolded s.c.c. standard rectangular clockwise_oriented FinSequence of the carrier of (TOP-REAL 2)
LeftComp (SpStSeq (L~ C)) is non empty Element of bool the carrier of (TOP-REAL 2)
L~ (SpStSeq (L~ C)) is non empty closed boundary nowhere_dense compact bounded bounded non horizontal non vertical Jordan Element of bool the carrier of (TOP-REAL 2)
S-bound (L~ (SpStSeq (L~ C))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (SpStSeq (L~ C))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (L~ (SpStSeq (L~ C))) is non empty Relation-like the carrier of ((TOP-REAL 2) | (L~ (SpStSeq (L~ C)))) -defined REAL -valued Function-like total V30( the carrier of ((TOP-REAL 2) | (L~ (SpStSeq (L~ C)))), REAL ) complex-yielding V174() V175() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ (SpStSeq (L~ C)))),REAL:]
the carrier of ((TOP-REAL 2) | (L~ (SpStSeq (L~ C)))) is non empty set
[: the carrier of ((TOP-REAL 2) | (L~ (SpStSeq (L~ C)))),REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [: the carrier of ((TOP-REAL 2) | (L~ (SpStSeq (L~ C)))),REAL:] is non empty non trivial V35() set
lower_bound (proj2 | (L~ (SpStSeq (L~ C)))) is V11() real ext-real Element of REAL
(proj2 | (L~ (SpStSeq (L~ C)))) .: the carrier of ((TOP-REAL 2) | (L~ (SpStSeq (L~ C)))) is V183() V184() V185() Element of bool REAL
lower_bound ((proj2 | (L~ (SpStSeq (L~ C)))) .: the carrier of ((TOP-REAL 2) | (L~ (SpStSeq (L~ C))))) is V11() real ext-real Element of REAL
C is non empty non trivial Relation-like NAT -defined the carrier of (TOP-REAL 2) -valued Function-like non constant V35() FinSequence-like FinSubsequence-like V262( the carrier of (TOP-REAL 2)) special unfolded s.c.c. standard clockwise_oriented FinSequence of the carrier of (TOP-REAL 2)
C /. 1 is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
L~ C is non empty closed boundary nowhere_dense compact bounded bounded non horizontal non vertical Element of bool the carrier of (TOP-REAL 2)
N-min (L~ C) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
N-most (L~ C) is Element of bool the carrier of (TOP-REAL 2)
NW-corner (L~ C) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
W-bound (L~ C) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ C) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj1 is non empty Relation-like the carrier of (TOP-REAL 2) -defined REAL -valued Function-like total V30( the carrier of (TOP-REAL 2), REAL ) complex-yielding V174() V175() Element of bool [: the carrier of (TOP-REAL 2),REAL:]
proj1 | (L~ C) is non empty Relation-like the carrier of ((TOP-REAL 2) | (L~ C)) -defined REAL -valued Function-like total V30( the carrier of ((TOP-REAL 2) | (L~ C)), REAL ) complex-yielding V174() V175() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ C)),REAL:]
the carrier of ((TOP-REAL 2) | (L~ C)) is non empty set
[: the carrier of ((TOP-REAL 2) | (L~ C)),REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [: the carrier of ((TOP-REAL 2) | (L~ C)),REAL:] is non empty non trivial V35() set
lower_bound (proj1 | (L~ C)) is V11() real ext-real Element of REAL
(proj1 | (L~ C)) .: the carrier of ((TOP-REAL 2) | (L~ C)) is V183() V184() V185() Element of bool REAL
lower_bound ((proj1 | (L~ C)) .: the carrier of ((TOP-REAL 2) | (L~ C))) is V11() real ext-real Element of REAL
N-bound (L~ C) is V11() real ext-real Element of REAL
proj2 is non empty Relation-like the carrier of (TOP-REAL 2) -defined REAL -valued Function-like total V30( the carrier of (TOP-REAL 2), REAL ) complex-yielding V174() V175() Element of bool [: the carrier of (TOP-REAL 2),REAL:]
proj2 | (L~ C) is non empty Relation-like the carrier of ((TOP-REAL 2) | (L~ C)) -defined REAL -valued Function-like total V30( the carrier of ((TOP-REAL 2) | (L~ C)), REAL ) complex-yielding V174() V175() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ C)),REAL:]
upper_bound (proj2 | (L~ C)) is V11() real ext-real Element of REAL
(proj2 | (L~ C)) .: the carrier of ((TOP-REAL 2) | (L~ C)) is V183() V184() V185() Element of bool REAL
upper_bound ((proj2 | (L~ C)) .: the carrier of ((TOP-REAL 2) | (L~ C))) is V11() real ext-real Element of REAL
|[(W-bound (L~ C)),(N-bound (L~ C))]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
NE-corner (L~ C) is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
E-bound (L~ C) is V11() real ext-real Element of REAL
upper_bound (proj1 | (L~ C)) is V11() real ext-real Element of REAL
upper_bound ((proj1 | (L~ C)) .: the carrier of ((TOP-REAL 2) | (L~ C))) is V11() real ext-real Element of REAL
|[(E-bound (L~ C)),(N-bound (L~ C))]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
LSeg ((NW-corner (L~ C)),(NE-corner (L~ C))) is non empty closed closed boundary nowhere_dense connected compact compact bounded bounded horizontal convex Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b1) * (NW-corner (L~ C))) + (b1 * (NE-corner (L~ C)))) where b1 is V11() real ext-real Element of REAL : ( 0 <= b1 & b1 <= 1 ) } is set
(LSeg ((NW-corner (L~ C)),(NE-corner (L~ C)))) /\ (L~ C) is closed Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | (N-most (L~ C)) is strict TopSpace-like SubSpace of TOP-REAL 2
proj1 | (N-most (L~ C)) is Relation-like the carrier of ((TOP-REAL 2) | (N-most (L~ C))) -defined REAL -valued Function-like total V30( the carrier of ((TOP-REAL 2) | (N-most (L~ C))), REAL ) complex-yielding V174() V175() Element of bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ C))),REAL:]
the carrier of ((TOP-REAL 2) | (N-most (L~ C))) is set
[: the carrier of ((TOP-REAL 2) | (N-most (L~ C))),REAL:] is complex-yielding V174() V175() set
bool [: the carrier of ((TOP-REAL 2) | (N-most (L~ C))),REAL:] is non empty set
lower_bound (proj1 | (N-most (L~ C))) is V11() real ext-real Element of REAL
(proj1 | (N-most (L~ C))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ C))) is V183() V184() V185() Element of bool REAL
lower_bound ((proj1 | (N-most (L~ C))) .: the carrier of ((TOP-REAL 2) | (N-most (L~ C)))) is V11() real ext-real Element of REAL
|[(lower_bound (proj1 | (N-most (L~ C)))),(N-bound (L~ C))]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
LeftComp C is non empty Element of bool the carrier of (TOP-REAL 2)
p is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
p `2 is V11() real ext-real Element of REAL
p . 2 is V11() real ext-real Element of REAL
SpStSeq (L~ C) is non empty non trivial Relation-like NAT -defined the carrier of (TOP-REAL 2) -valued Function-like non constant V35() FinSequence-like FinSubsequence-like V262( the carrier of (TOP-REAL 2)) special unfolded s.c.c. standard rectangular clockwise_oriented FinSequence of the carrier of (TOP-REAL 2)
LeftComp (SpStSeq (L~ C)) is non empty Element of bool the carrier of (TOP-REAL 2)
L~ (SpStSeq (L~ C)) is non empty closed boundary nowhere_dense compact bounded bounded non horizontal non vertical Jordan Element of bool the carrier of (TOP-REAL 2)
N-bound (L~ (SpStSeq (L~ C))) is V11() real ext-real Element of REAL
(TOP-REAL 2) | (L~ (SpStSeq (L~ C))) is non empty strict TopSpace-like SubSpace of TOP-REAL 2
proj2 | (L~ (SpStSeq (L~ C))) is non empty Relation-like the carrier of ((TOP-REAL 2) | (L~ (SpStSeq (L~ C)))) -defined REAL -valued Function-like total V30( the carrier of ((TOP-REAL 2) | (L~ (SpStSeq (L~ C)))), REAL ) complex-yielding V174() V175() Element of bool [: the carrier of ((TOP-REAL 2) | (L~ (SpStSeq (L~ C)))),REAL:]
the carrier of ((TOP-REAL 2) | (L~ (SpStSeq (L~ C)))) is non empty set
[: the carrier of ((TOP-REAL 2) | (L~ (SpStSeq (L~ C)))),REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [: the carrier of ((TOP-REAL 2) | (L~ (SpStSeq (L~ C)))),REAL:] is non empty non trivial V35() set
upper_bound (proj2 | (L~ (SpStSeq (L~ C)))) is V11() real ext-real Element of REAL
(proj2 | (L~ (SpStSeq (L~ C)))) .: the carrier of ((TOP-REAL 2) | (L~ (SpStSeq (L~ C)))) is V183() V184() V185() Element of bool REAL
upper_bound ((proj2 | (L~ (SpStSeq (L~ C)))) .: the carrier of ((TOP-REAL 2) | (L~ (SpStSeq (L~ C))))) is V11() real ext-real Element of REAL
C is TopSpace-like TopStruct
the carrier of C is set
bool the carrier of C is non empty set
p is Element of bool the carrier of C
WH is Element of bool the carrier of C
C | p is strict TopSpace-like SubSpace of C
the carrier of (C | p) is set
bool the carrier of (C | p) is non empty set
p12 is Element of bool the carrier of (C | p)
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
bool the carrier of (TOP-REAL C) is non empty set
p is Element of bool the carrier of (TOP-REAL C)
WH is Element of bool the carrier of (TOP-REAL C)
p ` is Element of bool the carrier of (TOP-REAL C)
the carrier of (TOP-REAL C) \ p is set
(TOP-REAL C) | (p `) is strict TopSpace-like SubSpace of TOP-REAL C
the carrier of ((TOP-REAL C) | (p `)) is set
bool the carrier of ((TOP-REAL C) | (p `)) is non empty set
Euclid C is non empty strict Reflexive discerning symmetric triangle Discerning MetrStruct
REAL C is non empty functional FinSequence-membered FinSequenceSet of REAL
C -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = C } is set
Pitag_dist C is non empty Relation-like [:(REAL C),(REAL C):] -defined REAL -valued Function-like total V30([:(REAL C),(REAL C):], REAL ) complex-yielding V174() V175() Element of bool [:[:(REAL C),(REAL C):],REAL:]
[:(REAL C),(REAL C):] is non empty set
[:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() set
MetrStruct(# (REAL C),(Pitag_dist C) #) is strict MetrStruct
the carrier of (Euclid C) is non empty set
bool the carrier of (Euclid C) is non empty set
p12 is Element of bool the carrier of ((TOP-REAL C) | (p `))
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
bool the carrier of (TOP-REAL C) is non empty set
p is Element of bool the carrier of (TOP-REAL C)
WH is Element of bool the carrier of (TOP-REAL C)
p ` is Element of bool the carrier of (TOP-REAL C)
the carrier of (TOP-REAL C) \ p is set
(TOP-REAL C) | (p `) is strict TopSpace-like SubSpace of TOP-REAL C
the carrier of ((TOP-REAL C) | (p `)) is set
bool the carrier of ((TOP-REAL C) | (p `)) is non empty set
Euclid C is non empty strict Reflexive discerning symmetric triangle Discerning MetrStruct
REAL C is non empty functional FinSequence-membered FinSequenceSet of REAL
C -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = C } is set
Pitag_dist C is non empty Relation-like [:(REAL C),(REAL C):] -defined REAL -valued Function-like total V30([:(REAL C),(REAL C):], REAL ) complex-yielding V174() V175() Element of bool [:[:(REAL C),(REAL C):],REAL:]
[:(REAL C),(REAL C):] is non empty set
[:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() set
MetrStruct(# (REAL C),(Pitag_dist C) #) is strict MetrStruct
the carrier of (Euclid C) is non empty set
bool the carrier of (Euclid C) is non empty set
p12 is Element of bool the carrier of ((TOP-REAL C) | (p `))
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
bool the carrier of (TOP-REAL C) is non empty set
p is Element of bool the carrier of (TOP-REAL C)
p ` is Element of bool the carrier of (TOP-REAL C)
the carrier of (TOP-REAL C) \ p is set
WH is Element of bool the carrier of (TOP-REAL C)
p /\ WH is Element of bool the carrier of (TOP-REAL C)
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
bool the carrier of (TOP-REAL C) is non empty set
p is Element of bool the carrier of (TOP-REAL C)
WH is Element of bool the carrier of (TOP-REAL C)
p12 is Element of bool the carrier of (TOP-REAL C)
(C,p12) is Element of bool the carrier of (TOP-REAL C)
{ b1 where b1 is Element of bool the carrier of (TOP-REAL C) : (C,p12,b1) } is set
union { b1 where b1 is Element of bool the carrier of (TOP-REAL C) : (C,p12,b1) } is set
(C,p12) is Element of bool the carrier of (TOP-REAL C)
{ b1 where b1 is Element of bool the carrier of (TOP-REAL C) : (C,p12,b1) } is set
union { b1 where b1 is Element of bool the carrier of (TOP-REAL C) : (C,p12,b1) } is set
C is ordinal natural V11() real ext-real non negative V35() cardinal V116() V117() V183() V184() V185() V186() V187() V188() Element of NAT
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
bool the carrier of (TOP-REAL C) is non empty set
p12 is Element of bool the carrier of (TOP-REAL C)
p is Element of bool the carrier of (TOP-REAL C)
WH is Element of bool the carrier of (TOP-REAL C)
p12 ` is Element of bool the carrier of (TOP-REAL C)
the carrier of (TOP-REAL C) \ p12 is set
(C,p12) is Element of bool the carrier of (TOP-REAL C)
{ b1 where b1 is Element of bool the carrier of (TOP-REAL C) : (C,p12,b1) } is set
union { b1 where b1 is Element of bool the carrier of (TOP-REAL C) : (C,p12,b1) } is set
C is closed Element of bool the carrier of (TOP-REAL 2)
(2,C) is Element of bool the carrier of (TOP-REAL 2)
{ b1 where b1 is Element of bool the carrier of (TOP-REAL 2) : (2,C,b1) } is set
union { b1 where b1 is Element of bool the carrier of (TOP-REAL 2) : (2,C,b1) } is set
bool the carrier of (TOP-REAL 2) is non empty Element of bool (bool the carrier of (TOP-REAL 2))
bool (bool the carrier of (TOP-REAL 2)) is non empty set
WH is set
p12 is Element of bool the carrier of (TOP-REAL 2)
WH is Element of bool (bool the carrier of (TOP-REAL 2))
p12 is Element of bool the carrier of (TOP-REAL 2)
C is Element of bool the carrier of (TOP-REAL 2)
C ` is open Element of bool the carrier of (TOP-REAL 2)
the carrier of (TOP-REAL 2) \ C is set
(2,C) is Element of bool the carrier of (TOP-REAL 2)
{ b1 where b1 is Element of bool the carrier of (TOP-REAL 2) : (2,C,b1) } is set
union { b1 where b1 is Element of bool the carrier of (TOP-REAL 2) : (2,C,b1) } is set
bool the carrier of (TOP-REAL 2) is non empty Element of bool (bool the carrier of (TOP-REAL 2))
bool (bool the carrier of (TOP-REAL 2)) is non empty set
WH is set
p12 is Element of bool the carrier of (TOP-REAL 2)
WH is Element of bool (bool the carrier of (TOP-REAL 2))
p12 is Element of bool the carrier of (TOP-REAL 2)
C is Element of bool the carrier of (TOP-REAL 2)
C ` is open Element of bool the carrier of (TOP-REAL 2)
the carrier of (TOP-REAL 2) \ C is set
C is compact bounded Element of bool the carrier of (TOP-REAL 2)
(2,C) is Element of bool the carrier of (TOP-REAL 2)
{ b1 where b1 is Element of bool the carrier of (TOP-REAL 2) : (2,C,b1) } is set
union { b1 where b1 is Element of bool the carrier of (TOP-REAL 2) : (2,C,b1) } is set
C is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
west_halfline C is connected convex Element of bool the carrier of (TOP-REAL 2)
C `1 is V11() real ext-real Element of REAL
C . 1 is V11() real ext-real Element of REAL
C `2 is V11() real ext-real Element of REAL
C . 2 is V11() real ext-real Element of REAL
bool the carrier of (Euclid 2) is non empty set
C is bounded Element of bool the carrier of (Euclid 2)
r is V11() real ext-real Element of REAL
2 * r is V11() real ext-real Element of REAL
(C `1) - (2 * r) is V11() real ext-real Element of REAL
|[((C `1) - (2 * r)),(C `2)]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
0 + (C `1) is V11() real ext-real Element of REAL
(2 * r) + (C `1) is V11() real ext-real Element of REAL
|[((C `1) - (2 * r)),(C `2)]| `1 is V11() real ext-real Element of REAL
|[((C `1) - (2 * r)),(C `2)]| . 1 is V11() real ext-real Element of REAL
EX1 is Element of the carrier of (Euclid 2)
|[((C `1) - (2 * r)),(C `2)]| `2 is V11() real ext-real Element of REAL
|[((C `1) - (2 * r)),(C `2)]| . 2 is V11() real ext-real Element of REAL
p1 is Element of the carrier of (Euclid 2)
|[(C `1),(C `2)]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
dist (EX1,p1) is V11() real ext-real Element of REAL
the distance of (Euclid 2) is non empty Relation-like [: the carrier of (Euclid 2), the carrier of (Euclid 2):] -defined REAL -valued Function-like total V30([: the carrier of (Euclid 2), the carrier of (Euclid 2):], REAL ) complex-yielding V174() V175() Element of bool [:[: the carrier of (Euclid 2), the carrier of (Euclid 2):],REAL:]
[: the carrier of (Euclid 2), the carrier of (Euclid 2):] is non empty set
[:[: the carrier of (Euclid 2), the carrier of (Euclid 2):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[: the carrier of (Euclid 2), the carrier of (Euclid 2):],REAL:] is non empty non trivial V35() set
the distance of (Euclid 2) . (EX1,p1) is V11() real ext-real Element of REAL
[EX1,p1] is non empty set
{EX1,p1} is non empty V35() set
{EX1} is non empty trivial V35() 1 -element set
{{EX1,p1},{EX1}} is non empty V35() V39() set
the distance of (Euclid 2) . [EX1,p1] is V11() real ext-real set
(C `1) - ((C `1) - (2 * r)) is V11() real ext-real Element of REAL
((C `1) - ((C `1) - (2 * r))) ^2 is V11() real ext-real Element of REAL
K37(((C `1) - ((C `1) - (2 * r))),((C `1) - ((C `1) - (2 * r)))) is V11() real ext-real set
(C `2) - (C `2) is V11() real ext-real Element of REAL
((C `2) - (C `2)) ^2 is V11() real ext-real Element of REAL
K37(((C `2) - (C `2)),((C `2) - (C `2))) is V11() real ext-real set
(((C `1) - ((C `1) - (2 * r))) ^2) + (((C `2) - (C `2)) ^2) is V11() real ext-real Element of REAL
sqrt ((((C `1) - ((C `1) - (2 * r))) ^2) + (((C `2) - (C `2)) ^2)) is V11() real ext-real Element of REAL
C is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
east_halfline C is connected convex Element of bool the carrier of (TOP-REAL 2)
C `1 is V11() real ext-real Element of REAL
C . 1 is V11() real ext-real Element of REAL
C `2 is V11() real ext-real Element of REAL
C . 2 is V11() real ext-real Element of REAL
bool the carrier of (Euclid 2) is non empty set
C is bounded Element of bool the carrier of (Euclid 2)
r is V11() real ext-real Element of REAL
2 * r is V11() real ext-real Element of REAL
(C `1) + (2 * r) is V11() real ext-real Element of REAL
|[((C `1) + (2 * r)),(C `2)]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
0 + (C `1) is V11() real ext-real Element of REAL
(2 * r) + (C `1) is V11() real ext-real Element of REAL
|[((C `1) + (2 * r)),(C `2)]| `1 is V11() real ext-real Element of REAL
|[((C `1) + (2 * r)),(C `2)]| . 1 is V11() real ext-real Element of REAL
p1 is Element of the carrier of (Euclid 2)
|[((C `1) + (2 * r)),(C `2)]| `2 is V11() real ext-real Element of REAL
|[((C `1) + (2 * r)),(C `2)]| . 2 is V11() real ext-real Element of REAL
EX is Element of the carrier of (Euclid 2)
|[(C `1),(C `2)]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
dist (p1,EX) is V11() real ext-real Element of REAL
the distance of (Euclid 2) is non empty Relation-like [: the carrier of (Euclid 2), the carrier of (Euclid 2):] -defined REAL -valued Function-like total V30([: the carrier of (Euclid 2), the carrier of (Euclid 2):], REAL ) complex-yielding V174() V175() Element of bool [:[: the carrier of (Euclid 2), the carrier of (Euclid 2):],REAL:]
[: the carrier of (Euclid 2), the carrier of (Euclid 2):] is non empty set
[:[: the carrier of (Euclid 2), the carrier of (Euclid 2):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[: the carrier of (Euclid 2), the carrier of (Euclid 2):],REAL:] is non empty non trivial V35() set
the distance of (Euclid 2) . (p1,EX) is V11() real ext-real Element of REAL
[p1,EX] is non empty set
{p1,EX} is non empty V35() set
{p1} is non empty trivial V35() 1 -element set
{{p1,EX},{p1}} is non empty V35() V39() set
the distance of (Euclid 2) . [p1,EX] is V11() real ext-real set
(C `1) - ((C `1) + (2 * r)) is V11() real ext-real Element of REAL
((C `1) - ((C `1) + (2 * r))) ^2 is V11() real ext-real Element of REAL
K37(((C `1) - ((C `1) + (2 * r))),((C `1) - ((C `1) + (2 * r)))) is V11() real ext-real set
(C `2) - (C `2) is V11() real ext-real Element of REAL
((C `2) - (C `2)) ^2 is V11() real ext-real Element of REAL
K37(((C `2) - (C `2)),((C `2) - (C `2))) is V11() real ext-real set
(((C `1) - ((C `1) + (2 * r))) ^2) + (((C `2) - (C `2)) ^2) is V11() real ext-real Element of REAL
sqrt ((((C `1) - ((C `1) + (2 * r))) ^2) + (((C `2) - (C `2)) ^2)) is V11() real ext-real Element of REAL
((C `1) + (2 * r)) - (C `1) is V11() real ext-real Element of REAL
(((C `1) + (2 * r)) - (C `1)) ^2 is V11() real ext-real Element of REAL
K37((((C `1) + (2 * r)) - (C `1)),(((C `1) + (2 * r)) - (C `1))) is V11() real ext-real set
((((C `1) + (2 * r)) - (C `1)) ^2) + 0 is V11() real ext-real Element of REAL
sqrt (((((C `1) + (2 * r)) - (C `1)) ^2) + 0) is V11() real ext-real Element of REAL
C is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
north_halfline C is connected convex Element of bool the carrier of (TOP-REAL 2)
C `1 is V11() real ext-real Element of REAL
C . 1 is V11() real ext-real Element of REAL
C `2 is V11() real ext-real Element of REAL
C . 2 is V11() real ext-real Element of REAL
bool the carrier of (Euclid 2) is non empty set
C is bounded Element of bool the carrier of (Euclid 2)
r is V11() real ext-real Element of REAL
2 * r is V11() real ext-real Element of REAL
(C `2) + (2 * r) is V11() real ext-real Element of REAL
|[(C `1),((C `2) + (2 * r))]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
|[(C `1),((C `2) + (2 * r))]| `1 is V11() real ext-real Element of REAL
|[(C `1),((C `2) + (2 * r))]| . 1 is V11() real ext-real Element of REAL
p1 is Element of the carrier of (Euclid 2)
0 + (C `2) is V11() real ext-real Element of REAL
(2 * r) + (C `2) is V11() real ext-real Element of REAL
|[(C `1),((C `2) + (2 * r))]| `2 is V11() real ext-real Element of REAL
|[(C `1),((C `2) + (2 * r))]| . 2 is V11() real ext-real Element of REAL
EX is Element of the carrier of (Euclid 2)
|[(C `1),(C `2)]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
dist (p1,EX) is V11() real ext-real Element of REAL
the distance of (Euclid 2) is non empty Relation-like [: the carrier of (Euclid 2), the carrier of (Euclid 2):] -defined REAL -valued Function-like total V30([: the carrier of (Euclid 2), the carrier of (Euclid 2):], REAL ) complex-yielding V174() V175() Element of bool [:[: the carrier of (Euclid 2), the carrier of (Euclid 2):],REAL:]
[: the carrier of (Euclid 2), the carrier of (Euclid 2):] is non empty set
[:[: the carrier of (Euclid 2), the carrier of (Euclid 2):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[: the carrier of (Euclid 2), the carrier of (Euclid 2):],REAL:] is non empty non trivial V35() set
the distance of (Euclid 2) . (p1,EX) is V11() real ext-real Element of REAL
[p1,EX] is non empty set
{p1,EX} is non empty V35() set
{p1} is non empty trivial V35() 1 -element set
{{p1,EX},{p1}} is non empty V35() V39() set
the distance of (Euclid 2) . [p1,EX] is V11() real ext-real set
(C `1) - (C `1) is V11() real ext-real Element of REAL
((C `1) - (C `1)) ^2 is V11() real ext-real Element of REAL
K37(((C `1) - (C `1)),((C `1) - (C `1))) is V11() real ext-real set
(C `2) - ((C `2) + (2 * r)) is V11() real ext-real Element of REAL
((C `2) - ((C `2) + (2 * r))) ^2 is V11() real ext-real Element of REAL
K37(((C `2) - ((C `2) + (2 * r))),((C `2) - ((C `2) + (2 * r)))) is V11() real ext-real set
(((C `1) - (C `1)) ^2) + (((C `2) - ((C `2) + (2 * r))) ^2) is V11() real ext-real Element of REAL
sqrt ((((C `1) - (C `1)) ^2) + (((C `2) - ((C `2) + (2 * r))) ^2)) is V11() real ext-real Element of REAL
((C `2) + (2 * r)) - (C `2) is V11() real ext-real Element of REAL
(((C `2) + (2 * r)) - (C `2)) ^2 is V11() real ext-real Element of REAL
K37((((C `2) + (2 * r)) - (C `2)),(((C `2) + (2 * r)) - (C `2))) is V11() real ext-real set
((((C `2) + (2 * r)) - (C `2)) ^2) + 0 is V11() real ext-real Element of REAL
sqrt (((((C `2) + (2 * r)) - (C `2)) ^2) + 0) is V11() real ext-real Element of REAL
C is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
south_halfline C is connected convex Element of bool the carrier of (TOP-REAL 2)
C `1 is V11() real ext-real Element of REAL
C . 1 is V11() real ext-real Element of REAL
C `2 is V11() real ext-real Element of REAL
C . 2 is V11() real ext-real Element of REAL
bool the carrier of (Euclid 2) is non empty set
C is bounded Element of bool the carrier of (Euclid 2)
r is V11() real ext-real Element of REAL
2 * r is V11() real ext-real Element of REAL
(C `2) - (2 * r) is V11() real ext-real Element of REAL
|[(C `1),((C `2) - (2 * r))]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
|[(C `1),(C `2)]| is non empty Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
p1 is Element of the carrier of (Euclid 2)
EX is Element of the carrier of (Euclid 2)
dist (p1,EX) is V11() real ext-real Element of REAL
the distance of (Euclid 2) is non empty Relation-like [: the carrier of (Euclid 2), the carrier of (Euclid 2):] -defined REAL -valued Function-like total V30([: the carrier of (Euclid 2), the carrier of (Euclid 2):], REAL ) complex-yielding V174() V175() Element of bool [:[: the carrier of (Euclid 2), the carrier of (Euclid 2):],REAL:]
[: the carrier of (Euclid 2), the carrier of (Euclid 2):] is non empty set
[:[: the carrier of (Euclid 2), the carrier of (Euclid 2):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[: the carrier of (Euclid 2), the carrier of (Euclid 2):],REAL:] is non empty non trivial V35() set
the distance of (Euclid 2) . (p1,EX) is V11() real ext-real Element of REAL
[p1,EX] is non empty set
{p1,EX} is non empty V35() set
{p1} is non empty trivial V35() 1 -element set
{{p1,EX},{p1}} is non empty V35() V39() set
the distance of (Euclid 2) . [p1,EX] is V11() real ext-real set
(C `1) - (C `1) is V11() real ext-real Element of REAL
((C `1) - (C `1)) ^2 is V11() real ext-real Element of REAL
K37(((C `1) - (C `1)),((C `1) - (C `1))) is V11() real ext-real set
(C `2) - ((C `2) - (2 * r)) is V11() real ext-real Element of REAL
((C `2) - ((C `2) - (2 * r))) ^2 is V11() real ext-real Element of REAL
K37(((C `2) - ((C `2) - (2 * r))),((C `2) - ((C `2) - (2 * r)))) is V11() real ext-real set
(((C `1) - (C `1)) ^2) + (((C `2) - ((C `2) - (2 * r))) ^2) is V11() real ext-real Element of REAL
sqrt ((((C `1) - (C `1)) ^2) + (((C `2) - ((C `2) - (2 * r))) ^2)) is V11() real ext-real Element of REAL
|[(C `1),((C `2) - (2 * r))]| `1 is V11() real ext-real Element of REAL
|[(C `1),((C `2) - (2 * r))]| . 1 is V11() real ext-real Element of REAL
0 + (C `2) is V11() real ext-real Element of REAL
(2 * r) + (C `2) is V11() real ext-real Element of REAL
|[(C `1),((C `2) - (2 * r))]| `2 is V11() real ext-real Element of REAL
|[(C `1),((C `2) - (2 * r))]| . 2 is V11() real ext-real Element of REAL
C is compact bounded Element of bool the carrier of (TOP-REAL 2)
(2,C) is connected Element of bool the carrier of (TOP-REAL 2)
{ b1 where b1 is Element of bool the carrier of (TOP-REAL 2) : (2,C,b1) } is set
union { b1 where b1 is Element of bool the carrier of (TOP-REAL 2) : (2,C,b1) } is set
C is compact bounded Element of bool the carrier of (TOP-REAL 2)
C ` is Element of bool the carrier of (TOP-REAL 2)
the carrier of (TOP-REAL 2) \ C is set
(2,C) is non empty connected Element of bool the carrier of (TOP-REAL 2)
{ b1 where b1 is Element of bool the carrier of (TOP-REAL 2) : (2,C,b1) } is set
union { b1 where b1 is Element of bool the carrier of (TOP-REAL 2) : (2,C,b1) } is set
C is compact bounded Element of bool the carrier of (TOP-REAL 2)
(2,C) is non empty connected Element of bool the carrier of (TOP-REAL 2)
{ b1 where b1 is Element of bool the carrier of (TOP-REAL 2) : (2,C,b1) } is set
union { b1 where b1 is Element of bool the carrier of (TOP-REAL 2) : (2,C,b1) } is set
p is connected Element of bool the carrier of (TOP-REAL 2)
(2,C) is Element of bool the carrier of (TOP-REAL 2)
{ b1 where b1 is Element of bool the carrier of (TOP-REAL 2) : (2,C,b1) } is set
union { b1 where b1 is Element of bool the carrier of (TOP-REAL 2) : (2,C,b1) } is set
(2,C) \/ (2,C) is non empty Element of bool the carrier of (TOP-REAL 2)
C ` is Element of bool the carrier of (TOP-REAL 2)
the carrier of (TOP-REAL 2) \ C is set
[#] the carrier of (TOP-REAL 2) is non empty non proper Element of bool the carrier of (TOP-REAL 2)
C \/ (C `) is Element of bool the carrier of (TOP-REAL 2)
(2,C) \/ (2,C) is non empty Element of bool the carrier of (TOP-REAL 2)
C ` is Element of bool the carrier of (TOP-REAL 2)
the carrier of (TOP-REAL 2) \ C is set
C is compact bounded Element of bool the carrier of (TOP-REAL 2)
(2,C) is non empty connected Element of bool the carrier of (TOP-REAL 2)
{ b1 where b1 is Element of bool the carrier of (TOP-REAL 2) : (2,C,b1) } is set
union { b1 where b1 is Element of bool the carrier of (TOP-REAL 2) : (2,C,b1) } is set
p is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
west_halfline p is connected convex Element of bool the carrier of (TOP-REAL 2)
C is compact bounded Element of bool the carrier of (TOP-REAL 2)
(2,C) is non empty connected Element of bool the carrier of (TOP-REAL 2)
{ b1 where b1 is Element of bool the carrier of (TOP-REAL 2) : (2,C,b1) } is set
union { b1 where b1 is Element of bool the carrier of (TOP-REAL 2) : (2,C,b1) } is set
p is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
east_halfline p is connected convex Element of bool the carrier of (TOP-REAL 2)
C is compact bounded Element of bool the carrier of (TOP-REAL 2)
(2,C) is non empty connected Element of bool the carrier of (TOP-REAL 2)
{ b1 where b1 is Element of bool the carrier of (TOP-REAL 2) : (2,C,b1) } is set
union { b1 where b1 is Element of bool the carrier of (TOP-REAL 2) : (2,C,b1) } is set
p is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
south_halfline p is connected convex Element of bool the carrier of (TOP-REAL 2)
C is compact bounded Element of bool the carrier of (TOP-REAL 2)
(2,C) is non empty connected Element of bool the carrier of (TOP-REAL 2)
{ b1 where b1 is Element of bool the carrier of (TOP-REAL 2) : (2,C,b1) } is set
union { b1 where b1 is Element of bool the carrier of (TOP-REAL 2) : (2,C,b1) } is set
p is Relation-like NAT -defined REAL -valued Function-like V35() 2 -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL 2)
north_halfline p is connected convex Element of bool the carrier of (TOP-REAL 2)
C is ordinal natural V11() real ext-real non negative V35() cardinal set
Euclid C is non empty strict Reflexive discerning symmetric triangle Discerning MetrStruct
REAL C is non empty functional FinSequence-membered FinSequenceSet of REAL
C -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = C } is set
Pitag_dist C is non empty Relation-like [:(REAL C),(REAL C):] -defined REAL -valued Function-like total V30([:(REAL C),(REAL C):], REAL ) complex-yielding V174() V175() Element of bool [:[:(REAL C),(REAL C):],REAL:]
[:(REAL C),(REAL C):] is non empty set
[:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() set
MetrStruct(# (REAL C),(Pitag_dist C) #) is strict MetrStruct
the carrier of (Euclid C) is non empty set
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
p is V11() real ext-real Element of REAL
WH is Element of the carrier of (Euclid C)
0* C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
C |-> 0 is Relation-like empty-yielding NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of C -tuples_on REAL
Seg C is V35() C -element V183() V184() V185() V186() V187() V188() Element of bool NAT
(Seg C) --> 0 is Relation-like Seg C -defined INT -valued RAT -valued {0} -valued Function-like total V30( Seg C,{0}) V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() V176() Element of bool [:(Seg C),{0}:]
{0} is non empty trivial V35() V39() 1 -element V183() V184() V185() V186() V187() V188() set
[:(Seg C),{0}:] is INT -valued RAT -valued V35() complex-yielding V174() V175() V176() set
bool [:(Seg C),{0}:] is non empty V35() V39() set
r is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
p12 is Element of the carrier of (Euclid C)
p * r is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of the carrier of (TOP-REAL C)
p * r is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() FinSequence of REAL
p multreal is non empty Relation-like REAL -defined REAL -valued Function-like total V30( REAL , REAL ) complex-yielding V174() V175() Element of bool [:REAL,REAL:]
id REAL is non empty Relation-like REAL -defined REAL -valued Function-like one-to-one total V30( REAL , REAL ) complex-yielding V174() V175() increasing V179() Element of bool [:REAL,REAL:]
multreal [;] (p,(id REAL)) is set
r (#) (p multreal) is Relation-like Function-like V35() complex-yielding V174() V175() set
C is Element of the carrier of (Euclid C)
dist (WH,p12) is V11() real ext-real Element of REAL
the distance of (Euclid C) is non empty Relation-like [: the carrier of (Euclid C), the carrier of (Euclid C):] -defined REAL -valued Function-like total V30([: the carrier of (Euclid C), the carrier of (Euclid C):], REAL ) complex-yielding V174() V175() Element of bool [:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:]
[: the carrier of (Euclid C), the carrier of (Euclid C):] is non empty set
[:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[: the carrier of (Euclid C), the carrier of (Euclid C):],REAL:] is non empty non trivial V35() set
the distance of (Euclid C) . (WH,p12) is V11() real ext-real Element of REAL
[WH,p12] is non empty set
{WH,p12} is non empty V35() set
{WH} is non empty trivial V35() 1 -element set
{{WH,p12},{WH}} is non empty V35() V39() set
the distance of (Euclid C) . [WH,p12] is V11() real ext-real set
p * (dist (WH,p12)) is V11() real ext-real Element of REAL
dist (WH,C) is V11() real ext-real Element of REAL
the distance of (Euclid C) . (WH,C) is V11() real ext-real Element of REAL
[WH,C] is non empty set
{WH,C} is non empty V35() set
{{WH,C},{WH}} is non empty V35() V39() set
the distance of (Euclid C) . [WH,C] is V11() real ext-real set
C is ordinal natural V11() real ext-real non negative V35() cardinal set
Euclid C is non empty strict Reflexive discerning symmetric triangle Discerning MetrStruct
REAL C is non empty functional FinSequence-membered FinSequenceSet of REAL
C -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = C } is set
Pitag_dist C is non empty Relation-like [:(REAL C),(REAL C):] -defined REAL -valued Function-like total V30([:(REAL C),(REAL C):], REAL ) complex-yielding V174() V175() Element of bool [:[:(REAL C),(REAL C):],REAL:]
[:(REAL C),(REAL C):] is non empty set
[:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() set
MetrStruct(# (REAL C),(Pitag_dist C) #) is strict MetrStruct
the carrier of (Euclid C) is non empty set
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
bool the carrier of (TOP-REAL C) is non empty set
p is V11() real ext-real Element of REAL
p12 is Element of the carrier of (Euclid C)
0* C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
C |-> 0 is Relation-like empty-yielding NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of C -tuples_on REAL
Seg C is V35() C -element V183() V184() V185() V186() V187() V188() Element of bool NAT
(Seg C) --> 0 is Relation-like Seg C -defined INT -valued RAT -valued {0} -valued Function-like total V30( Seg C,{0}) V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() V176() Element of bool [:(Seg C),{0}:]
{0} is non empty trivial V35() V39() 1 -element V183() V184() V185() V186() V187() V188() set
[:(Seg C),{0}:] is INT -valued RAT -valued V35() complex-yielding V174() V175() V176() set
bool [:(Seg C),{0}:] is non empty V35() V39() set
C is Element of bool the carrier of (TOP-REAL C)
WH is V11() real ext-real Element of REAL
Ball (p12,WH) is bounded Element of bool the carrier of (Euclid C)
bool the carrier of (Euclid C) is non empty set
p * C is Element of bool the carrier of (TOP-REAL C)
{ (p * b1) where b1 is Element of the carrier of (TOP-REAL C) : b1 in C } is set
p * WH is V11() real ext-real Element of REAL
Ball (p12,(p * WH)) is bounded Element of bool the carrier of (Euclid C)
C is ordinal natural V11() real ext-real non negative V35() cardinal set
Euclid C is non empty strict Reflexive discerning symmetric triangle Discerning MetrStruct
REAL C is non empty functional FinSequence-membered FinSequenceSet of REAL
C -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
{ b1 where b1 is Relation-like NAT -defined REAL -valued Function-like V35() FinSequence-like FinSubsequence-like Element of REAL * : len b1 = C } is set
Pitag_dist C is non empty Relation-like [:(REAL C),(REAL C):] -defined REAL -valued Function-like total V30([:(REAL C),(REAL C):], REAL ) complex-yielding V174() V175() Element of bool [:[:(REAL C),(REAL C):],REAL:]
[:(REAL C),(REAL C):] is non empty set
[:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() complex-yielding V174() V175() set
bool [:[:(REAL C),(REAL C):],REAL:] is non empty non trivial V35() set
MetrStruct(# (REAL C),(Pitag_dist C) #) is strict MetrStruct
the carrier of (Euclid C) is non empty set
TOP-REAL C is non empty TopSpace-like V130() V195() V196() V233() V234() V235() V236() V237() V238() V239() strict add-continuous Mult-continuous RLTopStruct
the carrier of (TOP-REAL C) is non empty set
bool the carrier of (TOP-REAL C) is non empty set
WH is V11() real ext-real Element of REAL
p12 is V11() real ext-real Element of REAL
C is Element of the carrier of (Euclid C)
0* C is Relation-like NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of REAL C
C |-> 0 is Relation-like empty-yielding NAT -defined REAL -valued Function-like V35() C -element FinSequence-like FinSubsequence-like complex-yielding V174() V175() Element of C -tuples_on REAL
Seg C is V35() C -element V183() V184() V185() V186() V187() V188() Element of bool NAT
(Seg C) --> 0 is Relation-like Seg C -defined INT -valued RAT -valued {0} -valued Function-like total V30( Seg C,{0}) V35() FinSequence-like FinSubsequence-like complex-yielding V174() V175() V176() Element of bool [:(Seg C),{0}:]
{0} is non empty trivial V35() V39() 1 -element V183() V184() V185() V186() V187() V188() set
[:(Seg C),{0}:] is INT -valued RAT -valued V35() complex-yielding V174() V175() V176() set
bool [:(Seg C),{0}:] is non empty V35() V39() set
r is Element of bool the carrier of (TOP-REAL C)
p is V11() real ext-real Element of REAL
Ball (C,p) is bounded Element of bool the carrier of (Euclid C)
bool the carrier of (Euclid C) is non empty set
WH * r is Element of bool the carrier of (TOP-REAL C)
{ (WH * b1) where b1 is Element of the carrier of (TOP-REAL C) : b1 in r } is set
p12 * r is Element of bool the carrier of (TOP-REAL C)
{ (p12 * b1) where b1 is Element of the carrier of (TOP-REAL C) : b1 in r } is set